THE PERSPECTIVE O F RCHITECTURE. IN TWO PARTS. A WORK ENTIRELY NEW; Deduced from the Principles of Dr. BROOK TAYLOR; And performed by Two Rules only of Univerfal Application. PART the FIRST, CONTAINS The Defcription and Ufe of a new Inftrument called the Architedlonic Se&or. PART THE SECOND, A New Method of Drawing the Five Orders, Elegant Stru&ures, &c. in PERSPECTIVE. BEGUN BY COMMAND of His Prefent MAJESTY, WHEN PRINCE of WALES. B Y Joshua Kirby, Defigner in Perfpedtive to His Majesty. LONDON: Printed for the AUTHOR, in Duke-Street, Grosveno r-Squar e, By R. Francklin, in Ruflel-Street, Covent-Garden; AND SOLD BY T. Payne, at the Mews Gate; Meffieurs Knapton and Horsefield, in Ludgate Street; Meffieurs Do dsley, in Pall-Mall; T. Longman, in Pater-Nofter Row; T. Davies, in Ruflel-Street, Covent-Garden; and J. G r e t t o n, in Bond Street. M DCC LXI. PREFACE. if^j’ HOEVER attempts to go out of the common road of fcience, or to tread in an y new and unbeaten path, muft expeft fuch a fcrutiny from the public, as is confiftent with the nature of his fubjeft : and however trivial their opinion may have been thought by felf-fufficient writers, yet I have always efteemed it the very belt, if not the only criterion, by which a modeft author would defire to be tried. The following work, which I have treated in a manner entirely new, and which relates to a mod delightful fcience, may poflibly merit the attention of fuch perfons as are any ways verfcd in the arts of defign ; fuch as fill up their vacant hours with the ftudies of architefture and painting ; and particularly thofe, who purfue them for profit or reputation. It is to their candour and judgment, that I lubmit the fol¬ lowing fchemes and defigns, as new principles for a compleat fyftem of the Perfpec- tive of architedhire, both as it relates to the true delineation of objects, and the doc¬ trine of light and fhadow. Of the many treatifes, which have been wrote upon this fubjedf, very few have met with the public regard. Some were the labours of other men, or tranflations from injudicious writers, or elfe the produS of perfons, who did not feem to confi- der what were the proper materials, of which fuch works ought to be compofed. Indeed, it would be almoft endlefs to give a lift of the various authors, who have at different times (within this laft century) wrote upon Perfipeflive : and to examine and point out the excellences of fome, and the many miftakes and errors of others, might make a large volume, and probably would be of little moment to the world. But the principles invented and publilhed by Dr. Brook Taj lor, being now univer- fally eftabhlhed, I lhall think myfelf lafe m the mam point, if I proceed in his track j and (hall have little more to do, than to keep his demonftrations conftantly in my eye, and to invent fuch fchemes as may be eafily underftood, and applied to general practice. But, even this is a difficult and expenfive undertaking, and what I ffiould by no means have attempted had not a Munificent HAND held forth its alliftance, and enabled me to do that, which otherwife would have been almoft impracticable. Under P R E F A G E. Under fuch favourable and happy circumftances, even the mod indolent would be rouzed into action, and the moll unpromifing genius might be infpired ; and, it to this be added the folicitations of my friends on this occafion, and the kind recep¬ tion my former work has met with, I had every inducement that could be propofed, for exerting my utmoft abilities in the fervice of the public ; and I can with great truth aver, that to be any way ufcful to mankind, is of more weight with me, than lucrative confiderations. The work is indeed large, and from the great number of fchemes, very elegant¬ ly engraved, mufl necelfarily be expenfive *. But to write upon fo extenfive and difficult a luhjecl, without properly connecting, and thoroughly explaining, the prin¬ cipal parts of it, would have been like attempting to eredb a perfedl, and convenient building, without any regard to a necclfary quantity of materials, the dilpofitions of its parts, and the utility of the ftrudlure. All the figures, which are produced as general rules in this work, I have ven¬ tured to call my own ; not hav ing had any other aliiftance herein, than fome elegant deligns for the Perfpedlive ; and likewife all the prints which particularly relate to the architeftonic fector, which is an inftrument of a new and curious conftruftion ; and by which, perfons wholly unacquainted with archite£lure, may be enabled to delineate any part of it, with elegance and exadfnefs. Now if any one lhould fay, that my rules (ftriftly (peaking) may all be obtained from the ftudy of Dr. Taylor, I would anfwer, that the fame kind of remark will hold good againft every mathematician, that has wrote fince the time of Euclid. And I would at lead defire him to confider, whether the digefting theorems into a regular order, deducing proper corollaries from them, and illuftrating them by new fchemes and examples, has not as juft a claim to the title ol original, as any thing that can be produced in an age like this, when almoft every fubjefl feems to be quite exhaufted. I MAKE no doubt, however, that the method for drawing many of the finifned examples, will at lead be confidered as new ; and they may feem calculated to over¬ turn an opinion, which has long fubfifted, though (as I apprehend) founded on erro¬ neous principles ; I mean the making the perfpefliive reprefentations of columns, that '* And it would have been more fo, but for the reafon above-mentioned. preface. that are placed parallel to the plane of the pifture, increafe in their apparent magni¬ tude, in proportion to their diftance from the center of it. This (as I * have obser¬ ved before) has occafioned much controverfy, amongft painters, mathematicians and other ingenious men; this, therefore, being neither a new, nor lingular opinion 1 appeal to the fenfe of feeing, as a mod faithful guide on this occafion, and to the unbiafled judgment of thofe, who can belt determine from practice and experience. I HAVE nothing more to add by way of Preface, than to requeft a candid and im¬ partial examination of this work, which I have endeavoured, with much care and affiduity, to make as perfeft as I was able. With thefe hopes, I flatter myfelf, that the intenfe pains, and ftrift application of fome years, will neither be entirely thrown away, nor cenfured undefervedly. * See Dr. Brook Taylors Perlpeffive made eafy, andpubli/hcd by me in one vol. in i 75J , page 6,- “a®* CHAP. I. Introduction to the Ufe of the SECTOR. j3|l!-OtO S the following Treatife is entirely applied to Architecture, we muft of neceflity begin with defcribing the different Orders, and the method of drawing the various parts, before ^.D A we attempt the perfpeCtive reprefentation of them. The meafures made ufe of have QIOIQ been all laid down from an Architectonic SeCtor ; an accurate defcription of it’s ufes will anfwer ail the purpofes of an introduction. We owe to Revilio Bruti the form of the Architectonic SeCtor, who adapted>it'tcf Scamozzi’s archi¬ tecture ; he, for reafons belt known to himfelf, carefully fuppreffed the manner of laying down the diffe¬ rent divifions; to us they are unknown, and we have reafon to believe that the one, we propofe to treat ot, is conflruCted upon new principles, § and comprehends all the neceffary meafures for delineating the principal parts of architecture. A A § Owing to the ingenuity of that excellent workman Mr. George Adams, Mathematical Inftrument-maker to His R yal Highnefs the PRINCE of WALES, in Fleet-ftreet, London; who makes thofe Sedtors in filver, ivory, or wood; and who can wich great accuracy, by the fame principle, lay down on the vacant fpaces any other meafures, which the inftrument is capable of receiving. A G [ ^ ] ciicral Defcription of the Inftrument. The orders are taken chiefly from Palladio, correfled however by tire pureft examples of antiquity T„r. lnffrument is compofcd of a Sedtor and Limb; on each fide are laid down two lines one of fl 1 d'f- I t r f hCreaftCr mCnti ° n) thC ° thCr ° f 6 °- Each ° f th * divifions are u -dmded tnto 6 wh,eh renders rt an univerfal fcale of modules for drawing the different orders ■ for let the Seftor be opened, fo that the diameter of the intended column be fet off between 6o and 6o (the number of minutes, a module or diameter of a column is fuppofed to be divided into) and the exadt meafure of any one moulding, & c. may be taken to the 6th, and even to the x«h of a minute ; which is amply fufficient for the greateft accuracy. On the bevel or chamfered edges of the Seftor are placed the numbers of the circular lines on e limb, viz from r to aa on one fide, and from a 3 to +3 on the other, with the initial letters of the orders belonging to each of thofe lines. The limb has two fades or faces, each containing four intervals of circular lines, the general contents of which are engraved on the beginning and end of the arch. Five circular line,, comprehending the five orders, form for tire mol part an interval; though the fiiif and fourth on the firft face, and the fourth on the fecond are compofed of fix. The intervals are frequently fob-divided into two, three, or more fpaces, called bars ■ thofe are dif tmguifhed by two perpendicular lines that crofs the divifions at the b- ■ • ■ ° %»d .lid, ,h, leg. or ,1,0 saw „ „ . Fn ;r K j;i rir”"' • - “-—* * ~ .-...«... ,.„i Firft Face of the LIMB. Lines i to 5, Contain the heights of the five orders in colonnades and arches. Line 6, Is divided into two bar= • t-V- fiirfl- .1 1 • , the Done leffer H^ ^^ 5 ^ ^ Second ft of five Lines, and feven Bars. 7 IUJ ' hr colonnades, viz. of columns without pedeftals, and t ,!C dufcrent intcrcolumniations to each order. ^' nd V ''"’ Pr °j ections ° r g ,au colonnades with pedeftals. ft liird Car, P ; actions of leffer arches. fourth Car, Projections of greater arches, fifth Bar, Heights of Pedeftals. .Sixth Bar, Heights of entablatures. Seventh Bar, Half heights of confoles. Third Interval of five Lines and two Ears. 1 “ 10 11 llk 8> m the iulf widths, Widths, and heights of doors, their entablatures, confo.es, &c. proportioned to the five orders. Second Bar, Heights of columns, with their capitals and bafes. fc, ' ChaS brenufedto!ake hr the entire heights of orders, with their great parts; . - nS dmfiom COnKln men bets of carl, ofthefe parts, on a larger fcale. Fourth Lines 17 to 21, [ 3 ] Fourth Interval of Six Lines. Are divided into fix Bars. Firft Bar, Heights of the entablatures of doors. Second, The projections of the cornices of doors. Third, Heights and projedions of the architraves of doors. Fourth, Heights of architraves, and widths of confoles. Fifth, Heights of ballufters, proportioned to the five orders. Sixth, Projections of ballufters. Line 22, Conlifts of five Bars. Firft Bar, Doric flutes in piano. Second, - upright flutes. Third, Flutes and fillets of columns in piano. Fourfl^-of upright columns. Fifth,-of pilafters. Second Face of the LIMB. Firft Interval of Five Lines and Six Bars. Line 23 to 27, Firft Bar, Contains the heights of the different members of imports to the letter arches. Second, Contains the heights of impofts to the greater arches. Third, Gives the widths of leffer archivolts, and projections of the leffer impofts. Fourth, Has the widths of greater archivolts, and projections of greater impofts. Fifth, Projections of leffer archivolts. Sixth, Projections of greater archivolts. Second Interval of Five Lines and Six Bars. Line 28 to 3 2 Firft Bar, Contains the greater half diameters of columns and the projections of bafes. Second, Leflcr half diameters of columns, and projedions of capitals. ' Third, Projedions of friezes and architraves. Fourth, Projedions of friezes and cornices. Fifth, Heights of block cornices, proportioned to the five orders. Sixth, Projedions of block cornices. Third Interval of Five Lines and Five Ears. Line 33 to 37, Firft Bar, Heights of bafes. Second,-of bafes of pedeftals. Third, - of cornices of pedeftals. Fourth, Projedions of bafes of pedeftals. Fifth, Projedions of cornices of pedeftals. Sixth, Half heights of the die of pedeftals. Fourth Interval of Six Lines. Line 38 to 42, Divided into Three Bars. Firft Bar, Heights of capitals. Second,-of architraves and friezes. Third,-of cornices. B Line [ + J Line 43, Contains the heights and projections of the modern Ionic capital and entablature. It is divided into Five Bars. Firft Bar, Height of the capital. Second,-of architrave and frieze. 1 bird, of modillion cornice. Fourth, Projection of capital. » Fifth, Projection of modillion cornice. CHAP. II. The Ufe of the Inftrument in drawing the Tufcan Order. W E arc now to 1,1 ew the of the inftrument in drawing Orders, &c. for which purpofe we begin with the Tufcan Order, through all it’s different applications, whether in fimple columns, co- lonnades, arches, doors, See. But we mu ft firft explain a circumftance that may feem attended with difficulty, yet is however as fimple in it s operation, as any other part of the feale. Thb fub-divifions, that mark off the different members on the limb, are little lines,, ranged for the nioft part on the upper fide of the circular projeftions, called forward divifions; but fometimes they are placed below the.circular hnes pointing downwards, inftead of upwards; thefe lad we term backward divifions, and are occafioned by the minutenefi of the members, at the beginning of the bar, that arc too fmail to be taken oft the Scflor, even .when the legs are ffiut. Now, as the common method of fetting oft the d.vtirons of a bar is to fix one leg of the Seftor at the beginning, and to open it till the other leg cuts the laft d.vrfion of the order in this bar, which gives the total height or width, and then bnngmg back that leg, which we call the moveable one, to all the different forward divifions, there re- matns nothmg but the backward ones to work off; which is effefled by fixing the moveable leg at the warddtl'* ft and unferewing the fixed leg, making that cut each back- ward divifion. But all this will become plain by practice. . „ L " US bCg ;“ With thc S eneral hci S hts ° f this Order, as laid down on the firft face of the inftrument, firft interval, and firft line. / 1 11 UL ^ OM k S 8f the fet °r *= beginning of the line, No. i, then move the other fill it cuts the laft divifion, No. , 8, and this is the total height of the order. Ba.NO the moveable leg back to r 7 , this cuts off the bafe of the pedeftal, pafs over .6, which we ffia'l explain ptefently, and to , s is the dye of the pedefta, ; to rp is the cornice of the pedeffia, ; to 13 af of thc CO U then pafs over the divifion marked with letters that belong to doors or arches ^gthemoeabelegtosthetopofthetrunkS; to + the capital, to , the Lhitrave 5 ,0 2 frieze, and alfo the cornice. 5 ° 2 !' 7 Ch °° rC “ f "I' ° rder Wkh of a pedeftal, then the Sector opened from plinth Whcrcthcl —-ffedandbroughtbaokto rp, omitting i 5> cuts off the height of the It mal tronk . b '«ufe we look upon the (haft to include the upper cinfhire, whereas in working with this inftromen, it is more convc moulding whatfoever. the aftrat nient to ;al below the capital, as well as keep the trunk diftimft Aom any [ 3 ] lx is hardly worth mentioning, that the moveable leg carried to i 4) gives the height of the column •with it’s entablature, without either pedeftal or plinth. In like manner the moveable leg brought to 4 > cuts off the entablature without the column. Of INTER COLUMNIATIONS. Plate HI. Fig. A. Having thus obtained the heights of the principal parts of this Order, we now proceed to the projeftions; to which we fhall join the different diftances, or intercolumniations Anted to it; and as thofe intercolumniations are different in columns placed without pedeftals, or with them we have projedions proper for each on two different bars, viz. the ill and ad upon the ad interval of the i ft face. The firft bar gives us, befides the projeftions of the columns and entablatures, two different inter- columniations, one of 3 and r- 3 d modules, the other of 4 modules, or diameters. We will begin with the .ft bar, yth line; the Seftor opened from the beginning No. r, (which an- fwers to the axis of the column) to the kft divifion No. 8, we ff all have the greater half intercolum nation for columns, without pedeftals; .toy gives the leffer intercolumnation; . to 6 the projediou of the cornice which in this and all the other Orders is transferred from 6 to pc); the remaining num- bers are backward divifions. Now to prevent miftakes, we will obferve in this place, that whenever we reverfe the legs of the Seder to take off a backward divifton, we muft alfo reverfe the laying down our meafures upon paper. For example, to put down the forward divifions in this figure, we fix our compaffes at 1, and by ex¬ tending them to 8, we get the greater half intercolumniation; but for the four backward divifions of the plinth and column, we fix one point of our compaffes at 8, anfwering to the end of the bar on the mftrument, and then from thence to the firft backward divifion No. 2, will give us the piojedion of the top of the trunk; to 3 the bottom of the trunk, and alfo the capital; to 4. the bafe; and to 5 the plinth. And we will alfo obferve, that in reckoning the number of divifions on the inftrument, comffpond- ing to thofe on the prints, we always count the beginning of the bar r, the neareft backward divifion 2, and fo on with all the backward divifions in their order ; then we continue all our numbers from the firft forward divifion to the laft number of all, which is conftantly the end of the bar. The columns with pedeftals and two intercolumniations, one of 5, the other of 4 modules. The Seftor opened from the beginning of the bar No. 1 to 8 the laft divifion, marks the greater half intercolumniation ; i to 7 the leffer intercolumniation ; 1 to 6 the projeftion of the cornice ■ 1 to 5 the projection of the plinth and cornice of the pedeftal: the remaining are backward divifions ’there¬ fore from 8 to 4 is the dye of the pedeftal, and bafe of the column; 8 to 3 the greater diameter, and alfo the capital• 8 to 2 the leffer diameter. We have now the heights and projeftions of this Order, with or without pedeftals; we fhall next employ the inftrument in the formation of .arches. The heights of thefe are on the firft interval, and firft or Tufcan line, firft face; this we have al¬ ready done but as far as it relates to the Order itfelf: upon the fame line, however, there are feveral di- vffions marking the heights of arches, &c. which were omitted in forming colonnades, but become at prefent neceffary. Plate IV. F:g. C and D. Open the Seftor, and from the beginning of the line No. i to 6, marked k, gives the bottom of the key-ftone to the leffer arch. 1 to 7 k, I he bottom of the key-ftone to the greater arch, i to 9 i, Top of the impoft to the leffer arch. l to i o l, Bpttom of the impoft to the leffer arch, and top of that of the greater arch. 1 to 12 i, Fixes the bottom of the impoft to the greater arch; and thefe are all the general heights neceffary for drawing Tufcan arches. C We We will next take the projections of arches, which are on the fecond interval, third and feinth bars, and Tufcan line. Proje&ions of ldTer ARCHES. And firft for the leftcr arch, from i (which anfwers to the middle of the arch) to 13 gives the projection of the cornice. pig, c. 1 to 12, The greater half diameter, and projection of the capital. 1 to 11, The leftcr half diameter. 1 to 10, The axis of the column. 1 to 9, The greater half diameter. 1 to 8, The greater projection of the archivault. 1 to 7, The bafe of the column. 1 to 6, The plinth. 1 to 5, The piiafter, and infide of the archivault. 1 to 4, Projection of import. The remaining are backward divirtons, therefore from 13 to 2, is the bottom of the key-ftone. 13 to 3, is the top of it. Projections of greater ARCHES. Fig. D. 1 to 13, The projection of the cornice. 1 to 12, The greater half diameter, and projection of the capital. 1 to 11, The leffer half diameter. 1 to 10, The axis of the column. 1 to 9, The greater half diameter. 1 to 8, The greater projection of the archivault. 1 to 7, The dye of the pedeftal, and bafe of the column. 1 to 6, The bafe and cornice of the pedeftal. 1 to 5, The pedeftal and leffer projection of the archivault. 1 to 4, The projection of the import. The remaining are backward divirtons, from 13 to 2, is the bottom of the key-ftone. 1 3 to 3, the top of it. If only a fingle pedeftal, column, or entablature be wanted, we are to proceed in the following manner. Firft, for the pedeftal, the heights of which are on the firft face, fecond interval, fifth bar, Tufcan, or feventh line. A Single PEDESTAL. Plate XX. Fig. I. Fix one leg of the SeCtor at the beginning of the bar No. 1, and carry the moveable leg to the laft divirton, and we fhall know the entire height of the pedeftal ; brought back to the divirton 4 cuts off the plinth ; pals over the 3d divirton then, becaufe the heights of the dye and cornice are fixed by a backward divirton, therefore now fix the moveable leg at the end of the bar No- 1 bi the < hei leg to No. 2, which cuts off the dye and cornice required. Jr only a plinth is wanted, and not a pedeftal, then from 1 to 3 determines the height of it. Having thus obtained the general heights of a fingle pedeftal, there now remains to fhew how to cut off the genera: projections* which are placed on the firft lace, fecond interval, fecond bar, Tufcan line ; [ 7 ] lme ; for, to avoid a repetition, thofe meafures mull be taken from „ , of the inftrument at No. i, and carry the other to No 8 which ' L “ Fk °" e !cf from t to 5 cuts off the plinth and cornice; the remaining is a 1 mterCO,umnk ^. the dye. remam.ng ,s a backward divtfion, therefore 8 to 4 Is Of a Single COLUMN h„e?r“ 0UtPedeflaJS> 0rentibW - « * third interval, fecond bar, twelfth gives the entire Light IflhTcolZTIromNo ^:r tTj cL'T i^bT' '° ^ “ dil ' ifi “. verfed for the backward diviftons we take front ^2 il l ^ ^ ~ height of the column, and alfo the bottom of the capital ' N *’ g ‘ m thc "rr:::" •—* -.- divilions, therefore 8 to a is the top of the triLk “gT TT" ' ^ "* backward capital; and 8 to 4 the bafe. ’ 3 * e b ° tt0m of tile tr ™k, and alfo the , °f an ENTABLATURE Foa the general heights of an entablature only, firft face fecond ■ , , ' The inftrnment fixed as before, then ’ ’ ^ Tufcan iine ' t to 4 ’ tT °V he e “ ire bCight ° f the “Mature. 1 to ji i architrave. „ 1 t0 2 ' T,le fricze - and alfo the cornice.- Fo» the general projeaions of an entablature only • firft fie r a ■ F “ S ^r at the beginning of the bar, then ’ fCC ° nd ^ ^ • to 8, Is the greater intercolumniation 8 '° 6 ’ I'’ 6 “ miCe; aDd the faack '™d divifion ° a, Gives the frieze, and alfo the bottom of the architrave. ° f ever y particular MEMBER. to fliew the method ^^' tW remains We (hall begin with the bafe of the pedefta, the h 'T ^ of the limb, third interval, fecond bar, thirty-third linL“ W ^ ^ ^ —-—- Oder feparate, and to the fcale of 30 to , 0 . thouuh th 7' l ” W therefore ™de every prints about 29 1-half to 29 1- LL t0 3 ° ; th0USh tfaC fbrinking 0f tbe F a P er in printing has madeUe D Plate [ 8 ] Height of the Bafe of the PEDESTAL. FlateHH. Fig. A. The Sector being fixed as before, then 1 to + cuts oit die height of the baft. 1 to 3, The Doric cyma. l to 2, The fillet, and alfo the height of the plinth. The Dye of the PEDESTAL. The half height of the dye of a pedeftal is laid down on the fecond face, third interval, fixtli bar, thirty-third line. The Sebtor opened from the beginning i, to the end of the Tufean line 3, gwes half the height the dye. The PLINTH Only. Ir only a plinth is to be added to the column, and not a pedeftal, then the SeSor opened from the beginning of the Tufean line to the feeond divifion, mark'd with P, gives half the height of the plinth. Cornice of the PEDES! A L. Cornice of pedeftals, third interval, third bar, thirty-third line. The Sebtor opened from the beginning of the bar 1, to the laft divifion 3, gives the entire cornice of the pedeftal. I to 2, Gives the height of the cyma reverfa, and alfo of the regula. Bale of the COLUMN. Base of the column, third interval, firft bar, thirty-third line, fecond face. One leg of the Seftor placed at the beginning of the bar. No. 1, the other carried to the laft divi¬ fion 4, marks the entire height of the bafe. 1 to 3, Cuts off the lower cincture. 1 to 2, The heights of the tore and plinth. Heights of the CAPITAL. Foe the heights of the capital, we muft take the fourth interval, of the fecond face. The capital is laid down on the firft bar, thirty-eighth line. One leg of the Seder fixed to the beginning of it, No. 1, the other carried to the laft divifion 7> give the entire height. 1 to 6, Is the bottom of the abacus. 1 to 5, That 'of the ovolo. 1 to 4, The fillet. The reft are backward divifions. 7 to 3, Is the bottom of the neck of the column. 7 to 2, That of the aftragal, and the upper cindum. Architrave and Frieze. The next or fecond bar on this fourth interval, and the thirty-eighth line, gives the heights of the 1 ufcan architrave and frieze. Opening marks the entire [ 9 ] Opening the SeCtor as ufual from the beginning No. i, to the laft divifion 5, height of both thofe parts. 1 to 4, That of the frieze. 1 to 3, Fillet of the architrave. 1 to 2, The heights of the iirft and fecond fafcia. The CORNICE. Heights of cornices are to be found on the third bar of the fourth interval, thirty-eighth, or Tufcan line, fecond face. The SeCtor being opened from the beginning, No. 1, to the laft divifton, thews the entire height. 1 to 7, The upper fillet. 1 to 6, The cyma. 1 to 5, The fillet. 1 to 4, The corona. 1 to 3, The ovolo. 8 to 2, Being a backward divifion, gives the height of the fillet and cavetto. Proje&ions of the MEMBERS. These are all the heights of this order. We fhall now take, in the fame manner, the projections, which are all fet off from the axis of the column ; and from thofe points in the plates, where the afte- rifks are marked within a circle. The PEDESTAL. And firft for the bafe of the pedeftal; fecond face, third interval, fourth bar, Tufcan line: The SeCtor opened from the beginning, No. 1, to the laft divifion 7, gives the projection of the plinth. 1 to 6, That of the fillet. Fig. A. 1 to ja The projection of the Doric cyma; paffing by the fourth divifion, marked P, 1 to 3,3 which is the projection of the plinth as in Fig. B. 1 to 2, That of the dye. Projections of cornice of pedeftah, fecond face, third interval, fifth bar, Tufcan line. The SeCtor opened from the beginning, No. 1, to the laft divifion 5, is the projection of the fillet, or corona. 1 to 4,) a n d > That of the cyma reverfa. 1 to 3,5 1 to 2, That of the dye. The C O L U M N. Base of the column ; fecond face, fecond interval, firft bar, Tufcan or twenty-eighth line. The SeCtor opened from the beginning, No. 1, to the laft divifion 4, gives the projection of the plinth and tore. 1 to 3, That of the cindture. 1 to 2, The greater half diameter of the column. Lesser half diameter and capital; fecond face, fecond interval, fecond bar, Tufcan line. The SeCtor opened from the beginning, No. 1, to the laft divifion 5, contains the projection of the abacus. 1 to 4, That of the ovolo. 1 to 3, The fillet of the ovolo, the upper cindture, and the center of the aftragal. 1 to 2, The neck, and lefier half diameter of the column. E Frieze [ ] The ENTABLATURE, Frieze and architrave ; fecond face, fecond interval, third bar, Tufcan line. The Se&or opened as ufual, from the beginning, No. i, to the laft divifion 4, gives the projection of the fillet of the architrave. 1 to 3, The upper fafcia. 1 to 2, The lower fafcia and frieze. Frieze and cornice; fecond face, fecond interval, fourth bar, Tufcan line. The Sector opened from 1 to the laft divifion 9, gives the fillet of the cyma, or entire projection of the cornice. 1 to 8, The lower part of the cyma, with it’s fillet. 1 to 7, The corona. 1 to 6, The tooth of the corona, or end of the cyma. 1 to 5, The part of the corona, broke by the cyma. 1 to 4, The lower part of the cyma, or ovolo, and fillet, alfo the top ol the cavetto. i to 3, The cavetto. 1 to 2, The frieze. Heights and Projections of IMPOSTS, Sec. We have now laid down the heights and projections of all the parts of this Ordci ; which hold equally in fingle columns, colonnades, or arches: but in this laft difpofition there are two capital parts, viz. imports, archivaults, and key-ftones, whereof we have only had the general meafures; remains there¬ fore the particular mouldings. Plate XVII. Thofe of the imports are laid down on the fecond face, firft interval; and the heights of thofe adapted to the leffer arches are marked on the firft bar, twenty-third, or Tufcan line. Let the Sedtor be opened from the beginning of the line 1, to the laft divifion 7, and we ftiall have the entire height of the impoft. 1 to 6, Cuts off the plat-band or fafcia. 1 to 5, The Doric cyma. 1 to 4, The fillet. Then for the two backward divifions. 7 to 3, Gives the height of the corona. 7 to 2, That of the cavetto, and alfo the fillet above it. The heights of imports for greater arches are on the fecond face, firft interval, fecond bar, Tufcan line. The Sector opened from the beginning 1, to the laft divifion 8, gives the entire height. 1 to 7, Cuts off the lower fafcia. 1 to 6, The upper fafcia. 1 to 5, The fillet. 1 to 4, The cyma. 1 to 3, The fillet. And laft:'-, the backward divifion. 8 to r, Gives the height of the Doric cyma, and fillet above it. Proje&ions [ « ] Projections of Imports, and Width of Archivaulcs. The projeflions of thefe impofts are on the firft interval of the fecond face, third and fourth bars: and as archivaulrs always fall upon the impoft, we fhall at the fame time take off the different members belonging to them. And firft for the lefler impofts, and archivaults; third bar, Tufcan line. The Seflor opened from the beginning i, to the laft divifion 12, gives the entire breadth of the archivault, and projection of the impoft. 1 to n, That of the cavetto. 1 to 10, The corona. 1 to 9, The fillet. 1 to 8,£ and r The Doric cyma. 1 to 7,^ 1 to 6, The fafcia. 1 t° 5> The pilafter, and total width of the archivault. 1 to 4, Cuts off the firft fafcia of the archivault. Then follow the backward divifions. 12 to 3, Is the fecond fafcia. 12 to 2, The Doric cyma, and alfo it’s fillet. We next come to the greater impofts, and archivaults, fourth bar, Tufcan line. The Sector opened from the beginning i, to the laft divifion 12, gives us the width of the arclii- vault, and entire projection of the impoft. Is the projedlion of the Doric cyma. 1 to 10, J 1 to 9, The fillet and cyma. 1 to 8, The lower part of the cyma and fillet. 1 to 7, That of the upper fafcia. i to 6, The lower fafcia. 1 to 5, The projedlion of the pilafter, and total width of the archivault. 1 to 4, Cuts oft the firft fafcia of the archivault. And now for the backward divifions. 12 to 3, Is the fecond fafcia. 1 2 to 2, The Doric cyma, with it’s fillet. Thus we have the widths or heights of archivaults; the projections of their members are feldom diawn in plans, but yet abfolutely neceffary to be known ; they are therefore on the fifth and fixth bars, of the firft interval, fecond face. Projections of Archivaults. N. R. As thefe projections take up too fmall a portion on the fcale, to admit of their being laid down by themfelves, it was neceffary to affix fome arbitrary width before them ; the method we have followed is to repeat the height or width of each archivault, which is followed by the projections. Thf re fore in drawing any of their projections upon paper, we mull always have an eye to this additional width, which, though neceffary in the conftrudtion of the inftrument, and fetting off the diviiions, is of no ufe in the drawing. F First Ti-ir Sector opened from the beginning, No. i, to the laft divifion 6, gives (as we have fed belore) the width of the archivault, and it’s projection. 1 to 2, ' Projections of archivaults of greater arches; fixth bar, Tufcan line. The Sector opened from the firft to the 6th divifion, as belore, gives the width and projection of the archivault. are of five kinds, one adapted to each order; on die fecond face, fecond interval, fifth and fixth bars, Tufcan line. First for the heights; fifth bar. Plate XVlll.The Sector opened from the beginning of the firfh bar, to the laft divifion 9, gives the entire height. 1 to 8, The upper fillet. 1 to 7, The cyma. 1 to 6, The fillet. 1 to 5, The corona. 1 to 2, The top of die modilion- Project 1 6ns of the block cornice; fixth bar. The Sector opened from the beginning 1 , -to the laft divifion 8, gives the entire projection of the cornice beyond the upright cf the wall. Of the three backward divifions. 8 to 4, Cuts off half of the breadth of an inward modilion. [ r 3 ] Of BALLUSTERS. We come next to ballufters, which are alfo adapted to the five Orders; thefe are on the firft face, fourth interval, fifth and fixth bars. Heights of ballufters; fourth interval, fifth bar, Tufcan line. N. B. Thefe are drawn by the fcale of fixty. Plate XIX. The Sedtor opened from the beginning i, to the laft divifion i6, gives us the entire height. I to 15, Cuts off the upper fillet, or abacus. I to 14, The ovolo. I to 13, The fillet. I to 12, The neck. 1 to 11, The aftragal. I to 10, The fillet. I to 8, The height of the vafe. (And obferve that 1 to 9 gives only the line on which the greateft projection of the vafe is to be marked; but this divifion is of no other ufe in the heights, and therefore marked with a crofs on the bar) 1 to 7, The lower aftragal. 1 to 6, The fillet. 1 to 5, The fcotia. 1 to 4, The fillet. 1 to 3, The tore. 1 to 2, Cuts off the plinth, and gives, at the fame time, the height of the fub-plinth. Projections of ballufters; fixth bar. The SeCtor opened from the beginning 1, to the laft divifion 10, on the Tufcan line, gives the pro¬ jection of the entire ballufter. In all the other fcales of this inftrument, the projections are marked from the central line of the bottom, (arches excepted) but here jt is neceffary to fet off the projections of the ballufter from A or C,on each fide of it’s axis. This width, 1 to 10, the total projection of the fub-plinth put on paper, we bifedt, which gives us the femi-diameter of this ballufter, which could not be laid down upon the limb ; then from A towards C, 1 to 9, Is the projection of the plinth and tore of the bafe, and the abacus alfo of the capital. 1 to 8, The ovolo of the capital. 1 to 7, The greater projection of the vafe, and the lower fillet of the fcotia belong¬ ing to the bafe. 1 to 6, The fillet of the capital, and aftragal, at the neck. 1 to 5, The fillet to the top of the vafe. 1 to 4, The lower aftragal beneath the vafe. 1 t,o 3, The upper fillet of the fcotia, top of the vafe, and neck of the capital. 1 to 2, The narroweft part of the fcotia. We have now given an example of every thing that can be drawn from the inftrument, except flutes, which do not belong to this Order ; and doors with their ornaments. G Of [ 14 ] Of DOORS. Doors are fometimes placed in colonnades, as in porticos of temples; and then their heights mud be proportioned to the columns. To do this upon the fcale; after having drawn the Order, as laid down -on the fird face, fird interval, Tufcan line, one leg of the Sedfor fixed at the beginning of the Tufcan line i, let the other be opened to n, marked d, upon the limb, then we fhall cut od' the height o! doors proportioned to colonnades, without pededals. i to 8 marked alfo d, cuts oft the height of doors for colonnades with pededals. Thefe two divifions, 8 and ii, were not mentioned when we were drawing the heights of the Order, being of no ufe, except for the purpofe mentioned. If doors are to be placed in arches, their height is fixed, which we diall explain in the Ionic Order. Heights of doors, and their entablatures; fird face, third interval, fird bar, feventeenth, or Tufcan line. Having determined either the height, width, or half width of a door intended to be drawn, fix one leg of the Sector at the beginning of the bar, and open the other to any one of thefe given lengths, fuppofe the half width, then the meafure of that taken with the compaffes, from the fcale the plan is to be drawn by, mud be applied to the Sedtor, and where it coincides upon two oppofite numbers, which in this figure is 23, 23, will become the proper fcale for the general height of doors. General Heights of DOORS. Plate XX. The moveable leg of the Seftor carried to the laft divifion of the line 12, gives the entire height of the door with it’s entablature. I to 11, Cuts off the cornice. I to 9, The frieze. I to 8, Cuts off the architrave, and confequently i to 8 is the height of the door without the entablature. I to 3, The width of the door. I to 2, The half width, which we begun with. —— § If we make ufe of a kneed architrave, then after taking I to 8, The height of the door, I to 5, Gives the depth of the knee. Heights of C O N S O L E S. If a confole is to be added, it is generally made to fupport the cornice, and to terminate with the bottom of the knee, with a leaf falling from it. I to 11, Therefore gives the top of the confole. I to 10, The eye of the upper volute. I to 7, The top of the lower volute. 1 to 6, The eye of the lower volute. 1 to 5, The bottom of the lower volute. I to 4, Cuts off the length of the leaf. Having thus got the general heights of the entablatures of doors, we now come to the particular mouldings; which are on the fird face, fourth interval, fird bar. Heights of Entablatures of DOORS. Heights of entablatures of doors; fird bar, Tufcan line. The Sedtor opened from the beginning 1, to the lad divifion 13, is the entire entablature. 1 to 12, § We (hall confider this article more fully hereafter; for in this example the kneed architrave and confole are purpol'ely omitted. [ *5 ] Pi. a t e XXII. I to 12, Cuts off the upper fillet of the cornice, i to ii, The cyma. i to io, The fillet, i to 9, The corona. 1 to 8, The ovolo. i to 7, The fillet. i to 6, Cuts off the cavetto, and the entire cornice, i to 5, Cuts off the frieze, and gives us the top of the architrave. 1 t0 4 j The fillet of the architrave, i to 3, The Doric cyma. The backward divifion. 13 to 2, Gives the upper and lower fafcia. Projections of Cornices for D O O R S. Projections of the cornices of doors; fecond bar. The SeCtor opened from the beginning 1 to the laft divifion, is the greateft projection of the cyma and fillet. 1 to 6, The fillet. 1 to 5, The corona. 1 to 4, The ovolo. The backward divifions. 7 to 3, The fillet of the cavetto. 7 to 2, The bottom of the cavetto. Of Architraves for DOORS. Projections of the architraves; third bar. As the entire projections of architraves, are too fmall to be laid down by themfelves on the fcale, we are obliged here, as in archivaults, to add fome certain mcafure before them ; for which purpofe we choofe to repeat the height of the architrave itfelf. The SeCtor opened from the beginning of the bar to 6, the laft divifion, gives us both the height and projection of the architrave. 1 t° 5,) and r The projections of the Doric cyma. 1 to 4,' 1 to 3, That of the upper fafcia. 1 to 2, The lower fafcia. Of CONSOLES. Plate XXIII. Widths of confoles; fourth interval, fourth bar, feventeenth line, firft face. These, like the laft, contain too fmall a fpace to be laid down by themfelves; but as the confole is generally placed by the fide of the architrave, we add the height of the architrave to it 4 which fhall be more fully explained in the next Order. In this Order, the confole is plain without any members, fo that we have nothing but the entire width to lay down. H The [ 16 ] The Sector opened from the beginning r, to the end of the line 3, gives us (as we faid before) the height of the architrave, and breadth of the confole. 1 to 2, Cuts off the width of the confole. N. B. Since the different heights are at a conffderable diftance from each other, and would, if put at large on the Se&or, take up too much fpace, we have therefore laid down only one half of their real heights, which muff carefully be remembered. Half heights of confoles; firft face, fecond interval, feventh bar, Tufcan line. Fix one leg of the Se&or at the beginning of the bar 1, and the moveable leg carried to 7, gives one half of the entire height of the confole. 1 to 6, Repeated, The eye of the upper volute. 1 to 5, Repeated, The bottom of this volute. 1 to 4, Repeated, The top of the lower volute. 1 to 3, Repeated, The eye of the lower volute. 1 to 2, Repeated, The bottom of the lower volute, and alfo the top of the leaf. f.a-5^ i he The U S E of the ARCHITECTONIC SECTOR, In drawing the DORIC ORDER. General Heights of the ORDER. CHAP. III. E fhall next fhew the ufe of the inftrument in drawing the Doric Order, &c. - « * We begin with the general heights of this Order, which are upon the firft face of the ioc § W >• 1 '; <2 limb, firft interval, fecond line. f f M fcTf § Screw one leg of the Setftor to the beginning of the fecond line, No. i : then move the other till it cuts the laft divifion, No. 18 ; this is the total height of the Order. Plate V. Fig. A. B. Bring the moveable leg back to 17, this cuts off the bafe of the pedeftal. 1 to 16, The dye. 1 to 15, The cornice. 1 to 14, The bafe of the column. Then palling over the divifions marked with letters which belong to doors, or arches, carry the moveable leg from 1 to 5, The top of the trunk. 1 to 4, The capital. 1 to 3, The architrave, including the tenia. The remaining number is a backward divifion ; therefore unferew the fixed leg, and place the move- able one to No. 18 the laft divifion on the line, then bring the other to the backward divifion, which will cut off the frieze, and alfo the cornice. See an article in page 4, and alfo in pao-e 5, backward divifions. The moveable leg carried to No. 15, gives the height of the column, with it’s entablature, without a pedeftal. In like manner the moveable leg brought to 4, cuts off the entablature, without a column. Proje&ions of COLONNADES. Thus having obtained the heights of the principal parts of this Order, we now proceed to the pro¬ jections, and the different diftances or intercolumniations fuited to it which are on the firft and fecond bars of the fecond interval, fecond line, firft face. [ IS ] The firft bar gives, befides the projections of the column and entablature, two different intercolum- niations, one of two modules, the other of one module, and fifteen minutes. Wf. fhall begin with the firft bar, eighth line. The Sector, opened from the beginning of the bar, No. r, (which anfwers to the axis of the column) to the lafl: divifion 8, we fhall have the greater half intercolumniation. i to 7, Gives the leffer half intercolumniation. i to 6, The projection of the cornice. The remaining numbers are backward divifions, fo that 8 to 5, Is the projection of the plinth, or bafe of the column. 8 to 4, The capital. 8 to 3, The greater half diameter of the column. 8 to 2, The leffer half diameter, and neck of the capital. Second bar, fecond interval, eighth line. The Doric column with pedeftals, and two intercolumniations, one of two modules and a half the other of one module, fifty-two minutes and a half. The Sedor opened from the beginning of bar No i, to 9 the lafl: divifion, marks the greater half intercolumniation. 1 to 8, The leffer half intercolumniation. i to 7, The projection of the cornice. 1 to 6, The plinth, and cornice of the pedeftal. The remaining numbers are backward divifions, therefore 9 to 5 > Gives the projection of the dye, and bafe of the column. 9 to 4, The projection of the capital. 9 to 3, The greater half diameter. 9 to 2, The lefler half diameter. We have now the heights and projections of this Order, with, or without pedeftals, with their different intercolumniations; alfo the height of columns, and pedeftals feparately : we fhall next employ the inftrument in the formation of arches. The heights of thefe are on the firft interval, and fecond, or Doric line: this we have already done, as far as relates to the Order itfelf ; upon the fame line, however, there are feveral divifions, marking the heights of arches, &c. which were omitted in forming colonnades, but become at prefent neceffary. Plate V. Fig. D. G. Open the Sector from the beginning of the Tufcan line, No. 1 to 6, marked k, this gives the bottom of the key-ftone to the leffer arch. 1 to 7 k, The bottom of the key-ftone to the greater arch. 1 to 8 i, Top of the impoft to the leffer arch. 1 to 10 i, Bottom of the impoft to the leffer arch. 1 to 11 i, Top of the impoft to the greater arch. 1 to 13 i, Bottom of the impoft to the greater arch. These are all the general heights neceffary for drawing Doric arches; we fhall next proceed to their projections, which are on the third and fourth bars of the fecond interval, on the firft face of the limb. Projections [ '9 ] Projections of Doric Arches, without Pedeftals. First face, fecond bar, third interval, eighth line. Plate V. Fig. G. From i to 12, (which anfwers to the middle of the arch) is the projeaion of the cornice ; from i to ii, The capital, i to io, The leffer half diameter. 1 i to 9, The axis of the column, i to 8, The greater half diameter, i to 7, The outfide of the archivault: i to 6, The bafe of the column. I to 5, The pilafter and infide of the archivault. i to 4, The impoft. And the backward divifions, Are for the upper and under part of the key-ftone. Projections of Doric Arches, with Pedeftals. First face, fecond interval, fourth bar. Fig. D. From i to 13, Is the projection of the cornice. 1 to 12, The capital. 1 to 11, Lefler half diameter. 1 to 10, The axis of the column. 1 to 9, The greater half diameter. 1 to 8, The outfide of the archivault. 1 to 7, The bale of the column. 1 to 6, The bale and cornice of the pedeftal. 1 to 5 j The pilafter and infide of the archivault. 1 to 4, The impoft. And the backward divifions, and C Are the upper and under part of the key-ftone. 13 to 2,3 J Heights and Projections of the Doric Leffer ARCH. Plate VI. Heights of Doric leffer arch are laid down on the firft face, fix* line, firft bar. i to 10, Is the entire height of the order. 1 to 9, The trunk. 1 to 8 i, The bottom of the impoft. 1 to 7 i, The top of the impoft. 1 to 6 k, The bottom of the key-ftone. 1 to 5, The top of the trunk, 1 to 4, The capital. 1 to 3, The architrave. 1 The laft is a backward divifion, io to 2, Which gives the top of the frieze, or bottom of the cornice, Projections of Doric lefler arch, firft face, fecond bar, fixth line. 1 to 11, Projedtion of the cornice; 1 to 10, The capital. K 1 to 9, [ 2 ° ] i to 9, The leffer half diameter. I to 8, The axis of the column. i to 7, The greater half diameter, and the outfide of the archivault. i to 6, The bafe. i to 5, The pilafter and infide of the archivault. i to 4, The import. And the backward divifions, to 3 > ^ ^ Are the upper and under part of the key-rtone. Of Single Pedeftals, Columns, or Entablatures. If only § a rtngle pedeftal, column, or entablature be wanted, we may proceed in the following manner. And firft for the height of the pedeftal. Fix the leg of the SeCtor at the beginning of the fifth bar, eighth line, fecond interval, firft face. The moveable leg carried to the lart divifion No. 4, of that line, marks the entire height of the pedeftal. Brought back to No. 3, cuts off the bafe ; but the height of the dye and cornice is a backward divifion, therefore 4 to 2, Will cut off' the cornice, and alfo the dye. Plate V. Fig. B. The general projections of the pedeftal; firft face, fecond interval, fecond bar, Doric line; where we have the projections of great colonnades: therefore fix the inftrument at No. 1, and carry it to No. 9, and we fhall have the greater half intercolumniation. I to 6, The bafe and cornice. The other is a backward divifion, therefore 9 to 5, Is the dye. Columns, without entablatures or pedeftals, are placed upon the third interval, fecond bar, firft face ; the thirteenth line is the Doric Order. The fixed leg placed at the beginning of the bar No. 1, and the moveable one carried to the laft divifion No. 4, gives the height of the column ; brought back to 3, the bafe; and the legs of the SeCtor reverfed for the backward divifion, then 4 to 2, Fixes the top of the trunk, and bottom of the capital. The general projections of the column. The SeCtor fixed as in the laft article ; then 1 to 9, Is the greater half intercolumniation. The others are backward divifions, fo that 9 to 2, Is the top of the trunk. 9 to 3, The bottom of the trunk. 9 to 4, The capital. 9 to 5, The bafe. For the general heights of an entablature only, fix the inftrument at the fixth bar, fecond interval, eighth line, firft face. 1 to 4, Cuts off the entire height. I to 3, The architrave. The § See this article fully explained in the Tufcan Order, Page 7, Plate XX. Fig. 1. [ « ] The laft is a backward divifion, therefore 4 to 2, Cuts off the frieze, and alfo the cornice. General projedions of an entablature only, are on the firft face, fecond interval, fecond bar, Doric line. The Sedor fixed at the beginning of the bar, then i to 9, Is the greater half intercolumniation. i to 7, The cornice. The remaining is a backward divifion, therefore 9 to 2 Cuts off the frieze, and alfo the bottom of the architrave. Heights and Projections of the M E M B E R S. Thds far the general meafures of this Order: we will now fet off the heights and projedions of every individual member. Of the Bafe to the PEDESTAL. Plate VII. Fig. A. The bafe of the Doric pedeflal hath it’s heights laid down on the fecond face of the Sedor, third interval, fecond bar, thirty-fourth line. The Sedor being fixed as before, i to 6, Cuts off the height of the bafe. i to 5, The cavetto. i to 4, The fillet, i to 3, The cyma reverfa. i to 2, The fillet, and alfo the height of the plinth. Of the Dye of the PEDESTAL. The half height of the dye of pedeftals; fecond face, third interval, fixth bar, thirty-fourth line. The Sedor opened from the beginning No. i, to the end of the Doric line No. 2, gives half the height of the dye. The Cornice of the PEDESTAL. Cornice of pedeftals; third interval, third bar, thirty-fourth line. The Sedor opened from the beginning of the bar No. i, to the laft divifion 6, gives the entire cornice of the pedeftal. i to 5, Cuts off the fillet, r to 4, The corona. The remaining numbers are backward divifions; therefore, 6 to 3, The ovolo. 6 to 2, The fillet, and alfo the cavetto. Bafe of the C O L U M N. Base of the column ; fecond face, third interval, firft bar, thirty-fourth line. L One I ** ] One leg of the Sedlor placed at the beginning of the bar No. i, the other carried to the laft divifion '8, marks the entire height of the bale. i to 7, The height of the lower cindture. i to 6, The upper tore. i to 5, The upper fillet of cavetto- i to 4, The cavetto. i to 3, The lower fillet of cavetto. i to 2, The lower tore, and alfo the plinth. Of the CAPITAL. Fig. B. For the heights of capitals, we mull take the fourth interval of the fecond face. The Doric ■capital is laid down on the firft bar, thirty-ninth line. One leg of the Sector fixed at the beginning of it No. i ; the other carried to the laft divifion No. ii, gives the entire height. i to io, The fillet, i to 9, The Doric cyma. i to 8, The corona, i to 7, The ovolo. i to 6, The firft annulet, i to 5, The fecond annulet. i to 4, The third annulet. The remaining are backward divifions, therefore ii to 3, Gives the neck of the capital. ii to 2, The upper aftragal, and alfo the upper cindture. The next, or fecond bar of this fourth interval and thirty-ninth line, gives the heights of the Doric architrave and frieze. Of the ARCHITRAVE and FRIEZE. Open the Sedlor as ufual, from the beginning, No. i, to the laft divifion, No. 9, and you have the entire height of both thefe parts. 1 to 8, The top of the channel of the triglyph.. 1 to 7, The bottom of it. 1 to 6, The tenia, or band to the architrave. 1 to 5, The lower part of it. 1 to 4, The fi let to the drops. 1 to 3, The drops. 1 to 2, The bottom of the upper fafcia, and alfo the top of the under fafcia. Of the C O R N I C E. Heights of cornices are to be found on the third bar of the fourth interval, thirty-ninth or Doric line ; fecond face. The Sedlor being opened from the beginning No. 1, to the laft divifion No. 10, gives the entire height. 1 to 9, The fillet. 1 to 8, The cyma. 1 to 7, The fillet. 1 to 6, The Doric cyma. 1 to 5, [ 2 3 ] i to 5, The corona. I to 4, The ovolo. i to 3, The fillet. The laft is a backward diviflon. 9 to 2, Gives the height of the cavetto, and band of the triglyph capital. Projections of the MEMBERS. These are all the heights of this Order: we fhall now take in the fame manner the projedions, which are all fet off from the axis of the column. Bafe of the PEDEST AL. Fig. A. And firft for the bafe of the pedeflal; fecond face, third interval, fourth bar, Doric line. The Sector opened from the beginning No. i, to the laft divifion 6, gives the projeftion of the plinth, i to 5, That of the fillet, and cyma reverfa. i to 4, The fillet, i to 3, The cavetto. i to 2, The projection of the dye. Cornice of the PEDESTAL. Projections of cornice to pedeftals; fecond face, third interval, fifth bar, Done line. The Seftor opened from the beginning No. i, to the laft divifion 7, gives the projeSlon of the fillet, i to 6, The corona. 1 to 5, The top of the ovolo. i to 4, The fillet and bottom of the ovolo. 1 to 3, The cavetto. 1 to 2, The dye. Bafe of the C O L U M N. Ease of the column ; fecond interval, fecond face, firft bar, Doric or twenty-ninth line. The Seflor opened from the beginning No. x, to the laft divifion No. 6, gives the projeaion of the plinth and tore. ! to 5, The lower fillet to the cavetto. I to 4, The upper fillet to the cavetto, and center of upper tore, i to 3, The lower cinCture. 1 to 2, The greater half diameter of the column. Of the CAPITAL. Fig. B. Leffer half diameter and capital; fecond face, fecond interval, fecond bar, Doric line. The Secftor opened from the beginning of the bar No. 1, to the laft divifion io, contains the pro- jedtion of the upper fillet. 1 to 9, The top of the Doric cyma. 1 to 8, The bottom of it. 1 to 7, The corona. 1 to 6, The top of the ovolo. 1 to 5, The bottom of the fame, and the firft annulet. 1 to 4, The fecond annulet, and center of the upper aftragal, and upper cin&ure. M 1 to 3, [ 2 + ] i to 3, The third annulet. i to 2, The neck of the capital, and letter half diameter of the column. Of the FRIEZE and ARCHITRA V E. Frieze and architrave; fecond face, fecond interval, third bar, Doric line. The Sector opened as ufual from the divilion No. i, to the lad divilion No. 13, gives the projection of the band of the triglyph. 1 to 12, The fide drop and it’s fillet. I to 11, The top of the drop. 1 to 10, The upper fafcia. 1 to 9, The frieze and lower fafcia. 1 to 8, The capital of the triglyph. 1 to 7, The fide channel. 1 to 6, The fillet and bottom of the outer drop. 1 to 5, The top of the drop. 1 to 4, The other fide of the channel, and middle of the drop. The remaining numbers are backward divifions, therefore 13 to 3,p a n d C Are the middle ol the two other drops, and alfo the fides of the whole channel. 13 to 2,3 Cf the FRIEZE and CORNICE. Frieze and cornice; fecond face, fecond interval, fourth bar, Doric line. T he Sector opened from 1 to the laft divifion 21, gives the fillet of the cyma, or entire projection of the cornice. 1 to 20, The cyma and fillet. 1 to 19, The top of the Doric cyma. 1 to 18, The bottom of it. 1 to 17, The corona. 1 to 16, The tooth of the cornice. 1 to 15, The fillet. 1 to 14, The ovolo. 1 to 13, The fillet. 1 to 12, The cavetto. 1 to 11, The band to the triglyph capital. 1 to 10, The fide triglyph. 1 to 9, The bottom of it’s channel. 1 to 8, The frieze. 1 to 7, The triglyph capital. 1 to 6, ) a n d > The half channel. 1 to 5,) The remaining numbers are backward divifions, therefore 21 to 4, The fide of the whole triglyph. 21 to 3, It’s middle. 21 to 2, It’s other fide. Heights [ ^5 ] Heights and Proje&ions of I M P O S "T S, &c. Those of the imports are laid down on the fecond face, firft interval; and the heights of thole adapted to the leffer arches are marked on the firft bar, twenty-fourth or Doric line. Plate XVII. The Sector opened from the beginning of the line No. i, to the laft divifion No. io, gives the entire height of the import. i to 9, The fillet, i to 8, The aftragal. i to y, The neck. i to 6, The fillet, and bottom of the cyma. i to 5, The fillet, and top of the cyma. i to 4, The corona. Then for the two backward divifions, io to 3, The cyma. io to 2, The fillet. The heights of the imports for greater arches, are on the fecond face, firft interval, fecond bar, Doric line. The Sector opened from the beginning No. i, to the laft divifion No. ix, gives the entire height, i to ii, The fillet. I to io, The aftragal. I to 9, The neck, i to 8, The lower fillet. I to 7, The upper fillet, and alfo the bottom of the ovolo. i to 6, The top of the ovolo. i to 5, The fillet and bottom of the cyma. The remaining numbers are backward divifions; therefore, 12 to 4, The top of the cyma and filleL 12 to 3, The bottom of the upper cyma. 12 to 2, The top of the cyma, and upper fillet. Projections of Imports and Archivaults. The projections of imports are on die firft interval of the fecond face, third and fourth bars; and as archivaults always fall upon the imports, we rtiall at the fame time, take off the different members belonging to them. And firft for the leffer imports and archivaults ; third bar, Doric line. The Sector opened from the beginning No. i, to the laft divifion No. 12, gives the entire breadth of the archivault, and projection of the import. 1 ton,) a n d > The cyma. I to 10,) 1 to 9, The corona. 1 to 8, The fillet and cyma. 1 to 7, The fillet and lower cyma, and the lower fillet jmd 'center of the aftragal 1 to 6, The neck, and alfo the pilafter and total width of the archivault. 1 to 5, Cuts off the firft fafeia of the archivault. N Then [ ^6 ] Then follow the bacl^ward divifions, 12 to 4, Is the fecond fafcia. 12 to 3, The aftragal. 12 to 2, The cyma and fillet. Projections of greater Impofts and Archivaults. We next come to the greater impofts and archivaults; fourth bar, Doric line. The SeCtor opened from the beginning i, to the laft divifion 14, gives us the width of the arclu- 1 to 13,) and h The cyma. 1 to 12,; 1 to 11, The fillet and top of the cyma. 1 to 10, The bottom of the cyma and fillet. 1 to 9, The ovolo. 1 to 8, The bottom of the ovolo, and upper fillet, and alfo the lower fillet and center of the aftragal. I to 7, The next fillet. 1 to 6, The pilafter, the neck, and total width of the archivault. 1 to 5, Cuts off the firft fafcia. I to 4, The fecond fafcia. Now for the backward divifions, 14 to 3, The aftragal. 14 to 2, The cyma and it’s fillet. Thus we have the widths or heights of archivaults; the projedions of their members are feldom drawn in plans, but yet abfolutely neceffary to be known; they are therefore on the filth and fixth bars, firft interval, fecond face. See the remark, at the bottom of page II- Projections of leffer ARCHIVAULTS. First, projections of archivaults for the lefier arches; fifth bar, Doric line. The Seftor opened from the beginning No. i, to the laft divifion 6, gives (as we faid before) the width of the archivault, and it’s projection. I to c,/ a n d c The top and bottom of the cyma. I to 4,^ i to 3, The fecond fafcia. i to 2, The firft fafcia. Projections of the greater ARCHIVAULTS. Projections of the archivaults of greater arches; fixth bar, Doric line. The Sedtor opened from the firft to the fixth divifion, as before, gives the width and projection of the archivault. I to 5, The c ma. I to 4, The c ma and aftragal. i to 3 , The fecond fafcia. i to 2, The firft fafcia. Heights [ 2 7 ] Heights and Projections of BLOCK CORNICES.. The next thing is block cornices, which are on the fecond face, fecond interval, fifth and fixth bars, Doric line. First for the heights; fifth bar. Plate XVIII. The Seftor opened from the beginning of the bar i, to the laft divifion io, gives the entire height. i to 9, The fillet, i to 8, The cavetto. i to 7, The fillet. 1 to 6, The corona. 1 to 5, The cyma, and top of the modilion. The remaining numbers are backward divifions, therefore 10 to 4, The bottom of the modilion. 10 to 3, The drops to the modilion. 10 to 2, The top of the cyma, and the fillet. Projections of the Doric block cornices ; fixth bar. The Sector opened from the beginning 1, to the laft divifion 14, gives the entire proje&ion of the cornice, beyond the upright of the wall. 1 to 13, The cavetto. 1 to 12, The fillet. I to 11, The corona. 1 to IO,) a n d C The cyma. 1 to 9 ,S 1 1 to 8, The outward modilion. 1 to 7, ■ AND The cyma. 1 to 6,5 I to 5, The inward modilion, and alfo the fillet. Of the three backward divifions, 14 to 4, Cuts off the top of the lower cyma. 14 to 3, The inward modilion. 14 to 2, The bottom of the lower cyma. Of BALLUSTERS. We come next to ballufters, which are on the firft face, fourth interval, fifth and fixth bars, Doric line. Heights of ballufters; fifth bar. Plate XIX. The Se&or opened from the beginning 1, to the laft divifion 16, gives us the entire height. 1 to 15, The upper fillet. I to 14, The ovolo. 1 to 13, The fillet. 1 to 12, The neck. 1 to 11, The aftragal. 1 to 10, The fillet. O 1 to 9 [ =8 ] i to 9, Gives the line on which the greateft projection of the vale is to be marked; but this divilion is of no other ufe in the heights, and therefore marked with a crofs on the bar. i to 8, The bottom of the vafe. i to 7, The lower altragal. i to 6, The ovolo. i to 5, The fillet. Then for the three backward divilions, 16 to 4, The cavetto. 16 to 3, The fillet. 16 to 2, The ovolo, and alio the plinth. Projections of ballufters; fixth bar. N. B. The manner of fetting off the projections of ballufters is fully explained in page 13. The SeCtor opened from the beginning of the bar No. 1, to the laft divifion 8 on the Doric line, gives the projection of the entire ballufter. From 1 to 7, The lower ovolo, and utmoft projection of the vafe. t to 6, The upper ovolo and fillet. 1 to 3, The middle ovolo, the lower fillet, the upper ovolo and fillet. 1 to 4, The upper aftragal, and the fecond fillet. 1 to 3, The cavetto, the lower aftragal, and fillet to the upper aftragal. 1 to 2, The top of the vafe and neck. Flutes of COLUMNS in Plano. Plate VI. We have now given an example of every thing to be drawn in this Order, except flutes, and doors with their ornaments. Doric flutes in piano ; are on the firft face, twenty-fecond line, firft bar. Half the plan of the column being drawn, and therein the femi-diameter D R at right angles with the diameter C B, we jfhali divide it into two quadrants: take in your compaffes the chord B D of one entire quadrant, and apply this diftance to the SeCtor opened as before, and try on what oppofite numbers this opening will coincide ; and then from this number thus difeovered, we fet oft' the Doric flutes. The SeCtor opened from the beginning 1 to the laft divifion 7, gives one fourth part of the circum¬ ference, viz. C D or B D. i to 6, Being fet from B and D, gives the flutes 2 and 7. 1 to 5, From the fame points, the flutes 3 and 6. 1 to 4, Is the radius R D, or femi-diameter. 1 to 3, The flutes 4 and 5, 1 to 2, BifeCts the quadrant at A. Upright FLUTES. Doric upright flutes; fecond bar, twenty-fecond line. Open the SeCtor from the beginning No. 1, to the laft divifion 8, then take the femi-diameter of the column, and apply this diftance to oppofite numbers until it coincides therewith; and from this number fo difeovered we fet off all the flutes from the center line of the column each way. 1 to 7, [ 29 3 , to 7, The fide of the half flute. i to 6,~j 1 to 5,1 , . , i to 4,1 > Th e flutes m t ‘ ieir order ‘ A N D I 1 to 3>J The other being a backward divifion, therefore 8 to 2, Obtains the half flute. Of DOORS. Pi, ATE XX. Fig. 3. After having drawn the Doric Order as laid down on the firft face, firft interval ; one leg of the Seder fixed at the beginning the Doric line 1, let the other be opened to 12, marked d upon the limb, then we (hall cut off the height of the doors proportioned to colonnades without pe- deftals ; I to 9 marked alfo d, cuts off the heights of doors proportioned to colonnades with pedeftals. But if only a door is to be drawn, then this fcale is of no ufe, becaufe the height or width of the door being arbitrary, we need only to have a reference to them. Heights of doors, and their entablatures; firft face, third interval, firft bar, Doric line. Having determined either the heights, widths, or half widths of a door intended to be drawn, fix one lev of the Seaor at the beginning of the bar, and open the other leg to any one of thofe given lenvtht, fuppofe the half width K M, then the meafure of that taken in the compaffes mull be applied to die Seaor, and where the legs of it coincide upon oppofite numbers will give the proper heights of doors. The moveable leg of the Seaor carried to the laft divifion of the line 12, gives the entire height ot the door with it’s entablature. j to 11, Cuts off the cornice. 1 to 9, The frieze. 1 to 8, The architrave, and confequently the height of the door without the entablature. I to 3, The width of the door. 1 to 2, The half width K M, which we began with. If we make ufe of a kneed architrave, then after taking 1 to 8, The height of the door, j to 5, Gives the depth of the knee. Ir a confole is to be added to it, it is generally made to fupport the cornice, and to terminate with the bottom of the knee, with a leaf falling from it; therefore 1 to II, Gives the top of the confole. 1 to 9, The bottom of the upper volute. I to 10, The eye of the upper volute. 1 to 7, The top of the lower volute. 1 to 6, The eye of the lower volute. 1 to 3, The bottom of the lower volute. 1 to 4, Cuts off the length of the leaf. Having thus got the general heights of entablatures and confides to doors, we now come to the par¬ ticular mouldings, which we will deferibe at large 8 they are on the firft face, fourth rnterval, firft bar, Doric line. Heights cf entablature of doors j firft bar. p Plate [ 3 ° Pi, ate XXII. The SeCtor opened from the beginning i to the laft divifion 15, is the entire entablature. I to 14, Cuts off the fillet. 1 to 13, The cyma. 1 to 12, The fillet. 1 to 11, The cyma. 1 to 10, The corona. I to 9, The ovolo. 1 to 8, The fillet. 1 to 7, The cyma, and alfo the entire cornice. 1 to 6, The frieze. 1 to 5, The fillet. 1 to 4, The cyma. 1 to 3, The aftragal. The backward divifion, 15 to 2, Gives the upper fafcia. Projections of cornice of doors ; fecond bar. The Sector opened from the beginning 1 to the laft divifion 10, is the greateft projection of the cornice. 1 to 9, The cyma, and alfo the fillet. 1 to 8,7 and C The cyma. 1 to 7,) 1 to 6, The corona. 1 to 5, The ovolo. The backward divifions, 10 to 4, Cuts off the bottom of the ovolo, and fillet. 10 to 3,) a n d >■ The lower cyma. 10 to 2,' Projections of architraves of doors; third bar. As the entire projections of architraves are too fmall to be laid down by themfelves on the fcale, we are obliged here, as in archivaults, to add fome certain meafure before them, for which purpofe we choofe to repeat the height of the architrave itfelf. The Sector opened from the beginning 1 to the laft divifion 6, gives us both the height and pro¬ jection of the architrave. 1 to 5O and > The cyma, and alfo the aftragal. 1 to 4,) 1 to 3, The upper fafcia. 1 to 2, The lower fafcia. Of CONSOLES. Plate XXIII. Thefe, like the architraves, contain too fmall a fpace to be laid down by themfelves; but as the confole is generally placed by the fide of the architrave, we add the height of the architrave itfelf. 1 he half heights of confoles are laid down on the firft face, fecond interval, feventh bar, Doric line. Plate [ 31 ] Plate XXIII. The Seflor opened from the beginning No. i, to the left diviSon 7, gives half the entire height ; from 1 to 6, The eye of the upper volute. 1 to 5> The bottom of the upper volute. 1 to 4 > The top of the lower volute. 1 to 3, The eye of it. 1 to 2, The bottom of the volute, and top of the leaf. Width of conloles; firft face, fourth interval, fourth bar, Doric line. 1 to 7, Gives the entire width of the architrave and confole. 1 to 6, The fillet. 1 to 5, The cyma. 1 to 4, The aftragal. I to 3, The cyma. 1 to 2, The other fillet. Q The [ 3 2 ] % - - ss *^f jfkjwfkjf; *-*>; M r«3 ,ju * ■fifcf l**A SaSA £* A Nv< * «-- » -a AJA % # jr' > f H T.*,T *%*r , XjP* Ji W^te. k. * jif s ) /X''X\3 4' * T <*•>-vO > < !$> # < X * rjLi *W* Tv • >*<' <*T>; ?*> •> - * -ss -s^K .'« £ * The U S E of the ARCHITECTONIC SECTOR, In drawing the IONIC ORDER. GENERAL HEIGHTS. C H A P. IV. O R the aeneral heights, &c. of the ancient Ionic Order. They are upon the hr ft face t***! % of the limb, firft interval, third bar. F # $ ~, , ^ Plate VIII. Screw one leg of the SeCtor to the beginning of the third line, No. r, then ItejK'^te^ a'iHjt move the other till it cuts the laft divifton 17, which is the total height of the Order, Bring the moveable leg back to 16, this cuts off the bafe of the pedeftal. 1 to 15, The dye. 1 to 14, The cornice. 1 to 13, The bafe of the column. Then palling over the divilions marked with letters, which belong to doors or arches, bring the moveable leg from 1 to 5, The trunk. 1 to 4, The capital. 1 to 3, The architrave. 1 to 2, The frieze, and alfo the modilion cornice. The moveable leg brought to 14, gives the height of the column with it’s entablature, without a pedeftal. In like manner the moveable leg brought to 4, cuts off the entablature without a column. Of INTERCOLUMNIATIONS. First face, fecond interval, firft and fecond bars, ninth line. These bars gives us, befides the projections of the columniations, one of one module, thirty-feven minutes, minutes, i-4th. column, and entablature, two different inter- i_4thj the other of one module, twenty-one We fhall begin with the firft bar. The [ 33 ] The Sedtor opened from the beginning of the bar No. i, (which anfwers to the axis of the column) to the laft diviiion No. 8, we {hall have the greater half intercolumniation. 1 to 7> The lefler half intercolumniation. i to 6, The projection of the cornice. The remaining numbers are backward diviflons j therefore, 9 to 5 > fjives the projection of the plinth of the column. 9 to 4, The capital. 9 to 3, The greater half diameter. 9 to 2, The lefler half diameter. The Ionic column with pedeftals, and two intercolumniations, one of four modules and ten minutes, the other of one module, thirty-feven minutes and a quarter. Second bar, fecond interval, ninth line. The Sector opened from the beginning of the bar No. i, to the laft divifton 9, marks the greater half intercolumniation. 1 to 8, The lefler half intercolumniation. I to 7, The projection of the cornice. I to 6, The plinth, and cornice of the pedeftal. The remaining numbers are backward diviflons; therefore 9 to 5, The plinth, and bafe of the column. 9 to 4, The projection of the capital. 9 to 3, The greater half diameter. 9 to 2, The lefler half diameter. Of ARCHES. The heights of arches are on the firft interval, and the third or Ionic line; this we have already done in the intercolumniations, and as far as relates to the Order itfelf: but upon the lame line, there are feveral diviflons marking the heights of arches, 8cc. which were omitted in forming colonnades, but become at prefent neceflary. Open the Sedtor from the beginning of the Ionic or third line No. 1, to 6, marked k, this gives the bottom of the key-ftone to the lefler arch. 1 to 7 k, The bottom of the key-ftone to the greater arch. 1 to 8 i, Top of the impoft to the lefler arch. 1 to 10 i, Bottom of the impoft to the lefler arch, and top of that to the greater arch. 1 to 12 i, Fixes the bottom of the impoft to the greater arch. Projections of greater arches-. Open the Sedtor to the beginning of the Ionic or ninth line, fecond interval, third bar, firft face, to the laft divifion; then 1 anfwers to the middle of the arch, and 11 cuts o£F the cornice to the greater arch. 1 to 10, The capital. 1 to 9, The top of the trunk. 1 to 8, The axis of the column. I to 7, The bottom of the trunk, and alfo the outfide of the archivault. 1 to 6, The dye, and alfo the plinth of the column. 1 to 5, The plinth and cornice of the pedeftal, the pilafter, and confequently the inflde of the archivault. 1 to 4, The impoft. The R [ 3+ ] The remaining are backward divifions; therefore n to 2,) a n d > Cut off the top and bottom of the key-ftone. 11 to 3,) Projectticns of Ionic lefler arch are on the fecond interval, third bar, ninth or Ionic line, firft face. Open the SeCtor to the beginning No. i, to No. 12, then 1 anfwers to the middle of the arch, and 12 is the projection of the cornice. I to 11, The capital. I to 10, The top of the trunk. I to 9, The axis of the column. 1 to 8, The bottom of the trunk. I to 7, The outfide of the archivault. 1 to 6, The bafe of the column. 1 to 5, The pilafter, and alfo the infide of the archivault. I to 4, The import. The remaining are backward divirtons, 12 to 20 and f For the top and bottom of the key-ftone. 12 to 3,) Of a Single Tedeftal, Column, or Entablature. § A fingle pedeftal is on the firft face, fecond interval, fifth bar, ninth line. The Se&or being fixed as before, and the moveable leg carried to the laft divifion 4, gives the entire height of the pedeftal; brought back to 3 cuts off the bafe. No. 2 is a backward divifion, therefore from 4 to 2 gives the height of the cornice, and alfo the dye. Plate VIII. The general projections of pedeftals; firft face, fecond interval, fecond bar, Ionic line. Fix the inftrument at the beginning No. 1, and carry the other limb of it to 9, which cuts off the greater half intercolumniation; irom 1 to 6, The bafe, and alfo the cornice. And the backward divifion, 9 to 5, Is the dye. The heights of a fingle column are on the firft face, fecond interval, fecond bar, fourteenth line. The SeCtor placed at No. 1, then carried to the laft divifion 4, gives the entire height; brought back to 3 the bafe ; and the legs of the inftrument reverfed for the backward divifion, then 4 to 2 fixes the top ot the trunk, and the bottom of the capital. The general projections of the column, are on the firft face, third interval, fecond bar, Ionic line. The SeCtor being fixed as before; then 1 to 9, Is the greater half intercolumniation. The remainder are backward divifions; therefore 9 to 2, The top of the trunk. 9 to 3, The bottom of the trunk. 9 to 4, The capital. 9 to 5, The bafe. The heights of an entablature; firft face, fecond interval, fixth bar, Ionic line- I to 4, The entire height. I to 3, The architrave. 1 to 2, The frieze, and alfo the cornice. § See Plate XX, Pa*e 6. Projections [ 35 ] P.oject.ons of the entablature; firft face, fecond interval, fecond bar. i to 9, Is the greater half intercolumniation. 1 to 7, The cornice. And the backward divifion, 9 to 2, Cuts off the frieze and architrave. Of the MEMBERS. Wr (hall begin with the bafe of the pedeftal; the heights of which are laid down on the third interval, fecond bar, thirty-fifth line. fecond face, The PEDESTAL. barTthen*' °“ ^ ° f ^ ^ ^ ** " ufuaI ’ and the Mh “ « *e end of the i to 7, Cuts off the height of the bafe. i to 6, The cavetto. i to 5, The fillet, i to 4, The aftragal. 1 to 3> The cyma reverfa. 1 to 2, lhe fillet, and alio the plinth. The half heights of the dye ofpedeftals; fecond face, third interval, fixth bar. The Seder opened from the beginning i, to the end of the Ionic line, gives half the height of the dye. Cornice of pedeftals; third bar, thirty-fifth line. The Sedor opened from the beginning of the bar No. i, to the laft divifion 7 , gives the entire cornice of the pedeftal. i to 6, The fillet, i to 5, The corona. The remaining numbers are backward divifions j therefore 7 to 4, Gives the bottom of the ovolo. 7 to 3, The aftragal. 7 to 2, The fillet, and alfo the cavetto. The COLUMN. Ease of the column ; fecond face, third interval, firft bar, thirty-fifth line. One leg of the Sedor placed at the beginning of the bar No. i, and the other carried to the laft divifion No. 9, marks the entire height of the bafe. 1 to 8, The lower cinffure. 1 to 7, The lower aftragal. 1 to 6, The upper tore. 1 to 5, The upper fillet of the fcotia. 1 to 4, The fcotia. 1 to 3> The lower fillet. 1 to 2, The lower tore, and alfo the plinth. The CAPITAL. Fig. B. For the heights of the ancient Ionic capital and entablature, we muft take the fourth interval of the fecond face. S The [ 36 3 The Ionic capital is laid down on the firft bar, fortieth lme. 0 „ leg of the Sedtor fixed to the beginning of the bar No. x, the other earned to the laft dtvxfxon No. II, gives the entire height; and I is the bottom of the volute. 1 to 10, The fillet. ! to 9, The Doric cyma. 1 to 8, The lift of the volute. 1 to 7, The ovolo, and top of the fecond revolution. 1 to 6 , The aftragal, and top of the eye. 1 to 5, The center of the eye of the volute. 1 to 4, The bottom of the aftragal, and bottom of the eye. The remaining numbers are backward divifions, therefore 1 a to 3, Is the upper cindtare. 1 2 to 0 The height of another revolution of the volute. Fig c The heights of the modern Ionic capital and entablature, are laid down on the fivth hue o the fourth interval, firft bar, fecond face, and forty-third line. „ Ohe leg of the Seta fet to the beginning of the bar, the other carried to the laft divifio . , gives the entire height; and . is the bottom of the volute, i to 10, The fillet. 1 to o, The Doric cyma. 1 to 8, The band of the volute, the ovolo, and the fecond revolution. ! to 7, Another revolution. , to 6, The top of the aftragal, and the top of the eye of the volute. I to 5, The center of the eye. I to 4, The bottom of the aftragal, and of the eye. The remaining numbers are backward divifions, therefore II to 3, The upper cinfture. II to 2, Another revolution. Of the ARCHITRAVE and FRIEZE. THE fecond bar of the fourth interval, and fortieth line of the fecond face, gives the heights o the ancient Ionic architrave and frieze. - 1 Fio. D. The Sedlor opened as nfual from the beginning of the bar No. 1 to the a >u ion 9, m the entire height of both thefe parts. 1 to 8, The top of the architrave. 1 to 7, The fillet. 1 to 6, The Doric cyma. 1 to 5, The upper fafeia. 1 to 4, The aftragal. The remaining numbers are backward divifions, therefore g to 3, The middle fafeia. 9 to 2, The aftragal and ^ ^ of th e fixth line, The heights of the modem Ionic architrave, and frieze 1 fourth interval. Fic , c. [ 37 ] Flc - C. The Sector opened from the beginning of the fecond bar No. i on the forty-third line, to the laft division No. 9, is the entire height of both thefe parts. 1 to 8, The frieze. I to 7, The fillet. 1 to 6, The Doric cyma. 1 to 5, The upper fafcia. i to 4, The aftragal. The remaining numbers are backward divifions, therefore 9 to 3, The middle fafcia. 9 to 2, The aftragal and lower fafcia. Of the C O R N I C E. Heights of ancient Ionic cornices are to be found on the third bar of the fourth interval, fortieth line. Fig. B. The SeCtor opened from the beginning No. 1 to the laft divifion 12, fliews the entire height; 1 to 1 1, The fillet. 1 to 10, The cyma. 1 to 9, The fillet. 1 to 8, The Doric cyma. 1 to 7, The corona. 1 to 6, The ovolo. 1 to 5, The fillet. 1 to 4, The dental band. The remaining numbers are backward divifions; therefore 12 to 3, The dentals. 12 to 2, The fillet, and Doric cyma. The heights of the modern Ionic cornice is laid down on the third bar of the forty-third line. Fig. C. The Sector opened from the beginning No. 1 to the laft divifion 12, fliews the entire height. I to 11, The fillet. 1 to 10, The cyma. 1 to 9, The fillet. 1 to 8, The Doric cyma. 1 to 7, The corona. 1 to 6, The Doric cyma. 1 to 5, The modilions. 1 to 4, The fillet. The remaining numbers are backward divifions; therefore 12 to 3, The ovolo. 12 to 2, The fillet and cavetto. These are all the heights of the Ionic Order ; we fliall now take in the fame manner the projections, which are all fet oft from the axis of the column. The P E D E S T A L. And firft for the bafe of the pedeftals; fecond face, third interval, fourth bar, Ionic line. The Sector opened from the beginning 1 to the laft divifion 7, gives the projection of the plinth. T 1 to 6, [ 38 ] i to 6, The fillet, i to 5, The aftragal. I to 4, The fillet. i to 3, The cavetto. i to 2, The dye. Projections of cornice of pedeftals ; fecond lace, third interval, fifth bar, Ionic line. The Sector opened from the beginning No. i to the laft divifion No. 8, gives the projedion of the upper fillet. i to 7, The corona. I to 6, The ovolo. I to 5, The aftragal. I to 4, The fillet. I to 3, The cavctto. i to 2, The dye. Base of the column; fecond face, fecond interval, firft bar. Th:-. Sedor opened from the beginning No. i to the laft divifion 6, gives the projedion of the plinth and tore. i to 5, The lower fillet. 1 to 4, The upper fillet of the fcotia, and center of the upper tore; alfo die lower aftragal. i to 3, The lower cindture. I to 2, The greater half diameter of the column. Lesser half diameter, and ancient capital ; fecond face, fecond interval, fecond bar Ionic line. The Sedtor opened from the beginning of the bar No. i to the laft divifion No. io, contains the utmoft projedtion of the volute. i to 9, The fecond revolution. I to 8, The fillet. i to 7, The top of the Doric cyma, and another revolution, i to 6, The bottom of the cyma. i to 5, The eye of the volute, i to 4, The top of the trunk of the column. I to 3, The third revolution. I to 2, The infide of the volute. Lesser half diameter, and modern capital; fecond face, forty-third line, fourth bar. The Sedtor opened from the beginning of the bar No. i, to the laft divifion 13, gives the projedtion of the fillet and volute. 1 to 12,7 and C The Doric cyma. 1 to 11,3 I to 10, The fillet, and firft revolution. 1 to 9, A and C The Doric cyma. 1 to 8,S 1 to 7, The fecond revolution. 1 to 6, The third revolution. I to 5, [ 39 ] I to 5, The eye of the volute, i to 4, Another revolution, i to 3, The infide of the volute. The remaining number is a backward divifion; therefore, 13 to 2, Is the beginning of the volute. Of the FRIEZE and ARCHITRAVE. Frieze and architrave; fecond face, fecond interval, third bar, Ionic line- The Sedtor opened as ufual from the divifion No. 1 to the laft divifion 7, gives the utmoft projedtion of the fillet. 1 to 6, The top of the Doric cyma. 1 to 5, The bottom of it. 1 to 4, The upper fafcia, and aftragal. 1 to 3> The middle fafcia, and aftragal. i to 2, The frieze. Of the FRIEZE and CORNICE. Frieze and cornice; fecond face, fecond interval, fourth bar, Ionic line. The Sedtor opened from the beginning 1 to the laft divifion 17, gives the projedtion of the fillet, or entire cornice. I to 16, The cyma, and alfo the fillet. 1 to 15, The top of the Doric cyma. 1 to 14, The bottom of it. 1 to 13, The corona. 1 to 12, The tooth of the corona. 1 to 11, The fillet to the pvolo. 1 to 10, The ovolo. 1 to 9, The fillet. 1 to 8, The firft dental. I to 7, The cyma. I to 6, The next dental and Doric cyma. 1 to 5, The frieze. The remaining numbers are backward divifions ; therefore 17 to 4, Is one fide of the fifth dental. 17 to 3, The other fide of it. 17 to 2, One fide of the middle dental, and alfo a denticle. N. B. From the dentals already drawn the others are to be taken, and alfo the denticles. Modern FRIEZE and CORNICE. N. B. The frieze and architrave are the fame as in the ancient Order. The cornice ; fecond face, forty-third line, fifth bar. The Sector opened as ufual from the divifion 1 to the laft divifion 20, gives the projedtion of the fillet, or entire cornice. 1 to 19, The bottom of the cyma, and alfo the fillet. 1 to 18,) and > The Doric cyma. 1 to 17,’ i to 16, The corona, U 1 to 15, [ 40 ] I to 15,7 a n d > The Doric cyma. I to 14,^ 1 to 13, The modilion. 1 to 12, The tooth of the modilion. 1 to 11, AND I to 10, I to 9, The modilion and fillet to the ovolo. 1 to 8, The ovolo. 1 to 7, The fillet. 1 to 6, The cavetto. 1 to 5, The frieze. The remainder are backward divifions.' 20 to 2, The fide of the middle modilion. 20 to 3,7 a n o C it’s cyma. 20 to 4,) Of IMPOSTS. The heights and projections of imports are laid down on the fecond face, firft interval; and the heights of thole adapted to the lefler arches are marked on the firft bar, twenty-fifth or Ionic line. Plate XVII. The SeCtor opened from the beginning of the line No. 1 to the laft divifion 10, gives the entire height of the import. 1 to 9, The fillet. 1 to 8, The aftragal. 1 to 7, The fillet, and bottom of the cyma. 1 to 6, The fillet, and top of the cyma. 1 to 5, The ovolo. 1 to 4, The corona. Then for the two backward divifions, 10 to 3, The Doric cyma. 10 to 2, The fillet. The heights of the imports for greater arches are on the fecond face, firft interval, fecond bar, Ionic line. Plate XVII. The SeCtor opened from the beginning No. 1 to the laft divifion 12, gives the entire height. 1 to 11, The aftragal. 1 to 10, The neck. 1 to 9, The fillet. 1 to 8, The ovolo. 1 to 7, The fillet. I to 6, The cyma. 1 to 5, The fillet. 1 to 4, The corona. The remaining are backward divifions; therefore 12 to 3, The Dor c cyma. 12 to 2, The fillet. The cyma to modilion. The [ 41 ] The projeftions of thefe impofts are on the firft interval of the fecond face, third and fourth bars. And as archivaults always fall upon the impofts, we lhall at the fame time take off the different mem- bers belonging to them. And firft for the leffer impofts and archivaults; third bar, Ionic line. The Seftor opened from the beginning No. , to the laft divifion No. 14, gives the entire breadth of the archivault, and projection of the impofts. 1 to 1 3,^ and > The Doric cyma. 1 to 12,) 1 to 11, The corona. 1 to 10, The ovolo. 1 to 9, The fillet. 1 to 8, The center of the aftragal and fillet. 1 to 7, The lower fafcia, bottom of the cyma, and neck. 1 to 6, The aftragal. 1 to 5, The upper fafcia. Then for the backward divifions, 14 to 4, The aftragal. 14 to 3> The Doric cyma. 14 to 2, The fillet. We come next to the greater impofts and archivaults; fourth bar, Ionic line. The Seffor opened from the beginning 1 to the laft divifion 16, gives us the width of the archivault, and entire projection of the impoft. 1 to 15,) and > The Doric cyma. 1 to 14,) 1 to 13, The corona. 1 to 12, The fillet and cyma. 1 to ii, The bottom of the cyma and fillet. 1 to 10, The ovolo. 1 to 9, The fillet and center of the aftragal. 1 to 8, The bottom of the ovolo and fillet. 1 to 7, The lower fafcia, the neck, and alfo the pilafter. 1 to 6, The aftragal. 1 to 5, The upper fafcia. The remaining numbers are backward divifions, therefore 16 to 4, The aftragal. 16 to 3, The Doric cyma. 16 to 2, The fillet. Of ARCHIVAULTS. Projections of archivaults for the lefler arches; fifth bar, Ionic line. The Sector opened from the beginning No. i to the laft divifion 6, gives, as we faid before, the width of the archivault, and it’s projection. i to 5, The Doric cyma. i to 4, It’s bottom, and alfo the aftragal. i to 3, The fecond fafcia. i to 2, The firft fafcia. X Projections [ 4 2 ] Projections of the archivaults of greater arches; fixth bar, Ionic line. The Sector opened from the firft to the laft divifion 6, as before, gives the width and projection of the archivault. i to 5, The Doric cyma. i to 4, It’s bottom, and die aftragal. i to 3, The fecond fafeia, and aftragal. i to 2, The firft fafeia. Of BLOCK CORNICES. Heights of block cornices; fecond face, fecond interval, fifth bar. Plate XVIII. The SeCtor opened from the beginning i to 12, gives the entire height, i to i i, The fillet, i to io, The cyma. i to 9, The corona, i to 8, The ovolo. i to y, The fillet, i to 6, The dentals, i to 5, The denticle. The remaining numbers are backward divifions, therefore i 2 to 4, The bottom of the dentals. 12 to 3, The aftragal. 12 to 2, The fillet. Projections of block cornices; fixth bar. The SeCtor opened from the beginning i to the laft divifion 9, gives the entire projection of the cornice, beyond the upright of the wall. 1 to 8, The cyma. 1 to 7, The corona. 1 to 6, The ovolo. 1 to 5, The fillet. 1 to 4, The dental. Or the two backward divifions, 9 to 3, The infide of the dental, and center of the aftragal. 9 to 2, The fillet. Of BALLUSTERS. Ballusters are on the firft face, fourth interval, fifth and fixth bars, Ionic line. Plate XIX. Heights of ballufters ; fourth interval, filth bar. The SeCtor opened from the beginning 1 to the laft divifion 18, gives the entire height. 1 to 17, The fillet. 1 to 16, The ovolo. i to 15, The fillet, and top of the neck. 1 to 14, The bottom of the neck. 1 to 13, The fillet. 1 to 12, The fillet. 1 to 11, The inverted ovolo. 1 to 10, The fillet, and top of the vafe. 1 to 9, t 43 ] i to 9, The bottom of the vafe. I to 8, The fillet. i to 7, The aftragal or tore. i to 6, The fillet, and top of the cavett . The remaining numbers are backward divifions, 18 to 5, The bottom of the cavetto. 18 to 4, The fillet. 18 to 3, The cyma. 18 to 2, The fillet and plinth. Projections of ballufters; fixth bar. The Sector opened from the beginning i to the laft divifion 12, on the Ionic line, gives the pro¬ jection of the entire ballufter ; which put on paper we bifeCt, and this bife&ion gives the lemi-diameter of the entire ballufter, which could not be laid down upon the limb. 1 to 11, The plinth and upper fillet. 1 to 10, The lower fillet. 1 to 9, The fillet to the top of the vafe. i to 8, A fillet, and the ovolo. 1 to 7, The fillet to the bottom of the cavetto. 1 to 6, The top of the vafe. 1 to 5, The fillet, and top of the neck. 1 to 4, The aftragal or tore. 1 to 3, It’s two fillets. 1 to 2, The bottom of the vafe. Of FLUTES. Flutes and fillets of columns in piano are on the twenty-fecond line of the firft face, third bar. N. B. See the manner of taking off the Doric flutes, page 28. Plate VI. Fig. 1. The SeCtor opened from the beginning 1 to the laft divifion 10, gives one fourth part of the circumference of the column. 1 to 9, Two half flutes, i to 8, Two fillets. 1 to 7, Two flutes. 1 to 6, Two fillets. 1 to 5, The radius marked R. 1 to 4, Two flutes. 1 to 3, Two fillets, and the middle flute. 1 to 2, Half the quadrant A R. Fig 2. Flutes and fillets for upright columns are on the fourth bar, twenty-fecond line. The ScCtor opened from the beginning No. 1 to the laft divifion 14; then we take the femi-diameter of the column, and try on what oppofite numbers it coincides; and from this number fo difeovered, we fet off all the flutes and fillets from the center line each way. 1 to 13, The half flute. 1 to 12, The fillet. Y 1 to 11, [ 44- ] i to ii, The flute, i to io, The fillet, i to 9, The flute, i to 8, The fillet, i to 7, The flute, i to 6, The fillet. I to 5, The flute, i to 4, The fillet. Then the two backward divifions are fet from each fide of the column towards the center line. 14 to 3, The flute. 14 to 2, The fillet, and one half of the middle flute. Flutes and fillets for pilafters are on the fifth bar, twenty-fecond line. The Sedlor opened from the beginning No. 1 to the laft divifion 9, and the extent of the half breadth of the pilafter fitted to coincide on oppofite numbers; it is from this number fo difcovered that we fet off the flutes and fillets each way from the middle line of the pilafter. 1 to 8, The flute. I to 7, The fillet. 1 to 6, The flute. 1 to 5, The fillet. Then the two backward divifions are fet off from the fides of the pilafter, towards the middle. 9 to 3, The fillet. 9 to 2, One half of the the middle flute. Of DOORS. After having drawn the Ionic Order, as laid down on the firft face, firft interval ; one leg of the Sedlor placed at the beginning of the line 1, let the other be opened to 11, marked d upon the limb, then we fliall cut off the height of doors proportioned to colonnades without pedeftals; 1 to 9 marked alfo d cuts off the heights of doors proportioned to the colonnades with pedeftals. These two divifions 9 and 11 were not mentioned when we were drawing the heights of the Order, being of no ufe except for the purpofe mentioned. Heights of doors and their entablatures; firft face, third interval, firft bar, Ionic line. Having determined either the height, width, or half width of a door intended to be drawn, fix one leg of the Sector at the beginning of the bar, and open the other to any one of thofe given lengths, fuppofe the half width; then the meafure of that taken in the compaffes from the fcale the plan is drawn by, muft be applied to the Sector, and where it coincides upon two oppofite numbers, will become the proper fcale for the general heights of doors. The moveable leg of the Sector carried to the laft divifion 12, of the line, gives the entire height of the door with it’s entablature. r to 11, Cuts off the cornice. 1 to 9, The frieze. 1 to 8, The architrave, and confequently 1 to 8 is the height of the door, without the entablature. 1 to 3, The width of the door. 1 to 2, The half width, which we began with. If [ 45 ] 11 we make ufe of a kneed architrave, after taking i to 8, The height of the door, i to 5, Gives the depth of the knee. lF a Conr ° k is to bc added ’ “ is generally made to fupport the cornice, and to terminate with the bottom of the knee with a leaf from it; therefore i to n. Gives the top of the confole. I to io, The eye of the upper volute. 1 7i The top of the lower volute, i to 6, The eye of the.lower volute. 1 1° 5> The bottom of the lower volute, i to 4, Cuts off the length of the leaf. Having thus got the general height of the entablature of doors, mouldings; which are on the firft face, fourth interval. Heights of entablature of doors; firft bar, Ionic line. 1 HE Seflor opened from the beginning i to the laft divifion 18, is the entire entablature. I to 17, Cuts off the fillet. I to 16, The cyma. 1 to 15, The fillet. 1 to 14, The cyma. 1 to 13, The corona. 1 to 1 2, The ovolo. 1 to ii, The fillet. 1 to 10, The dentals. 1 to 9, The fillet. 1 to 8, The cyma and alfo the frieze.' 1 to 75 The fillet and bottom of the frieze. 1 to 6, The fillet. 1 to 5> The cyma. 1 to 4, The aftragal. 1 to 3) The upper fafcia. The remaining number is a backward divifion; therefore, 18 to 2, Gives the cyma, and top of the lower fafcia. Projections of the cornice of doors; fecond bar. The Seflor opened from the beginning 1 to the laft divifion 12, is the greateft projedion of the cornice. 1 to 11, The fillet. 1 to IO, ) a n d C The cyma. 1 to 9 ,S 1 to 8, The corona. I to 7, The ovolo. 1 to 6, The fillet. 1 to 5, The dentals. The remaining numbers are backward divifions; therefore 12 to 4, The fillet. £ The cyma. Z Projections [ + 6 j Projections of architraves of doors, are on the third bar, Ionic line. The Sedtor opened from the beginning i to the laft divifion 8, gives us both the height and projedtion of the architrave. 1 to 70 and C The cyma, and alfo the aftrao-al. i to 6,{ ] i to 5, The upper fafeia. i to 40 and The cyma. i to 3,) i to 2, The frieze and lower fafeia. Of consoles. Half heights of confoles; firft face, fecond interval, feventh bar, Ionic line- Plate XXIII. The Sedtor opened from the beginning i to the laft divifion 7, aives half the entire height. I to 6, The eye of the upper volute; 1 to 5, The bottom of it. 1 to 4, The top of the lower volute. 1 to 3, The eye of it. 1 to 2, The bottom of the lower volute, and alfo the top of the leaf. Widths of confoles; firft face, fourth interval, fourth bar, Ionic line. i to 9, Gives the total width of the architrave and confole. 1 to 8, The fillet. 1 to 7, The cyma. 1 to 6, The fillet. 1 to 5, The aftragal. 1 to 4, The fillet. 1 to 3, The cyma. 1 to 2, The fillet. eKA* e¥* 'x-ji W The [ 47 ] ^ ^ y y_. ,. n ' C >1 Cvi s& S3 .fjKp,, w & ;?:* ^31 * -aJ &&•£ W Ct-, 3 ^ jf' u l v> VVV r ^ ¥ # ^ v W“TU iM fcjfluj * P % r The U S E of the ARCHITECTONIC SECTOR, In drawing the CORINTHIAN ORDER. CHAP. V. The Ufe of the Inftrument in drawing the Corinthian Order, through all it's different Applications. E (hall begin with the general heights of this Order; which are upon the firft face of the limb, firft interval, fourth line. Screw one leg of the Seder to No. ,, the beginning of the fourth line, then move the other till it cuts the Iaft divifion 17 ; this is the total height of the Order, Bring back the moveable leg to 16, this cuts off the bafe of the pedeftal. 1 to 15, The dye. 1 to 14, The cornice of the pedeftal. 1 to 13, The bafe of the column. Then parting over the divifions marked with letters, which belong to doors or arches, bring the moveable leg from 1 to 7, The trunk- Here likewife pafs by No. 6 and 5, both marked with letters, and bring the moveable leg from i to 4, Which cuts off the capital. 1 to 3 j T^e architrave. 1 to 2, The frieze, and alfo the cornice. We fhall here, as in the preceding Orders, obferve that if the moveable leg be brought to 14 it gives the height of the column with it’s entablature without a pedeftal. In like manner the moveable leg brought to 4, cuts off the entablature without a column. Of INTERCOLUMNIATIONS. Thus having given the heights of the principal parts of this Order, we now proceed to the projedi- Ofis; to -which we fhall join the different diftances, or intercolumniations fuited to it. **’'*•*'> 4 hz} 5 [ 43 ] The firft bar give us, befides the projections of the column and entablature, two different interco- lumniations, one of one module one half; the other of fifty-three minutes. We fhall begin with the firft bar, fecond interval, tenth line, firft face. Flate XI. Fig. A. The SeCtor opened from the beginning No. i (which anfwers to the axis of the column) to the laft divifion 8, we fhall have the greater half intercolumniation. i to 7, The cornice. i to 6, The lefier half intercolumniation. 1 to 5, The capital. The remaining numbers are backward divifions; therefore 8 to 4, Is the plinth. 8 to 3, The greater half diameter. 8 to 2, The lefier half diameter. Second interval, fecond bar, tenth line. The column with pedeftals and two intercolumniitions; one of one module, forty-eight minutes; the other of one module and twelve minutes. Fig. B. The Sedor opened from the beginning No. i to 9 the laid divifion, marks the greater half intercolumniation. 1 to 8, The lefier half intercolumniation. 1 to 7, The projection of the cornice. 1 to 6, The plinth, and cornice of the pedeftal. x to 5, The projection of the capital. The remaining numbers are backward divifions, therefore 9 to 4, Gives the projection of the modilion band, the bafe of the column, and alfo the dye of the pedeftal. 9 to 3, The greater half diameter. 9 to 2, The lefier half diameter. Of A R C H E S. Plate XII. We have now the heights and projections of this Order, with or without pedeftals, with their different intercolumniations ; alfo the heights of columns and pedeftals feparately ; we fhall next employ the inftrument in the formation of arches. The heights of thefe are on the firft face, firft interval, and fourth or Corinthian line ; this we have already done, as far as relates to the Order itfelf ; upon the fame line however, there are feveral divifions marking the heights of arches, &c. which were omitted in forming colonnades, but become at prefent neceflary. Open the Sedtor from the beginning of the fourth or Corinthian line, No. i to 5, marked k j this gives the bottom of the key-ftone to the lefier arch. 1 to 6 k, The bottom of the key-ftone to the greater arch. r to 8 i, The top of the import to the lefier arch. 1 to 10 i, The bottom of the import to the lefier arch, and top of that to the greater. 1 to 1 1 i, Fixes the bottom of the import to the greater arch. These are all the general heights neceflary for drawing the arches of this Order ; we fhall next pro¬ ceed to their projections, which are found on the third and fourth bars of the fecond interval, firft face of the limb. Projections [ 49 ] Projections of Corinthian leffer arch; third bar, fecond interval, tenth line. Fig. A. Open the Seder from the beginning No. r to the left divifion 12, which cuts off one half of the arch. 1 to 11, The capital. 1 to 10, The leffer half diameter. 1 to 9, The axis of the column. 1 to 8, The greater half diameter. 1 to 7, The outfide of the arcbivault. 1 to 6, The bafe. I to J, The infide of tire archivault, and the pilafter. I to 4, The import. The remaining numbers are backward divifions, therefore 12 to 3, The top of the key-ftone. 1 2 to 2, The bottom of it. Projections of Corinthian greater arches, are on the fourth bar, fecond interval, tenth line. Fig. B. Open the Sedor from No. 1 to 13, which cuts off one half of the arch, i to 12, The capital. 1 to ii, The leffer half diameter. 1 to 10, The axis of the column. 1 to 9, The greater half diameter. 1 to 8, The outfide of the archivault. 1 t0 7 > The bafe of the column, and dye of the pedeftal. 1 to 6, The plinth and cornice of the pedeftal. 1 to 5, The infide of the archivault, and alfo the pilafter. 1 to 4, The import. The remaining numbers are backward divifions, therefore 13 to 2, h and Give the top and bottom of the key-ftone. 13 to 7,) 1 Of a Single Pedeftal, Column, or Entablature. If only a § Angle pedeftal, column, or entablature be wanted, we muft firft take the general heights ot each, and then their general projections. And firft for the heights of the pedeftal. Fix the leg of the Seder at the beginning of the fifth bar, tenth line, iecond interval, firft face. The moveable leg carried to the laft divifion No. 4, gives the entire height of the pedeftal; to 3 cuts lcijit ot the bafe, No. 2, being a backward divifion, fix the moveable leg to the laft divifion on t c ar, and bring the other to the backward divifion, which will cut off the cornice, and alfo the dye. Plate XL Fig. B. The general projedions of the pedeftal; firft face, fecond interval, fecond bar tenth line. ’ . Flx one lc S of the moment at the beginning of the bar No. i, and the other carried to No. 9, gives the greater half intercolumniation. 1 to 6, The projection of the bafe and cornice. B b § See the example in the Tufcan Order, Page 7, Plate XX, Fig. 1. Then Then for the backward divifion, 9 to 4, Is the dye. Columns without entablatures or pedeftals, are upon the firft face, third interval, fecond bar, the fifteenth line, is this Order. Tiif. fixed leg placed at the beginning of the bar No. r, and the moveable one carried to the laft divifion No. 4, gives the height of the column; brought back to 3 the bafe; and from 4 to 2 fixes the bottom of the trunk, and bottom of the capital, by a backward divifion. Plate XI. Fig. B. The general projections of a fingle column; firft face, fecond interval, fecond bar. The Sector fixed as before, I to 9, The greater half intercolumniation. 1 to 5, The capital. The remaining are backward divifions; therefore 9 to 2, Is the top of the trunk. 9 to 3, The bottom of the trunk. 9 to 4, The bafe of the column. The general heights of an entablature, are on the firft face, fecond interval, fixth bar, Corinthian line. 1 to 4, The entire height.- 1 to 3, The architrave. 1 to 2, The frieze, and alfo the cornice. The general projections of an entablature, are on the firft face, fecond interval, fecond bar, tenth line. 1 to 8, The cornice. 1 to 9, The greater half intercolumniation. The remaining is a backward divifion, 9 to 2, The frieze, and alfo the bottom of the architrave. Of the MEMBERS. We fliall begin with the bafe of the pedeftal; the heights of which are on the fecond face of the limb, third interval, fecond bar, thirty-fixth line. _ The PEDESTAL. Plate XIII. One leg of the Secftor placed at the beginning as ufual, and the other carried to the end of the bar; then 1 to 7, Cuts off the height of the bafe. 1 to 6, The inverted cavetto. 1 to 5, The fillet. 1 to 4, The cyma reverfa. 1 to 3, The fillet. 1 to 2, The tore and plinth. The half heights of the dye of pedeftals; fecond face, third interval, fixth bar. The Secftor opened from the beginning No. 1 to the end 2 of the Corinthian line, gives half the height of the dye. Cornice of pedeftals; third interval, third bar, thirty-fixth line. The Sector opened from the beginning No. 1 to the laft divifion No. 7, gives the entire cornice of the pedeftal. [ 5 . ] i to 6, The fillet. 1 to 5> The Doric cyma'. 1 to 4, The corona. Then for the backward divifions, 7 to 3, The ovolo. 7 to 2, The fillet, and alfo the Doric cyma. The COLUMN. Ease of the column; fecond face, third interval, firft bar, thirty-fixth line. One leg of the Sedor placed at the beginning of the bar No. r, and the other divifion No. it, marks the entire height of the bafe. carried to the laft i to ro, The lower cindture. i to 9, The aftragal. 1 to 8, The upper tore. i to 7, The aftragal. i to 6, The upper fillet of the cavetto. J to 5, The cavetto. i to 4, The lower fillet to the cavetto. 1 to 3, The aftragal. i to 2, The lower tore, and alfo the plinth- The CAPITAL. F,g. B. For the heights of the capital, we muft take the fourth interval of the fecond face. The capital is laid down on the firft bar, forty-firft line. One leg of the Sector fixed to the beginning of the bar No. i, 16, gives the entire height. the other carried to the laft divifion i to 15, The ovolo of the abacus. 1 to 14, The fillet. I to 13, The cavetto. I to 12, The lip of the bafket, and the fecond revolution of the volute. 1 to n, The eye of the volute. 1 to 10, The third revolution of the volute. I to 9, The bottom of the volute,, and the top of the upper leaves, i to 8, Ihe turning down of the upper leaves, ri to 7, The top of the fecond row of leaves. 1 to 6, Their reverfe. 1 to 5, The firft row of leaves. 1 to 4, Their turning down. - lIE remaining numbers are backward divifions; therefore 16 to 3, The bottom of the capital. 6 to 2, The aftragal., and lower cincture. c The [ 5 2 ] The ARCHITRAVE and FRIEZE. The next, or fecond bar of this fourth interval, and forty-firft: line, gives the heights of the archi¬ trave and frieze. Open the Sedtor as ufual, from the beginning No. i to the laft divifion io, which marks the entire height of both thefe parts. i to g, The frieze, i to 8, The fillet, i to 7, The Doric cyma. i to 6, The aftragal or bead, i to 5, The upper fafeia. i to 4, The aftragal or bead. The remaining numbers are backward divifions; therefore, io to 3, The middle fafcia. io to 4, The aftragal and lower fafeia. Heights of cornices are to be found on the third bar of the fourth interval, forty-firft or Corinthian line. The Sedtor opened from the beginning i to the laft divifion 15, fhews the entire height. 1 to 14, The fillet. 1 to 13, The cyma. I to 12, The fillet. 1 to 11, The Doric cyma. 1 to 10, The corona. 1 to 9, The fillet. 1 to 8, The cyma, and top of the modilions. 1 to 7, The bottom of the modilions. 1 to 6, The top of the ovolo. I to 5, The bottom of it. 1 to 4, The dental fillet. The remaining numbers are backward divifions; therefore, 15 to 3, The dentals. 15 to 2, The cyma. These are all the heights of this Order; we fhall now take, in the fame manner, the projections, which are all fet off from the axis of the column. The PEDESTAL. And firft for the bafe of the pedeftal ; fecond face, third interval, fourth bar, Corinthian line. The Sector opened from the beginning 1 to the laft divifion 6, gives the projedtion of the plinth and tore. 1 to 5, The fillet. 1 to 4, The cyma and fillet. 1 to 3, The cavetto. 1 to 2, The dye. Projections of cornice of pedeftals; fecond face, third interval, fifth bar, Corinthian line. The [ 53 3 The Sector opened from the beginning i to the laft divifion 10, gives the projection of the fillet, i to 9, The top of the Doric cyma. i to 8, The bottom of it. i to 7, The corona, i to 6, The ovolo. i to 5, The fillet, i to 4, The top of the Doric cyma. i to 3, The bottom of it. i to 2, The dye. The C O L U M N. Base of the column ; fecond face, fecond interval, firft bar, Corinthian or thirty-firft line. The SeCtor opened from the beginning i to the laft divifion 6, gives the projection of the plinth and tore. I to 5, The lower aftragal. i to 4, The lower fillet of the cavetto. I to 3, The upper fillet of the cavetto, and the center for the two aftragals, and upper tore. i to 2, The greater half diameter of the column. The CAPITAL. Second face, fecond interval, fecond bar, Corinthian line. The SeCtor opened from the beginning i to the laft divifion 19, contains the projection of the ovolo. 1 to 18, The fillet. I to 17, The ovolo. I to 16, The fillet, and cavetto, and outfide of the volute. 1 to 15, The cavetto. I to 14, The outfide of the firft revolution of the volute. 1 to 13, The fecond revolution of the volute. 1 to 12, The eye of the volute, and alfo the aftragal. I to 11, The third revolution of the volute, and alfo the upper cinCture. 1 to 10, The infide of the volute, the lefler half diameter, and the outfide of the lower leaf. 1 to 9, The middle of the outward leaf. 1 to 8, It’s infide. 1 to 7, The middle of the long leaf. 1 to 6, The outfide of the next lower leaf. 1 to 5, It’s middle, and alfo of the ftalk to the volute. T«e remaining numbers are backward divifions; therefore, 19 to 4, One fide of the ftalk. 19 to 3, The eye of the middle volute. 19 to 2, The infide of the lower leaf. The FRIEZE and ARCHITRAVE. The frieze and architrave ; fecond face, fecond interval, third bar, Corinthian line. The Scflor opened as ufual, from the beginning i to the laft divifion 7, gives the projeftion of i to 6, [ 54 ] i to 6, The cyma. i to 5, The aftragaL i to 4, The upper fafcia and aftragaL i to 3, The middle fafcia, and aftragaL i to 2, The lower fafcia, and frieze. Of F R I E Z E and CORNICE. Frieze and cornice; fecond face, fecond interval, fourth bar, Corinthian line. The SeCtor opened from i to the laft divifion 23, gives the projection of the fillet of the cyma, or of the entire cornice. 1 to 22, The fillet. 1 to 21, The top of the Doric cyma. 1 to 20, The bottom of it. 1 to 19, The corona. 1 to 18, The fillet. 1 to 17, The cyma of the modilions, above. 1 to 16, The cyma of the modilions, below. 1 to 15, The outward modilion. 1 to 14, The ovolo. 1 to 13, The dental fillet. 1 to 12, The dental band. 1 to li, The top of the Doric cyma. 1 to 10, The modilion. I to 9, The cyma. 1 to 8, The frieze. The remaining numbers are backward divifions, therefore 23 to 7, The fillet to the cyma of the middle modilion; 23 to 6,-) and C The cyma. 23 to 5 ,S 23 to 4, Half a modilion 23 to 3, The denticle. 23 to 2, Half a dental. We have now laid down the heights and projections of all the parts of this Order. Of 1 m p o s t s. The mouldings of the imports are laid down on the fecond face, firft interval; and the heights of thofe adapted to the lefier arches are marked on the firft bar, twenty-fixth or Corinthian line. The SeCtor opened from the beginning No. 1 to the laft divifion 12, gives the entire height of the import. 1 to I I, The lower fillet. I to 10, The a ft rs gal. I to 9 > The neck of the import. I to 8, The fecond fillet. I to 7 > The fecond aftragaL 1 to 6, The large cyma. 1 to 5, [ 55 ] i to 5, The fillet, i to 4, The ovolo. The remaining numbers are backward divifions, therefore i 2 to 3, The corona. 12 to 2, The cyma and upper fillet. The heights of imports for greater arches, are on the fecond face, firft interval, fecond bar, Corin¬ thian line. The Sedor opened from the beginning No. i to the laft divifion 12, gives the entire height. i to ii, The lower fillet, i to io, The lower aftragal. i to 9, The neck of the import, i to 8, The fecond fillet, i to 7, The fecond aftragal. I to 6, The large cyma. i to 5, The fillet, i to 4, The ovolo. The remaining numbers are backward divifions, therefore 12 to 3, The corona, i 2 to 2, The cyma, and upper fillet. Projections of thefe imports are on the firft interval of the fecond face, third and fourth bars ; and as archivaults always fall upon the imports, we ftiall at the fame time take off the different members belonging to them. And firft for the leffer imports and archivaults ; third bar, Corinthian line. The Sedor opened from the beginning No. i to the laft divifion 16, gives the entire breadth of the archivault, and projedion of the import. i to 14,) 1 to 13, The corona. 1 to 12, The ovolo. 1 to 11, The third fillet, and alfo the cyma. 1 to 10, The firft and fecond fillet, and alfo the center of the aftragal*. I to 9, The infide of the archivault, and neck of the import, i to 8, The firft fafcia. 1 to 7, The firft aftragal. 1 to 6, The fecond fafcia. 1 to 5, The fecond aftragal. 1 to 4, The fillet. The remaining numbers are backward divifions j therefore 16 to 3, The ovolo. 16 to 2, The cyma, and alfo the fillet. We next come to the greater imports, and archivaults; fourth bar, Corinthian line. The Seder opened from the beginning 1 to the laft divifion 17, gives us the width of the archivault, and entire projedion of the import. E e The cyma. 1 to 14, [ 56 ] i to 14, The corona. 1 to 13, The ovolo. i to 12, The fillet, and alfo the top of the cyma. 1 to 11, The lower fi let, and center of the lower aftragal. 1 to 10, The fecond fillet, and center of the aftragal. 1 to 9> Fhe inhde of the archivault, and neck of the impoft, 1 to 8, The fir ft fafeia. 1 to 7, The aftragal. 1 to 6, The fecond fafeia. 1 to 5, The middle aftragal. 1 to 4, The fillet. The remaining numbers are backward divifions; therefore, 17 to 3, The ovolo. 17 to 4, The cyma and fillet. Of ARCHIVAULT S. The widths and heights of archivaults, and the projection of their members are on the fifth and fixth bars, firft interval, fecond face. First, Projections of archivaults for the lefler arches; fifth bar, Corinthian line. The SeCtor opened from the beginning 1 to the laft divifion 7, gives, as we faid before, the width of the archivault, and it’s projection. 1 A The cyma. 1 to 4, The ovolo. i to 3, The fillet, and middle fafeia. 1 to 2, The lower fafeia. Projections of the archivaults of greater arches; fixth bar, Corinthian line. The SeCtor opened from the beginning 1 to the laft divifion 7, as before, gives the width and pro¬ jection of the archivault. 1 to 6, and > The cyma. 1 to 5,) 1 to 4, The ovolo. 1 to 3, The fillet, and middle fafeia. 1 to 2, The lower fafeia. Of BLOCK CORNICES. Block cornices are on the fecond face, fecond interval, fifth and fixth bars, Corinthian line. First, for the heights; fifth bar. Flat XVIII. The SeCtor opened from the beginning 1 to the laft divifion 13, gives the entire height. 1 to 12, The fillet. 1 to ir, The cyma. i to 10, The fillet. 1 to 9, The middle cyma. 1 to 8, The corona. I to 7, The fillet. 1 to 6, [ 57 ] 1 to 6, The cyma to modilions. • I to 5, The modilions. 1 to 4, The modilion band. I he remaining numbers are backward divifions ; therefore i 3 to 3, The cyma. 13 to 2, The aftragal, and alfo the lower fillet. Projections of block cornices; fixth bar. 1 iif. SeCtor opened from the beginning No. 1 to the laft divifion 13, gives the entire projection beyond the upright of the wall. 1 to 12, The fecond fillet. 1 to 11, AND k 'J'Jjg C y ma> I to IO,) i to 9, The corona. 1 to 8, The fillet. 1 to 7 >) and > The cyma to modilion. I to 6 ,5 1 to 5, The modilion. Of the two backward divifions, 1 3 to 3, The modilion, and bottom of the cyma. 13 to 2, The lower fillet. Of BALLUSTERS. Ballusters are on the firft face, fourth interval, fifth bar, Corinthian line. Heights of ballufters; fourth interval, fifth bar, Corinthian line. The Sedor opened from the beginning 1 to the laft divifion 9, gives half the height of the ballufter. 1 to 8, The bottom, and confequently half of the middle aftragal. 1 to 7, Gives only the line on which the greateft projection of the vafe is to be marked; but this divifion is of no other ufe in the heights, and therefore marked with a crofs. 1 to 7 > Gives likewife only a line for the leaft projection of the concavity of the vale. The remaining numbers are backward divifions; therefore, 9 to 5, The bottom of the vafe. 9 to 4, The fillet. 9 to 3, The lower aftragal. 9 to 2, The fillet, and top of the plinth. Projections of ballufters ; fixth bar. 1 he SeCtor opened from the beginning 1 to the laft divifion 8, gives the projection of the entire iballufter, or utmoft projection of the vafe; which put on paper vve bifeCt, and this gives the femi- diameter of the ballufter, which could not be laid down upon the limb. 1 to 7, The plintv. 1 to 6, The fillet, and middle aftragal. 1 to 5, The ower aftragal. 1 to 4, The bottom of the vale. j to 3, The fecond fillet. 1 to 2, The leaft projection of the vafe. r f Of [ SB 1 Of FLUTES. The flutes and fillets of columns in piano, as well as thofe for upright columns and pilafters, are the fime for this Order as in the Ionic, which fee in that example. Of DOORS. After having the Order, as laid down on the firft face, firft interval, one leg of the Seftor fixed at the beginning of the Corinthian line No. i, let the other be opened to 12, marked d, upon the limb, then we fliall cut off the height of the door proportioned to colonnades without pedeftals; 1 to 9, marked alfo d, cuts off the heights of doors proportioned to colonnades with pedeftals. These two divifions 1 2 and 9, were not mentioned when we were drawing the heights of this Order, being of no ufe, except for the above purpofe. Heights of doors and their entablatures; firft face, third interval, firft bar, Corinthian line. Having determined either the height, width, or half width of a door intended to be drawn ; fix one lea of the Sector at the beginning of the bar, and open the other to any one of thofe given lengths, fup- pofe the half width ; then the meafure of that taken in the compaffes from the fcale the plan is drawn by, muft be applied to the Sedtor, and where it coincides upon two oppofite numbers, will become the proper fcale for the general heights of doors. Pi.ate XXI. The moveable leg of the Sedtor carried to the end of the line 12, gives the entire height of the door with it’s entablature. I to 11, Cuts off the cornice. 1 to 9, The frieze. 1 to 8, The architrave, and confequently 1 to 8 is the height of the door, without the entablature. 1 to 3, The width of the door. 1 to 2, The half width, which we began with. If we make ufe of a kneed architrave, then after taking 1 to 8, The height of the door, i to 11, Gives the top of the confole. 1 to 10, The eye of the upper volute. 1 to 9, The bottom of the upper volute. 1 to 7, The top of the lower volute. 1 to 6, The eye of the lower volute. 1 to 3, The bottom of the lower volute, and alfo the bottom of the knee. 1 to 4, Cuts off the length of the leaf. N. B. In Fig. A we have drawn the architrave, and at Fig. B is a plan of it. We now come to the particular mouldings for the entablature of doors ; which are on the firft face* fourth interval. Heights of entablatures of doors; firft bar, Corinthian line. The Sedtor opened from the beginning 1 to the laft divifion 21, is the entire entablature, 1 to 20, Cuts off the fillet. 1 to 19, The cyma. 1 to 18, The fillet. 1 to 17, The cyma. 1 to 16, The corona. 1 to 1 5, [ 59 ] I to 15, The ovolo. 1 Co *4> The filler, i to 13, The dentals. 1 to 12, The fillet. 1 to 11, The cyma. I to 10, The aftragal, and alfo the frieze, t to 9, The frieze, and top of the architrave. 1 to 8, The fillet, i to 7, The ovolo. 1 to 6, The fillet. 1 to 5, The cyma. 1 to 4, The aftragal. The remaining numbers are backward divifions, therefore 21 to 3, Gives the upper fafcia. 21 to 2, The cyma, and alfo the lower fafcia. Projections of cornice of doors; fecond bar. The Seftor opened from the beginning 1 to the laft divifion 12, is the greateft projeftion of the cornice. 1 to 11, The fillet. 1 to 10, The top of the cyma. 1 to 9, The bottom of it. 1 to 8, The corona. 1 to 7, The ovolo. 1 to 6, The fillet. 1 to 5, The dentals. The remaining numbers are backward divifions, therefore 12 to 4, The fillet. 12 to 3, The top of the cyma. 12 to 2, The bottom of it, and alfo the aftragal. Projections of architraves of doors; third bar. The Seftor opened from the beginning No. 1 to the laft divifion ,0, gives us both the height and projedtion of the architrave. 1 to 9, The ovolo. 1 to 8, The fillet. I to 7, The top of the cyma. 1 to 6, The bottom of it, and alfo the aftragal. 1 to 5, The firft fafcia. 1 to a n d ^ The cyma. 1 to 3,) 1 to 2, The lower fafcia, and frieze. Of CONSOLES. The half heights of confoles, are on the firft face, fecond interval, feventh bar, Corinthian line. Plate XXIir. The Seftor opened from the beginning 1 to the laft divifion 7 , gives half the height of the entire confole. ° 1 to 6, [ 6 ° ] i to 6, The eye of the upper volute, i to 5, The bottom of it. I to 4, The top of the lower volute, i to 3, The eye of it. i to 2, The bottom of the volute, and top of the leaf. Widths of confoles; firft face, fourth interval, fourth bar, twentieth line. The Se£tor opened from the beginning i to the lad; divifion 13, gives us the height of the architrave, and breadth of the confole. 1 to 12, The fillet, i to n, The cavetto. 1 to 10, The fillet. 1 to 9, The cyma. 1 to 8, The fillet. 1 to 7, The aftragal. 1 to 6, The fillet. I to 5, The cyma. 1 to 4, The fillet. 1 to 3, The cavetto. 1 to 2, The fillet. ¥9 /OKo &A i The [ % # snRintf'tr'KsrT* ^ k jkTjbl jI .... k * .> C, <*> * <*>€*> * <*> > f" „ AT „ n k-f-jK k-fsji % kkkjKk-wkjs! -t- v- P 'S' 'S' ^Wgl 5 ^ 0 ^.a*PW* J ■£• -S' ?T'KK''}r»'-3fK''S{ *4 , * £ &#> \ , r*j w ^ v C kk k 4 *^° a ®. <*»5 <*> * <*> * <*> _> p^ % . . y f k^k kfk F" '15 j? jckkkkkkjt * k^'^oif* *vt, >?• *$ The U S E of the ARCHITECTONIC SECTOR, In drawing the Compofite or Roman Order. GENERAL HEIGHTS. CHAP. VI. 5 if§!M §3 H E “ fe ° f the !nftru,ncnt in drawing the general heights of the Compofite or Roman ftw X WM Order, as laid down on the firft face of the limb, firft interval, and fifth line. »w *- shA Plate XIV. Screw one leg; of the SeCtor to the beginning; of the fifth line No. i, wfc£|HE3r«wE . o a » k^-sQ^^k then move the other till it cuts the laft divifion 18 ; this is the total height of the Order. Bring back the moveable leg to i y, this cuts off the bafe of the pedeftal. i to 16, The dye. i to 15, The cornice of the pedeftal. I to 14, The bafe of the column. Then palling over the divifions marked with letters, that belpng to doors or arches, bring the moveable leg from 1 to 7, The trunk. Here likewife pafs by No. 6 and 5, both marked with letters, and bring the moveable leg from I to 4, Which cuts off the capital. I to 3, The architrave. 1 to 2, The frieze, and alfo the cornice. Here as before, we fhall obferve, that if the moveable leg be brought to 14, it gives the height of .the column with it’s entablature without a pedeftal. In like manner the moveable leg brought to 4, cuts off the entablature without a column. Of intercolumniations. Thus having given the heights of the principal parts of this Order, we now proceed to the projecti¬ ons; to which we fhall join the different diftances, or intercolumniations fuited to it: we have pro-. jcCtions proper to .each, viz. on the firft and ftcond bars, fecond interval, firft face. H h The [ 62 ] Tr: fii fl bar gives us, befides the projections of the column and entablature, two different interco- lumniatior.s, one of one module and one half; the other of one module. We {hall begin with the firft bar, eleventh line. The ScCtor opened irom the beginning No. r (which anfwers to the axis of the column) to the laft divifion 8, we (hall have the greater halt intercolumniation. i to 7, The projection of the cornice. 1 to 6, The ltffer halt intercolumniation. 1 to 5, The projection of the capital. The remaining numbers are backward diviffons; therefore, 8 to 4, The plinth. 8 to 3, The greater hilf diameter. 8 to 2, The leffer halt diameter. Second bar, fecond interval, eleventh line. The Roman columns with pedeftals, and two intercolumniadons; one of two modules; the other of one module and ten minutes. The Seder opened from the beginning of the bar No. i to the laft divifion 9, marks the greater half intercolumniation. 1 to 8, The projection of the cornice. 1 to 7, The leffer half intercolumniation. 1 to 6, The bafe and cornice of the pedeftal. 1 to 5, The projection of the capital. The remaining numbers are backward diviffons; therefore, 9 to 4, Gives the projection of the bafe of the column, and dye of the pedeftal. 9 to 3, The greater half diameter. 9 to 2, The leffer half diameter. Of A R C II E S. We have now the heights and projections of this Order, with or without pedeftals, with their diffeient intercolumniations; alfo the heights of columns and pedeftals feparately; we fhall next employ the inftrument in the formation of arches. Thi heights of thefe are on the firft interval, and fifth or Roman line ; this we have already done, as far as relates to the Order itfelf; upon the fame line however, there are feveral diviffons marking the liei'dits of arches, See. which were omitted in forming colonnades, but become at prefent ncceflary. Plate XV. Open the SeCtor from the beginning of the fifth or Roman line No. i to 5 marked k ; this Tves the bottom of the key-ftone to the leffer arch. 1 to 6 k, The bottom of the key-ftone to the greater arch. 1 to 8 i, The top of the impoft to the leffer arch. 1 to 10 i, The bottom of the impoft to the leffer arch. 1 to 11 i, The top of that to the greater arch. i to 12 i, Fixes the bottom of the impoft to the greater arch. These are all the general heights neceffary for drawing the arches of this Order ; we fhall next pro¬ ceed to their projections, which are found on the third and fourth bars of the fecond interval, fiift face of the limb. Projections [ 63 ] Projections of lefler arches, are on the third bar, fecond interval, eleventh line. Fix the SeCtor as before, to No. i, and open it to No. 12, which cuts off half the width of the whole arch, and the projection of the cornice. 1 to 11, The capital. 1 to 10, The lefler half diameter. 1 to 9, The axis of the column. 1 to 8, The greater half diameter. 1 to 7, The outflde of the archivault. I to 6, The bafe of the column. I to 5, The pilafter, and infi.de of the archivault. 1 to 4, The import. Then for the backward divifions, *a n°d 3 ’1 Give the top and bottom of the key-ftone. 12 to 2, ) Projections of greater arches, are on the fourth bar, fecond interval, eleventh line. Fix the inftrument as before, and move it to No. 13, which gives half the whole arch, and pro¬ jection of the cornice. 1 to 12, The capital. 1 to n, The lefler half diameter. 1 to 10, The axis of the column. 1 to 9, The greater half diameter. 1 to 8, The outflde of the archivault. 1 to 7, The bafe of the column, and dye of the pedeftal. 1 to 6, The plinth, and alfo the cornice of the pedeftal. 1 to 5, The pilafter, and alfo the inftde of the archivault. i to 4, The import. The remaining are backward diviflons; therefore n d ’ r- Cuts off the top and bottom of the key-ftone. 13 to 2 > Of a Single Pedeftal, Column, or Entablature. If only a § fingle pedeftal, column, or entablature be wanted, we mull firft take the general heights of each, and then their general projections. Fix the leg of the Seflor at the beginning of the fifth bar, fecond interval, eleventh line, firft face. The moveable leg carried to the laft divifion No. 4. gives the entire height of the pedeftal; to 3 cuts off the height of the bafe ; No. 2, being a backward divifion, fix the moveable leg to the laft divifion on the bar, and bring the other to the backward divifion, this will cut off the cornice, and alfo the dye. Plate XIV. Fig. B. The general projedions of the pedeftal; firft face, fecond interval, fecond bar, fifth line, where we have the projeflions of great colonnades. Fix one leg of the inftrument at the beginning of the bat No. 1, and the other carried to No. 9, will ^ive the greater half intercolumniation. 1 to 6, The projection of the bafe, and alto the cornice. The remaining number is a backward divifion ; therefore, 9 to 4, Is the dye. I i § See this example fully explained in the Tufcan Order, Page 7, 1 late XX, Fig. 1. Columns 1 to o, L the greater half intercolumniation. i to 5, The capital. The remaining numbers are backward divifions ; therefore 9 to 2, Is the top of the trunk. 9 to 3, The bottom of the trunk. 9 to 4> The bale of the column. The remaining number is a backward divifion; therefore, 9 to 2, Cuts oft the frieze and architrave. fecond face of the limb, third interval, fecond bar, thirty-feventh line. The PEDESTAL. I to 7, Cuts off the height of the bafe. i to 6, The upper fillet. 1 to 5, The aftragal. i to 4, The cyma reverfa. 1 t0 3 j The lower fillet, i to 2, The tore, and alfo the plinth. 1 HE halt heights of the dye of pedeftals ; fecond face, third interval, fixth bat. The Sedor opened from the beginning i to the end 2 of the Roman line, c the dye. Cornice ofpedeflals; third interval, third bar, thirty-feventh line. The Sedor opened from the beginning No. , to the laft divifion No. 8, give the pedeftal. i to 7, The fillet. [ 6s ] I to 6, The cvnu 1 to 5, I he corona, i to 4 , The fillet. Tu * rcm; ™ing numbers are backward divifions; therefore $ to 3, 1 lie cyma. b to 2, The aftragal, and alfo tile lower fillet. The COLUMN. Bass of the column; f.cond face, third interval, firft bar, One leg of the Seder placed at the beginning of the bar No. divihon 15, marks the entire height of the bafe. thirty-feventh line. x, and the other carried to the laffc i to 14, 1 he height of the lower cintfture. 1 to 13, The upper aftragal. 1 to 12, The upper tore. I to 11, The hollow moulding. 1 to 1 o, I he upper fillet of the cavetto. 1 to 9> The cavetto. 1 to 8, The lower fillet of the cavetto. 1 to 7, The upper aftragal. 1 to 6, The lower aftragal. 1 to 5> 'l he upper fillet of the lower cavetto. 1 to 4, The lower cavetto. 1 to 3> The fillet of the lower cavetto. i to 2, The lower tore, and alfo the plinth. The CAPITAL. For the heights of the capital and entablature, we mud take the fourth interval of the fecond face. The capital is laid down on the firft bar, forty-fecond line. One leg of the Seder fixed to the beginning of the bar No. ,, the other carried to the laft divifion 15, gives the entire height. i to 14, The ovolo of the abacus. 1 to 13, The fillet, and top of the volute. • to I 2 , ^ he cavetto, and top of the fecond revolution of the volute. 1 to 11, The ovolo, and top of the eye of the volute. 1 to 10, The aftragal, and bottom of the eye of the volute. I to 9, T he cinflure, and bottom of the the third revolution of the volute. 1 to 8, I he bottom of the fecond revolution of the volute.. 1 to 7, The bottom of the volute, and top of the upper row of leaves. 1 to 6, The turning down of the leaves. 1 to 5, The top of the lower leaves. 1 to 4, Their turning down. The remaining numbers are backward divifions; therefore, 1 5 to 33 The bottom of the capital. 15 to 2, 1 he aftragal, and alfo the lower cin&ure. K k The [ 66 ] The A R C H I T R A V E and FRIEZE. T. : next, cr fecond bar oi this fourth interval, and forty-fecond line, gives the heights of the Roman architrave and frieze. Open tire SeCtor as ufual, from the beginning No. i to the laft division 9, this marks the entire height of both thefe parts. 1 to 8, The frieze. 1 to 7, The fillet. 1 to 6, The cavetto. 1 to 5, The Doric cyma. 1 to 4, The aftragal. I to 3, The upper fafeia. 1 to 2, The Doric cyma, and lower fafeia. Heights o. 1 cornices are to be found on the third bar of the fourth interval, forty-fecond or Roman line. The SeCtor opened from the beginning 1 to the laft divifion 15, fhews the entire height. 1 to 14, The fillet. 1 to 13, The cyma. 1 to 12, The fillet. 1 to 11, The Doric cyma. 1 to 10, The corona. 1 to 9, The ovolo to modilions. I to 8, The aftragal to modilions. 1 to 7, The upper modilion band. 1 to 6, The cyma to modilions. The remaining numbers are backward divifions; therefore, 15 to 5, Gives the bottom of the modilion. 15 to 4, The modilion band. 15 to 3, The Doric cyma. 15 to 2, The aftragal, and alfo the fillet. These are all the heights of this Order ; we fhall now take in the fame manner, the projections, which are all fet off from the axis of the column. The PEDESTAL. And firft for the bafe of the pedeftal ; fecond face, third interval, fourth bar, Roman line. T h e SeCtor opened from the beginning No. 1 to the laft divifion 6, gives the projection of the plinth and tore. 1 to 5, The fillet. 1 to 4, The aftragal. 1 to 3, The fillet. 1 to 2, The dye. Projections of cornice of pedeftals; fecond face, third interval, fifth bar, Roman line. The SeCtor opened from the beginning 1 to the laft divifion 9, gives the projection of the fillet. 1 to S,) a n d - The cyma. 1 to 1 to 6, [ 6 7 ?! I to 6, The corona. 1 to 5 > The fillet, and top of the cyma. 1 to 4, The aftragal. 1 to 3, The fillet, and bottom of the cyma. i to 2, The dye. The COLUMN. Base of the column; fecond face, fecond interval, firft bar, Roman or thirty-fecond line. and T " £ re Sea0r ° pcned fr0m the be S innin g No - * *<= M divifion 7> gives the projedion of the plinth i to 6, The lower fillet of the cavetto. i to s , The upper fillet of the cavetto, and the center for the two aftragals, and projection of the upper tore. I to 4, The fillet to the upper cavetto, and lower cindure. ^ 3, The hollow moulding. I to 2, The greater half diameter of the column. The CAPITAL. Second face, fecond interval, fecond bar, Roman line. The Seder opened from the beginning No. i to the laft divifion , 9> contains the projedion of the ovolo. J i to 18, The fillet. I to 17, The ovolo, the outer cavetto, and the outfide of the volute, i to 16, The fillet. 1 to 15, The inner cavetto. 1 to 14, The firft revolution of the volute. 1 to 13, The reverfe of the outer lower leaf. 1 to 12, The aftragal, and fecond revolution of the volute: 1 to 11, The third revolution of the volute, and alfo the cinCture. 1 to 10, The eye of the volute, the outfide of the lower leaf, and alfo the lelfer half diameter of the column. 1 to 9, The infide of the third revolution, and the middle of the outer leaf. 1 to 8, The infide of the fecond revolution of the volute. 1 to 7, The width of the lower outward leaf. 1 to 6, The infide of the firft revolution, and the middle of the long leaf. 1 to 5, The outfide of the next lower leaf. 1 to 4, The middle of the leaf, and alfo the ftalk to the ornament between the leafs. 1 he remaining numbers are backward divifions; therefore, 19 to 3, One fide of the ornament between the leafs. 19 to 2, The infide of the lower leaf. The FRIEZE and ARCHITRAVE. The frieze and architrave ; fecond face, fecond interval, third bar, Roman line. The SeCtor opened as ufual, from the beginning No. 1 to the laft divifion 9, gives the projection of the fillet. L 1 1 to 8, [ 68 ] i to 8, The cavetto. i to 7, The cyma. 1 to 6, The bottom of the cyma, and the aftragal. 1 to 5, The fecond fafcia. 1 to 4,7 and b The cyma. 1 to 3,) 1 to 2, The fir ft fafcia, and frieze. Of FRIEZE and CORNICE. Frieze and cornice; fecond face, fecond interval, fourth bar, Roman line. The Sedor opened from the beginning 1 to the lad divifion 22, gives the fillet of the cyma, or entire projedtion of the cornice. 1 to 21, The cyma and fillet. 1 to 20, The top of the Doric cyma. 1 to 19, The bottom of it. 1 to 18, The corona. I to 17, The ovolo. 1 to 16, The aftragal. 1 to 15, The outward modilion. 1 to 14,) and > The cyma. 1 to 13,) 1 to 12, The bottom of the modilion. 1 to 11, The modilion band. 1 to 10, The cyma. 1 to 9, The aftragal. 1 to 8, The fillet. 1 to 7, The frieze. The remaining numbers are backward divifions, therefore 22 to 6 , The ovolo to the middle modilion. 22 to 5, The upper half of the modilion. 22 to 40 and The cyma. 22 to 3,) 22 to 2, The lower half of the modilion. Of I M P O S T S. The heights of impofts are laid down on the fecond face, firft interval; and the height of thof e adapted to the leffer arches, are marked on the firft bar, twenty-feventh or Compofite line. The Sedtor opened from the beginning i to the laft divifion 13^ gives the entire height 01 the impoft. 1 to I 2, The fillet. I to II, The aftragal. I to IO, The neck of the impoft. I to 9 > The fillet. I to 8, The aftragal. 1 to 7 , The ovolo. 1 to 6, [ 69 J i to 6, The fillet. 1 to 5 > The cyma. i to 4, The fillet. The remaining numbers are backward divifions; therefore, *3 to 3, The corona. i 3 to 2, The cyma, and alfo the upper fillet. Heights of imports for greater arches, are on the fecond bar, firft interval, Roman or twenty- fevcnth line. The Sector opened from the beginning i to the laft divifion 13, (hews the entire height. 1 to 12, The lower fillet. 1 to n, The aftragal. 1 to 10, The neck. I to 9, The fillet. 1 to 8, The aftragal. 1 to 7, The ovolo. 1 to 6, The fillet. 1 to 5, The cyma. I to 4, The fillet. The remaining numbers are backward divifions; therefore, 13 to 3, The corona. 13 to 2, The cyma, and alfo the upper fillet. Projections of thefe imports are on the firft interval of the fecond face, third and fourth bars; and as archivaults always fall upon the imports, we Ihall at the fame time take off the different members belonging to them. And firft for the leffer imports and archivaults; third bar, Roman line. The SeCtor opened from the beginning 1 to the laft divifion 17, gives the entire breadth of the archivault, and projection of the import. 1 to 16,-) a n d C The cyma. 1 to 15,) 1 to 14, The corona. 1 to 13, The fillet and cyma. 1 to 12, The fillet, and bottom of the cyma. 1 to 11, The ovolo. 1 to 10, The upper aftragal, the center of the lower one, and the lower fillet. 1 to 9, The fillet to the upper aftragal. 1 to 8, The infide of the archivault, the neck, and pilafter. 1 to 7, The firft fafcia. 1 to 6, The aftragal. 1 to 5, The middle fafcia. 1 to 4, The aftragal. The remaining numbers are backward divifions; therefore, 17 to 3, The upper fafcia. 17 to 2, The cyma, and alfo the fillet. We ♦f M m [ 7 ° J V. come next to the greater impofts, and archivaults ; fourth bar, Roman line. The Sefior opened from the beginning i to the laft divifion 17, gives the width of the archivault, and entire projection of the import. I to 16, ^ and r" The cyma. 1 to 15,' 1 to 14, The corona. 1 to 13, The fillet, and cyma. ° i to 12, The fillet, and bottom of the cyma. 1 to 1 r, The ovolo. 1 to ro, The upper aftragal, the center of the lower aftragal, and it’s fillet. 1 to 9, The fillet, and center of the upper aftragal. 1 to 8, The infide of the archivault, the neck and pilafter. 1 to 7, The lower fafeia. i to 6, The aftragal. 1 to 5, The middle fafeia. 1 to 4, The aftragal Of the two backward diviftons, 17 to 3, The upper fafeia. 17 to 2, The cyma, and alfo the upper fillet. Thus we have the widths and heights of archivaults ; the projections of their members are feldom drawn in plans, but yet abfolutely neceflary to be known, they are therefore on the fifth and fixth bars, firft interval, fecond face. Of ARCHIVAULTS. First, Projections of archivaults for the lefler arches; fifth bar, Roman or twenty-feventh line. The Sector opened from the beginning No. i to the laft divifion 7, gives, as we faid before the width of the archivault, and it’s projection. 1 to 6, and C The cyma. 1 to 5,3 1 to 4, The upper fafeia, and aftragal I to 3, The middle fafeia, and aftragal I to 2, The lower fafcia. Projections of archivaults of greater arches; fixth bar, Roman line. The Sector opened from the beginning 1 to the laft divifion 7, as before, gives the width and projection of the archivault. 1 to 6,1 and > The cyma. 1 to 5 ,> 1 to 4, The upper fafeia, and aftragal. 1 to 3, The middle fafeia, and aftragal. 1 to 2, The lower fafeia. Of BLOCK CORNICES. 1 he next thing we ftiall take from the inftrument is the method of delineating block cornices which are on the fecond lace, fecond interval, filth and fixth bars, Roman line. FirsTj [ 7 1 ] First, for the heights; fifth bar. The Setfor opened from the beginning No. i, to the laft divifion 13, gives the entire height. 1 to 12, The fillet. 1 to 11, The cyma. 1 to 10, The fillet. 1 to 9, The cyma. 1 to 8, The corona. 1 to 7, The ovolo. r to 6, The aftragal. 1 to 5, The modilion. 1 to 4, The bottom of the modilion. The remaining numbers are backward divifions ; therefore 13 to 3, The modilion band. 13 to 2, The ovolo, and alfo the fillet. Projections of block cornices; fixth bar. The Sedtor opened from the beginning No. 1 to the laft divifion No. 18, gives the entire projedfion beyond the upright of the wall. 1 to 17, The fillet, and bottom of the cyma. 1 to 16,) and ^ The cyma. 1 to 15,3 I to 14, The corona. 1 to 13, The ovolo. 1 to 12, The aftragal. 1 to 11, The upper fafcia of the outward modilion. 1 to 10, The lower fafcia of it. 1 to 9, The ovolo to modilion. 1 to 8, It’s aftragal. 1 to 7, The upper fafcia of the modilion. The remaining numbers are backward divifions; therefore, 18 to 6, The bottom of the modilion. 18 to 5, The ovolo. 18 to 4, The lower fafcia of the modilion. 15 to 3, The upper fafcia of it. 15 to 2, The lower fillet, and bottom of the ovolo. Of BALLUSTERS. Plate XIX. We come next to ballufters, which are on the firffc face, fourth interval, fifth and fixth bars. Heights of ballufters ; fourth interval, fifth bar, Roman line. The Sedtor opened from the beginning 1 to the laft: divifion 11, gives half the entire height. 1 to 10, Half the middle fillet. 1 to 9, The fillet and cavetto. 1 to 8, The bottom of the cavetto. 1 to 7, The fillet, and top of the yafe. N n 1 to 6, 0 |l [ 7 * ] x to 6, Gives only the line on which the greateft projection of the vafe is to be marked ; fcut this divifion is of no other ufe in the Jieights, and therefore marked with a crofs. i to 5, Gives the leaf!; projection of the concavity of the vafe, or the narrowed part of it. The remaining numbers are backward divifions ; therefore ir to 4, The bottom of the vafe. ii to 3, The fillet. 3i to 2, The ovolo reverfed, and the plinth. Projections ol ball lifters; fixth bar. Tiie SeCtor opened from the beginning No. i to the laft divifion 6, gives the projection of the entire ballufter, which put on paper we bifeCt, and this gives the femi-diameter of the ballufter, which could not be laid down on the limb. i to 5, The ovolo reverfed. i to 4, The lower and upper little fillet, i to 3, The middle fillet of the cavetto. i to 2, The concavity of the neck. We have now given an example of every thing that can be drawn by the inftrument, except flutes with their fillets, and doors with their ornaments. Of FLUTES. The flutes and fillets of colomns in piano, as well as thofe for upright columns and pilafiers, are the fame for this Order as in the Ionic, which fee in that example. Of DOORS. Doors are fometimes placed in colonnades, as in porticos of temples, and then their heights mult be proportioned to the columns. After having drawn the Order, as laid down on the firft face, firft interval; one leg of the SeCtor fixed at the beginning of the Roman line No. r, let the other be opened to 13, marked d, upon the limb, then we (hall cut off the height of the door proportioned to colonnades without pedeftals, ; 1 to 9, marked alfo d, cuts off the heights of doors proportioned to colonnades with pedeftals. These two divifions 13 and 9, were not mentioned when we were drawing the heights of this Order, being of no ufe, except for the above purpofe. If doors are to be placed in arches, their height is fixed, becaufe the top of the entablature fhould always run in a line with the top of the impoft, and the impoft moulding ought by rights to form thofe .of the cornice, as we have ftiewn in plate XXI. Heights of doors and their entablatures; firft face, third interval, firft bar, Roman line. Having determined either the height, width, or half width of a door intended to be drawn ; fix one leg of the SeClor at the beginning of the bar, and open the other to any of thofe given lengths, fuppofe •the half width ; then the meafure of that taken in the compaffes from the fcale the plan is drawn by, mud be applied to the SeCtor, where it coincides upon two oppohte numbers, will become the proper fba'.e for the general heights of doors. [ 73 ] The moveable leg of the Seflor carried to the end of the line 12, gives the entire height of the door with it’s entablature. 1 to 11, Cuts off the cornice. 1 to 9, The frieze. 1 to 8, The architrave, and confequently the height of the door without the entablature. 1 to 3, The width of the door, i to 2, The half width which we began with. It we make ule of a kneed architrave, after taking 1 to 8, The height of the door, then 1 to 5, Gives the depth of the knee. _ If a confole is to be added, it is generally to fupport the cornice, and to terminate with the bottom of the knee,, wpth a leaf from it. 1 to 11, Gives the top of the confole. i to io* The eye of the upper volute. 1 to 7> The top of the lower volute. I to 6, The eye of the lower volute. 1 to s, The bottom of the lower volute. 1 to 4, Cuts off the height of the leaf. Havin-g thus got the general heights of door entablatures, we now come to the particular mouldings, which are on the firft face, fourth interval. Plate XXII. Heights of entablature of doors ; firft bar, Roman line. ? The Sedtor opened from the beginning i to the laft divifion 21, is the entire entablature. » to 20, The fillet. 1 to 19, The cyma. 1 to 18, The fillet. 1 to 17, The cyma. 1 to 16, The corona. I to 15, The ovolo. 1 to 14, The fillet. 1 to 13, The cyma. 1 to 12, The fillet. 1 to 11, The cavetto. 1 to 10, The aftragal. 1 to 9 > The frieze, and top of the architrave. 1 to 8, The fillet. 1 to 7, The cyma. 1 to 6, The aftragal. 1 to 5, The upper fafeia. 1 to 4, The aftragal. Then for the backward divifions, 21 to 3, Gives the middle fafeia. 21 to 2, The aftragal, and lower fafeia. O o Projections [ 7 + J Projections of cornice of doors; fecond bar. 'i ;ie SeCtor opened from the beginning x to the Iaft divifion 12, gives the greateft projection. I to ii, The fillet and bottom of the cyma. 1 to 10,) and (■ The cyma. 1 to 0,' 1 to 8, The corona. 1 to 7, The ovolo. 1 to 6, The fillet. I to 5, The top of the cyma. T;ie remainder are backward divifions. 12 to 4, The bottom of the cyma. 12 to 3, The fillet and cavetto. 13 to 2, The cavetto, and the aftragal. Projections of architraves of doors; third bar. As the entire projection of architraves are too fmall to be laid down by themfelves on the fcales, we are obliged here, as in archivaults, to add fome certain meafure before them; for which purpofe we choofe to repeat the height of the architrave itfelf. The Sector opened, from the beginning No. 1 to the laft divifion 7, gives us both the height and projedtion of the architrave. 1 to 6,J a n d ^ The cyma, and alfo the aftragal. 1 to 4, The upper fafeia and aftragal. 1 to 3, The middle fafeia and aftragal. 1 to 2, The lower fafeia and frieze. Of C O N S O L E S. The half heights of confoles, are on the firft face, fecond interval, feventh bar, Roman line. Plate XXIII. The SeCtor opened from No. 1 to the laft divifion 7, gives half the height of the entire confole. 1 to 6, The eye of the upper volute. 1 to 5, The bottom of it. 1 to 4, The top of the lower volute. 1 to 3, The eye of it. 1 to 2, The bottom of the volute, and the top of the leaf. Widths of confoles; firft face, fourth interval, fourth bar, twenty-firft line. The SeCIor opened from the beginning No. 1 to the laft divifion 15, gives us, as we faid before, the height of the architrave, and breadth of the confole. 1 to 14, The fillet. 1 to 13, The cavetto. 1 to 12, The fillet. 1 to 11, The cyma. 1 to 10, [ 75 ] i to io, The fillet. X to 9, The aftragal. i to 8, The fillet, i to 7, The aftragal. I to 6, The fillet, i to 5, The cyma. I to 4, The fillet, i to 3, The cavetto. i to 2, The fillet. p p CHAP. [ " 6 ] f|»8 | W? ’ *l±. 3 S±jg ^/ > (pv’. ’ c "tv: -:v k,.i. .-:::-:::::::i;::l::: ;;; chap. vii. ! ft 1$ $8$ S: . . W I A farther Defcription, ttnd other Ufa of the ArchitecW feeCeOr ; by various Examples. i" lNthe be giianmg of the defcription and ufe of this ind • P la.the two principal lines or fcafa t"l “ ‘ o ’ page *■ we mentioned that theHraof 6 o is an univl] fj c of , f “ ° ^ ° t ' d ’<= lin * S and obferved, - *. f-eft degree of accufi ^ ** ^ Orders of tuchi^ 7“ Sea ° r; thmf0K « trniverfaily 7l 77777i77 ^7'^ " ^ 1 *= cwn - that and the great ufe already made of it in a ° • ’ . 7 ” nC wbo “ ^“‘tinted with ■»-* W^eitre^nrdiartoL";- e ^ ^ ^ « .i*::;: £ - ™- * -»», the primary ones. ’ d fland ° l ' er cvl;r 7 four* divifion of “* “ f *! *« « aad «***■ to the Roman ftcondrry divifrons »ith ihort ftrokes, will anfwer to the^Iifth XXnX ^ ^ ^ “ mediate^rhTwy'divddonSj^being ^one 2 quartloiTa lb t X" T"’ °“ ^ ' *“ ** - K within tiie fame r F cc o! the flXo a 7’ , *“ “ d *« into half inches by dotted divifrons. ' ’ 111 ” ” ’ 3nd tbcfe la(d are alfo Pub-divided e »rrrir m ^i; h ;r^ i fr° f r^ **• «« twenty-fourth part of an inch ; by the fecund, any * V bnes:^^^ 1170 ^ Breton both the feales, from the did —-—- E X A M P L E I. Ta.lhTlenXf tbelhre "T "7^ ^ ^ ^ S ® P^ A B in your conrpaflbs, and make this diftance eotrefpond with the divifion [ 77 J divifion on the line of do; that is, dircdtly under the Roman figures IX, IX; keep the Sedtor fixed ; and from the fame line of 60, take the {pace between i and i, which will be the i-9th of the whole line, and confequently will divide it into the number of equal parts propofed. But the fame thing may be done by the line of 60 only, viz. fet the length of the line from 9 to 9, then from 1 to 1 is the i-qth required ; or, if the line be too long to be taken fo near the center of the inftrument, then doubling the number will anfwer the fame end: thus from iS to 18, and from 2 to 2 will have the fame proportion to each other, as from 9 to 9, and from 1 to 1. In like manner, a line may be divided into any number of equal parts, greater than what are ex- prefied on the inftrument; fuppofe for inftance, 120 parts; take the length of the line, and fet from 60 to 60, and the one half of the firfl: divifion between 1 and the center of the Sedtor is the part required. Fig. 2. To divide the line A B into two equal parts, take half of it, viz. A C, and fit it to 60, 60, then 1 to 1 is the fpace fought for. Again, if a line be too long for the compafs of the inftru¬ ment, then divide it into i-half, 1 -3d, i~4th, &c. and proceed as diredted in the laft paragraph. It will be obvious, that when the divifions (of what nature foever) are to be under 15, or when by bifedting a line, &c. any other number can be obtained, that the fcale of Roman figures is to be pre¬ ferred, becaufe the parts being larger and fewer, will therefore be extremely ufeful on many occafions. EXAMPLE II. Fig. 3. To encreafe or diminifti a line in any proportion. Let it be required to encreafe the line A C, from 30 to 50 feet ; that is, two thirds. Take the length of the line A C in the compaffes, and make the Sedtor correfpond with it at 30, 30; then take the diftancc from 20 to 20, and transfer it from C to B, and then B C being two thirds of A C, and added to A C, will increafe the line A C as was required, viz. from 30 to 50 feet. EXAMPLE III. Fig. 3. To diminifti a line, viz. from 50 to take away 20 feet. Fit the given length A B to 50, 50 ; take the diftance 20 to 20, and fet from B towards A, and then will A C be diminiftied 20 parts out of 50, that is, made fhorter by two thirds. If the lines are to be confidered as feales of feet and inches, or parts of either of them to be meafured in that manner, then the fcale of Roman figures, may be ufed with the greateft accuracy in the following manner. EXAMPLE IV. Fig. 4. To divide a line into feet, inches, and parts. Let it be required to divide the line A B into a fcale of 10 feet, and one of thole feet into 12 inches. By example I, divide A B into 10 equal parts, take one part A 1, and divide that alio into 12 parts, by the lines of 60; then the fpace A 1 fet from 12 to 12 will give one inch, and the fpace from 1 to the center of the Sedtor being divided into 6 parts, will give i-6th part of an inch; and thus fhall we obtain a fcale of feet, inches, and parts of an inch. If a fcale of more than ten feet be wanted, fuppofe 30, then, by taking i~3d of the propofed line, and dividing that into ten, &c. we fhall obtain what is required. Q.q EXAMPLE [ 7S ] EXAMPLE V. Fig. 5. To make a fcale of modules and minutes. Suppose A B is a given line, to be divided into 5 modules and 60 minutes; by the fcale of Roman figures, viz. from the dotted lines under VI, VI, we may divide the line into 6 parts, as in the firft example. And for the minutes, if the afligned length A C be not too fhort to reach from 60 to 60, when the Seftor is quite fhut; then by fetting the length of the line to thofe numbers, and taking the diftance from 1 to 1, we fhould have at once what was wanted ; but fince the given line is too fhort, we muft therefore take a leffer, but proportional number; fuppofe, the half of 60, which is 30, and make thefe numbers coincide with the compafles; then the half of the {pace between 1, 1, and the center of the inftrument, will be the i-6oth part of A C.-Or, having firft divided the line A C into 30 parts, and then taking the half of one of thofe parts, will anfwer the fame purpofe. EXAMPLE VI. Fig. 6. From three given numbers, viz. 8, 7, 5, to conftruft a triangle. Take any length, AB for the bafe, and fet it from the dotted lines under VIII, VIII; keep the Sedtor fixed, and, in the fame manner take the diftance from VII to VII; fix one point of the compaffes at A, and defcribe an arc at C ; then take the fpace between V, V, and from the point B crofs the arc C ; draw the lines AC, B C, and the thing propofed is done. EXAMPLE VII. Fig. 7. To bifedt an angle. From A, with any radius, defcribe the arc B C ; take the fpace B C, and divide it into two equal parts, by example I, and draw A D. EXAMPLE VIII. Fig. 8. From a given triangle, to make another of any proportion. First, From the triangle ABC, to make another a b c, that fhall be a third part of it. Meafure the lengths of all the lides A B, AC, CD, by the inftrument; thus, fuppofe A B is let from 15 to 15, on the fcale of 60 ; the Sector remaining fixed, then A C and C B being equal, they will both coincide at 12, 12 ; draw a b at pleafure, and take the diftance from 5 to 5, and transfer it to a b ; then take the fpace from 4 to 4, and with that fpace defcribe the triangle, as in the fixth example. Secondly, From the triangle a b c, to make one which fhall be 2~3ds bigger. Take the length of a b, and fet from 5 to 5 ; then make A B equal to the diftance 15, 15, and AC, B C, each equal to 12, 12, &c. E X A M P L E IX. Fig. 9- ere< ft a perpendicular A C, by the inftrument, from the point A of the line A B. 1 ake any length A a, and make it the diftance of 30, 30 ; take the diftance of 40, 40, and with it defcribe the arc b, from the point A; then take the diftance 50, 50, and from a in the fame man¬ ner, crofs the arc at b ; finally draw a line from A to b, and then A b is perpendicular to A b; for 3, 4, and 3, conftitute a right angle, as we.l as any multiple of them. example [ 79 ] EXAMPLE X. Fig io. From a given fquare, to conftruCt another of any fize. The manner of doing this mull be obvious, from the laft example, and therefore needs no explanation. EXAMPLE XI. Fig. ii. To draw any irregular figure; and from a fmaller, to conftruCt a larger. Let A BCD EF be the given figure, and let it be required to contract it to i~5th. Parallel to E D, draw e d at pleafure ; take the length of E D, and make it correfpond with 25, 25; let the SeCtor remain fixed, and make e d of the diftance 5,5; draw e f parallel to E F, and in the fame manner make E F correfpond with the numbers 25, 25, and then e f with the (pace 5, 5 ; and by repeating the operation for the remaining fides, the figure will be compleated. If it be required from a larger figure to draw a fmaller one, take any fide of the fmall figure (fuppofe e d) and make it correfpond at 5, 5 ; then draw E D parallel to e d, which we make equal to 25, 25 ; and then proceeding as above directed, we fiiall do what was required. EXAMPLE XII. Fig. 12. From a large column A B, draw the fmaller one a b to half the fize of A B. Take the length of A B, and divide it into two equal parts; make one of thefe parts the whole height of the column ; then by the firft face, third interval, fecond bar, find the general heights, &c. And to produce a large column from a fmall one already drawn, the proportion muft be increafed in the fame manner. EXAMPLE XIII. Plate XXV. Fig. 1. To form a fingle cornice. Give A B for the propofed height, and fix the inftrument to the third bar, fourth interval, fecond face, Tufcan line, and try where the fpace A B will coincide with correfponding numbers, viz. 30, 30, which number, thus obtained, muft be kept to, as in the former examples; and thus fhall we obtain the height of every member. For the projections of the mouldings, we muft go to the fecond face, fecond interval, fourth bar; upon which are the projections of the frieze and cornice ; thus B D is the projection of the frieze only, and B G the total projection of the cornice. EXAMPLE XIV. Fig. 2. From the cornice ABC, Fig. 1, to make a fmaller one; fuppofe i-half lefs. Divide A B of Fig. 1 into two equal parts; take the half of it, and try where it will correfpond with the numbers on the inftrument, viz. 15 and 15 ; which is the number for drawing all the mouldings; and by keeping to the fame numbers, and ufing the bar above-mentioned, we fhall get the projections alfo. It is hardly worth mentioning, that in the fame manner, a large cornice may be taken from a fmall one ; the operation being only the reverfe of the other. By thefe examples we may proportion a cornice to any given height; fuppofe, for inftance, we would draw a cornice for a room of 14 feet high, fo as to make it i-i6th part of this height. R r Take [ 8o ] Take the given height of the room, and fct it from VIII to VIII, (the half of iG) take alfo the difiance between the half of I and I on the Sedor, viz. 2, 2, on the lines of 60, which is the total height of the cornice; and having obtained this, proceed as above directed. EXAMPLE XV. To vary the members. As it may be neceffary fometimes to deviate from the Arid rules of putting invariably the fame mouldings to the fame parts of architedure, we will therefore Ihew how this may be perform’d by the inflrument. Suppcfe, for infiance, we would put the Attic, or Doric bafe, to the Corinthian Order. Take the height of the given bafe, then fct the Sedor to the Doric bafe, and find the correfponding numbers; with which compleat the drawing. In like manner, any other parts of an Order may be varied, with great facility and exadtnefs. EXAMPLE XVI. Fio. 2 and 3. If we would leave out any particular member; fuppofe the ovolo. Let it be required to leave out the ovolo of Fig. 2, and to form all the other members into a cornice, with fimilar proportions as Fig. 3. Firft, any where apart, draw a line parallel to A B, Fig. 2, viz. the lines 14, upon which mark off the heights of all the members except the ovolo. Secondly, give A B, Fig. 3. for the height of the propofed cornice, which is of the fame height as A B, Fig. 2. Thirdly, parallel to A B, Fig. 3, draw the lines iy, 17. Fourthly, upon the ihorteft, or outer line ot Fig. 2, fet off the heights of every moulding, but the ovolo, as it is done in the figure. Fifthly, take the fliorter fcale iy, and carry it to correfponding numbers on the Sedor, fuppofe 20, 20, keeping it fixed. Sixthly, take the longed fcale 1 to 7, or the given height A b’ and fee where it fits upon the Sedor, viz. 25. Seventhly, by Example the 2d, increafe the feveral parts upon the long fcale, from thofe of the fhorter. If the defcription of tills paragraph fiaould appear prolix, yet the operation will fhew the neceffity of it; fince by this means it becomes extremely eafy. But we null fhew likewife, how to proportion the projedions of the members. In the firft place, the projedion of the cornice is made equal to it's height; which is fet off from the point D to C. Draw a line, c a, Fig. 2, from the end of the fillet, which Ihews the projedion of the cyma ; then make C a the diftance of 20 to 20, and find the proportion of the height c a, which is 25 to 25 ; ■then make the height c a. Fig. 3, the diftance of 25 to 25 ; and C a will be from 20 to 20. In the fame manner find the other projedions. ^ A M I LL XVII. 'I o determine the height of pediments. The heights of this part of architcdure being in a great meafure arbitrary, we Ihall therefore princi¬ pally regard the manner in which pediments are conftruded. And this being an artic'e which we could not fo regularly explain before, we for that reafon have p..!!vl over the Ionic door within an arch, in the defcription of that Order, and referred it for this place ; and lnr the&nereafon > we have omitted to mention the Doric and Corinthian pediments over the doors’ u plates aX and XXL It has been (hewn how arches are to be drawn by the Sedor to all the five Orders; and the manner of placing doors within them is fo very obvious, from what has been before advanced, that this article needs no farther explanation. Fig. [ 8 : 1 Fig. 4. For an angular pediment. Let A 1 be the utmoft length of the upper fillet to the cyma; divide it into 9 equal parts, by example I; then bifeCt A 1 in B, and draw the perpendicular C D ; make B D equal to two parts of A r, and draw A D and D 1 ; which will form what is called a pitched pediment. And for the compafs pedi¬ ment ; bifeCt the line D 1 in E ; from D and 1 with any radius, make the crofiing of the arcs at F, r.ni from E draw E F through F, to cut D C in C ; and then is C the center for delcribing the pediment. Fig. 5. Secondly, by another method. BisrcT A D in B, and draw the perpendicular CE ; with the radius C A, defcribe the arc A E, &c. and then is E the top of the pediment. EXAMPLE XVIII. 1 ig. 6 and 7. To vary the heights of the principal parts of an Order, and at the lame time to preferve the proportion of the feveral members. If A B is a given entablature, and C D the fame height transferred for drawing of the other, which we will luppofe is to be of the following proportions, viz. four parts for the cornice, three for the frieze, and three for the architrave; then divide CD (or E F) into 10 equal parts, which will determine the proportions required. EXAMPLE XIX. Fig. 8. To adapt a capital, bafe, See. to a given trunk. Take the tota’ height, cr projection of either of the parts; and then by the inftrument, we may ob¬ tain proportional numbers to work with, and by this means be enabled to draw the part that is wanted. EXAMPLE XX. To meafure the Orders, &c. Let it be required to find the meafures of any colonnade already drawn ; fuppofing another was to be made in the fame proportions, but of a different height to that reprefented by figure 8, and let the required height be 15 feet. Take the height of the colonnade, and make the tranfverfe difiance between XV, XV ; fix both legs of the Sedtor with the ferews,. then the tranfverfe diftance of each member meafured on the SeClor will give the required meafures. To meafure the Orders after a more exaCt manner. To meafure an arch ; draw a line as long as the inftrument can contain within the open of the two legs, and maik all the heights upon this line with the inftrument; then draw another line, and mark the projections; and by fome of the foregoing methods, meafure every member marked on thefe lines, and then transfer thele meafures to the fmall draught, whence they will be more exaCtly meafured than ii they had been taken from the fmall one. S f Bur [ 82 J But arches and archi vaults mu ft always be reduced as follows, viz. before the circumference can be meafured, take the tranlverfe diftance between 7, 7, or VII, VII, and alio that at 11, 11, or XI, XI, mark thefe both apart, and keep them for a general rule, to meafure the circumference of any arch or archivault of half a cir cle. Then to meafure the circumference of the arch, fuppofe the diameter; fit the tranfverfe difiance of 7, 7, tranfverfiy over 5 feet, i-half, the fuppofed diameter of the arch ; the inftrument remaining thus fet, take the tranfverfe difiance of n, n, and fee where that fits upon the Sedtor, which will give the circumference of the faid arch in feet and inches. By the fame rule any room may be meafured. 7 , •-ivy Hn/nMi/iav- /b/l/MH l 7‘so/ss/roit. 0/ Ms Onviiss. ttMs. dfouY 1.6 /tmtfsnrt/f/vui //Vp.c. TsMu/o/’ \ t ofovo of-/6s fo/uum x. ^ .-i . —/rfirr . 7o/<•>■- so/nintut/to tt - .-) 6//ro/sr < 7/i/i r- co/nmil otio/t i (yivo/s r ,f/i/rr-i o/om mi /'/< ’// ,-M.rftsr Mu/sr-so/unination £ e ft VO 0 / /As Co/u/nn ’ - * '' 'S l/hyse/ion. of /As (onuss. so {/e J/tocs 1.6 /nritifsrrs:/f/vni J (0 p.c. ///.HY/// _ m < -a «mmh “■ ■ ■MJ-liiLiuiJ-L I -tfl.lJ. -— »- ^f— -. ^ — — , .—— I— —_ _ __ ' ~ _ I'/rrfr m ■HHHMIM| -v W- r./», iyJcMe ' ^yJ/r Hi k __ F/aie XX. JOLTY. -P/aJz XXV. THE PERSPECTIVE O F ARCHITECTURE. A WORK ENTIRELY NEW; » Deduced from the Principles of D r BROOK TAYLOR; And performed by Two Rules only of Univerfal Application. BEGUN By Command of His prefent MAJESTY, WHEN PRINCE of WALES. JOSHUA KIRBY, Defigner in Perfpettive to His MAJESTY. PART THE SECOND. PRINTED FOR THE AUTHOR. c INTRO D U C T I O N. T7 XT 1--U nn « U.J !..f-n fk a »-»-. — Cl- ,.r,.r..l JiC'/«foiiiDo Pifl^ctr kxr iff'pnrlin^r t-r\ flm /■*!'■» !■»-.trtrw* The belt method for inveftigating the perfpeCtive of architecture feems to be this, viz. to bring before the mind the various forms of buildings; to fort, or arrange them into feveral claffes; in order to obtain fuch rules for practice as may be eafily comprehended and made univerfai in their applica¬ tions. For, if clear ideas are once obtained, and we can form from them a fet of principles which are eafy, determinate, and comprehenlive; then, by the pow^r of language we can readily convey thofe thoughts to others, if we ufe common and exprefs terms for each idea, and lay them in the fame order as they are placed in our own minds. ’Tis owing to the want of fuch a regular manner of inveftigation, that many authors on this lubjeCt have miffed the point they aimed at. They drew out Plans and Elevations for every example, and made ufe of innumerable lines and points, even for the moll fimple Buildings, which mult neceffarily have perplexed themfelves, and embarraffed thofe they intended to inftruCt. But it fhall be our bufinefs to ftrike into a new path, and endeavour to eftablifh fuch principles for this part of perfpeCtive as fhall have a rational theory, and fully anfwer the end propofed by them. In order to do which, we will begin in a regular manner, and go on ftep by ftep, till wc have fully illuflrated whatever we fhall advance. All vifible objeCts, in refpeCt to their fize, fhape, colour, &c. convey the fame kind of ideas to different perfons. In nature, thefe characters or marks of figures are infinite ; but in works of art they are limited and confined within a much narrower compafs than is generally apprehended; and particularly fo in the geometrical forms or fhapes given to architecture. And therefore, in order to draw the reprefentation of any building, it becomes neceffary to know, in the firft place, what it is that marks or charaCterifes the whole; and fecondly, to confider very attentively its feveral conftituent parts, in a regular and progreffive manner. The moll general forms of architecture may be comprehended under the Triangle, the Square, and the Circle; and the feveral parts, which conftitute a compleat order, (a very few excepted) are of a fimilar conftruCtion with thofe geometrical figures. All thofe lines that are boundaries to the feveral parts of Architecture, are either ftraight or circular; and therefore thofe two different kind of lines varioufiy applied, may be faid to conftitute the principal parts of an order. a In [ S ] In like manner ; Buildings are either terminated by given angles, or by circular outlines, confe- ■quently to reduce a circle or any given angle into perfpeaive is all that feems neceffary for drawing the reprefentations of fuch Buildings; for if the body of an edifice be a cube or parallclopipedon, i's angles are right ones ; if a prifm, it's angles are acute ; and if a polygon, then it’s angles are ok :fe ; but if a cone or cylinder, then the plan is a circle; and fo alfo if the Building be a mix'd one, that is, partly triangular, partly fquare, and partly circular; then the perfpeaive of it is to be obtained by the fame rules, and with little more trouble than is required in drawing thofe, which are lefs complex. An order of architecture (as to it s mouldings only) may be confidered as a number of fquare and circular horizontal planes, of different diameters, laid in inch a manner upon one another, as to give the peculiar fhape or outline of each; and therefore to put the feverai mouldings into perfpedive, no¬ thing more feems neceffary than two general or univerfal rules, viz. one for drawing the reprefentation of a fquare, and the other that of a circle : and thefe we have deduced from the principles of Dr. Brook Taylor, in his Linear Perfpedive, and we have moreover fully explained it in the beginning of this work. Again, the Teeming great variety of mouldings, of which an order of architedure is compofed, is •reducible to feven only, viz. the Plinth, the Torus, the Ovolo, the Cindure, the Cyma, the Cavctto and the Scotia ; as for the Ionic, the Corinthian and Compofite capitals, the Doric Triglyphs, Modi- lions, Dentals, See, their reprefentations may be determined by the fame rules a little varied in their applications. In putting the orders into perfpeaive, we have ufed the fame method for the heights and widths as architects do in drawing elevations only; which manner of working will make each operation more eafily underftood, and more univerfally extenfive. 1 hus much, we apprehend, is fufficient for conveying a general idea of our defign in the following work. We will now give a (hort abftrad of the contents of it, and then proceed witli as much order and brevity, as the nature of the fubjed will admit of. This volume is divided into four books, and each of thefe into feverai Tedious. In the firll book we have given a few fimple, but general rules. In the fecond book we have (hewn how, with thefe rules, to put all the five orders of architedure into perfpeaive. The third book relates wholly to the dodnne of light and (hadow, which explains this part of perfpective in a new and familiar manner. In the fourth and Iaft book, we have (hewn the application of our general rules, beginning with fimple colonnades, and ending with elegant (fractures ; and with thefe we finiih what was principally intended ; however, this, in order to make the work yet more compleat, (hall be followed by another volume, if we arc fo fortunate as to meet with the public approbation. A CHAP. I. SECTION I. Of preparing the Picture, viz. the affuming a proper Diftance, and Height for the Eye. one that is unalterable The place of the eye is a;fo a charaCteriftic by which the different fpecies of projection may be diftinguifhed. Thus, for inflance, when the "eye is con¬ sidered as being at an infinite diftance from the plane of pro¬ jection, that is, the plane on which the required reprefentations are to be drawn, which in perfpeCtive is termed'the picture, it is called orthographic projection. When the eye is con¬ ceived as being only ninety degrees diftant from the plane of projection, or in the pole thereof, it is called ftereographic projection ; and when placed at the center, the projection is named Gnomonical: this laft is the foundation of dialing. The orthographical and ftereographical projections, were contrived by , the ancient allronomers, for their eafe in aftronomical affairs, and are particularly adapted to the projection of the fphere, and its fevera! circles in piano. By the orthogra¬ phical projection, a circle that is perpendicular to the plane of projection is reprefented by a right line equal to the diameter thereof : in the (iereographic, its reprefentation is a right line, which is infinitely extended both ways from the center of projection; and by the fcenographical projection, it is reprefented by a line, which is either longer or fhorter, ac¬ cording as the eve is nearer or farther off. Hence it appears, ti.at, generally ipeaking, there are only four varieties in the politicos that may be afligned to the eye ; that is, it may either be at an infinite diftance from the plane of projection,” in the pole, or in the center thereof; or laftly, at fuch a due diftance as is luitable for diftinCt vifion. The laft cafe belongs to per. fpeCtive, and admits of fome variety, as was obferved above • “ ■ eye be considered as being on, or any wl e VV 'n“n-n h L ‘ Urtace of the f P here . the circle before deferibed will (till be projected into a right line, extending itfelf on both fides thereof. This, and the feveral other aflertions here delivered, concerning the different reprefentations which are produced by thefe feveral projections, may be feen demon- ftrated by tnofe authors who have treated on them in the mathematical wav. The doCtrine of projection may there¬ fore, in genera], be coniidered as confifting of three diftinCt branches, whofe firft principles are effentiaily different, and by which the whole of any objeCt may be reprefented upon the lame plane, viz. Orthographies, ftereographics, and fcenographics, commonly ftiled PerfpeCtive. Having thus briefly fpecified the principles of thefe feveral kinds of pro¬ jection, and (hewn wherein they effentiaily differ from each oiher. it remains that we now proceed to the main defign intended by this remark, which is to explain more particularly me nature of perfpeCtive, or that part of mathematical pro- j'.ccon winch is concerned in inveftigating rules for producing representations proper to the various cbjeCts, pofitions, and the feveral other particularities which a”re herein coniidered. Now feeing that folids when reprefented on a plane can there be (hewn only by furfaces, that lurfaces are refolvable into lints, and lines into points, it follows, that the theory, or mathematical part of perfpeCtive, may be faid to depend chiefiy on a true and general foluhon of the following. PROBLEM. A plane being given, the polition of a point out of that Ir Pl'™- *"* ,1,c P ,ace ft thc '3* befag given , to find npon that plane tr.e apparent pofition of that given point. The folving this problem will be found of Angular advan¬ tage :n efiabhihing the theory of perfpeCtive; for the ao Da . rent pofition or perfpedtive reprefentuion of a p ,i„t beime determined, that of lines (they being terminated by points ? ' “ U "«. drbds, bee info bounded "> (ill faces) will follow as lo many corollaries evidently icfuli- ing trum it. The rules which mathematicians give fur pro during perfpedtive reprefentations, have therefore their origin or are primarily deduced from hence. But bccaufe the pofi’ U0 " ft a " ft. 1 cannot be determined otherwife than by comparing it with lnnie other objedt, whofe firuation is given, therefore it is, that in the cafe before us, beiides the fr - given in the problem, two other planes are alihmed e. h . h fcrve lor terms of comparifon. The given plane, now called the pldture, exhibits the reprefentations of the feveral objedls whole perlpedtive forms are required, according to their refpedive diftances from each other. Of the two af- fumed planes, one is to be conceived as a level plane, perpen- dicu ar to the picture, and parallel to the horizon : Ibis plane enables us to diltingufth the pofition of objects, with refpeCt to higher and lower, and is therefore called the horizontal plane; and the other afiumed plane affifts our perception, by pointing out to us the place of objeCls, with refpeCt to their being on the right hand, or on the left. This lalt-men.ioned plane is perpendicular both to the pidure, and alfo to the horizontal plane, and is therefore called a vertical plane • fee an iliuflration hereof, in plate 1. fig. 5. ^ ’ A B, the picture, or plane, on which the perfpeCtive re- prelentations are to be drawn. E, the place of the eye, which muft he at a proper diftance from the picture, as determined by the methods laid down in this work. F G the horizontal plane paflbs through the eye at E and HL 'by Euc P '?,“ re ] AB ’ “ righ ' a,lgIes ' ,hc ri 6 ht I™ H L the tight line, or fefiion, where the picTure and ho¬ rizontal plane anU each other, is railed the horizo a! line. D I, the vertical plane, pafies allu through the eve at E mterfeCls the picture A B at right angles, in the li e KM* and hkewife cuts the horizontal line F G, perpendicularly in the .me E 1 K M, the right line, or fiction, where the picture and vertical plane intellect each other, is called the vertical line E C, the line which express the diftance between the eye and the picture, is called the principal ray. ; C, the point where the vertical and horizontal lines inter- feCt each other, is the center of the picture. This being premifed, it is manifeft that if the pofition of the picture, horizontal and vertical planes, with refpeCt to each other be given, we (hall then know how the two affu- med, or laft mentioned planes are fituated, with refpeCt to the p.Cture And becaufe the line E C, or diftance between the eye and the picture is alfo fuppofed to be given, therefore if the diftance between any objeCt, and the laid three planes be known, its reprefentation may be eafily found. For in- ftance, let us luppde the pofition of the eye, and the three atore-mentioned planes, to be the fame as before deferibed amd that the place on the picture, or perfpeCtive reprefentation of any given point as S, were required, it may be readily round thus. ’ Draw the line Y S, perpendicular to the vertical plane D I. Draw alio S R perpendicular to the horizontal plane FG • then will Y S exprefs the diftance of the given point S from the vertical pane, and SR it's diftance from the horizontal plane. Draw alfo YE, S E, R E, QE, and the figure F Y S .■ill Uo „ .V n k • , . & Ult - ^ 1 5 RQ, .. r.’'t S R Q is the plane of it’s bafe and is perpendicular to the vertical plane , y s r C, is a feCtion of [ 3 ] It would be very difficult, if not impoifible, to affign one determinate diflancc, to be univerfally made ufe of; or fuch a one as fhould anfwer on all occafions; becaufe the different circumftances relating B of the (aid pyramid made by the pidture, or plane of projec¬ tion, confequently is para lei to YSRQ. Now feeing that the line Q C exprelfes the diftance between the pidture and bafe of the faid pyramid, it is therefore the diftance between the pidture and the given point S ; and becaufe the two pyramids El Y S R Q, Eys r C are fimilar, we therefore get the follow¬ ing proportions. EQ:YQ:: EC :y C, or, which is the fame, EC + CQ:SR::EC:ir, And E Q : Y Q : : R Q : r C, or E Q. : Y Q : : S Y : r y. From the above analogies, we obtain the two following general rules tor calculating the diftance of the perfpedtive re- prefentation of any objedt in the pidture, from the horizontal and vertical lines. 1. For die diltance from the horizontal line. RULE As EC + CQ, or EQ, the fum of the diftances of the eye, and given cbjrdt from the pidture, is to EC the diftance of ti e eye from the picture; (o is SR the diftance of the objedt Irorn the horizontal plane, tur the diftance of it's reprelen- tation in the pidture from the horizontal line. JJ. For ihe diftance from the vertical line. As EC + CQ, or E Q, the fum of the diftances of the eye and the objedt fom the pidture, is to E C, the diftance be¬ tween the eye and the pidture; fo is S Y, the diftance of the objedt from the vertical plane, to sy the diftance of it's repre- lentation on the pidture from the vertical line. Although the three planes here mentioned, have been confidered only as being perpendicular to each other, yet it is not abfolutely requilite that they fhould be fo policed ; for wiien other fnua ions are necelfary, the above rules will hold good. Bur if the given objedt be fituated between the eye and the pidture, thus, luppofe ( s ) were the objedt, and the plane Y 5 R Q. to be the pidture, then it is plain that the represen¬ tation of (j ) would be in (S), and may be calculated by the above rules; only by putting the word difference in the firft: term of each proportion, inftead of the word fum. EXAMPLE. Suppose the breadth of a pidture to be 6 feet; alfo let EC, the diftance of the eye from the pidture be 6 feet; C Q, the diftance of the objedt from the picture 4 feet; S R or YO, the diftance of the objedt from the horizontal plane 15 inches^ and let it be required to find ( sr ) the diftance of it's repre- lentation in the pidture from-the horizontal line H L. CALCULATION. As ico, the fum of the diftances between the eye and the pidture, and given objedt and pidture, reduced to inches, is to 72 inches, the diftance between the eye and pidture, lo is 1 ; inches, the given objedt’s diftance from the horizontal j'ltne, to g inches, it's diftance in the pidture from the hori¬ zontal line H L. 120:72:: 15: — — ■ ? = 9. Q^E. I. So likewffe fuppofing ( sy) the diftance of the reprefenta- tion in the pidture from the vertical line K M was required, S Y the diftance of the objedt from the vertical plane bting 10 inches, and the reft: as before. Then 120 : 72 : • 10 : — * '° = 6. Q;_E. I. By the firft of thefe operations it appears, that according to the ciaca of this example, the line sr— 9 inches, and the line sy — t> inches, wherefore the true pofition of the required re- pucfentation is hereby determined. Lf.t us now f.jppofs the objedt to be between the eye and tie pidture; for iuftance, let (r) be the objedt; the p ; ane Y o.R QjJre pidture ; the eye being at E as before : 'cis required to find the lines S R, S V, eftceming sr~g inches, and s in — 6, as found by the ab ve data. Hence th--d.fiance ot the eye from the pidture E Q^= 120. ini lies ; tlie diftance of the objedt from the pidture C Q = 48 inches; the diftance of the ctjedt from the horizontal plane s r = 9 inches ; the diftance of the objedt from the vertical plane s v = 6 inches. Therefore, E Q_— CQiEQ^ur: SR; . uoXi) or 72 : 120 : : 9 • - = 17. Again, EQ^- CQj E Q_: : jjy : SY;'" or 72 : 120 : : 6 : 6 — 10. Whence it appears that S R = 15 inches, and S Y =: 1 o inches, the lame as they were before given. PLATE I. Fig. 1. Because (a b) is by conftrudtion parallel to 13, therefore (Euc.'6. 2.) a P : 1 P: : ah: 13 j wherefore if the pofition of the point (a) be known, the reprefentation ab will beeufi'y determined ; for whatever ratio a P hath to 1 P, the fame ratio will the reprefentation ( ah', bear to the given original line 13. 1 hus if (a P) be two thirds of (1 P) then will (a b) be two thirds of 13, See, Or, if the point (6) be given, then becaufe * f : P 3 : : ah : 13, therefore if either of the extremes be given, the whole reprefentation is known as above. PLATE I. Fig. 2. Because the lines C L, a 2, are parallel, the angle CL 2 is equal to the angle a 2 L, (Euc. 1. 29 ) Also the angle L C a, is equal to the angle Ca 2. And the angle C b L, is equal to the angle a b 2 (Euc. 1.15) therefore the triangles C^L. 2 b a, are equiangular, wherefore (Euc. 6. 4.) bc\ CL : : a b: a 2, hence the point ( b ) being known the reprefentation (a b) of the original line a 2, is eafily found. PLATE I. -Fig. A. Because e c is parallel to ab, the triangles baf, ecf, are fimilar, therefore e C : C f : : a b : a f Or thus, luppofe («') the diftance of the eye from the picture to be 3 feet; ( b) the diftance of the object from the picture to be 1 foot, and alfo 1 foot from the horizontal plane; to find it's diftance from the horizontal line, 4 ■ 3 : : : 7 therefore aj is i*4th of a C. FIG. B. Because ab, and el are parallel, the triangles baf, elf, are fimilar ; therefore e l: If : : a b : af. FIG. D. Let hi be the horizontal line; c the center of the pic¬ ture ; ce the diftance of the eye frcin the picture.; and let it be required to find b and/, the vanifhing points of a fquare building, and correfponding with Fig. 3. Because by hypothefis the given angle is a right angle, and the given lides.d l, is alfo known. F I G. E, Let hi, be the horizontal line, c the center of the pic¬ ture, c e the diftance between the eye and the pidture, as before, and let it be required to find the vani(hing points h and /, they being at unequal diftances from the center c, and correfponding to Fig. 4. Suppofe h c — 2;, ce = 5. Then hc : ce ;: ce : cl ; that is, 2,5 : 5 : : 5 : — == io = cl. t' erefore whatever part h c is of ce, the f>me part is c e of cl. But the diftance of thofe vanifhing points, &c. may likewife be found mechanically, as is expreffed by the dotted lines of thefe figures. The fame way of reafoning might be applied to the repre- fentations of furfaces, folids, dec. hut what has been faid n?ay fuffice, for it was not intended by this Remark, to treat pro- feffedly on this fubjedt, but only to lhew biiefly the fource from whence the rules for calculating perfpedtive reprefenta- tions arc derived. [ 4 ] to pictures, will frequently render a rule of this kind abfolutely impracticable. This is a truth known to every artift, that has had much practice in the fcience of perfpeCtive; and fueh I would alk, whether experience is not the mofl certain, or at leaf!, the molt ready and convenient guide in this cafe ? I can however take fuch a diftance for the examples in this work as will bell: anfwer the purpofe ; and (hall at prefent make ufe of one common diftance, as a general method, for the fake of order and perfpicuity ; and when it may be neceflary to vary in this effential requiftte, I fhall give my reafons for fo doing, and make fuch farther obfervations, as may arife from the cafe before me. Plate I. Fig. i. Suppofe that A B D F was the fpace or ftze allow’d for a picture or drawing. Divide the height A D into three equal parts, and draw a line H L through the loweft divilion for the § hori¬ zontal line; divide the width of the picture into two equal parts, and call C the * center of the picture. Again, take the utmoft width I K of the picture, and from C fet this width to H and L ; then call C H and C L the diftance of the eye on both fides of C : all which being reduced into a more regular order will ftand as follows, viz. i. HL, the horizontal line. 2. C, the center of the picture. 3. C H or C L, the diftance of the eye. 4. H and L, the points of diftance. Now this is all that is previoufty neceflary for an explanation of the following fchemes, which I call univerfal rules for drawing the true perfpeCtive reprefentations of any buildings, whether they be regular or elegant pieces of architecture, or fuch only, as are of the moft plain and Ample conftruCtion. RULE I. Fig. r. To determine the perfpeCtive length of any given line ab, when it is drawn parallel to the horizontal line ; and to divide it fo as to have it reprefent any number of equal or unequal parts. 1. Divide the bottom A B of the picture into any number of equal parts (fuppofe ten parts) and call this line a fcale for adjufting the proportions ol fuch objects as are to be drawn upon the picture. 2. Give the point a, for one end of the line propofed, and from a, draw at pleafure the parallel ab. 3. From any point, as 1 on the fcale, draw a line through the end a, to cut the horizontal line in P. 4. G.ve the fpace between 1 and 3, for the real length of the propofed line on the fcale, and from 3 draw a line to P, cutting a b in b, then will a b reprefent a length equal to the fpace 13. In like man¬ ner, if we would divide a b fo as to have it reprefent any number of equal or unequal parts, we muft ftrft mark on the fcale the given proportions, and from thence draw a line to P, which will cut a b in the points propofed, as in the Agure. And fuppofe ab is a line given in perfpeCtive, and we would And what real length it reprefents; then draw a line from any point in the horizontal line through the ends ol a b, to the fcale ; which will fhew the real length. Thus ab reprefents Ax parts, which may either ftand for fo many feet, or for the like number of any other proportionable parts, and fuch as may be beft adapted to the nature of the deAgn. RULE II. Fig. 2. To cut off a part ab of the line aC, that vanifties into the center of the picture, fo as to reprefent any given length; and to obtain any number of perfpeCtive diviftons upon it. 1. From C fet off the width I K of the picture to L, for the diftance of the eye. 2. From § The horizontal tine is varioufly placed by different au- * The center of the picture flmuld (if poffible) be al ways thors, but this 1'ce.ns a medium between them. placed in, or near, the niid.i e of the in ii/.omal hue ; t a • deviation in this particular, will be fomeumts unavoidable. [ 5 ] 2. From L to any point (fuppofe) 2 on the fcale, draw L 2 cutting a C in b ; and then will ab re- prefent the length a 2. In like manner, lines drawn from any diviiions on the fcale to L, will cut a C fo as to give the per- fpeblive of fuch diviiions. RULE III. Fig. 3. To cut off a part a b of the line a H, that vanifhes into one of the points of diftance H ; and to divide it as above. 1. Divide the diilance C H or CL into five equal parts, and make the dot at Ph two parts and i-1 qtli from C. 2. From any divifion, as t on the fcale, draw to Ph, cutting a H in b; then will ab reprefent the real length a i. And to divide ab fo as to reprefent any particular part in perfpeflive; we muft fet off the real lengths of thofe parts on the fcale, and then draw to P h, which will cut a b in the propofed points. Again for the line ac, which vanifhes into the point of diilance L. 1. Make the dot at P 1 the fame diilance from C as P h is from C. 2. From P 1 draw to any point 2 ; and fo will ac be the perfpeftive of a 2, See. N. B. The points for cutting off are marked with the letters Ph, PI; becaufe Ph is for the lines that vaniih into 1 !, and P 1 for thole that vanilh into L. It is prelumed, that thefe three rules only will be fufficient for the reducing almoil every regular piece of architeaure into perfpeaive, and in a greater variety of fituations than has hitherto been attempted. The firfl rule is adapted to the fides of fuch buildings as direflly front, or are even with the eye; the fecond to thofe which run diredly from the eye ; and the third to fuch as are viewed angle-ways, and in fuch a manner that both Tides have an equal degree of obliquity. J But to make this work as univerfal as poffrble, I will add a fourth rule, which may occafionally be wanted, and which being infinite in its application (I am fpeaking of fquare buildings only) will anfwcr for every degree of obliquity that can be propofedhowever this needs not at prefent to be attended to, beino- of no ufe in this volume. RULE IV. Fig. 4. Having given a b for the bottom of one fide of any fquare building; to find the vanilhing points of both fides, and alfo the points P h and P 1 , for cutting off &c. For the fide a b. 1. From the center C, erect the perpendicular C E, and make it equal to the given diftance C H or CL 2. Continue a b to cut the horizontal line in R ; then is R the vanifhing point of the fide a b. 3. From R draw to E, and transfer the diftance R E, from R to P h; then is Ph the point for cut¬ ting oft any part of a R by means of the fcale a 2. For the fide a c. 1. From E, draw E (^perpendicular to RE, cutting the horizontal line in Q_; then is Qjhe vaniih- ine point of the fide a c, therefore draw a C 2. From + Unlcfs the reader perfectly underftands, and can enfily tions; not only in the next fecticn, but in all the examples ri collect, the preceding general rules, he may poffibly we Ihall herealter give as illuftracions of this l'ubject. find fome difficulty iif comprehending their various applica- [ 6 ] 2. From Qjranskr the diltauce C^E to P 1 ; and then is P 1 the point for cutting off any part a c of a from the fcale a 3. I rom hence it it obvious, that a b reprcfents the length a 2, and a c the length a 3 ; and that either ol tliele lines a b or a c may be divided ill perfp-ffive, by means of the points P h, PI, and the fcale al tin bottom ot the picture ; and in the fame manner as in the preceding examples: and had I be a an " dle l ' l(; ' c a c infend ot a b, the operation would have been the Tame. - For there is a material difficulty, which arifes from placing the vailidling point Q_ to frir out of the pieturc 5 and that is, the having an inaccelfrbie point, or at leaft, one at too great a diftance to be readdy brought into practice: .this inconvenience may indeed be fomewhat removed, by analogical pro¬ portion (as is Oleum in my former work +; but even here the remedy will be almoft as bad a° the dif- c.ilc ; and therefore when this happens to be the cafe, the fhorteft method feems to be that of making a lui.nl model, truly drawn upon paper, and then to transfer the feveral parts of this model to the picture, by the common method of reticulation or net-work, SECTION IX. 1 o ccterniine the p^erfpective of fquares, in various filiations, n X A M P L E, I. For fquares that are placed in an even fituation, with refpeft to the pidure. 1 late II. Fig. 3. A fquare with one fide at the bottom of the picture. 1. Give 6 B for one fide, and cut off B i to reprefent B 6 (by rule 2.) r- Draw the parallel in, and cut it off (by rule ij to reprefent B 6. F. .v A e,I P L E, II. A fquare by giving it's center c, and diameter, a b. I.rx the center be in the line 2 C, at the diftance of 3 feet, i. Make 2 C to reprefent 2.5 (by rule 2.) Thm ^ h <= drJW Pa*!ld a b (by rule r) and make it to reprefent + feet, viz. two feet, on Cticli fide of the center c- 3. From e and d, draw the parallels e f, d g. E X A M P L E, III. For any number of fquares, one behind the other. 1. Cut off i 1 to reprefent i h, and draw the parallel 1 k. 2. Cut off 1 n to reprefent 1 k, and draw the parallel n m, See. N. B. In this Example, the fpace between, reprefents the width of one fquare. E X A M P L E , IV - Fl g- 6 - For fquares at any diftance from each other; let one be 6, and the other 4 feet fpace. 1. Cut off A a, to reprefent A 3, and draw a b. 2. Draw aho 9 C, and then the parallel bi reprefents 6 feet (by rule 1. ) 3. Cut off b c to reprefent b i; then draw one parallel from c, and another from d. Again for the fpace of four feet between, the fquares. t . Draw from 7 to C, and alfo the parallel h e; then is h e -iheperfpeaive of 4 feet (by rule -t.) 2. Then draw the fquare as before. EXAMPLE, V. An oblique fquare, whofc fides vanilh into the points of diftance, and whofe neareft corner is 1 foot, 6 inches and an half from the bottom of the piflure. 1 * - ee f’ 1 '' E'-tnh Taylor’s Perfpective made eafy, 6cc. Plate [ 7 3 l’l.ATR III. Fig. 7. Let the Tides be 3 feet, 5 Inches and an half long. 1. Find the point b (by rule 2) and from thence draw lines to H and L. 2. from b draw • lie parallel b c, and make it to reprefent a 1, viz. 3 feet, 5 inches and an half (by rule 1) 3. Cut off b d to reprefent b c. (by rule 3) 4. Draw the parallel df, then from d to L, and from f to H. F X A M P L E, VI. An oblique fquare; by giving its center a, and the parallel diagonal b d, which diagonal we will make to reprefent 6 feet. Fig. 8. Let the center a be five feet from the bottom of the pidture. 1. Cut off 6 a to reprefent 6 1, viz. 5 feet, (by rule 2) 2 Ihrough a draw the parallel b d, and from 3 and 9 (viz. 3 feet on each fide of 6) draw to C, which gives bd to reprefent 6 feet, (by rule 1) 3. Draw alfo from H and L through bd, meeting in c ; and from H and L through bd, meeting in e. F. X A M P L E, \ II. For oblique fquares placed at different diflances from each other. Plate IV. Fig. 9. Let the point 4 be the corner of the firft fquare, aad let the Tides be drawn to repreli-..t 2 feet. 1. Draw from 4 to H and L; and then eut off 4 a to reprefent 42, and 4 b to reprefent 4 6, (by rule 3) 2. From b draw to H, and from a to L. 3. From 2 draw' to H, and then the parallel a k, which will reprefent 2 feet, viz. the fpace 2 4, (by rule 1) 4. Cut off a m to reprefent a 'k, and draw the parallel m p, then cut off m n for the pei-fpeftive of m p, (by rule 3) 5. from m and-n draw to I,, and fo will the fpace am, or cl reprefent the width of one fquare, viz. 2 feet; and 1 mno is another fquare. Again, for any other fpace between the fquares, fuppofe 4 feet, viz. from 4 to 8. 1- Draw from 8 to L, and then from b the parallel b d. 2. From d to P 1 cuts off b e to reprefent b d, viz. 4 feet. 3. Froni 6 (the given width of the firfl: fquare) draw to L, then from e the parallel ei will repre- fent 2 feet, (by rule 1) therefore draw from i to P 1 , which gives the fide e g. 4. From e and g draw to H ; and continue ac to L. E X A M P L E VIII. For -circles. Every point in the circumference of a circle being at an equal diftance from the center, therefore every line that can be drawn from the center to the circumference muft be equal: if therefore the center of a circle, and one parallel diameter be cither given, or determined in perfpedlive, then the reprefentations ot other diameters may be found by the rules already explained ; and having obtained a fufficient number of points to reprefent fo many dots in the diameter of a circle, the appearance of it may be drawn with great facility and exaffnds.—Indeed in large circles (fuch as the plans of temples, &c.) many points will become neceflary ; but fmaller circles, fuch as the plans of columns, and the like, eight points only will be found fufficient, and frequently not many more than half that number. Fig. 10. Fora circle, vvhofe center is 3 feet within the pidlure, and whofe diameter is to reprefent 4 feet. Let the center be fomewhere in the line 4 C. D 1. Cut [ 8 ] j. Cut oft the line 4. c, to reprefent the line 4 7, viz. 3 feet. 2. Draw from H through a, which will cut oft' c e to reprefent c a ; and from H to b will cut off c f to reprefent c b (by rule 2.) 3. Draw from H and L through the center c. 4. From P h to a, will cut off c h, to reprefent c a; and from P h through b, will cut off c g to reprefent c b (by rule 3.) 5 . In like manner, from P 1 through a, will cut off c i to reprefent c a ; and from P 1 to b will cut off c k to reprefent c b. 6. Through the eight points thus obtained, draw a curved line, as in the figure. By the fame means, the perfpedtive of all circles may be determined, viz. by giving their centers and diameters; as 1 m n, and o p q.-And by rule 1, their perfpedlive lengths may be adjufted : thus from any point S, on the horizontal line, draw lines from thence through o,q to the bottom, which will fhew the real fize of o q, and which in this cafe reprefents 4 feet. Having fhevvn how to apply thefe general rules, in finding the perfpe&ive reprefentations of fquares and circles ^fi "ires of the moft fimple conftruction, but neverthelefs of fuch importance in architecture, ls to conftitute the moft general forms of it; and therefore in a work of this nature, of great import¬ ance) we will now proceed to the confideration of a few bodies limply conftructed, as preparatory to : he main d-.fign. SECTION III For putting cubes and cylinders into Perfpective. ! X AM P L F, I. A parallel cube of 2 feet fquare, and placed at the bottom of the picture. Plate V. Ffi. 11. Draw the front fide a b 1 3 ; and lines from b,a,3 to C j then from 5 draw to H ; and from c the perpendicular c d ; from d draw another parallel as in the figure, (by rule 1. 2.) E X A M P L F, II. The fame figure placed at one foot diftance within the picture. From 6 to L gives the corner f, (by rule 2.) Draw from 5 to C, and the parallel f e ; then make f g equal to f e, and draw the front fide f i k g, from e to L gives the point h ; from h draw the perpen¬ dicular k 1, and from 1 another parallel. EXAMPLE, III. Several cubes one behind another. Fig. 12. Draw the front fide A a b 2 ; from a, b, 2, draw lines to C, then compleat the firft cube as above. Again, draw from 4 to C, and alfo the parallel c d ; then from d draw a line to H, which gives a fpace to reprefent the width of one cube ; from g draw the parallel g h, and a line from h to H will give the width of another cube ; therefore, from g and n draw perpendiculars cutting b C, and from thefe interfections draw the parallels for the top. (by rule 1. 2.) Having drawn the cubes on one fide, thofe on the other are to be obtained with great facility, and equal exactnefs, in the following manner. EXAMPLE, IV. For obtaining the fame number of cubes on the oppofite fide, from thefe already drawn. Fig. 1 2. Upon 8 B draw the front fide ; from 8 and the two upper corners, draw lines to C ; and from the feveral corners of the cubes already drawn, produce parallels, as c m, cutting 8 C ; from thofe interfedlions draw perpendiculars for the fides, and then the parallels for the tops, 8cc. N. B. [ 9 ] N. B. The tops and bottoms of cubes, are fimilar figures, placed diredly over, and parallel to each other; and therefore the fame rule which determines the pcrfpedtive appearances of the bottoms, muft determine thofe of the tops alfo. And this will hold univerfally true, not only in cubes, but in cylinders, and in any other figures that are conftrudted in this manner. EXAMPLE, V. For an oblique cube 2 feet fquare; and the neareft corner to be 1 foot from the bottom of the picture. Plate Vf. Fig. 13. Find, by the fecond rule, the corner a; by the fuff, the length ab; by the third, the depth a c; draw the parallel c d, which gives the other fide a d. From c, a, d, draw the perpendiculars c f, a e, d g; and a e equal to a b; then from e draw lines to H and L ; and from f and g draw lines to PI and L. EXAMPLE, VI. For feveral oblique cubes; like the laft figure, one behind the other ; both to the right and left. Fig. 14. Draw the firft cube from the point 5; draw lines from 5 to Hand L; and from 7 to PI gives the fide 5 b; draw the parallel be; then the perpendiculars for the upright edges; and make 5 a equal to 5 7, and draw the lines from a to H and L, and alfo from d to L ; laftly, draw from e. to H, which flnifhes one cube. Let the fpaces between the cubes be 3 feet. Draw a line from 8 to L; and another from b; and then the parallel b f, which is 3 feet {by rule 1) then from f to P 1 gives b g to reprefent b f. (by rule 3) From 7 draw a line to L ; and from g the parallel gh, which reprefents 2 feet (by rule 1) that is, the width of one cube; then from h draw a line to P 1 , which gives the fide g i; therefore draw a line from g to H, and from c to L, which will produce the other fide g m. Again, from g, m, i draw perpendiculars as in the figure, and then interfeiftions with the lines, drawn from the top of the firft cube to L, will determine the height of two fldes; and by drawing other lines to H, as n H we fhall compleat another cube; and fo on. T he figures on the right hand fide, are found from thofe which are already drawn by means of parallel lines, viz, in the fame manner, as thofe in example 4. EXAMPLE VII. For putting cylinders into perfpedtive. Fig. 15. Let the propofed cylinder be 4 feet in diameter, 6 feet high, 3 feet from the bottom of the picture, and let the center be in the line 3 C. Find the point c, by rule 2, and the diameter ab, by rule 1 ; with the diameter ab find the per- fpedtive of a circle, as in Fig. 1 o ; divide a b into 4 feet, by rule 1. From c draw the perpendicular c m, then take 1 foot from a b, and from c fet it fix times to m ; through m draw the parallel k 1, and make it equal to the lower diameter ab; with kl find the perfpedlive of another circle, then from the outer parts of each oval draw lines, as al, bl, which will compleat the propofed reprefentation. Fig. 16. For two cylinders one behind the other. Let the center c and nr of the cylinders be in the line 9 C ; and let each be 2 feet in diameter, and 5 feet high. Let the center of the firft cylinder be only 1 foot from the bottom of the picture, but that of the other 6 feet. By rule 1 and 2 we may obtain the center c and the diameter a b of the firft cylinder; and the whole operation is the fame as in the laft figure. By the fame rules we find alfo the center m, and diameter 1 n ol the fartlieft cylinder; and by drawing a line from f to c we fhall have the height of it. E SECTION [ 10 ] SECTION IV. Plate VIII. Introduction to the perfpedtive of fquare and circular mouldings, See. The variety of mouldings which compofe an Order of Architefture, are reducible to feven, viz. the Plinth, the Torus, the Scotia, the Cin&ure, the Cavetto, the Ovolo, and the Cyma. + Tiie regular mouldings ot an Order, may be conceived to be made up of many fquare and circular horizontal planes, like thin pafleboards of different widths, cut out, and laid in fuch a manner upon one another, as to give the peculiar form, or fhape of each moulding ; and therefore in order to produce them in Perfpedtive, nothing more feems neceffary, than general rules for finding the reprefentation of a fquare and a circle from given diameters. And to llluftrate this by familiar examples • let us firft obferve, that the cube and fphere (or as it is commonly called the globe) are figures of a more fimple conftrudtion than any of the other geometrical bodies; now it thefe can be reduced into perfpedtive, by two general, or univerfal rules only, it will greatly facilitate each fucceeding operation. I r is well known, that the cube is a body, contained under fix geometrical fquarcs, placed at right angles with each other. Now if we imagine all but the upper and under fquares to be taken away, as in Fio-. D, and the upper one to be fupported by props at the four corners; we fhall then have as perfect an idea of a cube, as we had before with it’s whole contents; therefore if we conceive a cube to be a figure contained under two fquare planes of the fame dimenfions, and placed exactly even, and at a determi¬ nate height from each other, then nothing more is required for compleating the reprefentation of it, than to hnd the perfpective appearance ol thofe two planes only. And the general rule for finding a fquare (as h'ig. 5 ) be fufUcicnt for this purpofe ; for the different fituations of the fquares, require only a repetition of the fame rule, viz. that for cutting off a line which vanilhes into the center of the picture, la as to represent a given length. See plate II. Ix like manner.we may imagine, (as was obferved above) how any mouldings which are placed about fquare bodies, may be compofed of many fquare planes, like thin pafteboards of different breadths, See. which is obvious by the figures of plate IX. Plate VIII. And fuppofe alfo that a globe was cut diredlly through it’s center, in a perpendicular direction, then the fection to each half, will be a circle ; fo that if Fig. A be made to reprefent that fection, then it may be confidered as the elevation of a globe of a given diameter. Again, imagine the globe to be cut in the fame manner, through it’s center, but in an horizontal direction- then this fection alfo will be a circle; which is reprefented by Fig. B, whofe parallel diameter is i k : and whatever fections are made parallel to this horizontal one, they will all be circles; whole diameters will be perpetually lefs and lefs, as they are farther and farther removed from c, the center of the globe; as is evident by the parallel lines within Fig. A. fiG. A. Now let the upper line H L be the horizontal line, with the feveral neceffary points put upon it, for determining the perfpective of a circle ; and let this circle be the given elevation of a globe, whofe utmoft height is a b. Dkaw a b perpendicular to the horizontal line, and fo as to touch the bottom of the circle at a • and from any point draw d in Fig. B, draw another perpendicular at pleafure ; then continue h g in Fig. A, through the perpendicular d c of Fig. b, and make i k of Fig. B alike, and equal to g h in Fig. A : with i k find the reprefentation of a circle. Again, take any other diameter from Fig. A, and proceed in the fame manner with Fig. B, and fo fhall we obtain the perfpcctives of as many circles from given diame¬ ters, (lee Fig. E) as will be neceffary ; and by then drawing one continued curved line fo exactly as to touch thole t As for the Ionic, Corinthian, and Compofite capitals, the Doric tri^Iyphf, dentals, modilions, and the like j thefe having various conltructions, and being of no conference in this place, are therefore omitted for the orefem ; but they fhall be iuily conlidered hereafter. [ II ] tliofc extremities we fiiall have the proje&ion of a globe on the perfpedive plane or piflure, which is compleated in Fig. F. From hence then, it is eafy to conceive, that if the feveral parallel lines within Fig. A are taken for the diameters ol fo many circular planes, which feverally extend themfelves exactly to the circumference of the globe, and are all fixed in their centers upon the line dh, as a common axis, like e f Fig. E; then this figure put into perfpective will give the fiiape of the projected globe to great exadtnefs; and the nearer thefe planes are placed to each other, fo much the more exadtly will the fhape be determined. This fufficiently (hews us in what manner a globe or fphere may be made of circular horizontal planes of different diameters, and from thence, how to draw its projection upon the picture. Now, if the projected reprefentation of the fimple and uniform figure of a globe, can be thus deter¬ mined, by a variety of imaginary circular planes placed in an horizontal direction, and perpetually varied in their diameters; then by the fame rule, the perfpeCtive of cylindrical, and conical figures may be ob¬ tained alfo. And all forms whatfoever, which are bounded by circular outlines, or which may be conceived to be conftruCted of horizontal circular planes, may be put into perfpeCtive by that one in¬ variable rule, which we have given for finding the perlpeCtive reprefentation of a circle only. And this one method will do for all kinds of circular mouldings. * SECTION V. Two general rules for the perlpeCtive of fquare and circular Mouldings. RULE, I. For Square Mouldings. I iie method, which architects make ufe of, for drawing the elevation of an order, or for any part of it; is the fame as we {hall follow in putting mouldings, ora whole order into perfpeCtive: for by this means we fhall have the given heights and widths of each objeCt, put at once in their proper places, and horn thence the perlpective of the whole may be determined, with great facility and exactnefs. Plate IX. Suppofe then, that H L is the horizontal line, C the center of the picture; H and L the points of difiance, A the elevation of a plinth below the horizontal line, and B the elevation of a fquare cyma. Above the horizontal line, draw within the cyma B any number of parallel lines, foas touch the extremities of the moulding. Then from any point D, draw the perpendicular D E; and from A, B trans¬ fer the feveral parallel lengths of the mouldings, and mark the end of each line fo as to make it very exact and difiinct. Now it is evident, that the two lines at D will give a perfect idea, and be the true dimenfions of the plinth ; and that the lines at B do as truly meafure and characterize the cyma. EXAMPLE I. Firft for the Plinth. Let us now imagine that Fig. A is an upright parallel fection (like 1245, Fig. G) made exactly through the middle of the plinth: and that Fig. B is a fection made in like manner through the cyma, with the feveral parallel lines drawn acrofs it, as in the figure. From any point G, of the line AG, draw the perpendicular G F atpleafure; transfer the feveral parallel lines from A and B to G and F ; as was done before to D and E. From C draw lines through 12, at pleafure; and from L draw a line through 3, cutting the lines 2 C and 6 C in 6 and 7 ; then draw the paral els 6 9 and 7 8, which finill.es the top. From 8, 6, 9 let fall perpendiculars at pleafure- and draw a line from C through the point 4, which will give the oblique end; and a line from the point a, parallel to 6 9, will compleat the reprefentation required. * Here I am aware of laying myfdf a little'open to thofe who perlift in keeping up to the ftri&eft mathematical prin- cioles of perfpedlive, in drawing the reprefentations of all objects whatfoever. Eu; if thole gentlemen will fufpend their criticifms for the prefent, I may poffibly place this matter in its proper light; or at lead give fuch hints, as may be thought of fome importance. I have here repeated the operation for determining the perfpeftive of a fquare; that is, the top of the plinth, for the lake of a regular procefs; but the reader will at once perceive, that it is no more than a fquare, found by it’s center and diameter ; as was fhewn before by the fecond example in Fig. 5, and with which, it is fuppofed, he is very well acquainted ; and therefore henceforward, I (hall only fay, land a fquare by it’s center and diameter. This figure is fufficient for (hewing, how any fquare moulding with even fides, may be put into perfpc&ive; and the operation will be the very fame, for finding the reprefentation of any fquare mould¬ ing, whofe fides are uneven, or which are conffrudtcd of different degrees ol curvature; fuch as the Ovolo, Cyma, &c. only the rule will be oftener repeated, as will be feen by the next example. EXAMPLE, IL For the Cyma. The feveral widths for draping the moulding having been transferred as before directed; find the under fquare, by it’s center and diameter ; which gives the bottom of the moulding, as feen above the horizontal line ; then by the fame method, find (in a regular fuccefiion) the perfpefiive of as many other fquares, as there are given diameters, which will determine the exact fhape of all the corners of the moulding ; fo that by drawing curved lines through thofe points, the reprefentation of the whole moulding will be obtained ; even to the mod; fcrupulous exactnefs. But fince the finding fo many fquares together, will occafion fome confufion, therefore this may be avoided, by drawing the under one fird ; then only fo much of the others, as are neceffury for obtaining the three vifible points of each fquare; marking thofe points with ink (as in the figure) and rubbing out the pencil marks as we go on. But a little practice will make all this very familiar, and particularly to thofe, who are tolerably (kill’d in drawing, for they will find that a very few fquares will be fuffi¬ cient, and efpecially for fuch fized columns, as are generally produced in drawings upon paper. RULE II. E X A M P L E, I. For Circular Mouldings. Plate X. Let A be a perpendicular fection, made through the axis, or middle of a circular plinth or cincture ; and B fuch another fection made through the ovolo. Now fince the plinth is even all round, we therefore need only find the upper circle, and part of the under one ; but fince the fide of the ovolo is a curved line, therefore three diameters, at lead, will be neceffary for obtaining the perfpective of this moulding, fo as to make it correct; all which lines are transferred to D E, that the fimilar lines on f G. may be didinguidred without confufion. For the Plinth or Cincture. With the given diameter 1 2, and the J points P h, Pi, for cutting off, find the perfpective of the upper circle, as directed by Fig. 10; which we (hall repeat in this place. The line 1 2 is the given diameter; and F is the center of the circle: from H, C, L, draw lines throngh the center F at plea- fure. From H or L, through 1 and 2, will give the points a and b on the line drawn from C through F : from P h, through 1 and 2, will give the points e and f, in the line drawn from H through F ; and irom P 1 , through 1 and 2, will give the points c and d, in the line drawn from L through F, 6cc. in the fame manner, find as many points as are neceffary for drawing the appearance of the under circle, from it s given diameter 35; and then a perpendicular on each fide, fo as to touch the extremities of the two circles, will compleat the reprefentation : which is the fame as in the example in Fig. 10, beginning with + See Piate I, Fig. 3. or Rule 3, Page 5. [ 13 ] with the fecond article. Or the points, for the under circles, may, in this cafe be found by letting fall perpendiculars from the points i, d,a/, in the upper circle, and then drawing lines from H, C, L, through the center f, to cut them ; thus from L through f, gives the point 4, See. EXAMPLE, II. For the Ovolo. From the given diameter 8 6, find the perfpedfive of a circle above the horizontal line ; do the fame from the other two diameters; then draw a curved line on each fide to touch the extremities of the three circles, which will give the true fhape of the ovolo in this fituation. Now it muft be obvious from thefe four examples of the Plinth, the Cyma, the Cindture, and the Ovolo, how any other fquare, or circular mouldings, may be produced in perfpedfive, by the very fame rules; and by reconfidering each operation, we fhall find that, after having given the propofed place and dimenfions of each moulding, its whole appearance is to be univerfally determined by one general principle, viz. that for cutting off part of a line, fo as reprefent any given length. For circular mouldings, we muft have at leaft three different lines drawn through the center of each circle to the horizontal line, and therefore there muft be three points for cutting off, which together comprehend the fecond and third general rules: but as for fquare mouldings, where one line only is neceffary for cutting off, &c. there one point only is required; which may be either the point H or L, (for both will anfwer the fame purpofe) and this is done by the fecond rule. In fhort, to fet down the regular procefs, it will ftand as follows. 1. Give the horizontal line, and the center of the picture. 2. Give a proper diftance for the propofed figures; that is, place the points H and L far enough from C. 3. Give the center of the moulding, and from thence draw the perpendicular for its axis. 4. Give the feveral lengths of the variable diameters, &c. 5. Find the points for cutting off, by rule 2 and 3. 6. And by the fame rules, find as many points in the reprefentation of the circumference as are required. 7. Draw regular out-lines, by means of thefe acquired points ; and fo may each figure be compleated. Plate XI. In thefe figures I had an eye to the bafket and tile, which is faid to have given the origi¬ nal hint for compofing the Corinthian capital: but it is here produced only as an example of a fquare and circular figure, joined together j which will ferve as a farther illuftration of the two general rules. For figure A is the fedfion through the middle of the objedt, with the parallel diameters for fhaping it. In figure B the tile only is finifhed in perfpedfive, and the fedfion of the bafket is placed under it. In figure D the reprefentation of the bafket only is drawn, by means of the perfpedfive of the circles. And in figure E the objedt is wholly compleated. By the fame method we may obtain the perfpective reprefentations of ballufters, &c. Plate XII. In this plate the figures are intended only by way of a preparatory hint for drawing the Tufcan column. For Fig. A is a fection of the whole order, with tire parallel lines drawn acrofs its axis A B. On the line D E are the feveral diameters transferred: and Fig. F is the column com¬ pleated. -f- G BOOK 4 This diftance of the eye, in thefe and the two preceed- being obliged to bring the diftance within the compafs of ing plates, being much too little, therefore the apparent the plates, for the fake of that clearnefs and precilion fo depths of all the figures do appear a little prepofterous: but neceiTary on this occafion. this was an inconvenience not to be avoided in this place. [ H 3 BOOK II. CHAP. I. An Application of the foregoing Rules, to the feveral Orders of Architecture. The TUSCAN ORDER. SECTION I. T m X X hX%\*Ji& {M H E methods by which any fingle mouldings, that are either direftly fquare, or exaftly T;| circular, may be put into perfpe&ive ; have been fo fully explained in the laft fe&ion of book I, and are fo eafily underftood, and retained in the memory; and withal are fo uni- verfally applicable in almoft every part of the five Orders, that thofe rules perfectly com¬ prehended, will make the examples in this chapter fo very plain and obvious, at firfh fight, as to appear in a great degree felf-evident; and will moreover fhew the advantages which may be obtained, from building the general practice of this fcience, upon the moft obvious and fimple principles. However, it is abfolutely necefiary for the learner not only to underftand, and perfectly remember the general rules; but alfo to apply them to practice, in delineating two, three, or more mouldings of each kind together, before he attempts to begin with drawing the reprefentation of the whole Order : for I now fuppofe that he is perfectly acquainted with thofe fundamental principles, in order to avoid a repetition of the fame thing for every moulding, and to prevent that confufion which would necefiarily be confequent upon it. Now, though there be no occafion for drawing the elevation of the objedt intended to be put into perfpective, but to take the feveral heights and projections from the Architectonic Sector, as they are wanted in each operation; yet, fince the explication of any new fyftem fliould be afiifted by every pofii- ble means, which may render it eafy and familiar ; therefore I have given many of the elevations to the examples in this chapter : for by this means the reader will fee the correfpondency between the parts in the perfpectives and their elevations, and from thence will the more readily comprehend my meaning. But thofe who fhall not choofe to draw out an elevation for every object, may fhorten the work by drawing fo much only, as is expreffed on the left hand of Fig. A B. Plate XIII. And that all the examples may have the moil: agreeable fhapes that the plates in this work will admit of, and that the learner may know the exact place of the vanifhing points to every figure ; I fhall in general make the diftance of the eye equal to the utmoft width IT L of each plate, as was obferved before in page i ; which length H L being fet from C to the right and left on the horizontal line, will give the points H, L. And as for the other two points, viz. P h and P 1 for circles, they have been fully explained before. For the Pedeftal and Bafe. Let D be the bottom of the plinth, and D E the axis of the column, i. Draw [ 1 5 ] ’• Draw A D P arallcl to the horizontal line, and continue it at pleafure: then from any point A draw the perpendicular A B; and thereon the elevation to any propofed bignefs. а. Upon the axis DE transfer the heights and projeSions of the feveral mouldings from the elevation A B ; in a regular fuccefiion as they are wanted. 3. Begin with the plinth, and by rule 1, example 1, for fquare mouldings find it’s perfpe&ive; then draw the lines which are to be vifible with ink, and then rub out the pencil marks. 4. By the fame rule, and in the fame manner, draw the fillet. 5. The Doric cyma reverfa is drawn by rule 1, example 2. б. The dye by the fame rule as the plinth, viz. rule i, example 1. 7. The Doric cyma by rule 2, example 2. 8. The other fillet by rule r, example r. 9. The plinth of the bafe by rule 1, example 1 ; or it’s projection by the dye already determined. 10. The torus by rule 2, example 2. 11. The cincture by rule 2, example 1. 12. And the bottom of the fhaft of the column by rule 2, example 1. Turs figure fhews how the pedeftal and bafe will appear, when they are lower than the eye, and on one fide of it ; and in the 14th plate, the fame figure is wholly finiflied, with another of the fame lize placed directly under the eye: and the method for finding this, from that already drawn, comes next under confideration. Pi. ate XIV. 1. From the center C draw the perpendicular A C, and from B the parallel A B. 2. Continue (by parallels) the feveral lines which form the front mouldings of Fig. B acrofs the line AC. 3. Take half the widths of each moulding from B, fet them on each fide of A C, and compleat the front mouldings. 4. From the end of each moulding draw a line towards C; and then parallels from the fartheft pro¬ jections, as a b, will give all the apparent depths. 5. For the bafe of the column, it will be neceflary (in order to draw it very correct) to repeat the operation as in the former figure. For the Tufcan capital and entablature, and to make it correfpond with the pedeftal already drawn. Pla t e XV. Here E G is the axis of the column continued, F is a given point near the top of it’s ftiaft, and A B the elevation, taken by the fame fcale as the former, from the Sector. 1. From the elevation, transfer the feveral lines as before directed to F G, for the heights and widths of the mouldings. 2. By rule 2, example i, draw the appearance of the ftiaft, the neck and cinctures in their fucceflive progrefiions. 3. By rule 2, example 2, determine the aftragal and ovolo. 4. By rule 1, example 1, The abacus, the architrave, the frieze, fillets and corona. 5. By rule t, example 2, find the perfpective of the cavetto, the ovolo and cyma, as they follow in their feveral Orders; and from hence compleat the outline. Plate XVI. Here we have this and another figure, as finilhed prints to correfpond with thofe in plate 14. H And [ 16 ] And now let me obferve again, that (not only in drawing this, but alfo all the other orders) the learner is debited to be perfectly matter of one thing, before he attempts the leaft pare of that which follows: for the w hole of this fyftem, though built upon two of the molt fimple rules, yet the tranfpofing and varying thole rules, will require fome degree of attention, and above all a regular way of inveftigation. He therefore who fhall attempt to learn this part of perfpedive, without regularly proceeding with the feveral fchemes, will be as unlikely to fucceed in it, as he would in learning any other fcience with an equal degree of inattention. The DORIC O R D E R. SECTION II. If T would be ufelels were wc to repeat the operation for the feveral mouldings of this, or the other jh t h r ee orders, becaufe it will be exadly the fame in all cafes; and as I fuppofe the learner to be per- fcClv acquainted with the perfpedive of mouldings, whether feparated or combined, therefore I fhall now lead him to thofe parts of an order only that are not direct fquares, or perfed circles; fuch as the Trigliphs, Soffits, the Capitals, Modillions, Dentals, &c. in the following examples: becaufe in thefe few infiances the general rules mu ft be a little varied in their applications j that is, the fame rule muft be oftener repeated in the fame place. EXAMPLE I. Plate XVII. For the Band of the Trigliph Capital, and for the Plinth of the Trigliph, &c. 1. Take the feveral heights and projections from the elevation, Fig. X. as they are expreffed on the line i--, and transfer them to Fig. G and D. 2. Fig. G, D. By rule i find the perfpedive of four fquares, from the feveral diameters 22, 33, 4 +) 5 5 ’ 3. Make a dot at every angle, or joining of the foffit, and from every vifible corner draw a perpen¬ dicular upwards, as in Fig. E. 4. Transfer the height 1 7, Fig. X. to 1 7 (or to 5 6) Fig. E. and draw from C through 6 to 8, and then from the point 8 draw the parrallel 8 9, See. Xow let the reader carefully obferve the difference between the method ufed for this, and that for producing fquare mouldings; and almoft one glance of the eye will fhew him,' that in Fig. D. four kiuares of different diameters are put into perfpedive upon the fame plane ; and that this is performed by the very fame rule as has all along been ufed for fquare mouldings, with this difference only, viz. here it is four times repeated upon the fame line 5 5. And any archited will immediately trace out the feveral angles or corners of the moulding, by confidering the perfpedive D as a plan or fedion of the entablature in this place, viz. that part of it which feparates the frieze and cornice. Fig. Z. Since the feveral widths of the plinths of the trigliphs exadly correfpond with thofe of the band and capital already determined, this part of the drawing may be cut very fhort, thus. Draw in its proper place the line e b, for the under part of the Tenia, and fet off the feveral breadths or projedions, viz. a, b, c, d, e, from Fig. X ; then lines drawn from C, through the points on eb, and alfo perpen¬ diculars irom the corners of the band, already drawn as mn, will give all the widths, as in the figure. EX AMPLE [ '7 ] EXAMPLE, II. For the Trigliphs. Pi .ate XVIII. This example having more work in it than the former, I have for that reafon made two feparate figures of the fame thing, as Fig. F and G; and we fnppofe that every part of thofe figures are already drawn, except the trigliphs and drops, which come in the laft place as ornaments for deco- rating and compleating the whole. N. B. The center of the pifture for Fig. F, is found by fetting the fpace A C from B to the right hand, on the horizontal line; and K is the point of diftance that belongs to this fecond center. In the firft place let us imagine, that the channels of the trigliphs, and the fpaces between them, are wholly taken off, or cut fmoothly away, like Fig. i ; for then the operation will differ but very little from the laft example. 1. The projections, &c. being transferred from the correfjionding points on Fig. D, then through the feveral points 4,4., 8, 6, Fig. F, draw lines from the other center of the pifture ; and from the vamlhing point K of the diagonal, draw through the axis 2, cutting the aforefaid lines, as in the figure. 2. From thefe points, fo obtained on the diagonal 7 8, draw parallels, which will determine a back or flat part for the trigliphs, like Fig. I, and alfo the top of the channels. 3. Set the height above the channels from 2 to 3, and the top of the infide of the channels fiom 2 to 1 ; and from thence determine their heights on the middle of the fide trigliph, as 7 8, &c. 4. For the channels, Fig. G. Divide the breadth of the top of the channels and the parallel for the bottom of them, each into 12 equal parts, and from thence compleat the channels of the front trigliph as expreffed by the lines at the bottom of it. 0 ’ 5. From C fet the diftance H L of the eye, to the right on the horizontal line, and from the point fo .obtained, draw to the feveral divifions on the front trigliph, which cutting the correfponding lines on the fide trigliph, will determine the perfpeflive breadth of the channels in that place. N. B. T he reader is defined to remember this rule, for finding the channels on the fide trigliph, fince it will be very ufeful, and will be more fully explained hereafter. EXAMPLE III. For the Drops and their Corona. 1. The Corona is found exadtly in the fame manner as was the capital of the trigliph, Fig. B, viz by fetting the feveral widths in their proper places ; then giving their heights, and then drawing from the center of the pidture C, and from the point of diftance K, Fig. F- z. The drops. From Fig. D transfer the widths on the line a b to their proper places on the line b d, Fig. F. 3. Draw as before from the center C, and from Kj which will give the points marked on the diagonal g h. 4. Through the points on the diagonal g h, draw parallels, which will produce little fquares in per- Ipedive, as in the figure, for the under parts of each drop. 5. Divide the front corona into twelve parts, which will give the place for the top of each drop, and the fide drops are obtained, like the fide channels. EXAMPLE IV. For the foffit to the corona of the cornice. •1. Take from a b, under the corona of Fig. D, and fet thefe feveral divifions for the ornaments on b b, Fig. E, as before; and through thefe divifions draw lines from C at pleafure. 2 . Produce [ ] 2. Produce the diagonal d e, cutting the lines drawn from C, and mark very diftin&ly, all the inter- feClions on it. 3. From the points on the diagonal d e draw parallels, which will give all the parallel fquares, and alfo the middle points for thofe which are viewed in an oblique manner. 4. Within all the fmalleft fquares, draw the appearance of fo many circles for the under parts of the drops, and the larger fquares are fufficient for compleating the ornaments in and about them. N. B. The fides of the oblique fquares muft be drawn to the points of diftance. 5. The heights for the drops, 8cc. are to be found by fetting thofe heights from b b upwards; as b f, 8cc. Plate XIX. This plate contains a compleat outline of the whole Order. Plate XX. Here we have the Order wholly compleated. Plate XX'. This exhibits a Doric entablature (drawn to the fame fize, as thofe in plate XVII, and XVIII) which is wholly compleated. N. B. In this as in all the other finifhed examples; I have begun with the loweft part, and fo worked upwards ; though it would be equally the fame thing, were we to begin at the top and work downwards. The ANCIENT IONIC ORDER. SECTION III. pLATE XXII. In this plate I have only to fhew how to produce the volutes of the capital, when they are viewed either fide-ways or in front; and to give a rule for determining the dentals, and fome other ornaments. EXAMPLE, I. For the volute in front. Fig. D contains the heights and projections of the abacus, the ovolo and aflragal; and alfo the ut- moft projection a b of the volute, it’s height g f, and the centers d,e&c. for defcribing it. § Fig. E. Firft draw the abacus by the method for fquare mouldings, and then find the.centers for the horns of the volute. 1. From Fig. D, transfer the point c, to the correfponding point c on Fig. E; which is the height for the center of the eye of the volute, that is, the middle of the aflragal,; then through this point c draw the parallel e e, and make c e, c e of this figure, refpeCtively equal to c e, of figure D. 2. From C draw lines through e and e; and from the point of diflance draw the line 1 3 through the points, and then the parallels 1 2 and 3 4 will give the perfpeCtive of a fquare, whofe corners 1, 2, 3, 4 will be the centers for the eyes of the four volutes; and the little fquares at thofe corners will be f or placing the centers, &c. which may be more clearly feen by Fig. G, where this part of the figure is enlarged. 3. By the line g o (which determines the bottom of the volute) we obtain the perfpeCtive of another fquare, whole corners will determine the bottom or loweft part of the volutes. 4. Through § The font of the volutes may either be deferibed from or they may be drawn by hand with the afllftance of the centers, which it the common method uftd by architects; Architectonic Sector. C '9 3 4- Through the center for the eye of each volute (Fig. F; draw a parallel line for the breadths, and then defcribe all the volutes that arc vifible by the common method of twelve centers. 5 - Give the projection of the ovolo (Fig. F) which will be a guide for the middle of the fide of the volute, and conlequently for finifliing that part of it: though in this particular a good deal mult depend upon a nicenefs in drawing. b. Andlaftly, find the peripeftive of the circular mouldings, viz. the ovolo, theaftragal, and cinflure, by the former rules; and then draw in with ink fo much of each, as appears between the volutes. EXAMPLE II. For the Volutes, when they are viewed fideways, like Fig. I. Fig. K is the elevation of half the capital in front; and Fig. L is the elevation of half the fide of it. i. In Fig. H determine the appearance of the abacus, and from the middle of the oblique fide at e, draw the perpendicular e d at pleafure. а. Through the axis of the column at k, (which is the height for the center of the eye of the volute) draw a parallel line a c at pleafure, cutting e d in b. 3. From b as a center, fet off the feveral divifions to the right and left, as they are mark'd with dots on a c (Fig. K j and do the fame by the line ed. 4 ; Fr0m C 2 O the lowcft horizontal line) draw through the center b at pleafure; and at the point i .lance (to the right hand) put a pin, -and lay a ruler to it; then by moving it to the dots on the line a c, and fucceffively croffmg g f we ihall obtain correfponding dots on the line f g; which dots will determine the breadths lor the revolutions of the volute, and confequently the two centers for the eyes of them ; therefore through thofe centers draw perpendiculars as in the figure. 5. From C 2, draw through the dots on the perpendicular d e; which will give correfponding dots on the perpendiculars that pafs through the centers of the eyes of the volutes. б. Having obtained the above dots on the perpendicular and tranfverfe lines, we may from thofe fini (h the two reticulated planes, which will be the perlpeflives of the reticulated elevation above, in Fig. K, and confequently from the reticulations, fo obtained in perfpedive, we Ihall be enabled to draw one face of the capital to great exadnefs. 7 . And laftly, having drawn the reticulated plane for the neareft volute, that on the right hand corner is produced from it, by means of parallel lines, &c. N. E. g i is the breadth of the band of the volute. F ‘S- 1 the fcrolls of the TOlut « are completed. We will now determine the middle of the fide : and to do this we need only draw the circular mouldings, then find the middle of the ovolo and aftragal, with the middle f of the under part of the abacus; for this will direfl us in drawing the curved hue f, e d, and will be a fufficient guide for complecting the capital: a fin.Ihed example of which we nave .exhibited m the next plate, 2 5, viz. Fig. I. EXAMPLE III. for Dentals. Fig. A contains the heights and projedions of the whole cornice; a b is the height of the dentals- and c d contains their feveral widths, 8cc. 5 ..At Fig B place the height a b of the dentals, and through b draw a parallel line, and then from Fig. A transfer the .feveral widths to c d. K 2. Then [»° ] 2. Now draw a line from C through the ends c and d, and another from the point of difiance through the center b ; which gives a fquare, See. as in the Doric foffit, Plate XVIII, Fig. E. v From C draw through the other divifions on c b, fo as to cut the diagonal, and to give the widths of the dentals in front. 4. Through the divifions on the diagonal draw parallels, which will give the fide denta.s, 5 cc. N. B. In Fig. C, the dentals are drawn larger, and denticles are put between them. EXAMPLE, IV. For the ornaments of Mouldings. Divide, the top and bottom of the mouldings (for inftance, the ovolo in Fig. B.) on the front fide at top and bottom, by the fame rule as is ufed for drawing ornaments in an elevation ; from whence the ornaments in front may be finifhed. And for thofe on the oblique fide, we fix a ruler at the point of difiance to the right hand, and move it fucceflively to the points on the front fide, which will give cor- refponding points on the oblique fide. In plate XXIII, is an outline; and in plate XXIV, is the Order compleated. The MODERN IONIC O R D E R. TIT7 E are now to apply our general rules to the moft difficult parts of architecture, for fuch (as they ’ * relate to perfpeCtive) are the abacus and volutes in this, and the Corinthian and Compofite Orders ; which from their various degrees of curvature, and the obliquity of their fituations, have always been eficemed very difficult undertakings: and I do not remember ever to have feen one example of this kind which was truly drawn. Let us firft of all confider how thefe particular parts of architecture are conftruCted, for that will lead to the method for determining their reprefentations. The fides of the abacus are deferibed from the fummit of an equilateral triangle, and it’s ends are the diagonals of fquares (which in the pofition we fiiall give to the capital will vanifh into the points of difiance) and the plan of the whole is always drawn within a fquare. Having therefore put the given fquare for the top of it into perfpeCtive, we lhall have the utmofi extent of the abacus : and by drawing lines in the plan, as in Fig. B, we fhall obtain feveral principal feCtions in the curvilinear parts, and from thence be enabled to produce a very correCt reprefentation of this part of the capital. Plate XXV. Let Fig. A be the elevation of half the capital, and Fig. B the plan of one quarter of tire abacus. From the corners e and d of the under part of the abacus, let fall perpendiculars to 1 8 ; do the fame from any other points, a, f, g. Then 1 8 is half of the utmofi projection of the abacus, viz. of the point c; 7 is the projection of the points b and e; 6 is the projection of the points d and t ; 5 is the projection of the middle of the top part of the abacus; 4 is the projection of the point g; 3 is the middle of the bottom of the abacus; and 2 is the projection of the two points at a. Having obtained as many points on the line 1 8 as are neceffiry for our prefent purpofe, we will from thence determine the upper part of the abacus; for which purpofe draw the axis of the column from any point 1 of Fig. D, and alfo the line 8 8 for the projections j then from the center 1 fet off (from Fig. B) on both fides (Fig. D) the difiance of the points 12,15, 1 6, 1 7, and 1 8, and draw a fquare, See. as in the [ 21 ]' the figure, and within that fquare draw lines from C, cutting the diagonal N M in correfponding points, as in the former examples. And having determined the places of fo many principal points in the top of the abacus, we (hall have fufficient guides for drawing its true reprefentation ; all which is evident by the figures. In the fame manner (fee Fig. E) is the under part of the abacus to be put into pcrfpearve : and the lines, which pahs from C through the center i, will (in both cafes) give the points a b; viz. the middle of the abacus for drawing the ornament, or rofe, in that place. In regard to the volutes; we will firft confider the manner in which they are conftrufled by architeas, and from thence deduce a method for drawing their perlpeftive reprefentations. The face of a volute we will fuppofe to be only one fpiral line, generated by twelve centers on one plane only. It begins at the top of the ovolo, from thence it takes three revolutions, and then finrlhes in a circle; which we call the center or eye of the volute. Through this center a perpendicular is drawn, for the heights of the revolutions, and a tranfverfe line to it, for their breadths, as c d and a b. Fig. A. Now if we can find the perfpeaive of thefe two lines, then the height and breadth of the face of the volute will be determined : and if we can alfo obtain the heights and breadths of the revolutions, or the points on the lines a b, and c d, then we fhall have fufficient guides for drawing the whole face of the volute ; as may be feen in Fig. G. But in order, to do this (Fig. G) let us imagine an horizontal and perpendicular feflion to be made through the eye of the volute, as a b c d, e f g h, and that the plan of them is laid down in Fig. C, where we have three breadths of the volute, viz. that part of it which is next the column, the part in the middle, and the outfide ; and therefore by transferring the neceffary points from the line ah of the plan Fig. C, to the line 10, ro, Fig. F, we can then proceed in the fame manner as in the former example for the abacus, taking care to fix the center r of the line in its proper place, and then drawing the reprefentations as expreffed in the figure; which we fuppofe to be four horizontal planes palling through the middle of the volutes, viz. in the line a b, Fig. A. Havino proceeded thus far, let us next determine the perpendicular planes for the thicknefs of the volute in the middle; which will neceffarily give the breadth of the top and bottom of it; as gh, ef, Fig. G. At a (Fig. G) is the place for the center, or the eye of the volute placed upon the axis, and taken from the elevation Fig. A; the heights of the revolutions are alfo taken from Fig. A, and fet off from the point 2, viz. from 2 to i, and from 2 to 3: now through the point 3 (that is in the line which goes from the center of the eyes) draw the perpendicular 46; and from the point of diltance (to the left hand) draw lines through . 2 and 3, &c. fo as to cut 4 & m the points marked on 4 &• Again through the center on the face of the volute, draw another perpendicular, 78; then from the other point of diftance (to the right hand) draw lines through the feveral points between 4 and 6, and then we fhall not only compleat the perpendicular plane, but fhall alfo have the true he.ghts of all the revolu¬ tions on the line 78; and from which this volute may be finilhed. Having thus obtained one of the volutes, the other two, which are vifible, may be drawn from it. thus, through the eyes of the other volute in front draw perpendiculars, as e g, fh; then parallels from the parts of the volute already drawn will give correfponding points in this ; and the parallels from 7 and 8 give the points e g, See. In like manner, if a ruler be laid to the point of diftance and to the feveral points on e g, we fhall obtain correfponding points on the line i k. Faow what has been faid (and by infpeaing the figures with a little attention) we may eafrly conceive how an outline Fig. Hof this capital may be drawn I though it mull be confeffed that with all thefe L nelps. [ 22 ] helps, much will depend on the fkill of the artift, and efpecially if he does not confine each face of a volute to one plane only. For if the revolutions are made to fpring out from the plane at the begin- ing, we fhall have fuch a variety of different curves as will vaftly furpafs my comprehenfion; and which (to reduce truly into perfpe&ive) might probably evade the utmoff efforts of the moft able mathema¬ tician. Indeed, the proje&ions of the middles of each revolution, might be obtained by the horizontal plane, which pafies through the eye of the volute ; but this would be of no great affiftance, fince any tolerable draughtffnan may, from what is already laid down, do fufficiently well without it. Before I conclude with this example, it may be neceffary to reduce the rules into fome order, which I have hitherto given in a promifeuous manner for the fake of keeping the parts more clear and diftind. And therefore 1. Give the elevation A. 2. Find the plan B, and draw the perpendiculars, &c. 3. Draw the plan C, See. 4. Give the axis of the column, and the top of the abacus as in D ; then find the top, and draw fo much of it as is vifible ; marking the middle of it in x, and rubbing out the pencil lines. 5. I loduce the under part of the abacus; draw in witli ink, and rub out the pencil lines, as in Fig. 6. Finifli the abacus as in Fig. E and F. 7. Upon the axis put the height of the eyes of the volute, and draw the horizontal planes as in Fig. F. 8. Set off the heights of the feveral revolutions upon the axis as in Fig. G, and determine one volute. 9- From this volute obtain the others, by parallels, See. 10. Finifli the outline as in Fig. H. 11. And compleat the capital as in Ficr. K. The CORINTHIAN ORDE R. I N t:,;s 0rds:r 1 M hare ]itt,e more to d o than to apply the general rules in drawing the leaves of the capital. For the abacus and volutes are to be obtained by the method which is fo fully explained | ■ XXV of the lad Order ; and the manner of drawing the moddions is much the fame as that tor determining the perfpeftive reprefentations of the dentals in plate XXII. Inde ed, 111 this capital there are fmaller volutes between thofe placed at the corners; but I appre¬ hend, that no new or material difficulty, cau arife on this occafion to any one who has the lead facility rn drawing, or that is tolerably (killed in architefture. And I moreover imagine, that a minute de¬ tail ol fo complex an objed as this, would be neither entertaining nor inftruaive. For, were I (like Pozzo) to aim at great exaflnefs, it might indeed amufe the eye, and at the fame time confound the undemanding: and after a tedious and intricate operation, we ffiould gain no more ground than what may immediately be acquired by thefe rules of much greater fimplicity ; for, in both cafes, much muff epen on t ic hand and (kill of the performer. And I believe there are very few artifts who will not rea 1 y ac -nowitdge, thrt a few ftrokes properly placed, will give a more pcrfefl idea, and be of much greater affiftance to his hand in drawing any objefl, then putting him into the leading firings of faience, and and guiding him ftcp by ftep, through the intricate mazes of lines and points. Thus much may fufficc, for my brevity in {hewing how to put the Corinthian and Compofite capitals into perfpedive. We will now proceed to the matter immediately before us. Flats XXVI. In Fig. i, I have given an elevation of the capital, with the parallel lines which determine the heights and projedions of fo many parts as are neceffary for the prefent purpofe: and at Fig. 2, one quarter of the plan for obtaining the abacus ; the general procefs of which is reprcfented by Fig. 3 and 4 ; and this brings us to Fig. 5, for the leaves, See. In the firft place, let us obferve that this capital is compofed of two fimilar rows of leaves, whofe heights and the turning down of the leaves are given in the elevation Fig. i. Each row contains e.ght leaves; and the fecond row of them is fo placed, as to have one leaf fall diredly in the. middle of each front of the capita], and confequently the other four leaves in tills row are placed diredly under t e corner of the abacus, and therefore the ftalks, or middle of thefe leaves will be exadly in the points which we have all along made ufe of for drawing the perfpedive of a circle, viz. book I, example .8, of fect.on 3. And fince the firft row of leaves are placed exactly between the ftalks of the former, therefore having determined the places for the fecond row, thofe of the firft may be drawn from thefe, as wi 1 beft appear by the operation. Let Fig. 5 be the center for the bottom of the capital, and p p the diameter for the balket, as taken from Fig. i. 1. Find the perfpective of a circle from the given diameter p p, and make the eight points as in the figure. 2. Take (from Fig. 0 the heights r g, r d, of the fecond row of leaves, and of their turnings down; (as expreffed by the curved lines s f c e) and transfer them on Fig. 5, from r to g, d. 3. Draw through g and d, the parallels ee.ee, and make them refpectively equal to the cor- refponding lines g e, d c on Fig. i. + . Take the projections of thefe lines from Fig. 1, and transfer them to e e, c c, Fig. 5, mark- ing each .with a dot, as c, £, 1. 5. With the diameters e e; f f; c c, draw the perfpective of three circles, expreffed by the dot¬ ted lines; and in each circle, mark the eight dots as before. 6. Through thefe dots draw curved lines, as expreffed in Fig. 6, which will give all the ftalks, or middle of each leaf that are viftble in this fituation of the capital. 7 . Having general fliape obtained the ftalks, and the heights of the turning down of the leaves, next {ketch in the of each leaf, as in F,g. 7 : and from thence this part may be compleated. Again ; for the firft row of leaves. The widths, as was obferved above, are obtained from the fecond row already drawn; and there¬ fore only the heights and turnings down are wanted for compleating thefe alfo : and for this purpo e, fet off the heights and projedions from the elevation Fig. . to F,g. S , and from thefe find the perfpefl- ive of two other circles, as in Fig. 6, which produces what was rcqmred. I (hall now Ihew how to determine the extremities of the outer volutes, which line will likewife be a guide for the upper leaves, viz. thofe which go diredly under the volutes. Now, imagine an horizontal fedion to be made through the middle of the volute, as a b, Fig. ,. , Transfer the line a b from Fig. 1 to its proper point b, Fig. 7 , and fet off the projedions b a, b o. 2. From M [ H ] 2. From tl'.cfc two given projections, find the appearance of two fquares, as exprefTed by the dotted lines in this figure; and the lines of the fmaller fquare being continued to the fides of the outer one, will give four little fquares, the diagonals of which will be for the thicknefs of the outer parts of the volute, which will tend to the points of diflance. I hus much, I prefume, is fufiicient for compleating the capital, as in plate XXVIII and XXIX. All that now remains to be confidered, is the method of drawing the modilions. Plate XXVII. In Fig. i. is the elevation of an entire modilion. At Fig. 2. the projections on F. F of the Jeverai parts are transferred, from the line a b, Fig. ,; and by this means (as in the Doric foffit, p.ate XVIII, Fig. E) I determine the top of the modilions as in the figure : and in the fame manner find one part alter another of the capital., to each modilion, till all of them are compleated. For the under parts, and for the lines which ferve as guides for the leffer volutes; we take the heiglr , and fet any where from a, Fig. 3, on the axis AB, and then by transferring the feveral projec¬ tions flora the line cde, Fig. 1. we (hall obtain all the blocks for the modilions, and then draw in the ornaments, as Fig. + : but we are to remember that the point a is fuppofed to coincide with the point B. Pi .a te XXVIII and XXIX, contains a perfed out-line of the whole order, and a finilbed exam- pie ol it. The COMPOSITE ORDER. P ^ A 1 , E XXX ' Wc ' {haU n0t takc U P the ]earaer ’ s A™. dewing him how to delineate this Order, becaufe Ins own regions will eafily point out the method for drawing the whofc of it, as tepre lei.ted in the out-line of this plate. a , as rtpre Foa he is fuppofed to know how to produce the bafe and pedeftal, from what he learned in the Tufcan Order, &c. and the leaves of the capital being of a fimilar nature with thofe of the Corinthian • and t h .° ut d ab fhe w as the modern Ionic cap . Ql . therefore the w u( . J tion for'even T’ 7 7 a ' r °' ^ d;fes “ » P- which demands atten- ’ he modilions muff appear very eafy from the rules laid down on plate XXVII ; •“ ° ! *• ■ - -a. * » ,« BOOK [ 25 ] BOOK III. CHAP. I. General Rules for determining the perfpective of Shadows. A V I N G fhewn how to delineate the five Orders of architecture, I am naturally led to V H M t ^ ie con 6 deration °f buildings, and therefore fhould now have proceeded with applying the rules in drawing more complex parts of architecture, fuch as colonnades, arches, See. but &eQBG0(30Q£g £ nce j p r0 pofe to give as much correCtnefs and elegance to thofe objeCts as I poffibly can, it therefore becomes neceflary, in the firft place, to fhsw how to determine the appearance oi fiiadows, which I (hall principally do by one general, or univerfal rule. That true principles for drawing the fhapes of fhadows upon a picture are of the utmoft confequence, is a truth I apprehend not to be controverted ; and therefore an attempt to carry this part of perfpect¬ ive farther than has yet appeared in any author, will have fome claim to the attention and candour of the public. I do not prefume to fay, that no deviation is to be made from the doctrine I fiiall advance on this part of perfpeCtive; for poflibly there may be fome cafes in which it will be better for the artiffc to be guided by his own diferetion only : but this can no more render the following examples unneceflary, than the ufe of fpeCtacles to alfift the eyes of him who cannot fee perfectly without them. In my former book upon perfpeCtive, I have particularly confidered the doCtrine of light and fhadow, and have there fhewn how to determine their projections upon a variety of planes, when they are either perpendicular, parallel, or inclined : and much more may be faid upon it. However, a fmall degree of knowledge in the theory of this part, will fully anfwer our prefent purpofe : for, as was obferved above, it may principally be deduced from one fimple rule only ; which we will now proceed to explain. § N Whoever § Plate XXXIII. Fig. A. viz. by Fig. i. Suppofe a b Let cf be a ray of light, having the fame degree of incli- to reprefent any given objedt perpendicular to the ground, nation as the ray be, then will the line cf be equal to b c, which is here reprefented by the indefinite plane adfe. and the angle fed equal to the angle e b a (Euc. i. 26) Let be reprefent a ray of light, having any given in- therefore the triangles bae, cdf are entirely equal, and clination, which is here exprefied by the angle aeb: then have their correfpondent fides equal each to each (hue. 1. 4) will the line ae be the length of the fhadow call upon the df is therefore equal to a e. Since the triangular planes bae, ground by the given objedt a b, whence by Trigonometry, cdf, are each perpendicular to the ground plane, and paral- S. L a e b : a b :: S. L e b a : a e. lei one to another (Euc. 1 1. 14) therefore d / is alfo parallel Therefore the length of the objedt a b being known, as alfo to ae, wherefore ef is equal and parallel to a d (Euc. 1.33) the angle of inclination aeb, which the ray of light makes and therefore e f and b c are alfo equal and parallel (Euc. r. 30) with the ground, the length of the projedted fhadow is readily Hence it appears, that the right lines a e, df, are the fedtions determined, as above. But if the length of the ray of light made by the indefinite, or ground plane, and the triangular were given inftead of the angle of inclination, then ae might planes bae, cdf, and that ad, ef a re the fedtions made by be found by (Euc. 1.47.) the planes abed, ebef, with the ground plane a dfe, there- Now let dc be alfo a given objedt equal and parallel to a b-, fore the fhadows of the points b, c, are pr jedted on the ground then are the lines be, ad, equal and parallel one to another, in the points e, f that of the lines ab, de, in the lines ae, (Euc. 1.33) and the common fedtion of the two planes a be d, df and the fhadow of the whole plane abed, is projedted adfe, is the right line ad (Euc. 1 1. 3) Now becaufe the in the plane a dfe. planes abed, adfe, are perpendicular to each other, the angle bae is a right angle, as is alfo the angle cdf. Plate [ *« ] Whoever will make obfer vat ions on the effc&s of fun-ffiine, as he paffes by buildings, will be greatly aflifled in comprehending the following fchemes ; for the original hints of every example were taken from nature, and the mathematical reader may fee, by the annexed note, that the manner of drawing them in this work is not inconfiftent with the principles of geometry. Shadow is caufcd by the interpofition of opaque objedls, which flop the rays of light in their paffage from the fun, or any other luminous body. But it is the rays that come from the fun only, which I fha'.l particularly attend to in this place. The fhadows, that are projected by the fun, are, in refpedt to it’s immenfe diftance from us, confx- dered as parallel: wherefore the fhadows of regular objedts, which are caft upon fmooth or even planes, will ^generally fpeaking) be fimilar to the objects that projedl them ; this may be conceived from obierv- ing the fhadow of a poff, a pillar, &c. upon the round. But fhadows that are projected upon round, cylindrical and uneven furfaces, will have various forms, and oftentimes will be fo very intricate, as to puzzle the moll acute and able mathematician; and there¬ fore I fhall content myfelf with fuch helps, in thefe difficult cafes, as may, if required, admit of de- mon ft ration ; but I will not give my readers the trouble and perplexity of it in the body of this work. Plate XXXII. Fig. i. Suppofe A L the horizontal line, and the figures A, B, E, F, G, M, to represent the fun gradually afeending from the horizon at A, to it’s meridian height at M ; or de¬ fending from its meridian M to the horizontal line at A, and in both cafes, fending forth it’s rays to the point N. Then the different angles made by the rays B N &c. with the horizontal line A N, will lhew the angles of the fun’s inclination. Now let us fuppofe that the fame objedt is placed in fuch a manner on the horizontal line A N, as to touch the feveral rays of light as they pafs from E, F, G ; and it will be evident that thefe objedts i, 2, 3, will fever ally caft a fhadow as far as the point N, upon the plane on which the objedts are lived. For fince the fun paffes over the top of each objedt, and makes a triangular plane with it and the horizontal line, therefore the whole fpace comprehended within that figure, may be confidered as fhadow, like Fig. X. But the fhadows of all the objedts will be either the whole, or elfe a part of the line 1 4. Again, by attending to the figure, we fhall perceive, that the length of the fhadow from the object a, reaches to 4 ; thofe of the objects 2 and 3, are terminated at 4 alfo : fo that the fhadow of the ob¬ ject 1 is longer than the fhadow of the object 2 ; and the fhadow of the object 2 is longer than the fhadow of the object 3. But the object 4 being placed directly in the meridian M N, it therefore can¬ not •’ late XXXIII. Fig. X. viz. by Fig. 4. The planes 1 * 4 - 5 6 7 s > arc l'uppofed to be parallel to each other, ai perpendicular to the ground, or indefinite plane 1.2.0 9. The plane 3 4 o 9, is a plane of rays of light ifi'uing fro the line 3 4 of the plane 1 234, fo as to interfedt the pla: 5678, as here in the line 7 8. Now becaufe the lines 3 7 8, are the common fedtions of thofe two planes, they a therefore parallel (Euc. 11. /6) And becaufe the’lines 4 3 7 are equal and parallel, therefore 34, 78, are alfo eqi and parallel (Euc. 1.33.) Now feeing the lines 13, 57, are parallel, the fidesof f triangles 3 i 9, 7 5 9, are proportional (Euc. 6. 2) therefc 95 : 9 I:: 57 :3 3 - for the fame reafun 06:02 9 8 : 2 4. And as 95:5706:68. But 9 5 is equal o 6 therefore 5 7 is equal to 6 8 ; and therefore 7 8 is equ and parallel to 5 6. And becaufe 9 5 is equal and parallel 06, therefore 09 is equal and parallel to 56, and alfo 7 8 ; whence it is m,unfed that the fhadow of the point 3 projected on the plane 5678 in the point 7, and tiiat of 4 the point 8 ; andtheref .re the line 7 8 is the proj dtion of 1 1 tlie original l:ne 3 4, when caft upon the paraf plane 6 7 8. Although what has been here advanced, with regard to fhadows projected on the ground, from objedts that are per¬ pendicular to the plane of the horizon, is true with relpedt to the bufinefs of perfpedtive; yet it is not to be inferred from hence, that, univerfally the fhadows fo projedted are right lines; for this, in mathematical ftiidtnefs, is otherwiie, the fhadow being in one cafe a right line, and in others is feme one of the comc-fedtions. For inftance, when the fun is di- redtly over the equator, the fhadow is projedted into a right line; but it is a parabolic curve, when the diftance between the zenith and the pole of the place is equal to the fun's de¬ clination ; and in other cafes it will be either an elliptical or hyperbolical curve. And here alfo it is to be farther obferved, that thofe curves will be concave to the objedt that calls the fhadow only when the latitude of the place, ar.d the fun's declination, are both of the fame name, that is, beth north, or both Couth; for when they are of different names, or one north and the other fouth, then thofe curves are projedted fo as to be convex to the objedt that produces them; but thele arc particularities that have no place in perfpedlive reprefenta- fons, but neverthelcfs neceffary to be mentioned' in this place. [ *7 ] not have any fhadow projected upon the ground. But this happens only in the torrid zone, for in this part of the globe, the fun is never vertical, and therefore there will always be a fhadow call: by him at noon ; though it will be then fhorter than at any other time of the day, and much more fo in the fummer than in the winter folflice. From hence we fee the reafon why the fhadows of objects are very long in a morning and evening, but fhorter and fhorter as the fun approaches it’s meridian altitude. There are three different directions in which the rays of light are fuppofed to come upon a picture, viz. 1. In a parallel direction ; in which cafe the fhadows will be parallel to the horizontal line like Fig. i. 2. When the light comes from before the picture, and confequently, falls upon the front of it; and then the fhadow is caft towards the horizontal, as in Fig. 2. 3. When the light is fuppofed to come from behind the picture, and fo projecting the fhadow towards the bottom of it; as in Fig. 3. If the fhadow upon a picture is to be obtained by example 1, then that fide of the objeCt only, which is towards the luminary will be enlightened, and the front part of it will receive what is called a half fhadow. And if the light is fuppofed to come from behind the picture, then the front fide of every objeCt will be wholly in fhadow; fince it cannot receive any other degree of light, than what is re¬ flected to it, from objects that are illuminated, and placed near to it. It is by this fecond rule, that the various degrees of light, and the directions of the fhadows, which are neceffary for reprefenting the effects of the rifing or fetting fun, and of moon-light, are to be determined ; for in other cafes an artift will not make this a rule for his light and fhadow, fince it muft neceffarily deftroy the whole effect of his picture. But it is the fecond example that I fhall particularly attend to; for it is this only which can fully anfwer my prefent purpofe: however, for the fake of regularity, I fhall juft fhew how to find the fhadows from each of the objects, Fig. 1, 2 and 3, and then tutn my attention wholly to the rule in the fecond figure. CASE I. When the light comes in a parallel direction. Fig. 1. Let I K be an object placed perpendicularly upon the ground, with the light falling upon the left hand, and projecting a fhadow in a parallel direction. From the bottom I of the object, draw the parallel I e ; and give any inclination for the light, as K g ; this being done, then K g cutting I e in g, will give I g for the fhadow of I K. The fame may be faid of the other inclinations of the rays of light, viz. K f, K e, K b and K a. N. B. T hefe inclinations, are drawn parallel to the rays A N, B N, &c, which fhews as above, the different lengths of the fhadow, and alfo that the fhadow will be of an infinite length when the fun is at A viz. when it is in the plane of the horizon. Observ. We may eafily comprehend the nature of this fhadow, by imagining either of the planes of rays, viz. I Kg, See. to be like the plane X, drawn upon the picture, as a triangular plane only that is the parallel to the eye; then confidering the perpendicular fide I K as the object; and the hypo- theuenfe K g as a ray of light cutting the bafe I g in the point g. And the fame obfervation will hold good as to the. two following cafes; fince the ray of light (which in both examples) produces the fha¬ dow of the object, is to be confidered as the hypotheuenfe of a right angular plane, which ftands perpen¬ dicularly upon the ground, but is obliquely fituated with refpect to the picture ; and for this reafon, the yanifhing point L of thefe rays will be fomewhere in the line S L, that is drawn from the vanifhing O point [ a* ] point S of the bale I k of the triangle I K k. In cafe 2, the vanifhing point L of the lays will be below the horizontal line; and in cafe 3 it will be above the horizontal line. The truth of all this is more fully explained in my former book upon this fubject. CASE II. When the light comes from before the picture. Fig. 2. Give I K for the object, whofe fhadow is fought; then from the bottom of it I, draw a line at pleafure (fuppofc to S.) From S let fall the perpendicular S L, and take the point L at pleafure alfo ; then from L draw a line to K, cutting I S in k ; and then the line I k is the fhadow of the line IK, &c. N. B. the plane X, annexed to this figure, is drawn to give an idea of the obliquity of the rays of light; which is exprefled by the plane’s being turned from the parallel line i 2. CASE III. When the light comes from behind the picture. Fig. 3. Through the bottom of the object draw a line, as before, to any point S in the horizontal line; draw alfo the perpendicular S L, and give the point L at pleafure; then from L draw through K to cut S k in k; and fo will the line I k be the fhadow of the line I K, Sec. Now that one rule only will in general be fufficient for a great variety of obje&s; and may, partly, be comprehended in the next figure. Fig. 4. To determine the fhadow of an Obelifk, 1. Find the feats of each of the upper corners A, B, C, D, as they are marked at the bottom with cor- refponding letters a, b, c, d. 2. From any point e, draw a line at pleafure to the horizontal line, and call S the vanifhing point of the fhadow. 3. Let fall the perpendicular S L, and take the point L at pleafure alfo; and call it the vanifhing point of the rays of light. 4. From L draw to C (which correfponds with c) and then is c b the fhadow of the line C c. 5. Do the fame from the other points a, d, b, See. 6. From the corners 2 and 4 draw lines to c and d; and from c through b to c; laftly, draw the parallel b d, which finifhes the fhadow. Fig. 5. In this figure I have attempted, not only to fhew how the fhadow on the ground is to be gradated, or made fainter and fainter the nearer it approaches the horizontal line; but alfo to adapt the peculiar degree, or tone of the fhadow to the peculiar colour of the parts 1, 2, 3, 4, 5, and 6. For this is a fundamental principle for producing a good effedl; but it being much eafier to conceive in theory, than to explain by pradtice, I fhall therefore only offer this hint upon it. From what has been already done, I fhall be enabled to proceed in a regular manner: and by putting the following fchemes under general heads, I fhall take in fome of the moft material cafes of light and fhadow, which we obferve in nature. In the firft place we muff confider the fhape and fituation of the object, whofe fhadow is wanted. And fecondly, the direction we propofe giving that fhadow, or which is the fame thing, the manner in which we propofe to make the light come upon the pictures. Now the three following examples will give a more perfect idea of thefe particulars. EXAMPLE c 2 9 ] EXAMPLE, I. Plate XXXIII. Fig. i. To find the perfpective reprefentation of the Ihadow, call by the parallel object A B D F, when the Ihadow vanilhes into the center C of the picture. 1. Letab (Fig. A) be confidered as A D (Fig. r) andletbe (Fig. A) be called a ray of light, pro- jecting the ihadow a e. 2. Any where apart, draw the line 2 3 at pleafure, but parallel to the horizontal line; in the fame manner draw the perpendicular 2 1 ; and at the point 3, with the line 2 3, make an angle equal to the inclination of the rays of light (that is equal to the angle b, Fig. A) then draw 3 I, cutting,2 in the point 1; and then is the triangle 1 2 3 fimilar to the triangle eab; and confequently the angle at 3 Ihews the inclination of the rays of light; that is the height we fuppofe the fun to be above the horizon. 3. From C (the vanilhing point of the Ihadow) let fall the perpendicular C L, and give CE for the diflance of the eye; then from E draw E L parallel to 3 1, cutting S L in L; and then is L the vanilhing point of the rays of light. § 4. Draw from B to C, and from F draw a line to L; and then is B f the ihadow of B F. Again, draw a line from A to C, and another line from D to L, which will give the point d, and thereby the line A d for the Ihadow of the line A D : and by joining d f, the whole ihadow will be finiihed. Observ. 1. Remember that this ihadow is obtained by twice repeating the rule in figure 2, plate XXXII, viz. by firil finding the ihadow of B F, and then of A D. Obsepv. 2. Becaufe the top D F of the objedt is parallel to the horizontal line, therefore the ihadow of it, viz. d f, will be parallel to the horizontal line alfo. Observ. 3. When the ihadow vaniihes into the center of the pidture, as in this figure; then the light comes from dire&ly before the pidture; and then the Tides, or parts of objedts, which tend to the cen¬ ter C will he enlightened ; hut the front fides will be the lighteft. EXAMPLE, II, Fig. 2. For the ihadow of a parallel objedt A BDF, when it does not vanifh into the center of the pidlure, but into any other point, as S. 1. Draw B S, and then the perpendicular S L at pleafure. 2. From the center C of the pifture, draw the perpendicular CE, and call C E the diftance of the eye ; then draw SE, which is the diftance of the eye from the point S. 3. From S, with the radius S E transfer the diftance to E 2 ; and at E 2 give the angle of inclination for the fun’s rays, and drawEaL, cutting S L in L ; then isL the vanifhing point of the rays of light. 4. Draw a line from F to L, cutting B S in f; and then is B f die fhadow of B F. In the fame man- ner find the fhadow A d of A D, and then join d f. Observ. From this, and example 1, we may conceive how the lhadows will encreafe or decreafe in length, as the point L is nearer to, or farther from the point S; for which reafon it is neceffary to make this point at fuch a diftance as will prevent the lhadows being either too fhort or too long. Observ. 2. And from hence alfo it follows, that the vanilhing point S of the Ihadow, fhould be carried at a confiderable diftance out of the pidure, fince by that means the various lhadows projeded upon it, will the better correfpond with each other- P EXAMPLE § See Dr. Brook Taylor's Periledive made eafy, &c. Book i. chap 5. fed. 1. lemma. 3. 7 [ 3 o ] EXAMPLE IH. Fig. 3. For the fliadow of an objedt A D F B that vanifhes into the center of the pidfure. 1. Draw at pleafure a line from one corner A, to the horizontal line at S. 2. From S let fall the perpendicular S L, and find the point L as in the laft example. 3. Draw a line from E to S, and alfo from D and F to L, cutting A S in d, and B S inf; then join d f, which compleats the fliadow. Observ. Since the top D F vaniflies into the center of the pidurc, therefore it’s fliadow d f will vanifh into that point alfo. This is fufficient for flawing how the fliadow, that is call upon the ground by any upright objeft, is to be determined upon the piftuie. For let it be ever ib complex a figure, we have nothing more to do than to find the'feats, or plans of fome principal points in the perfpeaive, as a, b, c, d, Fig. 4 of Plate XXXII; and then proceeding in a regular manner, by finding the fliadow of one point, or line at a time, till the whole be compleated. All which will be made very obvious in the courfe of this work. example:, IV. Fig. 4. For the fliadow of an upright objeft A B, when part of it is call: upon a wall F D, that intercepts it from the ground. 1. Give the points S and L at pleafure, and then draw A S cutting the bottom of the wall in i ; then from 1 draw the line 1 b parallel to A B ; or, which is the fame thing, perpendicular to the bot- tom of the wall. 2. From B draw to S, cutting i b in b; then is b the fliadow of the end B, and confequently a i b is the whole fliadow of a line A B, &c. In like manner, F e is the fliadow of F E ; and e d is part of the fliadow of the top E D, which is alfo parallel to it. If the wall was wholly taken away, then A a would be the fhadovv of A B. Observ. From hence we may fee, how any other fhadows, that are call; by fimilar objedts upon up¬ right planes, may be determined ; fince nothing more is required than a repetition of the fame rule; which is fully exemplified in the five following figures. EXAMPLE V. Fig. 5. For the fliadow of an objedt A B, when the light comes as in the laft examples; and to determine that of the crofs-piece at the top, viz. E D. 1. Find the fliadow A i b of A B, as before diredted. 2. Through A draw the perpendicular A 3, and make A 3 equal to B E ; then from 3 draw 3 2, cutting the bottom of the wall at 2. 3. From 2 draw 2 e parallel to 1 b, and from E draw to L, cutting 2 e in e; then is e the fliadow of E, therefore draw a line through e b, and continue it at pleafure; draw alfo a line from D to L, cutting e b continued in d; and then is e d the fliadow of E D. Observ. Since E D is parallel to the horizontal line; therefore the fliadow of it, e d, will be pa¬ rallel to the horizontal line alfo. EXAMPLE VII, VIII, IX. Fig. 7, 8, 9. It is quite needlefs to fhew how to determine the fhadows in thefe figures, becaufe one glance of the eye will fhew, that all of them are deduced from the laft example ; and the correfponding letters will point out the peculiar ftndow of each point, See. Plate [ 31 ] Observ. In Fig. 5, the line A B may be considered as a column, and D E as the abacus of a capital. In Fig. 7 I had an eye to a colonnade of two columns, with an architrave over it. Fig. 8 Shews the manner by which the Shadow of an angular pediment is to be obtained : and Fig. 9 points out the me¬ thod for determining a Shadow from the circular pediment. EXAMPLE, X. Fig. 6. For the Shadow of an upright objed, when it falls upon more than two planes; and to find the Shadow of any part of it; and alfo how to determine the Shadow of the whole figure upon the ground. 1. Draw a line from A to the horizontal line S, &c. cutting the bottom of the Slop in 1 ; then from 1 draw 1 2 parallel to A B; and from 2 draw to S, cutting the bottom of the wall in 3 ; then from 3 draw 3 b parallel to A B, and draw from B to L, cutting 3 b in b, which gives A 1 2 3 b for the whole Shadow, as was required. Again ; If from any points in A B, we draw lines to L, their interfedions with the Shadow already drawn, will determine the places of thofe points. EXAMPLE, XL Plate XXXIV. Fig. 1. For the Shadow of a parallelopipedon A F, as it is caft upon a wall. 1. The points S and L being taken at pleafure; draw from the lower corner A to S, cutting the wall in 1 ; and from 1 draw 1 b parallel to AB; then draw from B to L cutting 1 b in b ; and then ' will Aib reprefent the Shadow of the line A B. 2. From the other corners, as D, proceed in the fame manner, and find the Shadows e and f of E and F ; then join e f, and f b, which finishes the Shadow. Observ. i. All Shadows that are call by lines (or the edges of objects; upon planes parallel to therm will be parallel to thofe original lines; thus 1 b is parallel to A B; and e f is parellel to E F. Observ. 2. The Shadow e b of the fide E D that vanishes into C, will be parallel to the line L C, which is drawn from the vanishing point C of the object to the vanishing point L of the rays of light. N. B. Thefe two obfervations will be of great ufe in moft of the following figures. EXAMPLE XII. Fig. 2. For the Shadow of a cylinder upon a wall. 1. Give the points S and L ; then make any number of points on the top of the cylinder, and find the feats of thofe points by means of the dotted lines as in the figure ; thus A is the feat of B, and D is the feat of E, &c. 2. From A draw to S, and from B to L, &c. which gives b for the fnadow of B; the fame done from D and E will produce the point e ; and by repeating the operation quite round the figure, we lhall obtain the Shadows of all the points marked on the top of the objed; and from thence be enabled to draw die curved line as in the figure ; which will reprefent the Shadow of the top of the cylinder as projeded on the wall. The whole Shadow is expreSTed by Shading, &c. Observ. If we would find the Shadow of a circle only, (fituated like the top of a cylinder) we mull £rft find the feats of any number of points on the top upon the ground, and then proceed as above. EXAMPLE XIII. Fig. 3. For the Shadow of one cylinder, caft upon another; when the light comes in diredly before them. Find the feats of the points A, B, D, &c. Q_ 2. From [ 32 ] 2 From the feat i of the point A draw to C, cutting the bottom of the cylinder in 2 ; then from 2 (if need be) draw the line 2 a at pleafure, but parallel to A i ; and then, as before, A L gives the point a for tire fhadow of the point A ; and i 2 a for the lhadow of i A. 3. Repeat the operation quite round the figure, and fo obtain the perfpediive of the whole fhadow, as is expreffed in the figure : where the correfponding letters mark the fhadow of each point, and confequently the curved line that is drawn through them, will be the fhadow of the top of the cylinder, &c. 4. A line drawn from K to L, gives the fhadow k of K. on the ground, &x. Obsekv. In both the laft figures, the dotted lines drawn from the tops of the cylinders to L, may, in home meafure, give an idea how the cone of rays is interfefled by the plane that receive the fhadow. EXAMPLE XIV. Fig. 4. To determine the fhadows of Cylinders, when the light comes in a fianting diredion; and alfo of Soffit, or board laid upon the top of the Cylinders; and likewife to find the fhadow upon the ground. N. B. the cylinders vanifh into the center of the pidure, and the width of the board upon them is equal to the diameter of the cylinders. 1. From C, draw lines to touch the outer parts of the bottom of the firft cylinder at 6; and that part of it, which is between the cylinders, will reprtfont the feat of the board upon the ground. 2. From S draw a line to touch the bottom of the fartheft cylinder at 4, and alfo to cut the line 7 1 in the point i. 3. Then from i draw the perpendicular i B, cutting the outward edge of the board in B; then from B draw a line to L, and the line 4 b parallel to iD; and then is b the fhadow upon the cylinder of the point B; and the line 4 b determines the part where the upright fhadow meets the light. 4. Find the feat 2 of the point D, and from 2 draw to S; then from 3 (where 2 3 cuts the bottom of the cylinder) draw the perpendicular 3 a, and then draw a line from D to L, cutting 3 a in a.; fo will a be the fhadow of D; therefore draw a curved line through the points b, a, meeting the foffit; which will be the fhadow required. For the fhadow upon the ground. First, find the feats of the four corners of the board (as 5, which is the feat of A) then draw 5 S, and then A L gives d for the fhadow of A. In the fame manner find the fhadows of the other corners of the board, and draw lines from S, fo as to touch the bottom of the cylinders, as in the figure. Observ. Here the fhadows of the fides of the cylinders vanifh into S ; and becaufe the fides of the board vanifh into C, therefore the fhadows projected by them will vanifh into C alfo; but the ends of the board being parallel, will caft fhadows which are parallel alfo. EXAMPLE XV. For fhadows that are projected, either upon the concave or convex fide of a Cylinder. Firft, for the convex fide. Fig. 5. The figures that projedt the fhadows are X and Z. Now, from the preceeding examples it is evident, that the fhadow of the edge A B of the objedt Z, is A 1 b ; which with the other parts of the fhadow are obtained by one and the fame rule, viz. Fig. 4, plate 33. Secondly, for the concave fide. Fig. 6. Here the concavity of the objedt makes no alteration as to the rule, nor yet in the appli¬ cation of it. EXAMPLE EXAMPLE, XVI. For the fhadow of a perpendicular Plane A F, joined at right angles to another that is parallel to the eye; and to determine the appearance of the light when it paffes through a door, or window. Firft, for the perpendicular Plane. Fig. 7. From the corner A draw lines to S, See; and from G to L will give the fhadow g; therefore join g F, which is the fhadow fought. Or having drawn 4 g at pleafure, then from L draw through C, and then a line from F parallel to L C, which will give the fhadow F g of F G. Secondly, for the door. Draw lines from the bottom, then perpendiculars from 3,2 ; and lines drawn from D, E to L will give the fhadow e d of E D ^ therefore join e d. Here e d is parallel to L C; for E D vanifhes intoC„ Observ. This example is of ufe in finding fhadows that are proje&ed into rooms, &c. EXAMPLE XVII. For the fhadow of an horizontal Plane when it is joined to another at right angles, &c. Fig. 8. From L draw a line through C the vanifhing point of A B, and from A draw to L, then from B, a parallel to L C cutting A L in a ; then is a B the fhadow of A B ; and another line a d drawn from the point a, and parallel to A D, will give ad, for all the fliadow of A D that can fall upon the plane B d. And for the fhadow upon the ground : here 1 and 2 are the feats of A and D ; and the fhadow of D is the point 3, 8cc. EXAMPLE XVIIL For a variety of fhadows, which will be more particularly applied in feme of the following examples. Fig. 9. Firft, for the fhadows of three perpendicular objeds, A B, G E, H F, as they are projected on different planes. 1. Draw from A to S, and then from B to L will give b for the fhadow of B. Or from D draw a parallel to L C which will give D b ; and the fhadow of E B likewife. 2. A line drawn from G to S, 8cc. and another fromE, gives e for the fhadow of E; and e 3 G for the whole fhadow of G E. 3. From H to S, &c. and from F to L will produce f for the fhadow of F; and f 4 H for the fliadow H F. Secondly, for the fhadow of the line EF. The point e is the fhadow of E, and f is the fhadow of F; and fince F E is a parallel line, therefore its fliadow e 6, which falls upon a parallel plane, will be parallel alfo ; and another part of the fliadow is obtained by joining f 6. Or the vanifhing point of the fhadow f 6 may be found thus, viz. from C (the vanifhing point of the plane P R S O) let fall the perpendicular C M at pleafure, and from L draw a parallel M L, cutting CMinM; and then is M the vanifhing point of the fhadow f 6. Thirdly, for the fhadows projeded by the fide E N, and top N O of the figure. Draw from Qjo S, and from 2 the perpendicular 2 n at pleafure ; then a line from L to N, &c. will give n 2 Q^for the fhadow of N Q; and e n will be the fhadow of E N : and fince n is the fhadow of N, therefore the parallel e C will be part of the fhadow of E B, and the parallel n 5 will be part of the fliadow of O N, but the other part, viz. O 5, will vanifh into M. R Observ. C 3+ ] Observ. Tliis figure is calculated to anfwer many ufeful purpofes, and therefore the learner will do well to undcrfiand it pcrfedtly. EXAMPLE XrX. Plate XXXV. Fig. i. For the fhadow of a fquare objedt call upon a cylinder. Take any number of points on the under part of A B (for it is this edge which projects the fhadow) and draw lines to S ; and from where thefe lines cut the top of the cylinder, draw lines parallel to L S ; then from the feveral points on A B draw to L, which will feverally cut the upright lines, and thereby deter¬ mine the fhadow of each point on the cylinder; fo that by drawing a curved line, as in the figure, we fhall obtain what was required. Observ. r. The fhadow of this figure is projected on the ground, and the correfponding letters will point out that part of it which is cart by the fquare; and lines drawn from S as tangents to the bafe of the cylinder will produce the fhadow of that body. Observ. 2. If the point S was far removed from the fide of the cylinder, then the fhaded part of it would be much broader than in this figure; and if S was brought nearer to the cylinder, the fhadow would be narrower: but in all cafes, the line drawn from S, fo as to touch the bafe, will determine the breadth of the fhadow; that is, this point of contadl will always be the darkeft part of the fhadow. From whence it follows, that thefe kind of fhadows will appear proportionably broader or narrower, as the rays of light have a greater or lefs degree of obliquity with refpedt to the point of fight; and that when, the light comes upon the pidlure, from diredtly before it, then the fides of the object will receive only a half fhade, which, on both fides, will be equal. See the bafe of a column, Fig. 3, Plate XLV. EXAMPLE XX. Fig. 2. For the fhadow of the top of a wall that is placed againft a cylinder. 1. Take any points r, 2, 3, 4, on the top of the wall at pleafure, and draw the upright lines as in the figure. 2. From the correfponding points at the bottom, draw lines to S, cutting the bottom of the cylinder, where mark every interfe&ion with correfponaing figures; from thofe points draw the upright lines upon t. e cylinder, and continue them at pleafure; then from the points on the top of the wall draw to L, cutnug the upright lines on the cylinder, in the points 1, 2, 3 ; and then will 1 on the cylinder be t .c fhadow of 1 on the top of the wall, &c. Laftly, through the points 1, 2, 3, draw the curved line as in the figure, which will be the fhape of the fhadow, See. Observ. i. The fhadow of the point 4 on the wall falls within the fhadow on the cylinder, and therefore it has no reprefentation. The fhadow of the point 3, falling near the fhadow of the cylinder, gives that part of the object but a fmall degree of light, which we exprefs by the term half-fhadow. The fhadow of the point 2 marks that part which is the next to the higheft, or principal light, at the point 1 : fo that from hence we may conceive the gradation of light into fhade, &c. Observ. 2. As there is a gradation of light into fhade, fo, vice verfa, there is alfo a gradation of fhade into light. For as I obferved before, the darkeft part of the fhadow will always be above the point A, where the line drawn from S touches the bottom of the cylinder, and it will from hence gradate both ways, viz. on the right hand into light, and on the left hand into what is called a reflexion ; all which I have endeavoured to illuftrate by the finifhed examples of this kind, and have particularly attended to it in the ihafes of the columns already produced. Thefe are very ufeful hints for practice, and [ 35 ] and will moreover confirm what Mr. Hooarth has advanced, in his Analyfis of Beauty, upon light and fhade; where this very ingenious author has treated this part of fcience with the ftriaeft truth, good fenfe, and perfpicuity. Observ. 3. If we fuppofe the wall to be of different heights, as expreffed by the lines drawn acrofs it to C, and the fituation of light to remain the fame ; then the fhape of the fhadow, caff by the top of the wall upon the cylinder, will be varied by every different height. And if a line be drawn from L through C, and then the different fhades projeded, (viz. by the fame rule as the above example) we fhall find that all the fhadows above L B will bend upwards, and all thofe which are below L B will bend downwards; and they will have a greater or lefs degree of curvature, as they are farther off, or nearer to the line L B. But when the line L B is even with the top of the wall, then the fhadow will be projected into the direction of L B, and will therefore be a ftrait line. EXAMPLE XXI. Fig. 3. For a fhadow caff on the concave part of a cylinder, from any part above it. 1. Suppofe A B a flick over the top : make any number of dots in it, and draw lines from thofe dots to S, cutting the top of the cylinder ; and at thofe interfedions make other dots as in the figure. 2. From the dots on the top of the cylinder draw the upright lines, and then from L draw other lines to the dots on the top of the flick; and laftly, the curved line from a, through c to b, which will give the fhadow for the flick ; and fince b is the fhadow of B, therefore b d is the fhadow of B D, &c. 3. For the fhadow that is caft on the cylinder by it’s own top, viz. the fpace between 2 and B. For this, draw from any points as 3 4. to S, cutting the top in two other points towards the right hand ; then from thofe laft points, draw the two upright lines as in the figure, and then draw from 3 and 4 to L, which will cut the upright lines, and thereby give the points for drawing the fhadow of this part. EXAMPLE XXII. Fig. 4. For the fliadow of a round and horizontal plane, as projeded upon a cylinder. Make points on the under edge, as before ; and draw to L, cutting the top of the cylinder; from the points thus obtained, draw the upright lines, and then from L to the points that caft the fhadow, which will produce points on the cylinder, and through them the fhadow is to be drawn, 8cc. Observ. If the line D B reprefents a column, then f c is the fhadow of it. EXAMPLE XXIII. Plate XXXVI. Fig. 1. The application of fome of the foregoing examples. If the reader turns back the laft plate, Fig. 2, he will at once recoiled almoft the whole of this ope¬ ration ; and I have repeated it here to fhew the conformity between the outlines and the finifhed example. But I fhall fhew how to determine the fhadow within the hollow building. From D to S cuts the bottom in g ; draw the perpendicular g e, then a line from E to L will give e for the fliadow of E ; and by joining e f the fhadow will be compleated. In the finifhed figures, I have fhewn how to reprefent either a ftone or a brick wall, and have endea¬ voured at giving each part it’s proper tone of light, fhadow, and reflexion. Observ. i. The neareft edge of the brick-wall, and alfo the neareft part of the fhadow in the hollow building, muft be proportionably darker than thofe parts of them which are farther off; and for the fame reafon that the apparent fizes of objeds are diminifhed in perfpedive in proportion to their diftance from the eye. In like manner, the bottom of the brick-wall will be of a lighter fhade than the top of it, S becaufe '[ .36 ] becaufe the bottom being nearer to the ground that is enlightened, will receive a greater quantity ol refledted light, than thofc parts which are farther from it: but the fhadow in the hollow building will have nearly the fame tone of colour at top and bottom; for being almoft wholly oppofed to other fhadows, it can receive but a fmall degree of reflected light. Observ. 2. As the colour of fhadow grows fainter and fainter, in proportion to its diftance from the eye, fo on the contrary, the enlightened parts of objedts mull be perpetually diminifhed and made darker and darker as they are made to recede from the bottom of the pidture. And if a line be drawn from the nearefl part of any objedt that is turned towards the light, to the fpedlators .eye, it will determine where the higheft or ftrongeft fhould be placed. Observ. 3. When the objedt is fo placed as to have one part of it in light, and another part wholly in fhade (like the bottom of the cylinder in the laft example) then the right hand fide of it, which is op¬ pofed to the fhaded wall, mull be darker than the left hand fide of it, which is towards the enlightened wall: and the reafon of this is obvious from what was obferved above. But if both the walls were taken away, and the lower part of the cylinder received a fhadow in this manner from fome diftant objedt, as a cloud, or the like, then the middle part of the fhadow would be the darkeft, becaufe that is nearefl: to the eye, and therefore will appear flronger than thofe parts which are farther ofl. Of this we have an example in the finifhed figure, Plate XXXVII. From hence we fee the reafon of that well-known rule for the management of fhadows, viz. to make that part of any fhaded object the darkeft, which if placed in the light is the moft ftrongly illuminated. This may be better conceived by refering to the finifhed examples of the mouldings, Plate XL 1 V. EXAMPLE XXIII. For the heights of two fhadows, that are caft by fimilar objedts, or by parts which have the fame projections Fig. 2. Find the fhadows a and b of the point A, B, as before directed; then through a and b draw the parallels, as in the figure. Observ. i. Since the object B is nearer to the vanifhing point L, of the rays of light, than the object A, therefore the fhadow caft by B will not be fo high as the fhadow caft by the object A; for were we to remove B, fo as to be even with L, that is, to be as low as L, then the fhadow would be a ftraight line. Observ. 2. This method will ferve univerfally for all foffits, and is frequently applied in the fore¬ going examples. EXAMPLE XXIV. For the fhadows of feveral Cylinders, &c. Plate XXXVII. Fig. 1. Draw lines from S fo as to touch the outfide of the bottom of each cylinder for the breadth of the fhadow; and then we fhall find that the fhadow of the cylinder A falls upon the cylinder B, and the fhadow of the cylinder D will be projected upon the wall. But the board over the cylinders will caft fhadows upon different parts of the figure ; which we will now attend to ; though this is partly explained already in the 14th example, to which we refer the learner for the manner of drawing the fhadow upon the cylinder B, &c. The fhadow of the cylinder D is caft upon the wall, and the point q fhews the fhadow of its top; and the fhadow of the corner of the board is at the point 8, therefore the line 8 7 is the fhadow of the end of the board, and it is parallel to L V. Now, fuppofe the cylinder D was taken away; then the cylinder E would receive a fhadow from the foffit, which we determine by our former rule, thus; viz. find the plan of the edge of the board as re- pjefented at the bottom by the line 4 8, then, from S draw any lines through the bottom of the cylinder to [ 37 ] to cut the bottom of the board in the points 4, 5, 6 ; and from thefe points obtain the correfponding points at the top, viz. 4, 5, 6 ; then draw the upright lines upon the cylinder, and from the upper points 4, 5, 6, draw the top of the cylinder ; by which means the curved line may be drawn for the fhape of the fhadow, See. EXAMPLE XXV. Fig. 2. This figure contains a particular application of Fig. 9, in plate XXXIV; and all I fhall add to it is the method for finding the fhadows caft by pediments. First, for the angular pediment. Let the pediments be conftrudted only of a board, as that is moft proper for fhewing the applica¬ tion of the rule, and will be fufficient for the prefent purpofe. From the top d of the pediment, and from any other point a, draw a line to S; then draw the upright line c b, and from a, d draw to L, cutting b c in c ; and then is c the fhadow of the point a ; laftly, from e draw a line parallel to the other fide of the pediment, which compleats the fhadow. Secondly, For the circular pediment. Take any points on the top of the pediment, and proceed as above; and fo fhall we obtain the curved line for the fhadow; as in the figure. The two finifhed examples in this plate, are defigned as farther illuftrations of what we have advan¬ ced ; particularly in the oblervations upon the 23d example. EXAMPLE XXVI. Plate XXXVIII. Fig. 1. For a fhadow that is caft within a fquare entrance. Draw a line from A to S, cutting the bottom B 1 in 1 ; from 1 draw the upright line, and from D to L will give the point d for the fhadow of D, therefore join D E, and then is A 1 d the fhadow of A D ; and d E is likewife the fhadow of D E. Observ. If a perpendicular C K be drawn through C (the vanifhing point of the fide 1 E) then a parallel from L (the vanilhing point of the rays of light) to ,cut C K in K, will give K for the vanifhing point of d E. EXAMPLE XXVII. Fig. 2. For the fhadow caft by the jambs of a door, window, or the like. Draw a line from A to S, cutting the bottom of the wall in 1 ; then draw from B to L, which gives b for the fhadow of B ; laftly, draw the parallel b e. EXAMPLE XXVIII. Fig. 3. For the fhadow of an opening, with an angular top. From A draw a line to S, cutting the bottom edge in 1, and from 1 draw the upright line; then from B to L will give b for the fhadow of B ; and A 1 b for the fhadow of A B. Again, through C (the vanifhing point of the fide 1 F) draw the perpendicular E M; and through L draw the line L< M parallel to the edge E B, whofe fhadow is fought; and where L M cuts C M, will be the vanifhing point of that fhadow; therefore from M draw a line through b at pleafure ; and alfo from L draw to E cutting be in e ; then is e the fhadow of E, and e b is the fhadow of E B. Again, from L draw ano¬ ther line L N parallel to the edge E F (which cafts another fhadow) cutting CM in N; then is N the fhadow of F e, therefore draw F e which is the fhadow of F e. m- ji jij T The [ 3 * ] Here arc two finifhcd examples, and likewife a nich properly fhaded. EXAMPLE XXIX. Plate XXXIX. Fig. i. For the fhadow of another opening, having it’s top conftrucfted of three parts. 1. From A draw to S, and from i the upright line i d •, then continue the perpendicular CN down¬ wards at pleafure, and from L draw a line parallel to E D, cutting the perpendicular C N, and this point (which is out of the picture) will be the vanifhing point of d 2. 2. From L draw a parallel to E D, and from C another line parallel to F G; then the interaction of thofe two lines will determine the vanifhing point of the line 2 e; and fo likewife a line drawn from E to L will give e for the fliadow of E, and confequently d 2 e is the fhadow of D E. 3. From L draw L N parallel to F E, cutting C M (the parallel of G F) in M ; and then is M the var filing point of the fliadow eF, which is caft by the edge E F. J E X A M P L E, XXX. Fig. 2. For the fhadow of an arch that falls partly upon itfelf, and partly upon a door, wall, or the like. 1. Take any number of points a, b, d, See. on the circular part, and beginning at the bottom a or k. of the arch, find their feats on the line A H by perpendiculars; as in the figure. 2. From A, B, See. draw to S cutting the bottom of the wall in the points 1, 2, 3, 4, and the fide of the arch in 5 and 6 ; then from thofe points draw upright lines, as before. 3. From a, b, d, on the top, draw lines to L, which will give a, b, d on the door for the fhadows of a, b, d on the top of the arch; therefore draw the curved line to join the fide of the arch, as in the figure; and fo flial] we have drawn all that part of the fhadow which is call upon the door. Now, fince the plane which receives the fliadow, viz. the door is parallel to the front of the arch which projects it, Therefore the fliape of the fhadow upon the door will be fimilar to the arch; but the other part of the fliadow being caft upon a plane not parallel to that which projects it, will therefore have a degree of curvature, as reprefente.d by the line which is drawn from g to 6. And in order to obtain this, I mud firft fhew how to determine two perpendicular planes, which I imagine to Dafs through the arch, and to interfect each other. The one is F f 1 x 5, whofe bottom F5 vanifhes into S ; the other is I i p 4, which vanifhes into C. Now fince all I fhall advance upon the fhadows of this kind will be performed by the application of thefe, or fuch like planes ; it is therefore neccfiary for the learner to make himfelf a perfedt mafter of this article before he proceeds any farther. And as this is an abftrufe and very difficult part of projection, and is moreover what has not been confidered before, a little prolixity in this place will be pardoned by the curious and ingenious reader : but to proceed. Now if the dotted plane F f f x 5 be once obtained, and the line drawn on the fide of the arch from 5 (at the bottom) to f on the top of it, then this line will be the fection which the plane makes with the back part of the arch ; and therefore a line drawn from f at the top of the arch, to L the vanifhing point of the rays of light, will (by the former rules) give the point f (within the arch) for the fhadow of the point 1 (on the top of the arch) and by thus obtaining the fhadows of feveral other points, we fhall have guides for drawing the curved line that is to reprefent the fliadow. But I have not fhewn that f f o x is a lection for nearly fo) with the top of the arch, and therefore we will now attend to that article only. 1. From + ^ have not attempted to fhew how to draw thefe kind artift to difpofc the light and fliadow in a pidture to afufficient oflhadows, fo as to fiend the telt ot a very ftridt demonftra- degree of exadtnefs; or at leaft for avoiding errors ol this tun; tor I am not advancing a fyftem of mathematical kind, fo frequently to be met with in the works of the be# .pr-cjcdion, but only luch rules lor pradticc as may enable the mailers. [ 39 3 1. From any point i on the top, draw to C, cutting the infide of the top of the arch in p. 2. From i and p let fall the perpendiculars to I 4, and draw 1 4 to its vanifliing point C, cutting F 5 in 7 , and from 7 draw the perpendicular 7 o; then is lip 4 a plane which vanifhes into C, interfering the former, or dotted plane in the line 7 o, and confequently the point o is in the fedion which this latter makes with the former plane ; and therefore is one point in the curved line ffo x. 3. And by drawing a regular curved line from f through f to x, we fhall have the fedion which was wanted to a fufficient degree of exadnefs. If one point, as f, fhould not be thought enough for this purpofe, more may be obtained in the lame manner, viz. by drawing other lines between F G and G I to C, and then building planes upon them, like I i p 4 ; which will give other fedions on the dotted plane, and confequently more points for draw¬ ing the top of the curve, &c. And by proceeding as above, with the lines D 3, G 6, we fhall likewile obtain the points e and g within the arch ; and then by drawing the curved line 6 e f g, and continuing it with an even degree of curvature, we fhall lee where the light goes off the arch (or where the lhadow begins) and thereby com pleat what was required. Observ. Here we muff obfcrve, that the dotted plane (which in this and the two following figures we confider as a plane of rays) muft be taken on the right hand of the point D, and at a convenient diftance from it; for were this plane to be taken at D, or on the left hand of D, it would not be of any ufe for the curvilinear part of the lhadow ; becaufe the lhadow on that fide of D, &c. are projected upon the flat wall, or door. And I may farther remark, that the lhadow upon the door may be eafily determined thus, viz. find the lhadow a of the point a; then draw the parallel a q, and from the middle of the arch at D draw a line to S, cutting the bottom of the wall in 3 ; then draw the perpendicular 3 q, cut¬ ting a q in q, which will give q for the center, and a q for the radius of the lhadow a b d 6. EXAMPLE XXXr. Fig. 3. For the lhadow which falls wholly upon the inlide of an arch. 1. Take any number of points on the top of the arch (as in the former example) afid find their feveral feats on the bottom, viz. on the line A FI; and from thofe feats draw lines to S, cutting the bottom of the fide of the arch, as expreffed by the dots on H 6. 2. Draw lines from the points on the top of the arch to C; and from the dots on H 6 draw the up¬ right lines, cutting the bottom h 7 of the crown of the arch. 3. From the points A, B, D, E, F, G, draw lines to C, interfering all the lines which were drawn from thofe points to S, and mark thofe interfedions as in the figure. 4. From the points on A 7 draw upright lines, cutting the lines before drawn from the top of the arch to C, in the points 1, 2, 3, 4, 5, 6; then will thefe figures correfpond with the fame figures at the bottom, and will all be in the fame plane; and therefore a curved line drawn through thofe dots on the top, as in the figure, will compleat the plane Aaz 123 45 67, which paffes through, and interfeds the fide of the arch in the line drawn from the bottom at 7 to the top of the arch at a ; and confequently a line drawn from the point a to L, will give a, within the arch for the fliadow of a, upon the top of it. 5. In the fame manner proceed with the other lines drawn between A, H to S, till you have obtained all the curved lines, as drawn within the arch ; and then other lines drawn from b, c, d, on the top of the arch to L, will give the points b, c, d, within the arch, therefore draw the curve from a to b, which will be the fliadow of that part of the arch which is contained within the fpace a b. U 6. Draw [ 4° ] 6. Draw a line from e to L, which pafles over, or but juft touches the curved line within the arch, and therefore the light at this point enters the arch, and confequently, if the curved line for the fhadow be regularly continued from d to e, we fhall have drawn the whole fhadow. Observ. If we confider a a, b b, c c, d d, as chords of fevered arches, we may then conceive the manner in which four different planes pafs through, and cut the crown of the arch ; and alio fee how they are perpetually diminifhed in proportion to their degree of diflance from the chord a a of the firff arch a 7 6, &e. The dotted plane at F, lhews that no fhadow can fall from the point f, becaufe a line drawn from f to L cannot pafs through any part of this plane ; and it expreffes alfo (as was obferved above) a plane of rays. EXAMPLE XXXII. Fig. 4. For the fhadow of a nich caft within infelf. 1. Take any points on the top of the nich, and find their feats on the bottom line A L as before. 2. With the lines g e, h d, i c, k b, 1 a (as fo many given diameters, for finding the perfpedive of circles) draw the femi-circular horizontal planes, as in the figure ; and do the fame with the corref- ponding diameters at the bottom : now the perfpective of the femi-circles at the bottom of the nich will be the feveral plans, or feats of the correfponding femi-circular planes, which are drawn in the crown or top of the nich ; and, if a perpendicular plane whofe vanifliing point is S (viz. that which is dotted) be built upon the line F 5, it will cut the above femi-circles in the correfponding points 1, 2, 3, 4, 5, both at the bottom and top of the nich, and therefore the curved line from f to 5 will be the fedion, which this dotted plane makes with the crown of the nich, and confequently a line drawn from f to L, will fall within 'the dotted plane; and cut the fedion in f, and thereby give f for the fhadow of f above it. 3. By repeating the operation with perpendicular planes, built on the lines, drawn from G, H, T, K, L, viz. on the left hand of F, we fhall obtain the other points 1 , k, i, h, g, for the fhadows of 1 , k, i, h, g, on the top of the nich ; and therefore a curved line drawn through thefe points to f, will give fo much of the fhadow as is projeded by the part of the arch between 1 and f. 4. I x like manner a plane built upon the line from E, will give e for the fhadow of e; and another upon the line from D, will produce the fhadow of d; and confequently, the curved line being regularly continued through e and d, will not only compleat the fhadow, but likewife fhew, or determine the point upon the top of the nich, where the light enters into it; or, if you pleafe, the beginning of the fhadow. Observ. 1, In the two former examples, the fhadows on the middle of the arches were obtained by the interfedions of two perpendicular planes; but in this figure I have determined the points for draw¬ ing the fhadow by one perpendicular plane, and a fedion made with it by horizontal planes. Observ. 2. The inclination of the fun for this fhadow is only 30 degrees; and I have likewife added the fhapes of three other fhadows, as projeded by the nich, when the fun is at different heights from the horizon ; which inclinations are fpecified on the figure ; and when the fun is in the meridian, and fo fituated as to fhine diredly into the middle of the nich, then the fhadow will be a curved line bending downwards. 03 serv. 3. Thefe three laft examples will point out the errors that have been generally committed in reprefenting the fhapes of thofe kind of fhadows; and a careful obfervance of thofe things in nature v/ill amply confirm the truth of what I have advanced ; and although I have not attempted to demonftrate ; thefe projedions by mathematical reafoning, they will, upon a nice examination, be very near to the truth, and [ 4i ] and may give hints to a curious mathematician for extending this part of fcience much farther. What I have done is fufficient for the prefent purpofe, and an attempt to inveftigate fuch curious examples was not unneceflary in a work of this nature. EXAMPLE XXXIII. Plate XL. This plate contains two examples of light and fhadow ; the firft, when the light comes upon the pidture in an oblique direction ; the fecond, when the light comes in parallel to the pidture. The figures A and B are fchemes for fhewing how the quantity of light is perpetually varying upon the fame objedt; for as the fun is nearer to or farther from the horizon, the quantity of light that is call upon any plane will increafe or diminifh in proportion as the rays are more or lefs oblique. Suppofe at figure A that the -rays of light fall upon the objedt in the diredtion a 3, b .2, c 1, viz. fo as to make an angle of 45 degrees with the plane of the horizon ; then the line a c being drawn perpendicular to thefe rays will meafure the quantity of light which falls upon the fides 12, 23, of the fquare A. And the fame may be faid of Fig. B. Now in Fig. A, the rays to each corner r, 2, 3, fall in fuch a manner that the middle ray divides the perpendicular into two equal parts; and fince the line a b receives all the light which can fall upon die fide 2 3 ; and the line c b all the light that can fall upon the fide 1 2, therefore the quantity of light on each fide will be equal: and were the figure to reprefent any folid body, as a cube, or the like, then both fides of it fliould be made of an equal degree of brightnefs. But figure B receives a larger quantity of light upon the top 4 5 (as is evident by the fcheme, and from what has been faid above) than upon the fide 5 6, wherefore die top is more enlightened than the fide, and therefore muft be made of a lighter colour. EXAMPLE XXXIV. Plate XLI. This plate is defigned as a farther illuftration of light and fhadow, and the correfpond- ing letters to the figures will guide us in the operation ; the reader will perceive that I had columns, See. in my eye, when I defigned it. I have now fully confidered every example of light and fhadow that feemed to be neceflary, except one part of it, which does not appear to have been taken notice of •, and that is, a method for determin¬ ing the fhadow of mouldings. Now mouldings have either fquare, or curvilinear out-lines, viz. like the round mouldings to a column, or elfe fuch as are terminated by given angles, like a plinth, abacus, See. To give a rule for determining the ffiadows of round mouldings, would be attended with fome degree of difficulty, and we ffiould not acquire any real advantage from it. Befides, I have fliewn before how to find the fhaded fide of a column, and the diredtion in which a fhadow is cart, either upon a convex, or a concave furface. And thefe examples will ffiew how to avoid the miftakes generally committed by unfkilful artifts, by giving the fame kind of diredtion to the fhadow of every moulding, whether it be concave or convex. Thofe falfe reprefentations I have endeavoured to avoid in examples of this kind j and for the truth of this obfervation, I refer the reader to real objedts in fun-fhine, which will amply confirm what has been faid about it. But I ffiall ffiew how to determine the ffiadows of fquare mouldings, as the rules for drawing them are clear and fimple, and as thofe kinds of mouldings conflitute the far greater part of architedture. And fince all that will be faid upon this article is wholly deduced from what has been advanced before, I may be taxed with a degree of prolixity, which though neceflary in my opinion, others perhaps, may ihink fliould have been avoided. X EXAMTLE [ 42 ] EXAMPLE XXXV. Plate XLII. Fig. i. For lTiadows which are caff by fquare boards, &c. upon a fmooth plane, on which they are fuppofed to be fixed at right angles. From L draw L C, and from the points I,K draw lines parallel thereto ; then if lines are drawn from the corners G, H, See. to L, they will give the fhadows i g, See. Fig. 2. Here I have fhaped the boards into the form of a fedtion, made perpendicularly through the Tufcan capital; and having obtained the points f, b, See. as above, we may from thence, compleat the fhadow of every part.—The fame may be faid of the third and fourth figures. EXAMPLE XXXVI. Plate XLIII. Fig. i. For the fhadows of mouldings caft upon mouldings, and alfo for determining die height and breadth of the fhadow upon each particular moulding, which is enlightened. First, for a capital or cornice. In order to have a clear conception of the manner by which thefe fhadows are produced, I will fup- pofe that all the mouldings are taken away, except the upper one, which is fquare; for then this figure will be like figure.3 of plate XLII, and confcquently it’s fhadow is to be found as in that example ; and therefore I have nothing more to confider but the diredti m of the fhadow over the ovolo, the fillet and cavetto ; and alfo the height of the fhadow upon the enlightened part of the mouldings. Let us fuppofe that the mouldings are put in their proper places; and the miter joints D G, E F, See. are expreffed as in the figure. Now the fhadow of A B, pafTes from B, and is parallel to L C, and from the point c it will tend to C; but in palling over the ovolo it will make a curved line upwards; then over the fillet, in a diredtion parallel to L C; and from g it forms a curve downwards to h ; then it pafTes from h to a, in a line pa¬ rallel to L C. And to determine every part of this fhadow. Firft, from E (the feat of the fillet on the top of the miter joint) draw the parallel E e, cutting the line which is drawn from C to c in the point e; then from e draw a line parallel to L C, cutting the fillet at f, and palling over it in the line f g; then is f g that part of the fhadow which pafTes over the fillet. And a line drawn from the point e parallel to L C, and then another line from L to A, will give a, for the fhadow of A. And the upright line a d will be a part of the fhadow of A B. Now it might be eafily fhewn upon a feparate paper, how to obtain the exadt fhape of the fhadow on the ovolo and cavetto ; but I prefume that every perfon’s judgment will enable him to perform this part to a fufficient degree of exactnefs; only he muff obferve, that the one turns upwards, and the other downwards, as in the figure ; being oblique fedtions made by a plane of rays upon curvilinear mouldings, which are placed above the eye of the fpedlator. But if more exadtnefs, as to this particular, fhould be thought necdTary, the following example will fupply the defedt. Secondly, for a bafe, See. Draw the miter joints Mi, 56, and find the feats 1, 2, 3, of any number of points, viz. B, D, E, F, G, 1 ^, I, K. From 1, 2, 3, draw to C, cutting the miter joint in 5, 6 ; then draw M S, and find a, the fhadow of A • then from a, draw to C, and from 3 to S; draw alfo from B to L, which gives b for the fhadow of B; next draw from a to C, and from D to L, cutting M d in d ; then draw from E, cuttins [ 43 ] cutting the line drawn before from 3, and then from this point draw a curved line through d to b, which will exprefs all the fhadow of the tore that falls upon the ground: but part of this fhadow is caft upon the pi nth alfo, therefore draw a perpendicular at e, and from 2 draw to S, cutting the bottom of the plinth, from whence draw another perpendicular, and then lines being drawn from F and G to L, will give f, g for the fhadow of F, G; fo that by drawing the curve from f through e, &c. we fhall obtain this part of the fhadow alfo. Now all the remaining part of the fhadow is caft by the lines G I, IK, K O; and for this, proceed thus, viz. Draw from I to C, and from P the parallel P n; then from L through n to N, and from N draw the perpendicular N 9, which gives 9 for the feat of N ; then draw from 9 and 1 to S, cutting the parallels which are drawn from 5, o, 6, in the points t, r, s; then from t, r, s, draw upright lines, as in the figure; and if other lines are drawn from I, K, N, to L, their feveral interfedlions, with the upright lines drawn from r, s, t, will give the points i, k, n, for the fhadows of I, K, N. Again, draw a line from D to R, and then the parallel R x will cut the upright line drawn from t, in x, and thereby give x for that point of fhadow which falls upon the neareft part of the tore ; viz. upon that part of it which projects even with the plinth ; fo that a curved line, drawn as in the figure, will compleat the fhadow. I fhall now fhew how to find the heights of the fhadow, when they are projected upon thofe mouldings which front the light. Fig. i. From any point 1, in the abacus draw to S, cutting the top of the ovolo in 2, and the feat of the fillet in 3 ; then from the top and bottom of the ovolo, viz. 2 and 4, draw tl?e curved line to form the fection made through the ovolo in the direction i S. From L draw to 1, which gives 2 6 for the depth of the fhadow upon the top of the ovolo : again from L draw a line fo as to touch the outftde of the bottom of the ovolo in 5, and then the point 5 marks the darkeft part of the fhadow, &c. The fame may be faid of the tore in Fig. 2 ; for if lines be drawn from L through w, it will be a guide for drawing the depth of the fhadow upon that part. EXAMPLE XXXVI. Plate XLIV. This plate is to ferve as a farther illuftration of what I have advanced upon the fhadows of mouldings, when they are caft from them, upon a fmooth plane only; and this (after underftanding the laft example) will appear extremely eafy. I fhall only add an obfervation or two upon what has been faid, and then conclude this part of the work. Observ. 1. The fhadow of the ovolo (and fome other mouldings of the like contraction) is always lighter at the bottom than at a little diftance from it; but, neverthelefs I have, in conformity to general cuftom, and for the fake of diftinctnefs in thefe parts, made the bottom part the darkeft. Observ. 2. By attending to the figures in thefe examples, we fhall fee the manner by which the light, fhadow, and reflexion of each particular object is to be managed: and this fhould be carefully confidered, and fo firmly fixed in the memory, as to be ready at hand whenever we attempt to fhade thofe parts of architecture ; becaufe the neglect of this very eflential requifite will make our performances appear as the effects of ignorance or caprice, ftamp alefs value upon them, and expofe us to the cenfure of every judicious obferver. Y BOOK [ 44 J 1 f fX* * * PX*> ♦ Kr** $ pxv *; {v $ 'aj+oI )nj£ja i ¥ i y B O O K IV. Of Buildings in general. 5 f[j E E 0 R E I Ec g m w ‘th tl'is part of perfpefiive, it will be neceffury to confider of the apparent hjisfif EzL ‘ oE tEe trunks of columns that are placed parallel to the plane of the pichirc. Wh»t I am going to advance, upon this fingular part of peffpedtive, is not with any intention to revive a former controverfy about it, but only to ofFer feme farther reafons why columns, that are thus fituated, fhould be all drawn of the fame fize ; and to give an univerfal rule for this purpofe. Mv continuing of the fame opinion as formerly, as to this matter, is not owing to obftinacy, or Angu¬ larity, but becaufe the evidence of my own fenfes, a candid examination, and the experience of eminent artifts, have all united to confirm it. And therefore I cannot avoid differing from thofe ingenious gen¬ tlemen, who are pleafed to confider this circumftance in a different light, from that in which I have placed it. Every author fhould write with candor and impartiality ; and though he may not peremptorily determine in difputable cafes, he may, however, lend his aff.fting hand towards clearing up that fide of the queftion, which bed agrees with his own opinion. And 1 have been particularly careful to prevent any objeflion to the work itfelf on this account; becaufe the fame rule will anfwer univerfally : and the only real difference will confift in the working with a fmaller diameter inftead of a larger. Plate XLV. Fig. 2. In this plate I have invented a fcheme § for obtaining fuch a diameter to work with in drawing the perCpeftive reprefentations of columns (that are placed parallel to the plane of the piflure) as will occafion their being all of the fame fize; or fuch an approximate as not to have any obfervable difference, even in columns of a confiderable magnitude. This is, in my opinion, a material circumftance, and therefore it is neceffary to confider it thoroughly before we proceed to 'the perfpeflive of columns that are placed in this manner. Let A B and D F be the plans of two columns placed upon the line A I; and fuppofe E to be an eye, viewing one in its axis E C, and the other in the oblique direflion E G. ,. From E draw the lines E A, E B ; E D, E F, fo as to touch the circles +. 2 ‘ Fr ° m E Wlth the radlus E C ( which is the diftance of the eye from the pifture) deferibe an arc, cutting the lines E G in g, and the fide lines in d and f. 3. Through $ Since the engraving this fcheme I have been inform that one of the fame nature has been invented, fome time ac by Mr. Wright, an ingenious mathematician; but as I ne\ law, nor received any inftrudions from it, this may therefc be called my own invention, without the imputation plagiarilm. And the fame may be faid of the diagram. Fig. which will be particularly confidered by my friend Mr. Cowle in the next page. ■f This method of drawing lines to touch the circles is r mathematically true ; but it is neverthelefs exaft enough for this purpofe, and is eafier than the true way of drawing lines as tangents to the circles: however I will ihewhow that is to be done alfo. Bifeashe diftance EC inX; from X, with the radius XC, delcnbe an arc A B, cutting the circle inAE, then from E draw lines to A and B, which will be the tangents required. I his is a truth fo univerfally known as not to require any demonftration in this place. r 45 ] 3. Through the center G draw the line D F, and through g, the line d f parallel to D F. 4. Through g draw h i parallel to H I; then will h i meafure (very nearly) the apparent breadth of the column H I to the eye placed at E ; and alfo A B is nearly the apparent breadth of the column placed at C ; I fay nearly the apparent breadth, becaufe it is not ftriflly fo, as obferved above. Now when we look at the circle A B and H I, it is imagined that the eye refers the piaure in both cafes to the fame diilance ; and lince the circle C is placed in the eye’s axis, and by being fomewhat nearer is larger and more ftrongly impreffed, perhaps, upon the retina, than the other circle, which is at a greater diftance ; therefore the eye may take this as a flandard to meafure the diftance of the other by, and accordingly refer the piaure to the fame diftance. This Teems naturally to arife from the conclufion we make in our own minds, when we conftder the apparent fize of the columns that are placed even or parallel with the eve; for in this fituation I apprehend that they all appear of the fame height and lize, though in fa ft they cannot, fince thofe which are fartheft from the eye muft be leen under a left angle, and therefore will be painted in it of a fmaller fize than thole which are nearer: and this is evi¬ dent from ab, d f, which are above E, Fig. 1. Now the contray effect to this will be produced if we follow the ftnfl rules of projeflion ; for in this cafe, the farther columns will be larger in proportion as they are farther and farther removed from that column which (lands right before us. For A B may be confidered as the projeflion of the middle column on the piflure, and H I as the projeflion of another column upon it when viewed at a greater diftance, which will give H I for its projection upon the picture; and by meafurmg H I, we (hall find it much larger than the projection A B of the column A B, that is nearer by the fpacc G g: and by meafuring the parallel h i alfo, we (hall find it an approximate of D F, or A B. From hence I would infer, that this line h i does meafure (very nearly) the true apparent magnitude of the column DF, and therefore the picture fhould be referred to that place: for if the fection h 1 be made parallel to the H L, it will cut the plane of rays E D F in h i, and therefore h i will very nearly determine the fize which the column ought to be made of upon the picture; and what will ftrengthen this opinion, is, that h i is an approximate of A B. -f- Those therefore, who will embrace this opinion, and would draw columns thus fituated, fo as to make them all of the fame fize in perfpective, have this as an univerfal rule for doing it; and thofe, who lhall differ in their judgment, and will infill upon making them ftrictly confident with mathematical principles, will be referred to a former rule for that purpofe CASE 1. For drawing the trunks of columns, which are parallel to the plane of the picture, all of the fame fize. 1. Let the axis of the column be determined, as in Fig. 3, one of which is placed directly before the eye. 2. From the center of the picture, draw C I perpendicular to the diftance C E of the eye. 3. Take the diftance of the axis of one column from the other, and transfer it from C toG; then take half .the given diameter of the middle column, and with it deferibe the circles from the points C and G. z 4 Draw + Although the line K I is not equal to the line A B, the difference is fo inconsiderable, that no error nor improper effe£t can arife from confidering thofe lines as being equal to each other. For let us fuppofe E C = 6 feet, or 72 inches, C G = 3 feet, or 3 6 inches, AB = FD = i2 inches. Then by Trigonometry, E H= 77 , sl’ rlear, y> ai,d E,G = 8 °-, 5 nearly, (Euc. 57 . 1 ) Hence Kg = 6, 246, g l = S, «, Confequently KI = 12, 046. But becaufe the fractions were here taken a fmall matter greater than what they are accurately equal to, the error will be lefs than what is here afiigned, and therefore lefs than the forty-fix thoufandth part of an inch ; or an inch being divided into five hundred equal parts, the error, or inequality of thofe lines, does not amount to fo much as twenty-three of thofe parts, which may therefore be difregarded in die applications here made ol it. [ 46 ] + , Draw lines from E fo as to touch the circles as in the figure, anti alfo through G, the perpen- dicular D F. 5. With the radius E C (viz. the diftance of the eye) defcribe an arc, cutting EG mg; then through g, draw d f parallel to D F ; and then will D F be the diameter for finding the perfpeftive of the trunk of a column, fituated like D F, which is fimihed in the bafe L of Fig. 3 ; for here f d is taken equal to f d, ofFig. 2, by which means the apparent width of the bafe L, which is feen obliquely, will be nearly of the fame fize as the bafe of the column A, which direftly fronts the eye. CASE II. But if we would draw columns as they are mathematically projeaed, we mud then proceed by the fame method which was ufed in drawing all the five Orders, in the preceding part of this work. Thus the given diameter a b of the bafe I, is equal to the given diameter a b, of the bafe K ; and from this the appearance of the circle is to be determined. Now, by meafuring thefe three trunks, we mall find that L and K are of the fame fize ; but the trunk I is larger than either of the other, by the width M H ; and therefore this may ferve as one in- flance of the difproportion, which I apprehend will be unavoidable, if we follow the drift mathematical rules of perfpeftive, upon this occafion: but this will be much more evident, by the column D, on plate XLV 1 I, which is drawn by a proper didance, and is, 1 believe, as difagreeable a form as can well be produced, being no more than five diameters and 3-4*5 hi g h . an<1 wblch would bave bc ™ tbe fliape of the column B, for it is made to anfwer for that place. As to the difference, which may be occafioned by a too great projeftion of the bafes to the fide columns, when drawn by this leffer diameter; little or no objeftion can I apprehend arife on this account, fince they will not have an unnatural ap¬ pearance ; and for this I appeal to the finlflied bafe, which is under Fig. L : and, that I might be as fair and candid as poffibie, I have given the bafes under L and I the fame kind of light and fliadow, by which means, a more exadt determination may be made. That I might cut off all occafion for controvcrfy, thefe two methods are offered for drawing the trunks of columns; and I would not, on any account, peremptorily obtrude my own opinion upon others, but only offer my real fentiments in a diiputable cafe: and I here declare alfo, that I (hall not think myfelf obliged to give an anfwer to any remarks which may be made, upon what is here advanced : the opinion of candid and fenfible perfons will be thankfully attended to ; but the ftriftures of fnarllng and malevolent critics will be entirely difregarded. Plate XLVI. Fig. i. For a Tufcan colonnade. Give A for the center of the corner column, and through it draw the parallel line B F ; then front A, fet off the intercolumniation A B, of two columns in the front; and A E, E F, for the two co¬ lumns on the fide. Draw the axis A Z, and B D ; then upon the axis A Z and B D, fet off the heights and projeftions of the principal parts of the Order, as is expreffed by (hading in the figure. Now draw A C, then from L to E and F, which will obtain the centers G and I of the fide columns, therefore draw their axis alfo as G H, IK,; and then lines drawn from the axis A Z to C, will give the feveral heights as in the figure. And in tile fame manner, the projeftions are to be found alfo, viz. by drawing the projeftion on A Z to C, as is (hewn by the plinth and abacus. Now for adjufting the fize of the trunks of columns. Any where apart, take (for want of more room) half the given diftance C L, and transfer it to E C; and from C draw a perpendicular at pleafure; then take half the diftance of the column 1 from the center C (Fig. 1.) and transfer it from C to 1 (Fig. 2.) do [ 47 ] do the fame by the column 2 ; and then draw lines from 1 and 2 to E (Fig. 2.) through 1 and 2, draw the perpendiculars a b, c d, and taking 1 and 2 for the axis, 'make a b, and c d, each equal to half the given diameter of the trunk, both at the top and bottom, and draw lines to E; then with the radius E C defcribe an arc, cutting E 1 in n, and E 2 in m; then proceed as dire&ed in 44, 45, and fo will f e be half the diameter for producing the column 1 ; and h g will be half the diameter for the column 2. In like manner, we may obtain the diameters for the two fide columns; thus, take half the diameter of the column 3 in the compafles; then lay a parallel ruler to a b or f e, and move one fide of it till the half diameter in the compafles coincides with the lines drawn from a and b to E ; then at that place draw o p parallel to f e, which will give the diameter required ; and the fame may be faid of the column 4, &c. The next thing is the entablature ; and for this, the method in the jefuit’s perfpeCtive correfponds exaCtly with my general rule for fquare mouldings. And fir A for the top of the cornice: from L through the given height Z draw the line Z M at plea- fure; then from C (through the given projection L) draw a line cutting ZM in M, and fo will M be one corner. Again, draw a line from the center C, through the other projection P, on the left hand; and then it’s interleCtion by the parallel MQ, will give the other corner of the cornice, and confe- quently the utmoft width of it. The fame thing repeated for the frieze and architrave, or for each in¬ dividual moulding, will obtain the projections of thole parts alfo; thus from a, we obtain the point e, for the bottom of the fillet; and from R the point S for the top of the frieze, or bottom of the cornice, &c. Having determined the projections of the members in front, thofe on the fide may be eafily found alfo; thus from the top and bottom of the cornice, draw lines to C; then fet off the other point of difiance to the right hand (which would not come into the picture) and from that point draw to the heights marked with afterilks on N K, which, cutting the lines that are drawn to C, will give the pro¬ jections as in the figure ; thlis O W is the cornice, &c. Having thus determined all the principal parts, the others may be drawn by the rules which were made ufe of in Angle columns; and more, or fewer lines may be made ufe of, as the artift lhall think it neceflary, to be more or lefs exaCt. In many cafes a fmall number of lines will be found to anfwer the purpofe, efpecially to a perfon who is tolerably {killed in drawing. Here I am aware of an objection which may be made, on account of the extraordinary projections of both the upper and lower cinCture, which will neceflarily follow, from working with a lefs, inftead of the real diameter of the column; but he muft have a bad hand indeed, who cannot adjuft the drawing by his eve, fo as to give it an eafy or natural appearance. If the rule I have given for finding the diameter, fhould be attended with any trouble or incon¬ venience, for want of room upon the picture, it may be done by a fmall fcale upon paper, which will anfwer the fame purpofe; or if the artift ftiall chufe to proportion the fize of the trunks of columns to their given heights, his eye will direCt how they are to be placed, fo as to correfpond with the bafes and capitals. N. B. It is abfolutely neceflary for the learner to underftand this example thoroughly before he proceeds any farther; and to make it as familiar to him as poflibie, I will here fet down the regular procefs, viz. Firft, give the center of one column. Secondly, give the intercolumniation of the two neareft columns, A a and [ 48 ] and draw their axis; then upon the axis of column i, fet off the greater heights and projections from the bottom to the top: do the fame by the other corner of the entablature. Thirdly, find the center, and draw the axis of the fide columns; then transfer (from the corner column i) the feveral heights and pro¬ jections. Fourthly, adjuft the fize of each column by Fig. 2, and draw the trunks. Fifthly, find the general projections of the entablature. Sixthly, draw all the mouldings, and finifh the figure as on plate XLVII. Before I proceed any farther, let us examine how far the rules made ufe of in the preceding part ■of this work, and particularly thofe for drawing this order at large, have been applied in this example. In the firft place, the centers for all the columns have been determined by rule 1 and 2 of plate I. Secondly, the fquares for the bafes and abacus of the capitals, were obtained by the method of putting a fquare into perfpeCtive from a given diameter, as in Fig. 5. plate 2. which does likewife for all fquare mouldings; as hath been fhewn by the rule for that purpofe throughout every order, viz. plate IX. Thirdly, all the circular mouldings may be drawn by repeating the rule contained in plate IV. Fig. io. 4 and by the rule calculated for this purpofe, plate X. Fourthly, the entablature is produced in the fame manner as the entablatures to all the orders, with this difference only, that in the orders it is made perfectly fquare, as united to one column only; but in this example it is continued, fo as to be fuited to more columns than one. Now if all this be perfectly underftood, it will greatly facilitate the fucceeding operations. For a Doric Colonnade, like that on Plate L. Plate XLVIII. Before we begin with this colonnade, let us confider the principal requilites which are wanted, and particularly thofe which have not been applied in the laft example. In the firff place, we want the centers and axis of all the columns, their principal heights and pro¬ jections: all which has been done in the laft example. Secondly, we want the returns of the entablature, the breadths of the triglyphs and motops ; and for t''is purpofe we muft be careful to give a proper intercolumniation to each part, that the diflance of the columns may be fuited to the quantity of their ornaments. And having given all the proper interco- lumniations, the triglyphs, &c are found by the fame rule as was ufed for determining dentals, modilions, or the like. After thefe obfervations, it appears almoft needlefs to be very particular in firewing how to draw every part of the following figure; yet to make myfelf as intelligible as poffible, and to fix what has been laid the more firongly in the memory of my reader, I will carry him through this figure fiep by ftep till we have wholly compleated it. The parts that are ruled, exprefs all the general heights and projections that are wanted. Let A.L he a line for the axis of the neareft columns A and C, the centers of the two neareft columns A C and the intercolumniations adjufted for two triglyphs and an half; C Zanother intercolumniation for three triglyphs and an half; I K the intercolumniation for four triglyphs ; and K L the intercolumnia¬ tion for the end, which is to contain four triglyphs. Draw a line from C, and another from Z to L, which gives D lor the axis of one column •, therefore draw the parallel B M, and then from A, I, K, to cut it in B, E, G, M, then are B, E, G, the centers of three columns more; therefore draw the axis of thefe alfo, and from the column C P, transfer the heights and projections to the axis D S; then transfer the heights and projections from D S to the columns at 3 , D, E and G, from whence the columns B, D, E, G may be drawn; for having the heights and diameters of [ 49 1 of one column given, we can from thence Cor from the fedtor, or from another fcale) take off the feveral parts; and the quantity to be taken from each of thefe columns, by their being joined to the buildings, is determined by the lines B E and E F, which being in the axis of the column, takes away one half of each column. See the finifhed example in plate L, and alfo Fig. A, B, of plate LI. Now for the columns at F and H. From M draw to L, which obtains H, and the parallel H F obtains F; therefore draw the axis from H and F, and find fas before) their heights and projections. We now come to the entablatures. Here, the firft or neareft part, is found as in the Tufcan colon¬ nade ; and becaufe the miter-joint at S T is parallel to that at P therefore they will both vanifh into the point L; confequently, if lines are drawn from L, through the points on the axis, as S, P, they will cut the lines drawn from the neareft corner to C, and therby give the joining of the mouldings at Q^T. Again, for another corner X; draw from L through the axis V, and from C through the projection W, which gives X for the corner wanted. And from the top of the axis Z, to the diftance H (which is out of the picture) will obtain the corner Y, See. Thus have I fhewn how to find columns in various fituations, whether they are to appear as whole columns, or only as half ones. And likewife how to determine the miter-joints, or angles of an enta¬ blature, all which is performed at once in the very place where every part of the building is to ftand, and without making ufe either of a plan or elevation, but only the fimple rule of cutting off a line that va- nilhes into the center of the picture, by means of one of the points of diftance ; as I explained by Fig. 2, plate I, &c. In the fame manner every particular moulding may be drawn. But it now remains for me to determine the perfpeCtive of the triglyphs, metops, &c. and for this I will continue the axis of the firft column A,C at pleafure, above the cornice ; and then draw the p a- rallel a b ; then upon the line a b place the triglyphs and metops in their regular order, beginning at the axis c, d of each column ; then continue the axis of the other columns upwards, viz. D, E, G ; draw from c to C, and the line e i. Again, from L draw through c, and from C through a, which gives the corner g for the angle of the frieze : then draw the parallel g f, and from C, through the points on a b, will give f for the other end of the frieze, and likewife the width for all the triglyphs and metops, whifch is more fully explained in Fig. i, plate XLIX. In like manner, lines drawn from C to o, and from the points on the line a b (which meafure two triglyphs and a half, for the return of the fide g h) will cut the diagonal g n, and fo give the breadths of thofe parts. Again, for the other triglyphs; from a b, transfer the fpaces, &c. to the line e i, (viz. the line that is upon the axis of the columns at D, E, G) and then proceed as above directed, which will not only determine the triglyphs at the ends of the frieze, but thofe alfo which are between p and m, &c. Now again let the reader refer to the rules for drawing the Doric foffit, or thofe for dentals, modilions, &c. and he will find this to be the very fame in every refpeCt. Plate XLIX. Fig. i. In this plate I have transferred the meafures which were obtained before for the modilions and metops; and I have fhewn how to draw them upon the frieze, by means of perpendiculars, which were expreffed by dotted lines, &c. The angles for the infide of the architrave at s, is found by drawing from L through the top of the axis of the column, to cut the bottom of the architrave as in the figure. As to the niches, I need only refer the reader to that in plate XXXVIII and XXXIX, which fhews this to be only the perfpeCtive of half a circle. b In [ 5° ] In the two following examples I have fhewn how to find all the joinings of the cornices, which will be wanted in this work : but it may be neceffary fometimes to have a perpendicular feeftion, and therefore I will fhewthow to find that alfo. Fig. 2. From the center of the picture draw lines through e, h, k, viz. through the axis e k; then from L, through the points d, g, i, which feverally meafure the real projections, will obtain what was required. EXAMPLE I. Plate LI. Fig. i, For pilafiers j and any part of a column. Give A and B for the middle of the pilafiers, and let the firft (at A) be i- 4 th as thick as ’tis wide ; the fecond at B, half its width. Set off the heights and projections upon the lines A F, B G, and continue thofe lines both above and below the figure. Now I will firft determine the thicknefs of each pilafter below A, B, and then the greateft projection of the cornice; which will be fufficient for fhewing how all the other parts are to be produced, viz. only by repeating the fame rules. 1. For the thicknefs of the pilafter at A, which is to be i- 4 th of its width. Divide half the given width i, 2, into two equal parts; then through i and 3 draw lines from C, and from L draw through 4, which gives the thicknefs; and a parallel from thence will determine the breadth of the front. 2. for a pilafter which is to be half as thick as it is wide. Draw from C, as before, through 5 and 6; from L through 7, and then a parallel for the front of the pilafter. 3. for the projedions above. Continue the thicknefs of the pilafter to the top of the entablature, and then from the projedion b of the cornice, draw a line from the center C; do the fame through a, to e ; then is a e the fide of the pilafter where the top of the cornice reprefents the miter joints cutting the fide of the cornice in the line c a, which will be the thicknefs of it in that place: a parallel drawn from e willreprefent the top ofthe pilafter in front; and for the top d g, d c of the cornice, from C through , a, f and lrom L through a, G, will obtain thefe parts alfo; and fo ofthe other parts, which will be much better comprehended by drawing the figure at large, than by any explanation: and the operation emg repeated above, will help to explain my meaning more fully. As to the pilafter on the fide, whofe front tends to C; the breadth and thicknefs of that is obtained y lines drawn from the other points of diftance, to the corners of thofe which are in front: thus from k to hi give the point, &c. For parts of columns, vi 1. For an half column, lowed half of a circle. example II. z. an half column, and a three quarters column, in front, and at an angle. I Ig. A. Give a b for the diameter, and from it draw the perfpetftive of the 2. For a three quarter column in front, circje ; divide one half of the diameter, viz. parallel e f. From the diameter ab find the perfpedtive of a whole c b in d, and cut off c h to reprefent cd, then draw the 3 - Fora three quarter column at an angle, Fig. B. fcntation of a circle ; and omitting i- 4 th of it, as bed, From the given diameter a b, draw the repre- we (hall have what was required. EXAMPLE III. Here a b is give the fcveral Plate LIJ. Fig. i. For pilafters, or fuch like projeaions. the width of the wall, and e g, and s t, are the given projections, corners n, o, p, q, r, », u, w, of the pilafter, See. in front. And From C and L will for thofe on the fide, which [ 51 3 which are to correfpond with them. Continue parallels from the top and bottom, as in the figure, then ■om c and a draw lines to C, 8cc. and then lines from H (as f q) to the feveral parts of the piiafters, &c. will give the correfponding parts for the fides, &c. Under the out-une is a finithed example, with the light falling upon the angle. Fig. 2. Having drawn the trunks of columns, to find the apparent breadths of the flutes. Let A, B,D be three plain cylinders: at any convenient diftance, draw K M parallel to the horizontal me, and from the centers I, 2, .3 of the cylinders, perpendiculars to cut it in F, G, h; through C the center of the pidure, draw E K perpendicular to K M, and make K E equal to the diftance C H : then draw ines from E to F, G, h. At F, G, h, defcribe circles, whofe diameters are refpeftively equal to the three columns; (and which may be confidered as the plans of them) and from E draw lines to touch the circles, as in the figure; then draw as many flutes to each plan as can be feen within the lines drawn rom t e eye. Now take the width of the cylinder A in your compafles, and move a ruler parallel to K M, till the fpace a b coincides with the compaffes; then from the feveral flutes on the plan draw hues ending to the eye E, which will divide a b, and thereby give the apparent width of as many flutes as can be fan upon the column A. In the fame manner find thofe of the other cylinders, 8cc. Thus 1 WC ° b L tain > t0 2 fuffiaent exaaners “ d “ m °ft eafy manner, an elfential part of a column; which, to acquire by any other method, would exceed the utmoft degree of human patience. N. B. When the diftance, &c. happens to be too great to be readily brought into the pidure, then ta mg ,-half, l- 3 d, &c. of the objects, and l- 3 d of their diftance from the middle of the pifture viz. rom the hue E C ; and ufing , -half or 1 - 3 d of the diftance of the eye, will produce die fame thing. Plate LIU. Fig. 2. For Arches and plain Pediments. 1. Draw the front of the arch, and alfo the parallelogram, with lines in it to interbed the arch, as in the figure. 2. From the front already drawn, draw the oblique fide, where the cor-efponding letters and figure lhew how to determine the points for drawing the arch, &c. 3. In the fame manner find the depth of the infide of the front arch; then the parallel p q will give t re fide of the other : the parallel R S, and a line from F to C, will give S for the center, and S R for the radius of the back part of the arch. 4. For the pediments: Draw the parallel Ne, and then a line from e to C will interfed fn, and thereby given for the top of the fide pediment; the parallel n M, interfeded by N C, will determine the top and joining of the roof, &c. But the pediments being conftituted of inclined planes, I might in this place lhew how to find the vamlhing fines and vamlhing points of them ; but this would carry me into too large a field, without anfwering any real purpofe: however 1 may juft obferve, that if a perpendicular be drawn through C (the vamlhing point of the oblique fide) and lines drawn from L (viz. the point of diftance) parallel to the fides N O and N d of the pediment in front, fo as to cut the line drawn through C in V and W, then V and W'will be the vanifhing points of thefe pediments. For any thing further relating to the dodlrine of inclined planes, I muft refer the reader to my former work, where this part of perfpeftive is particularly explained. The fecond figure is drawn to one half of the fize of Fig. ,, and is defigned as an example of light and fliadow. And the pediment above it is given as a hint for drawing the mouldings; but this may he pa/Ted oyer till we come to plate LXV. ' Cc P, . xc . Plate [ 5 2 ] Plate LIV. For an arch with three-quarter columns placed on pedeftals. The manner of drawing plain arches may be eafily conceived from the laft figure j but I will now (hew, in the frrft place, how to divide the infrde of an arch into any number of pannels for ornaments, &c. and this admits of two cafes; firft, when the view is taken rn the middle of the arch ; and fecondly, when it is feen fide-ways. CASE I. When viewed in the middle, as in the figure. i. Divide the front into the proper parts for the pannels, &c. and from thence draw lines to C. a. Let r 9 exprefs the real depth of the arch ; and divide this line into the parts for the widths of the pannels, See. then lines drawn from the points on r 9, to the point of diflance, will cut r s m the perfpeftive breadths, as r v. From v draw the parallel v w, then w is the center, and w v the radius for defcrihing one pannel, and fo on. CASE II. Fig. B. When the eye is placed on one Tide of the arch. Here a b is the width f the arch : divide the top of the arch as before, and draw lines to C. 2. From b draw a line to the point of alliance, cutting off a e to reprefent a b ; do the fame for the pannels, &c. that are marked on a b, as c, which will obtain the points for the breadths of the pannels on the line a e, as e g. 3. From o draw toC; and from g the parallel g k ; then is k the center, and k g the radius for drawing one pannel as before. I WILL now drew how to delineate the other parts of this figure. The mod material parts (hall be put under two diftina heads, and then I will conftder each part in its regular order. Firft, I mull determine the perlpeftive of four three-quarter columns with pedeftals, and the pro- je&ions as given in the plan A. Secondly, The impofts, and their joinings to the column. First, for the columns. Give the line A F, and thereon place the centers of the columns, as A, D, E, F; and alfo the middle of the arch at H. 2. On A B put the heights and projeaions, and from thence finiftr the three-quarter columns, as {hewn in plate LV. 3. Take from Fig. A the feveral projedions 1, +, 5 > 6, 7> and transfer them from E to 7 ; and then draw a line from C through each point; and then a line, from the point of diflance (to the rig it hand) through E, will give one corner z of the plinth. а. From the plinth of the column at x, let fall a perpendicular x n, cutting the line drawn from C to 4 (viz. the projedion of the plinth) then from the above point of diflance draw through n, whrchw.il give the angle at y. 5. From y draw a parallel, then from the point of diftance draw through s, which gives the corner 7, See. б. From the points thus obtained, we may finilh the plinth j and fo have a fufficient guide for compleating the mouldings. Secondly, [ 53 ] Secondly, for the imports, &c. Upon any axis, fuppofe A B, fet the heights and projections of the imports at b d e ; then take the diftance i 2 (Fig. A) which is the diftance of the wall from the axis of the columns, and fet it from A to a ; then obtain the point 1, from thence draw a perpendicular 1 k, and on it transfer the utmoft heights and projections of the imports, from thofe which are given at b d e, and fo fliall we obtain the total height and projection of the imports, which will enable us to draw them correCtly in their proper places, viz. at a and r. Now to join the imports to the columns; place the height of imports on the axis of the column, viz. at K ; and with the diameter in that place draw the perfpeCtive of a circle ; then the top of the import being drawn to cut this curve, as at M, will be the joining at that place, &c. Plate LV. By this print I have endeavoured to teftify my efteem for the memory of Dr. Brook Taylor, and had my abilities been equal to my inclinations, I would have produced fomething more fuitable to the character of fo eminent a man ; who may be conrtdered as the parent of perfpeCtive. Plate LVI. For a plain houfe. 1. Give b d for the bottom of one fide, and anywhere under it, draw A E, to which let fall the per¬ pendiculars b B, d D. 2. Upon A E place the widths for the windows, and on d k put their heights, and alfo the height for the cornice ; and from hence draw the windows and cornice in front. 3. From A B obtain the windows, &c. on the end of the houfe b e. 4. From C draw through D, then from H through E, &c: 5. Lines drawn from C through the divifions on D E, will give the breadths of the windows on F G, that are on the front fide f g. 6. The lines at 1 2 and 3 4, fhew how the jambs of the windows are to be obtained. But in this example it is the roof and chimney that particularly require explanation. For drawing thefe, continue all the fides of the building upwards as in the figure ; then draw the parallel A B, and from B draw to C, cutting d k produced in G ; from G draw the parallel G K, and then from K to C, and fo fhall we have the feveral lengths of the bottom of the root. Now for the top of the roof. 1 . Continue A B at pleafure, and draw from H through G to F ; which will give B F for the real length of the fide B G. 2. Bifedl A B, and draw from D to C, cutting G i in 2 ; then will 2 determine the corner of the roof at t. 3. Do the fame by K M, which will give O for the corner p of the roof, if it was upright at the end, like 1 p n. 4. For finding the hips of the roof; give B E and K S for the depth of the hips; then, in this cafe, C direfls the fituation of the hip v, and 3 the fituation of the hip at S, therefore let fall perpen- diculars from r and 3. 5. Set the height of the roof from 1 to q, and draw q p to C, then is p the height of the root in that place ; therefore from p draw a parallel to cut 2 t; from C draw through t, to cut c v in v; then draw the fide of the roof, as in the figure. D d In [ 5+ ] In the fame manner, I find the perlpeCtive of the chimneys; for which purpofe all the lines and points are drawn that were neceffary for doing it. Plat e LVII. Here the houfe, which was explained in the laft example, is compleated. Plate LVIII. For flairs. Since thefc are parts of architecture, particularly adapted to houfes, I have therefore given them this place in the work. Fig. i. Give A B for the length of the flairs, at the bottom of the building, to which I fuppofe the flairs arc placed ; and B 4, 45, 5 D for the heights of three fteps; alfo B 1, 1 2, 2 3, for the widths of three fteps; and the operation is evident from the ficrure. Fig. 2. Give B E D for the ends of three fteps, and A B for the lengths, &c. Fig. 3. Give I O for the bottom of a building; I G, G F, See. for the heights and widths of the fteps. Through the feveral corners draw from C at pleafure; then make B 1 equal to F G, and by means of the point of diftance L, &c. find the feveral parts as in the figure. Fig. 4. Here I fuppofe a b is the bottom of the building, &c. and it is alfo given for the projection of the part D from the building; and the other part A is to be exaCtly fimilar to it; which toaether make a flight of two fteps. Draw from L through a, from C through b ; then from c the parallel c d, which gives the projection of the part D. Again, draw from L through d, from C through c, and then the parallel e f will m Ve the projection of the part A, See. Fig. 5. For three flights of fteps. Confider A B as the bottom of the building; a 1 as the width of one ftep.; A 2 as the projection of the middle flight. Now, draw lines from L and C through 1 and A, which gives the corner e ; therefore draw the parallel e g. Again, from C draw through e, r, at pleafure; then from L through e determines the projection of the fecond flight, viz. g h. Now draw the parallel h i, then from L through i gives the projection of the flight F, See. Plate LIX. The manner of drawing this building muft be obvious, from the example in plate LVI; lor 1 2 is given for the bottom of the building, and the feveral heights are fet off upon the line 1 4. By the line B A we obtain all the widths, and by 1 4 the feveral heights, &c. G H for drawing the roof; and becaufe the whole width of the roof, which tends to C, would be extended farther than the compafs of the plate ; I have therefore taken one half it, and likewife one half of the diftance C L (viz. C K) which anfwers the fame purpofe. Plate LX. Contains a finifhed example of the laft figure. 1 or drawing the banquetting-houfe at Whitehall, which was built by Inigo Jones, for part of a Royal Palace. Plate LXI. Fig. Z, is as much of the elevation as is wanted, which being fo fmall, I have therefore not given any part of the plan ; for the feveral general projections may be fufficiently comprehended from the pcrfpeCtive of the parts, as is expreffed above, and below the building. Upon the lower line A D is fet off the feveral widths and projections, viz, for the windows the axis of each column and pilafter, the bafes of the columns and pilafters, and of the middle of the projection in front, all which being regularly reduced into perfpeCtive, will give fufiicient guides for drawing as far as the top of the trunks of the lower columns, fxc. and in the fame manner find the entablature over them, uhich will be eafily underftood from what follows, viz. the manner of drawing the upper part of the building. [ 55 ] building. For this, draw three parallel lines at pleafure, viz. E F, G I, KM, and draw perpendicu¬ lars through them for the axis of the columns, 8tc. From thefe axis fet off the feveral projections and End the perfpeCtive of them as in the figure; and fo fhall we obtain the general projections of each part, from whence the whole drawing may be compleated. Plate LXII. And here we have a finiftied example, of a fmall part of that moft magnificent ftruc- ture, which was defigned by a native of this kingdom, as a Palace for the Kings of Great Britain, and which, were it ever to be carried into execution would be a ftriking proof of the great abilities of the architect, and of the refined dignity of a Britifh Monarch. Plate LXIII. For a houfc with a colonnade, &c. If the reader recolleCts what he has done before in plate LVI, he will readily draw all the building except the triglyphs, the columns, and the arch ; and to bring the method of working that example more eafily to his mind, I have given the places for the windows on the line A E, &c. And for the columns, we are to proceed as in the laft example, viz. by fetting the points marked c, for their axis on the given line A E, 8cc, For the triglyphs. Those in front are readily drawn, and for thole on the oblique fides, continue lines up at pleafure as in the figure; then find the length of 3 and give the fpaces for the triglyphs and metops, and then find the feveral perfpeCtive breadths on 3 4, &c. Above (on the left hand) I have found the roof and chimney, by a method fomewhat different from that in plate LVI and LIX. Continue up the fides of the building, and draw A B, B G i and alfo B E ; give g for the center of the chimney, h k for the width, g i for it s height, and E 1 for the incli¬ nation of the hip of the roof. Upon A B, is likewife placed the point a, for the top of the roof, and for the middle of the chimney alfo; a b is the height of the roof ; from e cuts off c for the corner of the hip, 6 cc. c d is it’s perfpeCtive height. The height of the chimney is m n, which may be obtained either from g i, or a b ; for I have put two ways for finding the chimney, viz. one upon the line B E, and another upon the line B A. Plate LXIV. This plate exhibits a finifhed print of the laft example; the Defign was made, and compleated for me, fo as to come within the compafs of the plate : and I hope I may take the liberty of faying, that This, and the laft finifhed Print in die book, are efteemed by me as the moft valuable parts of it. These examples of four houfes only, are, I apprehend, fufficient for the generality of buildings; for the ingenious architect will perceive, that they are calculated for drawing a variety of objeCts; whofe per- fpeCtive appearances may be truly obtained by fome one, or more of the general rules; and any one may readily find by practice, how to apply them univerfally. But there now remains fome particular parts of buildings, which feem neceffary to be confidered in this place ; I mean the angular and circular pediments; thefe are curious examples, that I do not re¬ member ever to have met with, though they are very ufeful, and therefore ought to be attended to. Plate LXV. Fig. 1, For an angular pediment. Having drawn the body of the building, and determined the mouldings of the cornices, as if no pedi¬ ments were to be placed over them ; we muft, for the pediments, proceed as follows, viz. First, for the pediment in front. E e Find [ 56 ] Find the perpendicular feAton made in the middle of the cornice, as e f d, which will determine the fhapes of the mouldings in that place; and fince thofe at the top of the pediment have exadly the fame projection (that is, are all even with the mouldings below) they will limit the projeaion of each moulding at the angle ol the pediment: but fince the line 1 n, which is the height of the angle of the pediment, is longer than the line d f, which is the real height of the cornice, therefore the heights of the feveral mouldings on 1 n, will be greater than thofe on f d ; but in both cafes, the lines drawn from C through the feveral points on f d, on 1 n, will, with the aforefaid perpendiculars, determine the perfpeflive of fuch lections, and confequently the fliape of each moulding in it’s proper place. So that all which is wanted, is a method for finding the heights on 1 n; and this is obtained by drawing a perpendicular g k, within the given height for the cornice, upon that fetting the feveral mouldings, and then drawing the parallels to cut oft' 1 n, as in the figure. Secondly, For the pediment on the oblique fide. Set the heights and projections upon c s; then determine the plane o p q in the middle, and from thence draw lines both ways to the ends of the cornice, as in the figure : or the mouldings may be drawn thus, viz. having found the plane o p q, draw a perpendicular through C; then draw a line through F q, and another through G q, cutting the perpendicular drawn through C; and then thole points (as Nj are the vanifhing points of the mouldings; which may be more clearly comprehended by the fecond figure. Pi. ate LXVI. Fig. i. For a circular pediment. First, For the front fide. Determine the planes 1 n m, and t r s, as in the laft example ; and let i be the center for deferi- bing the circular mouldings in front, I mean as an elevation only. From C draw a line through the center i, and let fall perpendiculars from the feveral mouldings of the plane 1 n m; then will i, 2, 3, 4 > 5 » be the feveral centers of the mouldings in perfpeCtive j thus 6 is the center, and 6 m is the radius for the upper fillet, &c. Secondly, For the pediment over the oblique fide. I- rom the corner G of the upper fillet draw the perpendicular G d; then take any number of points, as F, E, See. on the top of the pediment in front, and draw parallel lines to cut G d in o and d - 3 from o and d draw to C ; and from F, E, 8cc. other lines to the point of diftance ; which will give the cor- refponding points f, e, See. on the oblique fide ; through which points if we draw a curved line as in the figure, we {hall obtain the true fhape of the top of this pediment alfo; then by means of this and the plane r s t, we may compleat all the mouldings neatly by hand; and the projections of the cornice will be guides alfo. Fig. 2. A general rule for drawing confoles and key-ftones. Give the elevation, as A B, and draw lines at pleafure for the projections, as E F ; then take the feve¬ ral heights and projections, and reduce them into perfpeCtive, in their proper places, as in the annexed figure ; and fo lhall we determine the true fhapes of thofe parts. Plate LXVII. Here is the former example of a door finifhed. Plate LXVIII. For columns that are placed in a circular manner. Let Fig. 1 be a plan of one quarter of the intended defign, viz. of eight columns to a round building ; which is to be viewed by the eye directly in the middle of the building. Draw [ 57 ] Draw a b for the diameter of the middle of the building ; fix the center A, and draw the axis A B, upon which fet the feveral heights as they are wanted ; which will be a fcale for the other parts. Upon A b fet off the feveral projeftions (Fig. i.) as 3, 4, 5, 6, both ways, and from thefe diameters find the perfpedive of four concentric circles, as in the figure; then will g be the center for the axis of one column; 6 another, and n another. Again, take (from Fig. 1) the length 1 2, and fet from A (Fig. 2) to 4 ; then draw a line from C through 4, cutting one of the middle circles in d, m; then are d, m, the centers for the axis of two other columns. Now for the diameters of the columns; the line 5 7 is one diameter * therefore take the half of 5 7 and fet from A and 4 to 2 and 3, then draw from C through thefe points, which will give d e, f g, for half a diameter in thofe places. And having thus obtained the heights and diameters to work with, the next thing is to compleat the out-lines of all the columns, as in Fig. 3. I am next to fhew an univerfal method for determining the ftraight mouldings to columns thus fituated- and fince two fides of them are generally made to tend to the center of the building, therefore thefe parts may be obtained as follows, viz. Draw a circle equal to the middle diameter of fiich mouldings, like a b of Fig. 1 ; then from the center A (Fig. 2) draw lines to touch the reprefentations of thofe circles, like thofe in the figure; and this will give the apparent breadths of the mouldings, which I have exprefled in the figure, by fhading thole ;arts. But I would obferve that there is no nec .ifity for repeating this operation for every moulding, fince a few principal parts will be fufficient for drawing the whole ; and a little attention, improved by practice, will make all this much eafier than words can do. I would in general remark, that if the heights of the feveral parts are fet upon the axis AB, then thofe points will invariably be the centers for the correfponding parts; and if thofe lines are continued to the horizontal line, this will likewife give the vanifhing point of fuch lines: thus A is a correfponding point to o, and o A vanilhes into \_, f See. This rule will ferve univerfally for circular buildings ; and by this principally it is that the remaining figures to this work are produced, and therefore the lefs may be faid when I come to them. In the fourth figure, I have given a finifhed example ; and in the fifth figure (by taking away the fore part of the objedt) we have an example of columns that are placed in a concave manner ■ as the infide of a round temple, or the like. Plate LXIX. For a circular temple. This example contains an application of the rules in the laft plate, which are fo obvious as to need no farther explanation : for Fig. 1 is the elevation ; Fig. 2 is one quarter of the plan ; and the dome is found by the rules for drawing a globe in plate 8. Plate LXX. Here we have a finiihed example of the laft plate; and it is a view of a temple in the gardens at Kew, belonging to Her Royal Highnefs the Princess Dowager of W A L E S : it is called the Temple of Victory. Plate LXXI. For determining the perfpe&ive of columns, in any fituation ; even that variety of them, which is {hewn in the laft plate. Fig. 1. Either upon the pi&ure, or on a feparate paper, give the centers and diameters of the co¬ lumns, as they are difpofed upon the plan : thus 4 is the center of the firft column, a b it’s diameter • c is the center of another; and e that ol the fartheft column. Now if w’e make A 1 as a fcale for re¬ ceiving the feveral diftances of the columns, then we may by one rule find all their places in perfpedive ; F f therefore [ 5 » ] therefore from c, d, c, draw perpendiculars to A i ; which lines c 3, d 2, e i, will feverally meafure the diftance of each center from the line A 1, and alfo give the fpaces, or intercolumniations, of the columns, viz. 43, 32, and 2 r. At Fig. 2, make C A, CL, equal to C A, CL of Fig. 1, and draw A 1 parallel to C L ; then make A 1 (Fig. 2) equal to A 1 , Fig. 1) and from 1 draw to C ; now take the diftance 1 e of the center e ! Fig. 1) and transfer it from 1 to f (Fig. 2) then draw f L which gives the point e in per- fpeCtive, for the center of the column as placed in the plan at e (Fig. 1.) Again, for the height • place this upon 1 h, and draw to C, which gives e g for it s perfpeftive height. Again, for the diameter ; put one half of it at 1 a, draw the parallel b e, and then draw a line from a, to C, &c. f>me manner find all the other columns as in Fig. 3 ; where the fame rule only is repeated four 1 ,'nc" * the four columns. Oi', having determined the height and breadth of one column, the others may be drawn from this, w! the exn.jr „ e'h column is determined, provided there be room enough upon the picture ; thus from du. c m, to find the height of the column d n : draw through c and d to cut the hori¬ zontal lii. in K ; then fi . hi draw to m, which gives d n for the height of the column, &c. T • i r.# t C )1 '.ins a.e likev.ife to be found by calculation, viz. from given numbers, as exprefled in Fig. 1 : for thofe nsirv ers ;ch cxpreil given lines, may as eafily be taken from a fcale, as the lines themfelves can be taken from a plan, £cc. Now by attending to ti ..' res, and confidcring the application of this rule., in a variety of inftances, (or, which is much the be:!, . .\v. . ven! examples with it) we fhall find with what cafe and fa¬ cility, a great variety of columns, 11 all kind 3 of fituations (or other objects) may be produced, and that too with the greateft expedition. And after the learner has drawn feveral examples of this kind, and is a perfect mafter of the preceed- ing part of this work, he may then venture to attempt drawing that moft elegant flructure, for which he has the outlines, See. in the next plate ; and a finifhed print of it to conclude with. But previous to his doing this (and to help his reflexions upon it) I will give a few ufeful and neceflary hints, which may make the operation ftill eafier to him. Plate LXXII. Fig. 1. is one quarter of the plan, drawn to one third of the propofed fize of the building : and on the line 1—28 are placed the centers for each column, See. which are fet oft' (viz. three times as large) upon the bottom line 1—28 of Fig. 3. At Fig. 2, is as much of the elevation as is wanted: the perpendiculars which are dotted, contain the heights of the pedeftals, columns, and entablature in thefe places. Y Z is the axis of the dome, and K is it’s real height. A D is the given height for the columns, Sec. to the circular part; and the perpendicular from 20, contains the heights of the columns, 8cc. to the arch. The point a is the center of the colonnade (viz. the perfpeCtive of c, Fig. ij and a d is the axis to which all the modilions, the capitals, bafes, See. tend ■ as was fhewn in Fig. 2, plate LXV 1 II. Plate LXXIII. We have here a little more than one half of a moft magnificent defign, which was made and given me for this work - } and which (if well executed) would make an excellent piece of feenery for a theatre. Thus have I finifhed with all I propofe doing in this work, viz. giving new rules for drawing the five orders of architecture in perfpedtive, with facility and exa&nefs; alfo how to determine the perfpec- five of fliadows, and an application of all this to buildings in general. Now [ 59 ] Now what has been already done will fhew us how to delineate a variety of objedts, and in fuch fituations as are generally attended to by architects ; fo that in regard to fquare objedts, I have hitherto drawn one fide of them parallel to the plane of the pidture, becaufe then the center of the pidture became the vanishing point of the other fide. This manner of working comprehends the firft, and a moft eflential part of the perfpedtive of architecture, which has hitherto been treated by other authors with great labour and perplexity. But various are the fituations which may be given to objedts, and thole that are fquare will, it drawn angle-ways, make very agreeable forms in a pidture ; becaufe the lines have a tendency to contraft, or oppofe each other; and they are therefore preferred on many occafions. This is a part I have not hitherto confidered, and befides this there is alfo the perfpedtive of Domes and Cielings, of Scenes for Theatres, See. See. all which thould be fully explained and illuftrated by thefe new principles, before the whole of Perfpedtive (I mean as it relates to the imitative arts only) can be properly compleated. But this (as I hinted in the introduction) muft be the bufinefs of another volume; wherein I propofe giving for examples, fome of the antient Temples, and other buildings of antiquity ; and a few of the moft elegant modern ftrudtures: which would ma^e a work more pleaftng to the generality of readers, and if properly executed, a ufeful performance. However, before I fhall venture upon fuch an arduous and expenfive undertaking, it is neceflary to fee whether this part be worthy of public regard. And, left I fhould not be encouraged to proceed any farther in this moft delightful fcience, I will here fubjoin the following remark, from which the ingenious reader may eafily form to himfeif a method for drawing fquare objedts, that are obliquely fttuated, and to give each ftde of them any breadth he pleafes. REMARK. Now all that is neceflary for the above purpofe, is to find the proportion which the diagonal of a fquare has to its fides. And this figure being a right angled triangle, therefore if we call each fide 7, then (by the 47, 1 Euc.) we fhall find that the hypotheneufe is 9, 9-ioths. And having thus fettled thofe given proportions, we can by an application of the former rules, obtain the perfpedtive of any fquare building that is to have an oblique fituation. Indeed I fliall fuppofe that the fides are equally oblique, with refpedt to the pidture ; but by changing the pofition of the objedt to the right or left hand, we fhall fee more or lefs of each fide, and confequently be enabled to make the fides of it wider or narrower, as we fhall think proper. This is evident by Fig. 5 and 6, of plate 7 1. But for the operation. CASE I. Fig. 4. When the building is to be placed diredtly in the middle of the pidture. 1. Give a b for one fide of a fquare, and (with the compaflcs) fit a b to VII, VII on the archi¬ tectonic fector, or to 7, 7 on the line of lines upon the common fector; then take the diftance 9 and 9-ioths, and make A B equal thereto. 2. From the points of diftance H and L, draw lines through A, B, meeting each other in d ; then is A d the perfpective of one fide, and B d another. 3. Give ed for the height of the building; draw the perpendiculars A h, B g, and then from e to H and L, &c. And fuppofe we would divide the fides, as B d, into any parts in perfpective ; then from d draw the parallel d 1 ; and from P 1 through B will cut off d 1 for the real length of d B ; therefore by dividing d 1 (fuppofe in 2) and drawing from thence to P 1 , we fliall do what was required. G g Bv [ 6 ° ] By the Time operation, Fig. 5 is produced, with this difference only, that the line A B is taken on one fide of the center C. From hence then we fee how fquare buildings, that are obliquely fituated, or fquare mouldings of every kind, may be produced in perfpedive ; and with as much eafe and exaflnefs as thofe which are placed in a parallel direction. As for the manner of drawing circular planes of every fpecies; fince the diameters, in every fituation of a building, may be taken from a parallel fedion, therefore the fame rule for drawing a circle from a given diameter, will hold univerfaliy true. Thus if a b in either of the above figures, be the given fide of a fquare, it is likewife the diameter of a circle, that is inferibed within it. THE PERSPECTIVE O F ARCHITECTURE. A WORK ENTIRELY NEW; Deduced from the Principles of D« BROOK TAYLOR; And performed by Two Rules only of Univerfal Application. BEGUN BY. COMMAND of His Prefent MAJESTY, WHEN PRINCE of WALES. B Y JOSHUA KIRBY, Defigner in Perfpe&ive to His MAJESTY. VOLUME theSECOND. PRINTED FOR THE AUTHOR. Fig. 6. 7 J /. ,/r ///. ■tr/.g. ,s F/.i/v Iix V/'/,/ YV/f/,- .17//. i. 7/IX '/"A/ j Tin -Plalel JYafr JX. JZ,,A-X\'l _ Q (I jaxx ' '/%r Pta/eZSm Plate xxvnr Plate XXIX. 3%afc.XXX. ■£ _7'«! P/a/e JCJC^TV. F/ok xzxir Ptafe JX -T VJ11. fitlitr XXXTX.. fla/r JLLU . J« —l 1 ■»» JZZ72T JP/eUe. Xlir. -*-r- a 11/ATX V IYa/f xnx. r? 'ITT yv/,[ Tjate UJZ. T/ateLIV. lAT a/v/ c z \ F/attLrur. ITT. TA te L XI. PUtei^Jnir. Su/LpLd, Jfod. tX+,4y .%<# ZUJ6/. iM RUte X, XVZ. TlaltLim. \ 7Z7yUTT ^ l T/afc LJOX. T/ritc L XXL Flak LJZDU1 PJ.ATE LXXIII. Chap. I. The defcription and ufe of the Se&or. II. The application of this inftrument in drawing the feveral parts of the Tufcan Order. III. -in drawing the Doric Order. IV. -in drawing the Ionic Order. V. -in drawing the Corinthian Order. VI. -in drawing the Compofite Order. VII. Some other ufes of the Se&or explained. PART II. B O O K I. Se&. r. Of preparing the pi&ure, viz. the afluming a proper diftance and height for the eye, See. 2. Of planes only. 3. Of folid bodies. 4. Introdu&ion to fquare and circular mouldings. 5. Two general rules for fquare and circular mouldings. BOOK II. The Tufcan Order. The Doric Order. The Ancient Ionic Order. The Modern Ionic Order. The Corinthian Order. The Compofite or Roman Order. BOOK III. The perfpeftive of fhadows, illuftrated by a variety of examples, and particularly applied to Archite&ure. BOOK IV. Of buildings in general, viz. A method for drawing the trunks of columns, that are placed parallel to the plane of the pi&ure, all of the fame fize, 8cc. For a Tufcan colonnade. For a Doric colonnade. For pilafters, or any part of a column. The fame, by another example. For the flutes of columns. For arches and pediments. An arch with three quarter columns. I N D E X. Page. For a plain houfe. .. 1 5v> For flairs of various kinds. 54 An houfe from a defign of Inigo Jones. jbij. The banquetting houfe at Whitehall. jbid. An elegant houfe with a colonnade. ^ For angular pediments with mouldings. jbid For circular pediments with mouldings. ^ For confoles and key-ftones. j^id For columns when placed in a circular manner. jbid. A circular temple. ^ For determining the perfpe&ive of columns in any fituation. ibid. A feene for an amphitheatre. Conclufion of this part of Perfpe&ive. REMARK. Relating to fquare objedls, that are obliquely fituated, &c. errata. PART I. Page 5, line 39, for done but as, read done as—p. 6, 1. 38, for know, r. have— p. 1;, 1. 37, for confoles, r. confoles at large— p. 18, 1 . 34, dele out D G—p. 33, 1 . 25, at the beginning of the line put, Plate IX— p. 77, 1 . 13, for to d, r. To. P A R T II. Introduction, page 2, line 27, for each, read, fome—p. 2, 1 . 46, for line, r. plane—p. 4, 1. 33, for line, r. lines—p. 10, 1. 39, for point draw d, r. point d—ibid. 1, 43, for by then, r. then by p. 17, 1 . 30, for Fig. B, viz. r. Fig. E, Plate XVII—p. 18, 1 . 26, for a b of, r. a b of the fide— ibid. 1. 33, for points and, r. points e, e, and—p. 19, 1. 36, for next plate, r. plate—p. 27, 1. 18, for fince it, r. fmee this part—p. 32, 1. 13, for foffit, t. the foffit—p. 37, 1. 4, for draw the, r. draw lines to cut the—ibid. 1 . 40, for is N the, r. is N the vaniihing point of—p. 46, 1 . 5, for D F, r. d f —ibid, 1 . 40, for projedion, r. projedions—p. 48, 1 . 36, for C, r. A, C—p. 49, 1 . n, for therby, r. thereby—ibid. 1. 22, for column, r. columns—p. 51, 1. 15, for ending, r. tending_p. 53, 1. 37, for C, r. c ibid. 1 . 41, for fide, r. tides. There is alfo an unneceffary ufe made of the words chapter and fedion, in a few parts of this work, which the candid reader will overlook, as matters of no confequence. Directions for placing the PLATE S. F IIOSE marked B 1 to Plate XXV, fhould be placed f ril, as belonging to the Architedonic Sedor ; and if bound up with the letter-prefs, fhould follow at the end of the defeription and ufe of that inftrument. The other plates, from plate I, to plate LXXIII, fhould follow in their order, at the end of the letter-prefs, belonging to the Perfpedive. But the bell method by far, is to bind the letter-prefs and plates in feparate volumes.