Qkn> [ ] \_J5 :*•- jfl ja ■ THE GENTLEMAN’S and BUILDER’S REEOSIT O RYj, eA'allhvn OR, C J/awni^^> S4i Z/SS ARCHITECTURE DISPLAV'D. Containing the moil Ufeful and Requiiite PROBLEMS in GEOMETRY. AS ALSO The moil Eafy, Expeditious, and Correct Methods for attaining the Knowledge of the Five Orders of Architecture, by equal Parts, and fewer Divifions, than any Thing hitherto publiilied. TOGETHER With all fuch Rules for Arches, Doors, Windows, Ceiling-Pieces, Chimney- Pieces, and their particular Embelliihments, as can be required. likewise A laro-e Variety of Designs for Truss Roofs •, with the Method of finding the Hip, cither Square or Bevel. ALSO The moft certain and approved Methods of forming a Number of different Stair-Cases, with their Twisted Rails, &V. The Whole embelliihed, not only with Eighty-four Plates, in Quarto, but fuch Variety of ' Cieting-P teas , Shields , Compartments , and other curious and uncommon Decorations, as muft needs render it acceptable to all Gentlemen, Artificers, and others, who delight in, or pra&ice, the Art o i Building. The Defigns Regulated and Drawn by E. IIoppus, Surveyor, and Engraved by B. Cole. The Third Edition, carefully Reviled and Re-examined from the Prefs ; vith^ the Addition of a new Frontispiece, representing the intended Front of the New Mansion-House for the Lord Mayors of the City of London *, and a Complete laoit of Contents, alphabetically digefted by E. Ii. aforeiaid. LONDON : Printed for C. Hitch, in PatermJler~Rov> J. Hodgf.s, Lmden-Bridgc-, and B. Cole, id llclborn. MdccxlViii. THE PR E F A C E. INCE the Study of the fever al Sciences relating to Building j has, of late Years , been fo univ erf ally en~ couraged and praElifed by Perfons of the highejl Rank and DiJlinEHon , it would be needlefs , if not impertinent , to fay any thing to recommend it : And \ fince there have been fo many able and elaborate Differ, tations, in order to demonftrate the Ufefulnefs of each individual Branch of it , there may befome Perfons , perhaps , ready , at firfi View, to cenfure our prefent Undertaking as unneceffary , atid of very little^ if any ^ Importa?2ce . Such partial and prejudiced Judges, however , w/// /'W doubt not) upon matyre Deliberation , find , that ?20 Yreatife was ever better form'd, or better calculated for toe Service of the Publick ; they will be obliged to acknowledge, that the Rules and Methods for the Attainmmt of the Art above - ® mentioned i PREFACE. mentioned, are not to be met with in any one fingle V< olume , how large fioever, which has been hitherto written on the Subject, and that the young PraBitioners mufi, of Necefftty, have Recourfe to a Variety of Books, and put themfelves to a large Expence, be - fore they can be able to form a jufl Idea of fo ufeful an Art in all its various Branches- In order, therefore, to bring the Sub- fiance of the whole into a moderate Compafs, and thereby fave them abundance of Time, and cafe them of fo great a Charge by the Sale thereof at a reafonable Price, I have ventured to offer to the Publick this New Magazine, which, I flatter myfelf, upon a fair and impartial examination, will be allowed to contain, not only all the Geometrical Problem that are moft ufeful and requi- site to be known, but the mofi eafy, expeditious, and cort eB Methods for drawing the Five Orders of Architecture, with all fuch particular Embelli foments of Doors, Windows, See. as befi fir ike the Eye, and are mofi agreeable to each refpeBive Order : The neweft, and mofi approved, Defigns for ereBing Trufs Roofs, -with the utmofl Strength and Beauty . ; and the mofi commodious Manner of forming a Variety of Stair-Cafes, with their twilled Rails, &c. All which, together with the different Kinds of Cielinsr-Pieces . Shields, Compartments, and other curious and uncommon Decorations, herein particularly deferibed, will, I hope, f nve univerfal SatisfaBion, and prove, upon the Perufial, to be the mofi copious and compleat, as well as the coeapefi. Performance of the like Nature hitherto extant . A D I S- DISSERTATION O N Practical Geometry. Rules for the Defcription of Polygons, Problem I. For the Ere&ion of a Perpendicular on the Middle of a Right Line given . UPPOSE C to be the Point propofed in the Middle of the Line A B. Defcribe, as you think proper, on the given Point C, the Semicircle DE; make the Se&ion I on the two Points D and E, from the Point C ; then draw C O, being the Line demanded, thro’ the Section I, and that line C O will be perpendicular to A B, the Line given, and be eredled upon C, the Point propofed. JProt'lem . T A- -D E B Problem 4 A Dissertation om Problem II. For the Ere&ion of a Perpendicular on the Extremity of a Line given . Suppofe ah to be the given Line, and b the End, or Point, whereon the Perpendicular is to be ereded. From the Point b , upon the Line ab y five equal Divifions muftbe made towards a upon b\ with four of them, as b d y defcribe the Arc/, on the Point c ; with five Divifions, as b e>, defcribe the Arc g ; from the Point b , thro’ the Interfedion f g, > draw the Line b h ; which will be perpendicular to the Line a b upon the Point b ^ Problem IIL Another Method of ere&ing a Perpendicular on the Extremity of a Line given, Suppofe a b to be the Line given* and a to be the Point propoled. On the Point a defcribe the Arc c/with a c, the Radius ; from the Point c towards f y upon the Arc c f make the Points d and e ; upon thofe lafi Points defcribe the Arcs^ and h ; from the Point a , thro’ the Interfedion g h y draw the Line ai y and that Line a i is the Perpendicular propofed. Problem IV. How to let a Perpendicular fall on a Line given , from a Point without the Line,, Suppofe C to be the Point from whence a Line is to falls perpendicular to A B» Defcribe, Practical Geometry. S Defcribe, as you think proper, on the given Point C, the Arch D E, interfering the Line A B in the Points D and E ; make the Serion F on the Points D and E ; draw the Line: C F, and the Line C O will be the Line demanded. Problem V. How to draw a Parallel Line thro a Point given , to a Line- given . Suppofe A to be the Point given, thro’ which a Parallel Line to that of B C is to be drawn. Draw, as you think proper, upon the Point A, the Oblique Line A D ; defcribe the Arc DE) upon the Point D defcribe the Arc A F ; make the Arch D G equal to the Arch A F ;; draw ihe Line M N thro 5 the Points A G, and that is the Lins demanded. * c pro.mr. Froblkm _Pro1>/ssm JT . 4 " ^\3>/ • Problem VI. For the Di'vifion of a Right Line given , into what Number of equal Parts you think proper. Suppofe A B to be the Line which you propofe to divide into fix equal Parts. From the Point A draw, as you think proper, the. Line A C thro 5 the extream Point B ; draw the Line B D parallel to the Line A C from the Points A and B, and along the Lines A C and BD; let any fix equal Parts, viz. efghik , be carried along the Line AC, rqpon'tn along the Line B D ; draw the Lines en , fo , g p, h q, ir , then the Line AB will be divided into fix equal Parts at the Sections STVXY. v Problem VII. How to draw a Spiral Lme round a Line given . Suppofe I L to be the Spiral Line round which fuch Spiral Line is to be drawn. Divide half the Line I L into as many equal Parts as you propofe to make Revolutions. Example for the making four Revolutions . Divide the Half B I into four equal Parts B C, E, O, X ; di- vide likewife B C into two equal Parts in A ; upon the Point A defcribe the Semicircles B C, D E, F G, HI; upon the Point B defcribe the Semicircles CD, E F, G H, XL, and you will have the Spiral Line demanded. Problem Practical Geometry, 7 Problem VIII. For making an Equilateral Triangle on a Line given . Suppofe A B to be the Line given, whereon the Triangles are to be made. On th^ extreme Points A, with AB the Radius, deferibe the Arc B D ; on the extreme Point B, with B A the Radius, deferibe the Arc AE ; from the Interfedion C draw the Line C A, C B ; and ABC will be the Triangle demanded. Problem IX* For making of a Triangle , the Sides whereof are equal to Three given Lines . Suppofe ABC to be three given Lines. Dravv the Line D E equal to the Line A A ; on the Point D, with B B the Radius, deferibe the Arc GF ; on the Point E, with C C the Radius, deferibe the Arc H I ; from the In- terfedion O draw the Line OE, O D, the Triangle DEO, will confift of three Sides, equal to thofe given A A, B B, C C. 8 ^Dissertation on PROBLEM X. For making a Square on a Right Line given « Suppofe A B to be the given Lines. Let the Perpendicular A C be ereded on the Point A ; de- fcribe the Arc B C on the Points B and C, with AB the Ra- dius ; make the Sedion D ; from the Point D draw the Lines DC, DB; A BCD is the Square propofed to be made. Problem XI. For making of a Regular Pentagon on a Right Line given . Suppofe A B to be the given Line, On the extreme Point A, and with A B the Radius, defcribe the Arc B D F ; ered the Perpendicular AC; divide the Arc into five equal Parts IDLMB; draw the Line A D ; divide A B the Bafe, into two equal Parts in O > ered the Perpendi- cular O E, on the Interfedion E ; with E A the Radius, de- fcribe the Circle ABHGF; carry the Line A B five times round, in the Circumference of the Circle, and a regular equi- angular equilateral Pentagon will be made. PRORIEM XII. For making a regular Hexagon on a right Line given . Suppofe A R to be the given Line. On the extreme Points A and B, and with A B the Radius, defcribe the *Arcs AC, B C ; on the Sedion C defcribe the Circle Practical Geometry* 9 Circle ABDGFE; carry AB, the Line given* fix times round in the Circumference, and you will have, on the given Line A B, a regular Hexagon ABDGFE- Problem XIII. For finding the Center , and the two Diameters , of an Oval Suppofe A B C D to be the Oval, the Center and Diameters whereof are propofed to be found. In ABC D, being the Oval propofed, draw, as you think proper, the two parallel Lines AN, HI ; which halve in the Points L and M ; draw the Line PL MO, which halve in E, and the Point E will be the Center- On the Point E deferibe, as you think proper, the Circle FGQ^ cutting the Oval in F and G ; thro’ the Interfe&ions F and G, draw the right Line F G ; which alfo halve in R ; draw the largeft Diameter B D through the Points E R ; thro’ the Center E draw the fmalleft Diame- ter A EC, parallel to the Line F G, and the Thing propofed will be accomplifhed. Problem Problem XIV. For the Defcription of an Eliptic Arch by the Framed when the Length and Height thereof is given . Suppofe ABC / to reprefent the Tramel, the Leg C i being at ^ight Angles with AB the Head, there is a Groove in each of them (as reprefented in the Middle of each of them by the ftrong black Lines) for the Pins e and /, which are fattened to the Rule D M, of a greater Length than / K ; the Pins e and /, mu ft be fixed at fuch a Diftance, as that, when a Pencil, '&c. is put thro’ a Hole at^, the Length eg is equal to / K, the Half of the Bafe Line of the Arch, and the Length f g equal to / H, the Height which the Arch is propofed to rife. OPERATION : Fix the Head of the Tramel AB, on the Length of the Arch RL; fix likewife the Point of the Pencil g *, at the Point K, and the Pins f and e in the Grooves AB and i C ; with one Hand move the Pencil g , and with the other, dire eb , each of them into the fame Number of equal Parts ; draw the interfering Lines which are correfpondent, according to the Direrions before given, and the Arch required will be completed. Problem XXI. Another Method for the Defcription of the Gothic Arch reverfe . Draw a b equal to the Bafe propofed, and c d parallel to a b, and equidiftanf to the Height of the Arch required, and equal in Practical Geometry. 15 in Length to the Half of ab , and proceed as directed in Problem XVII* and the Arch required will be defcribed. Problem XXII. For the Defcription of an Oval. ' The Tranfverfe and Conjugate Diameters being given, and interfe&ed twice in the Middle in right Angles, operate as di- rected in Problem XVII. and the Ovals required will be de- fcribed* Prorlem XXIII. For the Defcription of an Arch of equal Height to a Semicircle , but of a longer Diflention- Suppofe eg d to be a Semicircle, and a b the Length required, whofe Elevation of an Arch is equal to the Semicircle ; draw e f parallel to a b ; let ef be equal to c d , and proceed as directed in Problem XXI. and the Arch required will be defcribed. A Dissertation on Problem XXIV. For the Defcription of an Oval that is propofed to be fmaller at one E?td than the other . Let the Tranfverfe and Conjugate Diameters be given, as a b and h g, and interfering each other in the Middle, draw e c and //parallel to hg ; let f d be equal to three-fourths of hg ; thro’ the Point f h and d g draw the Lines f e and d c , and proceed as direded in Problem XXII- and the Oval which was required will be defcribed. Problem XXV. For the Defcription of an Oblique Oval Suppofe ab) a *, e f and /£, to be the Sides of a Rhomboid, within which an Oval is to be infcribed. Draw the T ranfverfe Diameter c d parallel to a b and e f and the Conjugate Diameter g h parallel to a e and bf and proceed as direded in Problem XXII, and the Oval will be defcribed which was required. Procee-d to P .'Aio tu Prv6&m :< 2 t. J’S Rules Practical Geometry. 17 Rules for the Defcription of Gothic Arches , gene- rated by Segments of Circles. Problem I, dejcribe a Gothic Arch on a given Line. S UPPOSE a B to be the Line given ; on A, with the Interval A B, make a Defcription of the Arc B d ; make likewife on the Point B, with the Interval B A, the De- fcription of the Arc A e ; and the Arch required, viz. A C B, will be completed by the Interfeftion C. n Problem 1 8 A Dissertation on Problem II. . Another Way of defcribing a Gothic Arch. Suppofe A B to be the Line whereon the Arch is to be de- ferred. Divide the Line A B into three equal Parts at the Points C and D ; on that of C, with the Interval B, make your Defcription of the Arc B/ ; on that of D, with the Interval A, delineate the Arc A g ; and the Arc required, viz. AEB, will be completed by the Interfe&ion E. Problem III. Another Way to defcribe the Gothic Arch. Suppofe A B to be the Line whereon the Arch is to be de- fer ibed. Let A B be divided into three equal Parts at the Points C and D ; from* the Points A and B, let fall the Perpendiculars A E and B F, equal to A D and B C ; draw Lines, of what Length you pleafe, thro’ the Points F C and ED; on the Points C and D, with the Interval A C, or D B, make your Defcription of the Arcs A G and BA; on the Points E and F, with the Interval EH, or F G, make your Defcription of the Arcs H K and G L ; and the Arch required, viz . A, G, I, H, B, will be completed by the Interfe&ion. Problem IV. Another Way of defcribing the Gothic Arch. Let A B be divided into three Equal Parts at C and D ; on the Points A C D B, with the Interval A D, make four Arcs ; and Practical Geometry. 19 and thro' the Interfe&ion E, and the Point D, draw the Line EDH; thro' the Interfeftion F, and the Point C, draw the* Line FCGj on the Points C and D, with the Interval C A, or D B, delineate* the Arcs A G and B H, and on the Points E and F delineate the Arcs H K and G L j and the Arch required^ vi%. AGIDB, will be completed by the Interfe&ion I- Problem V. For the Defcription of a Gothic Arch another W ay. Let A B be divided into five equal Parts on the Points A, C, D, B ; and the Interval A D make your Defcription of the four Arcs, and then proceed as above dire&ed, and you will complete the Arch required. ao A Dissertation on Rules for the Defcription of the Angle or Mitre Arch or Groins both regular and irregular $ as alfo of a Center for a femicircular Window in a circular Wall: And how to form Niches , See. Problem I. How to dif cover the Angle , or Mitre Bracket , of a Cove. D RAW the Bafe A B ; on A draw A D at right Angles ; and equal to A B draw the Line DB; let the Line D A be continued to C ; make A C equal to A B ; on the Point A, with the Interval B, delineate the Arc BCj on the Points B D draw B E and D F ; at right Angles with the Line B D, and equal, to A D or AC, draw the Line F E* Let A B be divided into any Number of equal Parts, the more the better, and more exadt the Operation, and thro’ thofe Divilions draw Lines parallel to A C 5 on the Arc B C, carry them on to the Line B D ; from the Divilions on D B draw Lines parallel to D F and BE; let the Perpendiculars on D B be equal to thofe on A B, doling in the Arc B C 5 deferibe the Arc F B by a bended Rule, &?c. thro’ the Points on the Perpendiculars from B D, and the Mitre required will be completed. Problem Practical Geometry. 2 I Problem II. In cafe the lejfer Arch of a Groin> which is irregular , be a Semi- circle given , the Formation of a larger one , which is not a Semicircle , is required after fuch a matitier as that the In- ter fe8i ion of the two Arches Jhall make the Groins from the Angle hang perpendicular over the Bafe thereof. Suppofe A BCD to be the fp ringing Walls whereon the Arches are to be ereded, and AEG the femicircnlar Arch given. Draw the Line BC; let the Line A C be continued to I, and B D to K j on B and C ered the Perpendiculars B O and C N ; make B K, A I, CN, and B O, each of them equal to the Height of the Semicircle given, as F E ; draw the Lines K I and NO; let A C be divided into as many equal Parts as you think proper ; thro’ the Divifions on AC draw Lines parallel to A B and C D, ending in the Semicircle A E C, and on the Diagonal C B ; from the Points on C B, ered Perpendiculars parallel to C N and B O, and to B K and A I, and the Lines L M and g H will be equal to F E • let the Lines be made on each Side of L on B C, and on each Side of g on A B, equal in Height to the Lines which are correfpondent on each Side of F on A C, thro’ the Points whereof defcribe theArches AHB, and BMC, the Arch and Groin required. Obferve, that the Arch B, M, C, ferves alfo for D A the other Diagonal. ■ # A Dissertation on Prorlem III. When you have one given Center for a Rhombus Groin, to make a Defcription of the other injuch a Manner as that the Mitre Arch /hall he conflruEled by the Interfe&ion , and he perpendi- cular over the Bafe. Let the Diagonal AD and BC be firft drawn j fuppofe AFB to be the given Center, then proceed as before dire&ed on the four Sides, and the two Diagonals, and the Groins, will be conftru&ed, which are required. Problem IV. Tdhe Arch Line of a Cteling , or V auk , being ^ given , which is fuppofed to be Jemicircular ; for the Formation of the Curve of a lejjer Arch which J, hall interfeSl the Side of it , in order to receive either Doors or hAindows, in fuch a Manner as that the Groin floall he produced by their InterfeBion , and hang perpendicularly over the Bafe thereof ; as likewije for the For- mation of the Curve thereof . Suppofe A B C D to be the Angles of the fpringing Walls. Draw the Semicircle A OB and C L D > on the Side B D fet oli the Spand of the Arch V/, which interfeds* upon the Points V and /, ered the Perpendiculars V r and t u , equal to the Height intended of the Arch which interfeds; defcribe the Line r u y divide it in the Middle at % draw zy parallel to V r and ut j produce zy as you think proper from the Point y on the Line AB, and the Pointy, fet the Height zy ; on the Arch BOA, at the Point h, produce h g , till zy be interfeded at the Point Practical G eometry. 23 Point x \ draw the Lines u and x t ; on the Points ^ and t . ei e<£t the Perpendiculars x < w- and t J' equal to g h y draw the Line divide B g into what Number of equal Parts you think proper- Thro’ the Divifions on B g draw Parallels to S ^ '* 011 Arc B h , and the Lines x v y from the divifionary Points on the Line x v y by the Lines from B g ; on Vy eredt I erpendiculars to z r, and parallel to y z and v r y eredt on the fame Number of equal Parts onjr/and t x Perpendiculars paral- lel to y z y t u and t/ y x w, fet the Length of the Lines from to the B/6, on the correfpondent Perpendiculars from yv to z r, from j? t to z u y from x t to w f, thro’ the Points fet off on the Parallels, the Arches required may be defcribed (as in the preceding Lx ample) V z t and w V z t is the Arch which interfe&s, and w t the Curve Line of the Groin which is corref- pondent to it. The Arches K m z and K P are drawn after the fame Manner. Prom, km 24 l A Dissertation on Problem V. *Tbe Arch of a Circular TV all , in which there is intended to be fired a femicircular Window , being given ; for the Formation of a Center to turn their Arches . . Suppofe A F B to be the Arch given of the Circular Wall, defcribed by the Center E. From the Center E eredt the Perpendicular E F, at right Angles to A B, equally on each Side E F ; on the Arch A F B, fet the Width of the intended Window C D; draw LM parallel ♦ and equal to CD; let L M be divided at N into what Number of equal Parts you think proper ; produce EF thro’ the Point N as far as O from the divilionary Points ; on L N draw Perpen- diculars parallel to E O, and abutting on the Arcs LO and CF ; from the Point F draw F G, parallel and equal toHD; draw the Line H G. Let the Line H E be continued to I equal to H G; on the Point C let the Perpendicular C K fall equal and parallel to IT I; draw the Line IK; divide HC into what equal Number of equal Parts you pleafe to the Line L N ; from the divilionary Points on H C, draw Lines to I K, parallel to H I and C K ; from the Points of Divilion on the Arc C F, as continued from L N, draw Lines parallel to C D, and equal to the Lines which are correfpondent on the Line L N, to the Arc L O ; from the Points of Divilion on CH, draw Right Lines to the extreme Points of the Lines from CF j fet the Length of the Lines from C H to the Lines from the Arc C F, on the Line H C to the Line I K, as H I is equal toHG, and fo on towards C ; and fet off thro’ the Points on the Lines, from HC towards I K ; defcribe the Arc C I, which will hang perpendicular over the Arch C F, when it is let in its due Portion. Problem Practical Geometry. z z Problem VI. and VII. T 7 j>e Center being given, on which the Arch of a Bow-Window is turned, for the Difcovery of another Center parallel to it accor- ding to the upper Edge of the Arch's Surface. Deferibe B K C by the preceeding Problem ; fet the flat Surface, or the Width of the Arch from B to A • and hom C to D, draw the Lines AD and B C ; let them be divided in the Middle at E F ; draw the Perpendicular of Length, as you think convenient, to H, in any proper Place, as Fig. 7 ; draw a Line, as you pleafe, as AG; upon the Point A ered the Perpendicular AF; then take E I, in Fig. 6, and fet it from A to B in Fig. 7, and E F from B to C t take the Semi-diameter BE, or E C, Fig. 6, and fet it from A to D, Fig. 7 ; take likewife A B, or C D, Fig. 6, and fet it from D to E, Fig. 7, and draw the Line E C on the Point F with the l ength C E ; on the Line I H make the Point g. Take the Width of the flat Surface of the Arch A B, or C D, and fet it on K to 7 on the Line EH; and let the Remainder from 7 to g be divided into feven equal Parts ; let the Arch B K be divided likewife into feven equal Parts ; take K 1 on the Line E H, upon the Point 1 ; on the Arc B K, with the Interval K 1 deferibe the Arc 1, as you fee convenient ; with the Interval K 2, on E H, upon the Point 2, on the Arc B K, deferibe the Arc 2 ; take likewife K 3, K 4, K 5, and K 6, feparately, and deferibe the Arcs 3, 4, 5, and 6 ; make a Divifion upon thofe Arcs from A to g in feven equal Parts ; and thro’ the Points of thole equal Parts, deicribe the Arc A g, according to the Directions in Prob. I- and the Arc D g may be drawn after the fame Manner, by which the Arch- Line required is com- P leted v E * Problem 26 A Dissertation ««■ Problem VIII. For the Formation of a Semi-circular Nich , with Ribs , as is cuflomary when the fame is propofed to be plaiftered . Defcribe the Semi-circular Plate A B C, and the Semi-circu- lar Front Rib ADB, equal to ABC; fix the latter level where it is propos’d to be continued ; on A B fet the Front Rib ADB perpendicular ; defcribe the Quadrantal Ribs D C, D E, D F, D G, and D H, each of them equal to A D, or B D, and at a proper Diflance, on the Plate ACB, and at C, E, F, G, and H, in fuch a Manner as to meet in one Point at D, on the Crown of the Front Rib A D B y which completes* one Half of the Operation ; and the Remainder may be finifhed after the feme Manner. Problem Practical Geometry, Problem IX. For the Formation of a Semi-circular Niclo by the Thickneffes of Planks or Boards , and to difcover the Bevels to each refpeEHve Thicknefs . Defcribe the Semi-circle on the Front of the Nich A D B ; make a Divifion of the Height e D into equal Parts, in Propor- tion to the Thicknefs of the Plank or Board which you propofe to make the Nich of. Defcribe the Thicknefs from whence the Bevels mull be taken, and draw Lines at the End of the prick’d Lines in the Example : Take the prick’d Line r 2, in your Compafies, or the under Side of the Plank or Board where- of you propofe to make the firft Thicknefs ; defcribe a Semi- circle from 1 equal to ADBj the Semi-diameter being equal to the prick’d Line 1 2, ftrike a fquare Stroke on the Edge from 1 , in order to difcover the Center for the Semi-circle on the upper Side of the firft Thicknefs, as at 3 ; take the prick’d Line 3, 4, upon the Point 3, defcribe the Semi-circle, the Semi-diameter whereof is equal to the prick’d Line 3, 4 ; an Arch being firft defcrib’d on each Side of the firft Thicknefs ; cut diredtly thro’ the Arch-Line, with a narrow turning Saw, on each Side of the Plank or Board, and by that means you will have the true Bevel and Curve of it. In order to defcribe the Bevel of the fecond Thicknefs, defcribe the laft drawn Semi- circle on the under Side of it, in the fame Manner as you did on the upper Side of the firft Thicknefs 3, 4, being the Semi- diameter. Strike a fquare Stroke from 3 on the Edge of the Plank or Board, in order to difcover the Center for the Semi- circle on the upper Side of this fecond Thicknefs ; on the Point 5, with the Interval 5, 6, on the upper Side of the fecond E 2 Thicknefs 28 A Dissertation on Thicknefs defcribe the Circle, the Diameter whereof is equal to 5, 6; cut thro’ the two Arches in the firft Thicknefs with a turning Saw, and the Arch-Line and Bevel of the fecond Thick- nefs will be given. In order to difcover the Arch- Line and Be- vel of the third Thicknefs, you are to follow the fame Rule as in the firft and fecond, and fo of the reft. When you have your Thicknefs prepared, according to their exadt Arches and Bevels, let the Glue, in which you fet them, be good, and well made, and let it ftand till it be perfectly dry, and with a Compafs fmoothmg Plane , fomewhat quicker than the Arch of the Work, plane the Infide of it till it be fit for the Defign propos’d. Prorlem X, XI, and XII. For the Formation of the Eliptical Nich by Ribs for P laiflering ,&c. Defcribe the Plate whereon the Ribs fhould ftand ; K, m y Fig . ii, being a Semi-ellipfis, equal to ADB, or A e B, Fig. io, the pricked Lines / n y / o, l />, / y, /r, and l m , Fig. n, repre- fent the Bafe Lines of the Ribs D e, Df D g, D h, D i > and D B, Fig- iq. The Lines s /, s u> sw , s at, and sy , are Bafe Lines, and the Perpendiculars a /, b u y c v y dw y e x, and fy, Fig. 12, reprefent the Riling of the Ribs e D, /D, g D, hV, i D, andBD, Fig. io, which, in Length, is equal to C Di you muft obferve, however, that the different Arch of each Rib muft be defcribed within thofe Lines ; that is to fay, the Arch s a y Fig. 12, is a Quadrant of a Circle, which hath t for the Center of it, and is equal to the Arch of the Rib e D. The Lines u s, s z, equal to zb, h u> are the Semi-tranfverfe, and Conjugate Axes of a Semi-ellipfis, the Arch whereof, s b , Fig. 12, is equal to the Arch of the Rib/D, Fig. io, which may either Practical Geometry. 29 either be defcribed by the Tramel, or the Interfe&ion of Lines. The Lines f z, fv> equal to c are the Semi-tranfverfe and Conjugate Axes of a Semi-ellipfis> the Arch whereof is equal to the Arch of the Rib g D, and proceed in the fame Manner for the Remainder- When you have the Ribs all ready, fet the Front Rib AD B perpendicular on the Plate A e B, as at A B, and fix the Feet of the fhort Ribs on the Plate A e B> as at e> g y h> i, Fig, io,, which are correfpondent with the Points n> o , p y q , r, Fig . n y and their Points a , b> c, d> e , Fig. 12, to the Crown of the Front Rib at D, Fig. 10 - and after this Manner the Operation pro- pofed may be accomplifhed. S tcrvwx/ Problem: 3 ° ^Dissertation on Problem XIII, XIV, XV, and XVI, For the Formation of an Elliptical Nich by the Fhickneffes of Planks or Boards . Defcrihe the Figures 13, 14, 15, and 16, according to the preceding Problems. The Arch ABC and f g h are Semi-ellipfes, and equal to each other* The Arch / n is a Quadrant of a Circle, and the Arch O P is a Quadrant of an Ellipfis, which are the two mod: different Arches of the Nich* The Arch f g h reprefents the fir ft Thicknefs, and is equal to A C D. The Perpendi- culars m n and g p are equal to e B, and the Bafe Line l m is equal to ig. The Bafe Line 0 g is equal to i the Arches whereof / n , 0 />, with their Bevels, ftand perpendicularly over i g and i k. On the under Side of the Plank or Board whereof you propofe to make the firft Thicknefs, defcribe a Semi-Ellipfis equal to ADC, or f g h, the Semi-tranfverfe Axis whereof is equal to the pricked Line 1, 2, and Semi-conjugate to 1, 3 ; then ftrike a fquare ftroke at 1, on the Edge of the Plank or Board, in order to difcover the Middle of the Bafe to the Elliptic Arch on the upper Side of the firft Thicknefs at 4, the Semi-tranfverfe whereof is equal to the pricked Line, 4, 5, and the Semi-conjugate equal to the pricked Line, 4, 6, by Virtue whereof defcribe an Elliptic Arch on the upper Side of the firft Thicknefs ; then, by Virtue of thefe two Elliptic Arches thus defcribed, on the upper and under Sides of the Piece, faw out the Curve and Bevels of the firft Thicknefs with a turning Saw, in order to find the Arch and Bevels of the fecond Thicknefs ; on the under Side of the Plank or Board, whereof you propofe to Practical Geometry. ir to make it, defcribe an Elliptic Arch equal to that upon the upper Side of the firft Thicknefs, the Semi-tranfverfe and Semi- eonjugate Axes whereof are likewife equal to the pricked Lines, 4, 5, and 4, 6- Then ftrike a fquare Stroke on the Edge from 4, in order to difcover the Middle of the Bafe Line to the Arch on the upper Side of the Second Thicknefs, the Semi-tranfverfe thereof is equal to the pricked Line 7, 8, and the Semi- conjugate is equal to the pricked Line 7, 9 j and faw out the Arch and Bevels thereof with a Saw as before mentioned ; and fo proceed with refped to the reft xm. xnn . payeji Problenu 3 2 A Dissertation on Problem XVII, and XVIII. For the Formation of a Nich or Globe with thin Boards , in order for their being covered with Paper or Pa feboard. Suppofe a f /, Fig . 17, to be the Plan of a Semi-circula Nich, and c ef d , Fig • 18, to be the Board, Paper, or Pafte- board of a given Width, either that of c d, or e f f Divide the Semi-circle a f l into equal Parts according to the Breadth of Fig. 18, as a b, be , cd , de , eg, g h, hi , /i, and hl y draw the Lines b u, c u, du, g u, h u, i u , k u, and let Perpendi- culars fall on the Line a /, from the Points b , c , d , £, £*, ^ j y k. Defcribe Semi-circles upon the Center u, with the Intervals, 0, r, and / ; fet the Girt of the Arch a f or f /, on the Board, &c. Fig. 18, as c a , and d b , which divide into as many Parts as you obferve there are Semi-circles. Divide in the Middle, as by the Line u w, Fig. 18 ; take the Arch a b and fet it in equally on each Side the Line uw, as at ab\ fet the Arch m n after the fame manner on u w 9 as at m n, and fo on to tf\ then let fmall Tacks be Buck in at the Points a, m, 0 , r, t and u, on one Side of uw , and at the Points^, n , p , q and f on the other Side uw y by the Application of a thin Ruler from a to u , and b to u , the Curve Lines will be given which are on each Side, and may be drawn by a Pencil, &c- And this is the true Mold for every Piece in the Globe or Nich required. .r-Tt and (as is requilite fometimes, elpecially in Inch Works as are not expofed to the Weather) here is fhewn the Manner of making the Bells in the Mutules, which mult be fix in Front, and fix in the Projedure, being thirty-fix in each. Their Formation is manifeft by the Plate. 9972/MT) ARCHITECTURE. 4 * The Principal Parts of the Ionic O r d e r, Plate I. A NY Height whatever being given for this whole Order, divide it into ten Parts, allowing two to the Pedeftal, and divide the remaining eight into fix, giving one to the En- tablature, and five to the Length of the Column, inclufive of the Capital and Bale, 1 he faid Length being divided into nine Parts, one will be the Liameter of the Column, which muft be found to regulate fqme of the fmaller Members following. The Height oi the Entablatures is divided into fix, allowing two to the Architrave, one and am half to the Freeze, and two and. an half to the Cornice. The Architrave proje&s one-fourth of its Height, and the Cornice equal to its Height. The Height of the Pedeftal is divided into feven Parts, allowing two to the Bafe and Plinth, four to the Dado, and one to the Cap. The Column is diminifhed one-fixth of the Diameter, from onc-tmrd to the Length of the Shaft, in the fame Manner as the laft Order was, and the Bafe of the Column projects the fame, which gives likewife the Breadth of the Dado o'f the Pe- delta]. The Bafe of the Pedeftal is one- third of the two Parts riven ?' ® a * e ninth, and the Projedion thereof equal to Use Height, and the Cap projects three-fourths of its Height. G • The The Ionic Pedejlal and part of the Shaft of the Column , andl the Bafe . Plate VIII. The Height of the Bafe of the Column is half the Diame- ter, and the Projection one-fifth Part of the whole Diameter,, which gives the Breadth of the Pedeftal, The whole Height of the Pedefial’s Plinth, Bafe, and Cap, was before fully illuftrated ; but as for the particular Members, divide the Height of the Bafe into four Parts,, allowing half a Part to the Fillet, two to the Cymafe, one half Part to the Fil- let, and one to the Hollow. The Projection being equal to the Height, and divided into the fame Number of Parts, each Member appears by InfpeCtion, The Cap is divided likewife into four Parts, allowing one to the Hollow and Fillet, which is one-fourth, another to the Ovolo, another to the Corona, and one to the Ogee and Fillet, which is one- third.. The whole Projection is three of the four Parts of the Height, and each third being divided into three, they are fet off, as, by infpeCting the Plate,, may be feen. , The Height ot the Bafe of the Column is divided into three Parts, one being for the Plinth, and the other two are divided as in the Doric Order, The Bead above the upper Torus is part of the Column, and is double the Height of the Fillets, and the Fillet above the faid Bead is equal to the others. . The Projection likewife is the very fame as the Doric. When thefe Columns are fluted, they muft have twenty-four in Number, and they are a Semicircle in Depth, and the Lift, or Fillet, between each, are one-third; of the faid Flutes, as by the. Plan of one quarter of the Column very plainly appears. The. ARCHITECTURE. 43 The Capital of this Order being more difficult than the for- mer, the next Plate is- referved intircly for that Furpofe. "The Ionic Capital , Plate IX. The whole Height is half a Diameter, and being firft divided into three, the upper Part is for the Abacus, which is divided again into three, one being allotted for the upper Part, half a Part for the Fillet, and one and an half for the lower Part ; From the Middle of the faid Abacus downwards is divided into eight Parts, allowing two and an half from the Bottom to the Volute to the Fillet, half a Part to the Fillet, one to the Aft tragal, and two to the Ovolo ; the reft as before limited. This Column is diminifhed one-fixth of the Diameter, and the Aftragal projeds equal to the Body of the Column below : The Ovolo projeds equal to its Height. To find the Plan of this Capita], makes a Square from A to B, equal to one Dia- meter and an half, and draw the Diagonals, and from the Cen- ter C, on the faid Diagonals, fet off a Diameter each way, and draw the Cants at Right-Angles with the faid Diagonals ; then, lor the Curve of the Abacus, make an Equilateral Triangle (the Part of the Square cut off by the Cants being the Bafe) and the oppofite Angle is the Center for the faid Curve, The Flower is as high as the Abacus and Fillet, and projeds to the Side of the above-mentioned Square. In order to form the Volute, defcribe a Circle on the Center of the- Aftragal, equal to its Height, and make the particular Centers as illuftrated at large at the Bottom of the Plate, at D ; then fixing one Foot ot the Compafs in the Center marked i. extend the other to the Top of the Rim, and defcribe a quarter of a Circle \ then G 2 remove ISSERTATION 0/2 44 remove the Compaffes to the Center 2 : Defcribe ano- ther Quadrate ; and thus, by proceeding to all the reft, in pro- per Order, you will form the outer Line of the Scroll; but, for the Diminution of the Rim, each Diftance between the Centers, is divided into five, and the Part next to the old Center is a new one for the faid Diminution, Uje Ionic 'Entablature. Plate X. The whole Height of the Entablature is divided into fix Parts , (as before-mentioned) allowing two to the Architrave, one and. an half to the Freeze, and two and an half to the Cornice ; as for the particular Members, the Architrave being divided into two Parts, each is fubdivided into eight (viz.) in all fixteen, allowing three to the firft Face, four to the fecond, five to the third, one to the Bead, two to the Ogee, and one to the Fil- let : The Proje&ion is one-fourth of the Height, and the up- per Face hath one- third thereof. The Freeze is formed by making a Triangle on the middle Part of three in its Height, whofe oppofite Angle is the Center for the Curve, or Swel- ling. The Height of the Cornice is divided into eight Parts, al- lowing one to the Hollow and Fillet (which is one-fourth) ano- ther to the Ovolo, and two more to the Modillion and Cap (which is half a Part) the upper four Parts mull be fubdivided into five, giving two to the Corona, one to the Scima Reverfa and Fillet / which is one-fourth) one and an half to the Scima Re j/yj 77 ' .y 1 " iX> kif • „ i ■«•<►• f i *>*'M*> . > •• •*•*.• * ?> »•*. ’ V * ' *-■ * •* - *<»*. V.*<* . .-«■ -■■ • - ■•’ n*i» • ••, J? .».■ 4 I «T • «..•<*.•< ,* • <.<►•***«• •*#. ■*•<** * • •• V-. V • » • . ' . ****** ■■■ .... ,# * • *- *•»«» • • - *** , ” • 4 • ' ' " • • ■ I !»-- *• » * •! •- * i i** *■»—">* ~>* - V . *V«* • - ■+** •*- - "i- — - • » .- 14 , ■. ••• r* ■ , ■ • • •• • * • • * •** * 7* “ - . ! »;■ r divided each into fix Parts, and then, with fome fmall Sub-divifions in that of the Doric } all the Mouldings are fet off, as is plain on the Plate. The next two Orders (viz.) Ionic and Corinthian , are di- vided each into four Parts, and then fubdivided ; the Parts in the Ionic each into four, and thofe of the Corinthian into three, from whence the feveral Members are taken. As to the Compofite, it is divided into feven Parts, and the upper two fubdivided into five, which regulates the Members. All the Projections are fet off from the lower, or firft Face, and in the two firft Orders is one-fixth of the Height, in the two next one-fourth of the Height, and in the laft two-fevenths of the Height ; and as for the Particulars, they are plain by the Divifions and dotted Lines. 1 Impofts of Arches with their Architraves . Plate XXIII., T HESE Impofts are all of them in Height one-ei ghth Part of the Opening of each refpedive Arch to which they belong. And this Height will alfo appear hereafter to be equal to the Breadth of the Pilafter on each Side the Arches. The Height then divide into three principal Parts, and fub- divide each into three (/. e. nine Parts in the Whole) and, by what has been already fhewn, it cannot be difficult to fet off the feveral Members. For the Proje&ions, obferve the "Tufcan has one of the three principal Parts, but the remaining four hath four of the nine Parts of Heights •> and as to the feveral Members, they are feen by Infpe&ion. The Aftragal, at the Foot of them, is one of the nine Parts, and the Fillet half thereof ; the Projection of the faid Fillet is equal to its Height, and the Whole one and one-fourth of the faid Parts. For the Architraves that circumfcribe the Arch, they are formed by the felf-fame Divifions for the Breadth (which is- equal to the Pilafter) and the feveral Proje&ures will plainly appear by a due Infpe&ion of the Plate ; therefore more faid hereon were but Tautology. //yuW.) 0/ ///r/u’j wzd //nr flrc/t/'fawnd P/a/4 XX )|| c 9 a* udm/i / ? //c. on Pedeftals. Plate XLV. On the Top are two more Niches, on Pedeftals, differently dreffed ; and at the Bottom two Venetian Windows- That on the Left Hand, is of the Ionic Order ; the Side-openings are each equal to one-third of the Middle-opening, which is two Diameters to the Semicircle. That on the Right Hand is a Ruftic one ; the Side-openings being each equal to one-half the Diameter or Middle-opening- Plate XLVI. H Aving given a large Variety of Doors, Windows, and Niches in general, on this Plat;e you have the particu- lar Meafures of the Architrave, Freeze, and Cornice. The General Rule is, to be guided by the Breadth of the Architrave, whofe beft Proportion is one-fixth of the Breadth L 2 op of the Opening (as given before) but ought never to be lefs than that, nor more than one-fifth. Thefe three are not only different in the feveral Members, but in the general Proportion, and yet formed from the Archi- trave. No. i. Is of a Tufcan Kind ; the Breadth of the Architrave being divided into four Parts, three of fuch is the Height of the Freeze, and five of fuch the Height of the Cornice. No. 2. The Freeze is made equal to the Architrave, and that being divided into four Parts, five fuch is the Height of the Cornice, or (which is the fame Thing) if a Height were given and divided into thirteen Parts, the Architrave hath four, the Freeze four, and the Cornice five. No. 3 * Is different ftill ; if a Height be given, divide it in- to three, one is the Architrave, and the other two divide into feven, giving three to the Freeze, and four to the Cornice ; or the Architrave being given, divide double the Breadth into feven, will be the fame Thing. * Hereby, this Proportion will form the Architrave the Height of that in No. i- and the Cornice, the Height of that in No- 2. as appears by compare. As to the forming the feveral Members, they are fo obvious by Infpe&ion, and a right Knowledge of the former Rules, that it mult be needlefs to mention them any more, the Scales and Figures being fufficiently plain. /VtoeXEm. LI /to HIT Mate UV /°/a& L 77 pA/ft /7 y%A-IX ARCHITECTURE. 77 Of Chimney-Pieces . Plate XL VII. T HEY muft be made larger or fmaller, in Proportion to the Size of the Rooms were they are intended. On this Plate are four different Sorts ; the Opening of them all is a perfect Square, and the Architrave is one-lixth of the Opening, and the Pilafters the Half thereof • all which is plain by the dotted Lines. Plates XLVIII, XLIX, L, LI, LIL Contain twenty different Sorts of Chimney-Pieces, with various and uncommon Ornaments- Plate LIII, LIV, LV. On thefe are Ex different Manners of forming Chimney- Pieces, with Frames for Pi&ures over them, which are ex- ceeding rich and ornamental. Plate LVI. Is an exceeding grand Chimney-Piece, defigned by Mr- Kent, and executed at Sir Robert Walpole s, at Houghton in Norfolk. Plate 78 A Dissertation on Plate LVII. In this Plate there are three feveral Kinds of Mouldings for Pi&ure Frames, or Pannels, with the Method of their Carving. Their Breadth and Projection are divided and figured, fo that they mu ft be eafy to underftand. HIS Plate contains not only the Plans, but the Sections of Rooms, according to that great Mafter Palladio. The Proportions being as follows (viz.) Round, as A; Square, as B ; or the Length continued to the Diagonal of the Square, as C ; or a Square and one-third, as D ; or a Square and a half, as E ; or a Square and two-thirds, as F ; and laftly, of two Squares, as G. They are made either with an arched or flat Cieling ; when the latter is ufed, the Height from the Floor to the Cieling muft Plate LVIII. Contains four Kinds of Mouldings, for fmaller Pannels, which are to be ufed between the others for Variety. The Divifions For the Proportions of Rooms , and the Manner of Coving the Cie lings. Plate LIX. be AW** /y^LYin ^ XXXI XX XX XX XX JUCXX JC-XJUL * 3 n ^mmmmmmiMO It [71 ^-—---m 'k >5, ' f / IT 12 /^ixr r i I 1 L L 1 U K L, 79 be equal to their Breadth. If on the firft or principal Sto- ry, the Rooms over them may be one-fixth Part lefs in Height. Here are fix Sorts of Arches, viz, Croffed, Faciated, Flat (be- ing a Segment lefs than a Semicircle) Circular, Groined, and Shell-like ; all which are in Height equal to one-third of the Breadth of the Room ; the four firft were ufed by the Ancients, but the two laft are of a modern Invention. Of deling s , and their proper Ornaments . Plate LX. This is divided into fquare Pannels in the Corners, and a large Circle in the Middle, proper for Painting, Wc. The Borders, or Margin, are ornamented with Frets and Guilochi’s. Plate LXI. Are two more Defigns for Cielings, the laft being proper for a Gallery. Plate LXII. Here are different Defigns of Compartments for Domes, or Cupolas, and proper Ornaments for the Soffites of Ar- cades, A Dissertation -■ Winding Stairs . Fig. 5 Thefe are fuch as are always winding and never fly. They go round a folid Newel, whofe Diameter is equal to the Length of the Steps, or one- third of the whole Well-hole. Fig- 6. Thefe are alfo all Winders round an open Newel ; the Steps being in Length one-fourth, and the Opening half of the Well-hole. Thefe Kind of Stairs are moftly ufed in Church Steeples, Caftles, and fuch publick Buildings. Other Kinds of Stairs . Plate LXXXII. Fig. i. Thefe Sorts of circular Stairs are feldom or never ufed for Beauty, but rather becaufe they go up in lefs Room, and if contrived in the Middle of the Building, they admit of being better lighted from above than other Stairs. Fig- 2. This is a mixed Stair-cafe of Flyers and Winders, and hath a quarter Pace in the Middle, and may be lighted by a Bow Window in the Semicircle- Great Care fhould be taken in the forming this Sort of Stairs, that all the Steps, in the Mid- dle of the Length, be of one and the fame Breadth ; for by this Means, the Feet, going in the Middle, will feel no Difference, the broad Ends of the Winders next the Wall, or the narrow Ends next the Rail, being feldom in Ufe, except when two Per-fons meet, or go up, or down together. Fig. 3. This is a circular Stair-cafe, in two Parts, or rather two diftinct Stair-cafes, which may lead off, from the Landing Places, to contrary Apartments, and is to be lighted from above. ^ ft) ARCHITECTURE. 9S Fig. 4. Is an oval Stair-cafe, with a large Twift to the Rail at Bottom, and hath two Doors, or Entrances. Fig. 5. Is a large commodious Stair-cafe, partly like Fig. 2. Plate LXXXI. only hath a much grander Entrance by four feveral Ways, and, as the Steps fly round a folid Newel, the back, or private Stairs, are made (as it were) in the Bowels thereof. Fig. 6- The French Nation being very humorous in their Compofitions of Stairs, and being fo far different from ours, here is fhewn a Specimen of their Manner, which mult have an extream grand Appearance, though they are generally too much crouded up, and are very expensive. The Plan will explain it felf by Inlpe&ion, therefore it were needlefs to dwell any longer on this Subject of the Plans o i Stairs ; but, whereas, in many of them, Twified Rails are introduced, I fhall proceed, on the next Plate, to fhew the Manner of forming them. For the Formation of the Arch , or Mould , to the Rail of every St air- cafe which is to be circular , on Part of the two fir ft Steps , fo as it Jhall fta?id perpendicular over the Ground , or Flan , , with the Manner of fquaring the faid Rail without fetting it up in its Place till finified. ” Plate LXXXIII. Fig. 1. When you have made your Plan, and thereby found the Breadth, or Tread of the Steps, and having alfo fixed on the Bignefs of the intended Rail, with the Form and Proje&ion of the Mouldings, as Fig. 2 ; then the Front of the fecond Step, between A and B muft be continued out farther, and thereon defcribe a Circle, touching the Infide of the Rail, and whofe Diameter 96 A Dissertation on Diameter mu ft be equal to the Breadth of two Steps, which divide into eight equal Parts ; then on the Center of the Pud Circle deforibe another Circle equal to the Bignefs of the Rail, Fig. 2. and alfo another Circle to the Extremity of the Mouldings, as a , b , c, d . Draw the diagonal Line c F, and defcribe the Part of a Cir- cle a g ; and, dividing it into eight equal Parts, continue them from the Center to the Line F HI K L M NO fo will you have the diminifiiing; Scale for the Formation of the Scroll. Then, trensferring the relpedtive Diftances FH, FI, FK, FL, Wc. within the great Circle, on each eighth Part thereof, and taking theDiftance from the main Center C toF, find the Cen- ter in the Eye, or Block, as at /, for the firft eighth Part of the Scroll ; then the Diftance C H, for the next eighth, and fo proceed to them all, and you will have the whole Scroll compleated and finifhed in the Block, at one Revolution cf a Circle. But here it is to be obferved, That the infid e Scroll, though drawn from the fame Centers, muft not meet on the aforefaid eighth Parts of the great Circle, but a Line drawn from the outer Scroll to each Center refpectively ; and the whole eighth Part being marked with fmall Letters, the fame as the diminifiiing Scale, it cannot need farther Explanation. For forming the Scroll of the firft Step A, the fame Method is to be ufed as above ; only obferve, that as it begins to be circular from the fecond eighth Part, the Diftance to the Rail muft be divided into feven Parts, and gathering in one at a Time, it will be compleated. Should it be required to make the Scroll of a larger Revolu- tion, as Fig. 3. defcribe a Circle, whofe Diameter is equal to three Steps, and divide the diminiihing Scale into twelve Parts, and ARCHITECTURE. 97 and by proceeding, as before, to ftrike one-eighth of the great Circle at a Time, you will have the Scroll, at one Revolution and a half of a Circle. But wanting it ftill larger, make a Cir- cle whole Diameter is equal to the Breadth of four Steps, and the diminifhing Scale divided into fixteen Parts, the Scroll will be formed at two Revolutions of the Circle ; this mud needs be plain enough by barely infpe&ing the Letters, &?c- Plate LXXXIII. For fquaring the Rail A Mould mull be traced out to find a Sweep, which, if ap- plied on the Rake, will be perpendicular to the Ground of rfpq, as Fig. 4 ; but obferve, there will be required fome (extraor- dinary or) more Wood on the Top of the Rail, as at a b. Fig. 5. and alfo at the Bottom, as c d • To find how much it rnuft be, take Notice where the Tvvift begins in the Plan, Fig. 1. as r f and alio, that at k the Twill: ends; therefore the Diltance from r tok is divided into a Number of equal Parts, and they muft be transferred on fome Line, as from r to k. Fig. 6 ; alfo take the Diftance r t, and apply it to the Pitch-Board (which is the Tread and Rife of each Step) Fig. 7. as from a to b , and raife the Perpendicular b c ; then in Fig. 6. from r, the End of the Line, make the Triangle re d, equal every Way to that of a be, Fig. 7. Finally, from e to d, and from and to the extream Points b , d , /, &c. they bend round feveral thin Pieces of the Wood the Rail is to be of ; the architecture. ro , HitfSfxvm ‘ r™ be "' E j h ? Hdght rf the Rail fl,cwn "> T , • , L ^ XX , ; f 1 ?' 2 - aad r ° many of them as will make the 1 hicknefs ; thcfe being glewed, or otherwife fattened together T a L° n VJ T ^ °tf fwm the C 5' linder > wi]1 be the Rail R, ami exadly iquared to the right Twift by w - u *>”'*“ *v«r Note, Either this Way, fhould die Well-hole be an Plan. or the foregoing, is undeniable, Ellipfis, or any other Figure for its Juft Publijhed (Being the compleateft Book of its Kind extant) Printed for James Hodges, London-Bridge. Price Bound 3 s. t, np HE Builder's Guide, and Gentleman and Traders AxTiftant : Or, a Univerfa! Magazine of 1 Tables. Wherein is contained greater Variety than in any other Book of its kind, witn ieveral new and ufei ulTablFs, never before publilhed ; which render it the moil genera , complete, and « nl ^ er1 ^ 1 Companion, for daily Ul'e, extant; and highly neceflary for all Gentlemen, Builders, Purveyors ofXmld- ings, Timber Meafurers, Carpenters, Bricklayers, &c. Alio for Merchants, Shopkeepers, and all Tiadef- nen that deal either bv Wholefale or Retail : Containing Tables of Timber, Board, and Plank Meafure, of Square and Cubical 'Meafure in general, either by the Foot, Yard or Rod; the Loads contained im any Number of Feet, of either rough or fquar’d Timber, or of Plank of any Thicknefs .Of the Redudm Brick-work, from i Foot to 4828 Feet, and to any Thickneis required • What Number of Bricks > are re- quired to build any Piece of Brick- work, from 1 to 14000 Feet, and at any Thicknefs . W hat Number ot Bricks, Lumps, or Clinkers, laid flat or edge-ways, or of paving Tiles, orPammants of any Size, wiilpa e any Floor of ids than 6- o Feet : What any Number efodd Feet, in a fuperflcial or folid Yard, comes to ;, at any Price, from a Farthing to 10 1 . per Yard : The Value of any Number of odd Feet of Tiling, Slating, Roofln?-, Flooring, Sec. performed by the Square of 10 Feet iquared, at any Price from 3 s. o 5 or 1 . per YaTd : The Value of any odd Feet of Brick-work, or others, performed by the Rod fquare, at an} Price from 3 s. to 10 1 per Rod : What any Number of Feet, Yards, Pounds, Ounces, &c. come to any Price per Foot, &c. The Value of any odd Parts of a Hundred, at the Rate of 1 1 z or 120 to the Hundred, at any Price, from 2 s. 6 d. to 8 1 per Hundred : The Value of 1 Foot in Length, of any fort of Limber, when fquared and cut to any Scantling lit for Building, at any Price per Foot cubical A Reduaion ^ common Tables of Coins, Weight and Meafure ; and a perpetual Almanack. The Whole ilL.irated .by a creat Variety of Examples, applicable to the various Branches of Trade in general, and a ter oconci tliod, that render it ufeful to all Artifts, and eafy to e\ r ery Capacity . By W. Salmon, jun. arpen er, CJdeJfcr. * Where likeaxife muy hn had, jujl ■publijhed, by the fame Author. . 2 The Country Builder’s Eflimatot : Or, The ArvhUe&’s Companion for Eftimating of New Buildings, or Repairing of Old; in a concife, eafy Method entirely new ; and of life to Gentlemen or their Stewards, Mailer- Workmen, Artificers, or any Perfon that undertakes or lets out Work : Wherein the feveil Ar- tificers Work concerned in Building, and every Article belonging to each of them are fully, diftmaiy, and feparately confide red ; and the Prices thereof inferted, not only of the Workmanlhip but .of the Materials alio; and what Quantity of Materials are required to the Performance thereof ; with the ^ Man- ner of taking Dimenfions, Meafuring and Valuing the fame. To which is added. Several New Tables (never before publilhed) for the valuing of Oak, or any other Timber that is fquared and cut to any bcant- lincr or Size fit for Building. Price 1 s. 6 d. . . r x. ? A New Defcription of all the Counties in England and W ales: Containing, I. In every Diocefe, what Circumference of Miles, Number of Acres and Houfes, the Air and Soil, Rivers, Commodities and chief Seats of the Nobility and Gentry of each County. II. Market Towns, Market-Days, and Diftance from London. 111 . Members of Parliament. . IV. Fairs, fixed, and moveable. V. Coaches, Can lers, and Water hound. VI. What Days they go out of Town. VII. Roads from London to the chief lowns, and Crofs Roads. Each County diitinft by itfclf. Alphabetically, very plain and eafy ; the like not ex- tant. Likewife the Rates of Coachmen, Carmen, and Watermen, in and about the Cities of London and JVcfminfhr .. The Fourth Edition, carefully Corretttd. To which is added, A Compleat Index, for the more eaiy finding out what County each 1 own is in. Price I j. 6 if. Juft Publijhed , printed for B. Cole, Engraver, the Corner of King’s-Head Court, .near Fetter-Lane, Holborn, Price for fmall Paper in Sheets it. 10 s. and the large 1 apst 2 /. 2 s. A NDREA PALLADIO’S Architefture. In Four Books. Containing A Differtation on the Five Orders, and the moll neceflary Obfervations relating to all Kinds of Building. As alio, Fhe : different Con- iiJtuctions of Publick and private Houfes, Highways, Bridges, Market-Places, Xyftes, an emp es, \vi ^ their Plans, Sections, and Elevations. The Whole containing 226 Folio Copper ! lates. Carefully Reviled aud Redelincated by E. Hoppus, Surveyor to the Corporation of the London Ajjurance , and embellilhed with, a large V ariety of Chimney Pieces. Collected from the Works of Inigo Jones , and others.