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 in 2017 with funding from 
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A SURE 
 
 Guide to Builders : 
 
 Or, The PRINCIPLES and PRACTICE of 
 
 ARCH I TECTURE 
 
 Geometrically Demonftrated, and made Eafy, 
 
 For the Ufe of WORKMEN in generaL 
 
 WHEREIN 
 
 Such Geometrical Definitions, Theorems, Problems, &c. 
 as are the Bafis of Architecture, are render’d eafy and intelligible 
 to every Capacity. 
 
 As aHb their various USES illuftrated, in the Conftrudtion of Decimal 
 and Diagonal Scales, Meafuring and Drawing Geometrical Plans and Uprights 
 of Buildings $ deferibing all the Moldings uled in Architecture $ Diminifhing, 
 Fluting, Cabling, and Wreathing the Shafts of Columns and Pillafters ; 
 deferibing the Ionick Volute, Divifion and Proportion of Rufticks; delineating 
 the Five Orders of Columns according to any Proportions affign’d, and to 
 determine the Pitch of Pediments, l$c. 
 
 Together with the general PROPORTIONS of Pedeftals, Columns, 
 
 Entablatures, Imports, and their various Difpofitions or Intercolumnarions 
 in Portico’s, Columnades, Arches, Doors, Windows, &c. 
 
 Curioufly fele&ed and drawn 
 
 From the moft rare Antique, as well of Rome, and other Places where 
 Architecture has flourifh’d, as of Vitruvius, Palladio, Scamozzi, 
 Vignola, Serlio, Perault, JBosse, Angelo, and other celebrated 
 Archite&s, Antient and Modern. 
 
 To which is added, An APPENDIX. 
 
 Wherein the feveral ACls of Parliament, now in Force, relating to Builders, 
 Building, and Materials, are explain’d for the Service of Surveyors, 
 Master-Builders, Workmen, and Proprietors of Buildings. 
 
 The whole illuftrated with great V ariety of Grand Defigns for Frontilpieces 
 Doors, Windows , Cieling-pieces, Pavements , &c. with the Thermes and 
 Columns, enrich’d after the antient Grecian and Roman Archite&s, curioufly 
 engraven on Eighty-two large Copper Plates. 
 
 By B. LANG LE T. 
 
 LONDON: 
 
 Printed for W, Mears, at the Lamb without temple-bar ; J. Wilcox, 
 
 at the Green Dragon in Little Britain ; ThO- W RIGHT, Mathematical Inftrument- 
 maker, (to his Majefty) at the Orrery and Globe in Vleet-ftreet ; and by the 
 Author, at Palladio' sHead, near Exstcr-Change in the Strand. 1729. 
 

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T O 
 
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 Thomas Sc awn, E% 
 
 SIR, 
 
 H A T I take the Liberty to infcribe 
 to your Patronage the following 
 Sheets, containing the Principles 
 and Praiticeof Arch itect ur e Geome- 
 trically Demonftrated, &c. is with due 
 Regard to your Knowledge and great Abi- 
 lities in every laudable Science, but more 
 particularly in This ; which is illuftrated by 
 that mod magnificent Structure, now railing 
 at your delightful Villa at Carjhalton, which 
 will perpetuate your Name and Family to 
 Pofterity. 
 
 A 2 
 
 Thefe 
 
DEDICATION. 
 
 Thefe Difpofitions being happily joined 
 with a liberal Mind, a polite Education, an 
 affable and courteous Behaviour, render 
 you the Delight of your Country, as well 
 as an Ornament of the Britijh Nation. 
 
 May you long continue an Encourager 
 of Arts and Sciences, the common Patron 
 of the County you Reprefent, and a gene- 
 rous Benefactor to Mankind, are the lincere 
 Willies of, 
 
 SIR, 
 
 Tour mojl Obedient , and 
 
 moji Humble Servant , 
 
 Batty Langley. 
 
0C-Z^Q^c!— J^Q SC^D36€gg)Q S^ss^OOCaa^Q Q C^ QSi CIIS Q 
 
 POTlMTOiPW^OT^ll . _ 
 
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 A N 
 
 ADVERTISEMENT 
 
 T O 
 
 WORKMEN, 
 
 To be firft Read by them before they pro- 
 
 
 ceed to the following Work. 
 
 INCE my real Defign herein is to retider the (Propor- 
 tions and Practice of Architecture more accurate , eafy , 
 and familiar , than has been yet done by all the Authors 
 hereon extant , I have therefore digefted this Work in 
 the mofl infiruCtive , plain , and demon f native Manner 
 that I am capable of doing ; and which, I hope , will enable every 
 one , who delights in this noble Art , mofl eafily and mofl readily to 
 demon f rate the Reafon and EffeCts of all the Operations which 
 they are to perform. 
 
 And in Conji deration that Geometry is the very Bafts or Funda- 
 mental of Architecture , I have therefore , in the Firjt , Second, and 
 Third Chapters, laid down fuch filed Definitions, theorems, and 
 Problems, which mu ft be well under food by every one that is defi- 
 rous of being a found good JVorkman, before he can pofitbly arrive 
 thereto. 
 
 And in order to the young Student's Accomplfbment, I muft ad- 
 vife him , that he never read at any one Time, more than he compre- 
 hends, and well under ft ands, and which he mufi be very fire of be- 
 fore he proceeds any further • that is, he mufi not prefume to pro- 
 ceed to the fee on d Definition, Theorem, Problem, &Cc. before he 
 
 well 
 
PREFACE. 
 
 weft underfunds the Reafon and Operation of the fir ft ; left , by too 
 haftily pafftng it over , he imagines that he knows that , which he in 
 Fail doth not , whereby ever after every thing becomes difficult and 
 tinpleafant , which otherwife would be eafy and delightful. 
 
 if o be a good Workman , or a compleat Arfift , there’s requir'd a 
 very fober and clofe Application \ and when any Difficulties a rife, 
 the Student mufl not therefore be difhearten’ d, but emulated , and 
 vigoroujly labour until he has furmounted them , which , when com - 
 pleated , crowns his Endeavours with unparallel’d Satisfaction and 
 Delight. 
 
 And that nothing may eaftly flip away after known , he muf there- 
 fore ingraft all his feveral Operations by many and frequent Per- 
 formances thereof ; which will fo well eftablifo them with him , as to 
 make him moft readily perform and demo nft rate the fame at any 
 time when requir’d. 
 
 If young Students (for whofe Sake I have compiled this Work ) 
 would imphy their le'tfure Hours herein for the Space of one Month , 
 or two at moft, they might be fully inform’d in the Knowledge of 
 the fir ft three Chapters hereof ; after which , in the like Space of 
 firm , they would pafs thro’ all the remaining , wherein the preced- 
 ing are apply’ d to PraClice in drawing Plans , Uprights , describing 
 of the feveral Moldings and Ornaments ufed in Building, delineating 
 of Columns and 1 Wafers, with their Entablatures , enriching them 
 with their ref petdive Flutes, Fillets, Ru flicks, &£c. according to 
 the general Proportions of Vitruvius, Palladio, Scamozzi, Vignola, 
 Serlio, Perault, BofTe, and Michael Angelo, contain’d in the fol- 
 lowing Chapters to the End. 
 
 And for the Ufe of Gentlemen, Surveyors, Mafter Builders , and 
 Workmen , I have enrich’d the whole with great Variety of curious 
 and ufeful Defgns of Doors , Windows, Chimney-pieces , Cieling- 
 pieces , Pavements, Arches, Ruficks , &c. according to the grand 
 eftablifh’d Proportions of the moft celebrated Architects, as well 
 antique, as ant lent and modern'. And whereas no general Meafures 
 have been yet efablifh’d to determine the Proportions of the feveral 
 Parts of Doors and Windows miverfally, to any ajjtgn’d Breadth 
 whatfoever, I have therefore in Plates LI. LII. LV. deliver’d the 
 fame in a very concife and eafy Manner, as follows : 
 
 Firft, Having the Breadth or Diameter of the. Door or Window 
 given , you muf divide the fame into 6 equal Parts , and any one of 
 thofe 6th Parts into 1 0 equal Parts j and then fuppofng the other 
 
 5 Parts 
 
P R E F A C E. 
 
 5 Parts to be divided in the like Manner (which need not be 
 done) the whole Diameter will be divided into 60 equal Parts : And 
 as the Diameter of a Column is divided into 6 o equal Pdrts, call’d 
 Minutes, whereby all its Meafures are determin’d , fo in like Man- 
 ner I call the Breadth or Diameter of a Door or Window its 
 Module , and the 6 o equal Parts 1 call Minutes , by which I give 
 every Member its due Height and ProjeClure, according to the re - 
 fpettive Meafures placed upon the fever al Parts , as exhibited in the 
 aforjfaid Defigns. 
 
 The Heights of the fever al Windows and Doors following , are , 
 for the general Pari, of two Diameters in Height ', but where Ne- 
 cejftty requires, the Windows may be of leffer Heights, but not lefs 
 than the Diagonal of a Square, whofe Side is equal to the Breadth 
 of the Window, excepting in an Attic Story, and then their Heights 
 Jhould be fomething more than their Breadths, that thereby they 
 may appear to be truly fquare, which they never can do, zvhen they 
 are made exaClly fquare. 
 
 7 " his (feems to be a Parodox, and ) is caus’d by the Projection of 
 their Stools , whofe upper Surfaces eclipfe the lower Parts of the 
 Windows, and that more or lefs according to the Difance that they 
 are view’d ; and it is in fuch Proportion that their Heights Jhould 
 exceed their Breadths. 
 
 7 * he like is alfo to be obferv’d in the Architraves of Arches over 
 Impof s , which do never appear to be Jemicircular , as they Jhould 
 do, but when the Rye is level with the upper Fillet of the Impof ; 
 and therefore, Jince by the Projection of the Impof s, the Height of 
 the Semi-circle is diminifh’d, it is therefore very reafonable , that 
 the Architraves of Impof s, whofe Projections are any thing large, 
 f could be carry’ d up perpendicular to fuch Heights above the Impofls , 
 as for the Eye to plainly difcover the very frf Spring or Beginning 
 of the Jemicircular Arch \ and as this perpendicular Height is to be 
 determin’d difcretionally , according to the Difavce that the Impoft 
 is to be view'd, I have therefore omitted to reprefent the fame in 
 the two Plates of Impof s XXX. and XXXI. 
 
 And fince that many Windows are oftentimes adorn’d but with 
 Arches, or Ruficks of rubbed and gaged red Stock Bricks, I have 
 therefore, for the Uje of Bricklayers, in Plates LVII. and LVIII. 
 exhibited the various Kinds of freight, fcheme , femi- circular, and 
 femi-ovallar Arches , whofe ConfruClions are difcover’ d at fir f Sight, 
 thofe of the Semi- ovals excepted , whofe ConfruClions are as follow : 
 
 fo 
 
-PREFACE. 
 
 To make the frongefi Arch , you mu ft divide the upper Curves of the 
 Hunches and Scheme , Fig. I. Plate LVIII. as AC, C E, and 
 EH, into equal Parts , ( which muji not exceed the A hi chiefs of 
 your Bricks when rubb'd). 
 
 A he Courfes of the Hunches A C and H I, muf be drawn to their 
 Centers K and L, and the Courfes of the Scheme CE,EH^ M, and 
 thus will the center al Joints be compleated. 7* he circular Joints may 
 be divided at Bleafure ; but they have the bef Fffelt when they con- 
 ff of a Stretcher , a Header , and a Clofer , making every Header equal 
 to half a Stretcher , and every Clofer ' equal to half a Header . 
 
 By this Method of Confrudlion , thefe Kinds of Arches are much 
 f conger , than when they are made for their Courfes to appear all 
 equal , as Fig. III. where the Courfes in the lower Curve BEFG, 
 appear equal in Breadth to one another , as thofe in the upper Curve 
 ACDH; which the others , thofe of the Hanches A C and H I, 
 Fig. I. do not , being lefs than thofe of the Scheme G E H. 
 
 ‘The EUiptick Arch of Ru [ticks. Fig. II. is divided without any 
 Recourfe had to Centers , as Fig. III. and the femi-oval Arches in 
 Plate L VII. have their Courfes in each of them , one Side thereof 
 divided with Recourfe to the Centers of the Ovals , and the other 
 Sides from the equal Divifons contain'd in the upper and lower 
 Curves , without any Recourfe had thereto . 
 
 And whereas there are divers Adds of Parliament , now in Force , 
 for the Regulation of Builders , Buildings , and Materials , I have 
 therefore in an Appendix explain'd all the material Parts thereof 
 which are abfolutely neceffary to be made known to every one con- 
 cern'd in the Art of found Building. 
 
 And to compleat this /Fork, I have faithfully deliver’d the Five 
 Orders of Thermes and Columns , as they were originally made and 
 enrich’d by the old Grecian and Roman Architects, which, though 
 different from our prefent eflablifh'd Proportions, yet have their 
 peculiar Beauties and Fffedts, that are well worth the Notice of the 
 mof Curious, and perhaps may prove a good Help to Invention . 
 
 June 20. 1729= 
 
 Batty Langley. 
 
CONTENTS. 
 
 CHAP I. 
 
 E 0 ME TRI CA L 'Definitions 
 Def. i. Of a Point 
 
 2. Of Lines 
 
 3. Of an Angle 
 
 4. Of Superficies 
 
 Page 
 
 5 
 
 ibid. 
 
 6 
 
 ibid. 
 
 7 
 
 ibid. 
 
 5. Of Superficial Figures 
 
 6. Of a Circle and its Tarts * 
 
 7. Of Angles and their Kinds 
 S. Of the fever al Kinds of Triangles 
 9 . Of the fever al Kinds of four fide d Figures 
 
 1 o. Of regular Polygons 
 1 1 . Of circumfcrib’d and inf crib' d Figures 
 1 2 Of the Tower uf a Line , demonfirating the Pea fin of 
 Multiplication , See. 15 
 
 1 3 . Of Solid Bodies 1 7 
 
 14. Of the Altitude of Figures 21 
 
 9 
 1 1 
 
 12 
 
 13 
 
 14 
 
 CHAP. II. 
 
 Geometrical T heorems ; demonfirating the Rea fins of the Menfu, 
 ration of fuperficial Figures , as Triangles , Circles , Tolygons , 
 Parallelogram^ , Sc c. from 21 to 36 
 
 CHAP. III. 
 
 Geometrical Problems 3 7 
 
 Prob. 1. To raife a Perpendicular by feven different Methods 
 
 37 , 33, 39 , 40 
 
CONTENTS. 
 
 Prob. 2. To let fall perpendicular Lines pag. 41 
 
 3. To divide right Lines and Angles by Perpendiculars 42 
 
 4. To draw parallel Limes 4 3 
 
 5. To meafure the Quantity of Angles by the Line of Chords, 
 
 ProtraPlor , &c. 44 
 
 6. To defcribe Ellipfis’s or Ovals by various Methods 4 6 
 
 7. To defcribe an Equilateral Triangle 50 
 
 8. To defcribe an Ifoceles Triangle ibid. 
 
 9. To defcribe a Scalenum Triangle ibid. 
 
 io= To defcribe a Geometrical Square 5 1 
 
 11. To defcribe a Parallelogram ibid. 
 
 12. To defcribe a Rhombus 52 
 
 1 3 . To defcribe a Rhomboid ibid. 
 
 14. To defcribe any regular Polygon, as Pentagon , Hexagon , 
 
 Sept agon, 0 PI agon, Nonagon, and Decagon, having a 
 Side given 5 3 
 
 1$. To perform the preceding, having the Diameter given 54 
 
 CHAP. IV. 
 
 Wherein the preceding Problems are apply' d to PraPlice, in meafir - 
 ing and drawing the Geometrical Plans and Elevations of 
 Buildings, Columns , P Wafers, &c. 5 6 
 
 Prob. 1 . To make Decimal Scales of Feet and Duodecimal Scales 
 of Feet, and Inches ibid. 
 
 2. To delineate a right-lined Triangle by the Decimal Scale 
 
 of Feet 5 7 
 
 3. To delineate a right-lined Triangle by the Duodecimal 
 
 Scale of Feet and Inches 5 8 
 
 4. To meafure divers given Length's by the aforefaid Scales 
 
 ibid. 
 
 5. To make Angles equal to given Atigles 60 
 
 6 . To meafure the Quantity of Angles by the Help of a 
 
 common five or ten Feet Rod, &c. <51 
 
 7. To defcribe a Circle , whofe Circumference Jhall pafs thro' 
 
 any three given Points that are not in a right Line 6 2 
 
 8. To make the Plan of any irregular Curve, which is not 
 
 any Part of a Circle , Ellipfis, &c. ibid. 
 
 9. To lay down in Plano the Outlines of Buddings in ge- 
 
 neral 64 
 
 10. To 
 
CO N T E NTS. 
 
 Prob. io. To take the Dimenfions of Walls and Earth ions of 
 Buildings , and to delineate the fame by the 'Duodeci- 
 mal Scale of Feet and Inches pag. 68 
 
 11. To delineate Geometrical Elevations or Uprights of 
 
 Buildings in general 7s 
 
 12. To defer ibe Geometrically the fever al Moldings ufed in 
 
 Architecture 79 
 
 J 3 'To delineate the Tufcan Column 84. 
 
 14. To defer ibe Geometrically the Eggs and Anchors of the 
 
 Ovolo 94 
 
 15 -To delineate the wreath'd Shaft of the Dorick Order 9 6 
 
 1 6. To delineate the wreath'd Shaft of the Ionick Column 97 
 
 17. To delineate the wreath'd Shaft of the Corinthian Co- 
 
 lumn ibid. 
 
 1 5. To divide the Rnfticks of the Tufcan, Dorick, Ionick 
 
 Columns 9 g 
 
 1 9. To divide and draw the Flutes of the Dorick Column 1 o 1 
 
 20. To divide and draw the Flutes and Fillets of the Ionick 
 
 S haft 103 
 
 21 •To divide and draw the Flutes and Fillets ofTillaflers 1 04 
 
 CHAP. V. 
 
 Of general Troportions of the Five Orders of Columns in Archi- 
 tecture^ according to the 'Proportions of Vitruvius, Palladio, Sea- 
 mozzi, Vignola, Serlio, Perault, BoflTC, and M. Angelo 1 06 to 1 29 
 
 CHAP. VI. 
 
 Of Pede flats and their Ornaments ! , Q 
 
 A Table exhibiting the different Heights of Pedefals , as practis'd 
 by antient Architects r 3 1 
 
 A Table exhibiting the Proportions of the principal Tarts of Pede- 
 fals, viz. their Bafes , Dies, and Capitals , as practis'd by the 
 Antient s I3+ 
 
 A Table exhibiting the Project tires of the Bafes and Cornices of Pede- 
 fals, as practis'd by antient and modern Architects 137 
 
 CHAP. VII. 
 
 Of Columns , and their Ornaments. ' j 3 g 
 
 C b 2 1 A Table 
 
C O NT E N T S. 
 
 A fable of the antient and modern TrojeCtures of the Bafes of 
 Columns pag. 13 9 
 
 A Table of the different Heights of Columns , as practis’d by anti- 
 ent and modern Architects 1 4 1 
 
 A Table of the ‘Diminution of Columns , taken from the Ant lent s 1 4 3 
 
 CHAP. Yin. 
 
 Of Entablatures, and their Ornaments 14 ^ 
 
 A Table of the different Heights of Entablatures , practis'd by 
 
 antient and modern Architects 146 
 
 A Table exhibiting the different T’rojeCiures of Entablatures, accord- 
 ing to the proportions of antique and modern Architects 1 47 
 
 CHAP. IX. 
 
 Of Pit Infers, and their Elutings 14 8 
 
 CHAP. X. 
 
 Of divers Errors committed by fome Architects in their Manner of 
 placing Columns and 'Pill afters at the Angles or Quoins of Build- 
 ings, &c. 
 
 CHAP. XL 
 
 Of Pediments 15 3 
 
 CHAP. XII. 
 
 Of the Proportions of Halls, Antichambers , Chambers f Galleries , 
 Gates , Doors, Windows, &c. 155 
 
 CHAP. XIII. 
 
 Of Floors, Ceilings , Pavements , Chimnies, St air -cafes, &c. 157 
 
 THE 
 
C^V T^m^t 'j^*b -Jt>£iS i^*V j *yV 
 
 THE 
 
 PRINCIPAL MATTERS 
 
 Contain’d in. This 
 
 WORK. 
 
 A’ 
 
 BACUS 86 
 
 — its Etymology ibid. 
 
 Acute-angle, what io 
 
 ~— how meafured ibid. 
 
 Altitude of figures 21 
 
 Ambligonium Triangle 11 
 
 Angles 6 
 
 — their Kinds 9 
 
 B 
 
 Bale of Triangles, what 13 
 
 Bafe of Columns, why firft ufed 106 
 Black-led Pencils 4 
 
 Builders Didlionary ufclefs 2 
 
 — how meafured 
 
 10, 44 
 
 
 
 — how denoted by three Letters xo 
 
 Cathetus, what 
 
 IS 
 
 ■ — to divide 
 
 42 
 
 Cablings of Fluted Columns 
 
 103 
 
 • — how taken with five , 
 
 ten Feet. 
 
 Cariatides Order 
 
 105 
 
 &c.. Rods 
 
 6 1 
 
 Capital, its Etymology 
 
 86 
 
 • — Solid , how. taken 
 
 63 
 
 — with Mouldings 
 
 ibid. 
 
 Annulet 
 
 87 
 
 — with Ornaments 
 
 87 
 
 Antichambers, their Proportions 1 55 
 
 Capitals 
 
 126 
 
 Arched or Arch Lines 
 
 9 
 
 — their Heights 143 
 
 3 144 
 
 Architrave, what 
 
 90 
 
 Cantaliver 
 
 114 
 
 — its Etymology 
 
 ibid. 
 
 Caveto, how defcriV d 
 
 82 
 
 Arteoftyle 
 
 109 
 
 Chord Lines 
 
 8 
 
 Aftragal, its Etymology 
 
 89 
 
 Chapiter of Columns 
 
 86 
 
 Attic Bale 
 
 XII 
 
 
 
 Chambers^ 
 
A Table of tie Principal Matters. 
 
 Chambers, their Proportions i$$ 
 Chimneys 158 
 
 Circle 7 
 
 — how and why me afar d 32 
 
 Circumlcnb’d Figures 14 
 
 Cindhire, how delineated , and its 
 
 Etymology p. 85 
 
 Cima Redta, how defer ib’ d, with 
 its Etymology 92 
 
 Cima Reverfa , how def crib’ d 93 
 Compares 4 
 
 Corollary, what 21 
 
 Corona, its Etymology 93 
 
 Cone, what 17 
 
 ■ — how getter at ed ibid. 
 
 — its Axis , what ibid. 
 
 ■ — 'various Kinds ibid. 
 
 • — Bafe, what 1 8 
 
 Complement of an Arch 9 
 
 — • of Degrees and Minutes ibid. 
 • — of Angles 1 o 
 
 Column, its Etymology 78 
 
 — their Forms originally taken from 
 the taper Growth of frees ibid. 
 
 Columns of Brick , Stone, &c. firfi 
 made by King Dorns ibid. 
 
 — their Kinds ibid. 
 
 — their Parts ibid. 
 
 - — the centeral Lines , what 79 
 ■ — how meafur d and delineated ibid. 
 • — manner of placing 129 
 
 ■ — Pro] clotures of their Bafes 139 
 - — their entire Heights 141, 142 
 
 — their Diminution 143 
 
 - — Height of their Capitals 143,144 
 Corinthian Order, by whom infii- 
 
 tuted 10 6 
 
 — its Capital firfi form’d by Calli- 
 machus 107 
 
 — Shaft , how wreath’d 9 7 
 
 • — where to be ufed 123 
 
 — its Bafe 124 
 
 *— Manner of fluting the Shaft ibid. 
 — - Height of the Capital ibid. 
 
 — Diminution of the Shaft ibid. 
 
 — Architrave ibid. 
 
 — its Cantalivers andModilions ibid. 
 
 — to proportion it to any Elcight 
 
 affignd 125 
 
 — Ornaments of the Sopheta ibid. 
 
 — Intercolumnation p. 126 
 
 1 — Jmpofis ibid. 
 
 Compolite Order, by whom infii- 
 
 tuted 107 
 
 »— its Capital 108 
 
 — - its Cantali-vers 114 
 
 — where to be ufed 126 
 
 — Height of the Column ibid. 
 
 — its Bafe ibid. 
 
 — Shaft , ho-w fluted ibid. 
 
 — - Height of the Entablature 127 
 
 — to proportion it to any affignd 
 
 Height ibid. 
 
 — Intercolumnation ibid. 
 
 — Impofts ibid. 
 
 Cube, what 1 9 
 
 Curves irregular, how plan’d 62 
 Cylinder, what ig 
 
 — its Axis , what 1 9 
 
 D 
 
 Degree, what g 
 
 — - Number thereof in every Circle 
 
 ibid. 
 
 — how divided ibid. 
 
 Decagon j 3 
 
 Decimal Scale 56 
 
 — its 1 /fe S7 3 S8, &cc. 
 
 Diameter ox a Circle 
 Diameter of a Square 
 Diameter of a Parallelogram 
 Diameter of a Sphere 
 Diagonal of a Parallelogram 
 Diagonal of a Square 
 Dodecaedron, what 
 Dorick Order, by whom infiituted 
 
 106 
 
 — Height of its Shaft at its Inft na- 
 tion hi 
 
 — firfi 
 
 1 
 
 12 
 
 *3 
 
 *7 
 
 13 
 
 12 
 
 20 
 
A Table of the 
 
 — firft made without any Bafe , and 
 
 why ibid. 
 
 — the Bafe ufed when any ibid. 
 
 — its Shaft , how wreath'd 96 
 
 how fluted 1 0 1 
 
 — where to he ufed no 
 
 — its Capital 112 
 
 — its original Architrave ibid. 
 
 . — its Gutta s ibid. 
 
 — its Triglyphs ibid. 
 
 — its antient Ornaments of the 
 
 Freeze 114 
 
 «— Drops or Bells in the Mutils 1 15 
 
 — its modern Ornaments of the 
 
 Freeze 114 
 
 Denticles ibid. 
 
 — their Etymology - 1 1 5 
 
 — Diminution of the Shaft ibid. 
 
 — Height of Entablature 117 
 
 • — to proportion it to any afflgn d 
 
 Height ibid. 
 
 — its Inter columnation 1 1 8 
 
 — its Arches and Impofts ibid. 
 
 Doors 156 
 
 Drawing-Pen 4 
 
 Drawing-Table ibid. 
 
 E 
 
 Echinus 93 
 
 Eggs and Anchors 87 
 
 ■ — how defcrih'd 94 
 
 Ellipfis, how defcrih'd 46 
 
 Entablature, what 90, 145 
 
 Entablament 90 
 
 ■ — its Compoftion ibid. 
 
 — its Etymology ibid. 
 
 • — their Heights 146 
 
 — their Projeffures 147 
 
 Elevations of Buildings , how taken 
 
 and delineated 75 
 
 Epiftyle 90 
 
 Equilateral T riangle 1 1 
 
 Evelyns Parallel imperfcdl 2 
 
 Excefs of an Arch 9 
 
 Principal Matters. 
 
 Expofitions, heft 
 
 1 55 
 
 F 
 
 Fafcia 
 
 91 
 
 Fillet, how delineated 
 
 80 
 
 — its Etymology 
 
 87 
 
 Figures fuperficial 
 
 7 
 
 Fluted Columns 101, 
 
 103, 104 
 
 Flutes, why fir ft ufed 
 
 106 
 
 Freggio 
 
 88 
 
 Fuft 
 
 p. 89 
 
 Floors 
 
 157 
 
 G 
 
 Galleries 
 
 156 
 
 Gates 
 
 ibid. 
 
 Geometrical Square 
 
 12 
 
 — how defcrib d 
 
 5 * 
 
 Gorge or Gule 
 
 87 
 
 Greek Orders 
 
 107 
 
 Graveurs 
 
 xi3 
 
 Gutta’s 
 
 1 12 
 
 H 
 
 Halls, their Proportions 
 
 155 
 
 Heptagon 
 
 13 
 
 Hexagon 
 
 ibid. 
 
 Hypothenufe 
 
 11 
 
 Hypotracheliurn 
 
 I 
 
 Icofaedron, what 
 
 87 
 
 20 
 
 Impofts 
 
 no, 123 
 
 Inftruments necejfary for Drawing 4 
 
 Xnfcrib’d Figures 
 
 14 
 
 Inicrib’d Solids 
 
 20 
 
 Infcrib’d Circle within a 
 
 Square , its 
 
 Proportion 
 
 34 
 
 Intercolumnation, what 
 
 102 
 
 lonick Order, by whom 
 
 : inftituted 
 
 106 
 
 Height 
 
A Table of the 
 
 — Height of its Shaft 
 
 118 
 
 — how fluted 
 — - how wreath'd 
 
 103 
 
 97 
 
 — Number of Flutes 
 
 119 
 
 — its Safe by Vitruvius 
 
 ibid. 
 
 ■ — its Capital and Volute 
 
 ibid. 
 
 — hew defcrib’d 
 
 — its Height 
 
 121 
 
 — Architrave 
 
 ibid. 
 
 — Height of the Entablature 
 
 122 
 
 — to proportion it to any aflfign d 
 
 Height 
 
 ibid. 
 
 — jts Intercolimnation 
 
 123 
 
 • — its Impofls 
 
 ibid. 
 
 K 
 
 Kitchens, their Situations 
 
 159 
 
 L 
 
 Larmier 
 
 P- 93 
 
 Latin Orders 
 
 107 
 
 Legs of Triangles 
 
 11 
 
 Lines 
 
 5 
 
 — their Power 
 
 15 
 
 Line of Chords 
 
 45 
 
 Liftello 
 
 85 
 
 M 
 
 Metops 
 
 113 
 
 Modern Buildings 
 
 2 
 
 Module, what 
 
 79 
 
 Moldings, how defcrib’d 
 
 ibid. 
 
 Modilions 
 
 1 14 
 
 Mutils 
 
 ibid. 
 
 N 
 
 Nonagon 
 
 13 
 
 O 
 
 
 Obtufe Angle, what 
 
 10 
 
 Principal Matters. 
 
 O dragon 1 3 
 
 Qdaedron 19 
 
 Ogee, how defcrib’d 9 1 
 
 Orthigonium Triangle 1 1 
 
 Order Entire, what 79 
 
 Orders, their generalProportions 106 
 Ovals, how defend’d 46 
 
 Ovolo 87 
 
 Out-lines of Buildings, hew plan’d 
 
 64 
 
 Oxigonium Triangle 11 
 
 P 
 
 Parallel Ruler 
 
 4 
 
 Paper for Drawing 
 
 ibid. 
 
 Parallelogram, what 
 
 13 
 
 *— how delineated 
 
 5 i 
 
 Parallelopipedon, what 
 
 19 
 
 Parallel Lines to draw 
 
 43 
 
 Pavements 
 
 157 
 
 Pediment 
 
 152, 153 
 
 — Obfervations thereon 
 
 *54 
 
 Perfpedive neceffary to Architects 3 
 
 Perpendicular, what 
 
 10 
 
 — to raife 
 
 37 
 
 — to let fall 
 
 41 
 
 Pentagon 
 
 13 
 
 Perfian Order 
 
 p. 105 
 
 Pedeftals 
 
 13°, 1 37 
 
 — their Heights 
 
 131 
 
 — their principal Parts 
 
 134 
 
 — ProjeCtures of their Bajes and 
 
 Capitals 
 
 137 
 
 Pillafters 
 
 148 
 
 — their ProjeCture 
 
 148, 149 
 
 — their Flutes 
 
 104, 149 
 
 — their Capitals 
 
 150 
 
 — how to be plac’d 
 
 151 
 
 — • Errors therein 
 
 ibid. 
 
 — their ProjeCtme from the Build- 
 
 ing 
 
 128 
 
 Plain Scale 
 
 4 
 
 Platonick Bodies, what 
 
 20 
 
 flans, how taken and delineated 68 
 
 Plancere 
 
A Table of the Principal Matters. 
 
 PJancere 
 
 93 
 
 Septa^on 
 
 13 
 
 Plinth 
 
 85 
 
 Sector 
 
 4, 8 
 
 Point 
 
 5 
 
 Shaft 
 
 89 
 
 Portion of a Circle 
 
 8 
 
 Soffito 
 
 93 
 
 Polygons, what 
 
 13 
 
 Sphere, how generated 
 
 17 
 
 — their Area 
 
 30 
 
 — its Axis , what 
 
 ibid. 
 
 — how delineated 53 
 
 * 54 j 55 
 
 Stillicidium 
 
 93 
 
 Protra&or 
 
 4 
 
 Statues, their Heights , 
 
 how proper - 
 
 — its Ufe 
 
 44 
 
 tion d uponBuildiwjs when view'd 
 
 Prifm, what 
 
 18 
 
 from a given Point 
 
 129 
 
 Pyramis, what 
 
 ibid. 
 
 Stair-cafes 
 
 159 
 
 — its Vertex or Apex, 
 
 ibid. 
 
 Superficies 
 
 6 
 
 — its Axis , what 
 
 ibid. 
 
 Subtenle Lines 
 
 8 
 
 
 
 Supercilium 
 
 93 : 
 
 0. 
 
 
 x 
 
 
 Quadrant 
 
 8 
 
 
 
 Quarter-round 
 
 87 
 
 Talon 
 
 89:.: 
 
 
 
 Tailloir 
 
 ibid. 
 
 R 
 
 
 Tabulatum 
 
 90 
 
 
 
 Tetraedron, what 
 
 18 
 
 Radius of a Circle, what 
 
 8 
 
 Tenia 
 
 114 
 
 Rhombus, what 
 
 13 
 
 Theorems* what 
 
 21 
 
 — how delineated 
 
 52 
 
 Tondino 
 
 89 
 
 Rhomboides, what 
 
 13 
 
 Triangles, the Kinds 
 
 31 
 
 — how delineated 
 
 52 
 
 Trapezium, what 
 
 13 
 
 Right Angle, what 
 
 10 
 
 T riangles right-angled ', 
 
 their Area 
 
 Right-angled Triangle, what 11 
 
 
 p. 27 
 
 Right Line to divide 
 
 42 
 
 Triangles equilateral , 
 
 their Area 
 
 Rule for me a faring of Circle s, Se- 
 
 
 28 
 
 micircles , Quadrants , 
 
 Sectors , 
 
 Triangles Ifofceles 
 
 5 ° 
 
 &c. 
 
 34 
 
 Triangle Scalenum - 
 
 ibid. 
 
 Rufticks, how divided 
 
 p. 98 
 
 Trabeation 
 
 90 
 
 Roman Order 
 
 107 
 
 Triglyphs 
 
 1 12, 113 
 
 
 
 Torus 
 
 84. 
 
 3. 
 
 
 Tufcan Column, by whom infiituted 
 
 • 
 
 
 
 107 
 
 Scalene Triangle 
 
 21 
 
 — how delineated 
 
 84 
 
 Scotia 
 
 80, 1 12 
 
 — its Bafe 
 
 ibid. 
 
 Scapus 
 
 89 
 
 — its Capital 
 
 86 
 
 Segment, cr Section of a Circle 8 
 
 — where to be ufed 
 
 108 
 
 — how me a fur d 
 
 83 
 
 — Height of the Shaft 
 
 ibid. 
 
 Semicircle 
 
 10 
 
 — Height of the Bafe • 
 
 ibid.: 
 
 Segments of the Bafe of a 
 
 Triangle 
 
 — Diminution 
 
 ibid,: 
 
 
 iz 
 
 1 — height of Entablature ibid. 
 
 
 
 
 = how. 
 
Matters. 
 
 A Table of the 
 
 > — how to proportion it to any ajjignd 
 
 Height iog 
 
 — its Intercolumnation ibid. 
 
 ■ — its Arch no 
 
 • — its Impofi ibid. 
 
 V 
 
 V olutes of the Ionick Order , why 
 fir ft it fed I0 6 
 
 — how defcrib'd 120 
 
 W 
 
 Wreath'd Columns, how delineated 
 
 96 
 
 Windows 156 
 
 Z 
 
 Zoophorus, or Zophorus 88 
 
A SURE 
 
 GUIDE 
 
 T O 
 
 BUILDERS. 
 

 
 
 
THE 
 
 INTRODUCTION. 
 
 RCHITECTURE: Or, The Art of 
 Building, wholly depends on the Principles 
 and Practice of Geometry ; for thereby it 
 is, that their Parts, Angles, Area's, Soli- 
 dities, Proportions, &c. are meafured, de- 
 termined, fet out, executed, valued, &c. 
 And therefore thofe who are defirous to 
 well underftand the Reafons of all the 
 beautiful Proportions contain'd in Archi- 
 tedure, muft be firft acquainted with fuch Elements of Geometry 
 that are abfolutely neceffary thereto. 
 
 It is a common Saying, ( tho' a very much miftaken one ) 
 That Architedure may be underftood and performed without well 
 underftand mg the Principles of Geometry, which is abfolutely 
 falfe, and is utter d, either by Mafters who being ignorant them- 
 felves, are unwilling that their Apprentices fhould excel them in 
 their Arts ; or otherwife, ’tis reported by fuch, as know to the 
 contrary, who delight in training young Builders in the old, dark, 
 uncertain Methods of working, to prevent their acquiring an equal 
 Knowledge w'ith themfelves. 
 
 But be this ill-natur’d Ad, as it will, Yis very barbarous and 
 injurious to the Improvement of Youth. And it is therefore that 
 I take this Opportunity of mentioning it to the young Student, 
 that he may with vigorous Pleafure proceed to the Study of the 
 following Geometrical Definitions, Theorems, Problems, &c. 
 which will not only lead him into fine eafy Methods of Defin- 
 ing, Contriving, Delineating, &c. but enable him to well per- 
 form all his Undertakings with Accuracy and Strength in the leaft 
 Time. _ For he that well underftands the true Reafons of all his 
 Operations, will perform a Work, whilft another that works by 
 guefs, is thinking of Methods to perform it by. 
 
 The 
 
2 
 
 Introduction. 
 
 The feveral Authors, who have wrote on this Subject, are in- 
 deed very ‘numerous, and therefore it may very reafonably be 
 imagin’d that every Part thereof has been fully handled already : 
 But when we ftridly look into their feveral Works, we find, 
 that the Defign of every Author has been more to fhew the Theory 
 of his Works, than to lay down Pradical Rules for the Work- 
 man. There’s not one of them has laid down fo much as the 
 fimple Conftrudion of the Moldings, _ of which their five Orders 
 are compofod. Nay, fome have omitted fome of their Principal 
 Parts, of which the Parallel of Mr. Evelyn is one, he having 
 given the Proportions but of the Columns and Entablatuies of 
 thofeDrders which he has treated of 
 
 An entire Order of Architecture is compofed of three Principal 
 Parts, viz. the Pedeftal, the Column, and the Entablature ; of 
 which Mr. Evelyn has wholly omitted the firft : As alfo their 
 Arches, Impofts, and Intercolumnations ; and altho’ Vitruvius 
 was the very Father of Palladio , and all other Architects, yet he 
 has done no more than juft mentioning his Name now and then, 
 and has wholly omitted to exhibit the beautiful Proportions con- 
 tain’d in his Orders, which 1 have here moft accurately laid down : 
 As alfo thofe of the Pedeftals, Arches, Impofts, and Intercolum- 
 nation of Columns in general. Thofe fo much celebrated Archi- 
 tects Palladio and Scamozzi , whole Proportions and Orders are 
 vaftly beautiful and majeftick, yet both thofe Gentlemen have 
 omitted Pradical Rules for delineating the Moldings of the feve- 
 ral Members, of which their Orders are compofed. 
 
 The great Want of Architedonical Principles has caufed many 
 good-natur’d Workmen, fuch as Halfpenny, Hoar , &c. to com- 
 municate what little they knew for the Good of their P ellow- 
 Workmen, in as good a manner as they were capable ; but being 
 without Demonftration, they have left Workmen in the dark, and 
 all that they have done, is therefore of very little Service ; and 
 fbe Builders Didiionary (the moft furprifing, undigefted Mefs of 
 Medley that yet was ever put together ) confifts of nothing more 
 than Hear-fays, Reports of God knows who, and what, without 
 any re al Matters of Fad, that either Workman or Mafter can de- 
 pend on. . . , / . r 
 
 If we examine the Modern Buildings of this Kingdom, ( thole 
 
 built by the Right Honourable the Lords Burlington md Herbert 
 
Introduction. 
 
 excepted) a<d the Artificers thereof, ’tis very difficult to find one 
 in twenty that are good, or fcarcely fit to pafs Mufter in a 
 Crowd ; which undoubtedly is wholly due to the Want of well- 
 digefted Rules and Proportions to work after. 
 
 ’Tis true, that the Antients have left us excellent Patterns, yet 
 for want of their Pradical Rules being made publick, Our Work- 
 men feldom arrive to their Perfections of Strength and Beauty. 
 
 Having thus juftly obferv’d the many Abfurdities in all the 
 Authors extant ; and confidering the innumerable Complaints 
 among Workmen, for the want of plain and accurate Rules 
 well-digefted to work by ; I was therefore induc’d to compile 
 fuch a Work, which 1 have endeavour’d to render intelligible to 
 every Capacity, in a Style and Manner familiar and eafy. 
 
 The firft Part of this Work was publifh’d about two Years 
 ago, intitled, The Builders Che (1- Book : Or, A Key to the Five 
 Orders of Columns in Architecture, which I wrote purely for the 
 Ufe of young People at their firft coming to Bufinefs, and which 
 has been fo happy as to meet with its intended Succefs* to the en- 
 tire Satisfaction of the great Numbers of Builders and Artificers, 
 who have purchafed and read the fame. 
 
 This kind Reception, and the many Thanks that I have, and 
 do daily receive from Workmen in general for the Publication 
 thereof, induc’d me to communicate this fecond Work, according 
 to my Promife made in the End of my Builders Che/l-Book , con- 
 taining all fuch Geometrical Rules as occur to foi$nd Workmen, 
 in Pradice, throughout all the feveral Parts of their refpedive 
 Operations. 
 
 Indeed, I muft confefs that it may be expected, that I fhould 
 have here laid down fuch Elements of EerfpeCiivc as are requifite 
 for the drawing of PerfpeCtive Elevations , and Elans of Building, 
 which renders the Art of Defigning and Drawing compleat ; but 
 as fuch a Work would have fwell’d this Volume to a greater 
 Bulk and Price than intended, it will therefore foon appear in 
 Publick in adiftind Volume by itfelf : But excufc this Digreftion, 
 and proceed to the Matter in Hand. 
 
 The Excellency and Perfedion of an Art, confifts not in the 
 Multiplicity of its Principles, but contrarily, the more fimple 
 and few in Number they are, the better. Therefore I lhall endea- 
 vour to lay d«wn the following in as concife, but full and plain 
 a Manner, as the Art will conveniently admit of. 
 
 B a 
 
 And 
 
INTRODUCTION. 
 
 TI . ' 
 
 And in Confideration that Workmen fhould be furniftfd with 
 iuch Mathematical Inftruments as are neceflary for their feveral 
 Purpofes, I will, in the next Place, fpeak fomething thereof, and 
 then proceed to their Ufes in PraCfical Geometry. 
 
 The Inftruments requifite for thefe Purpofes, are moil accurately 
 made, according to the beft and lateft Improvements, and fold by 
 the Author at Andrea Palladio’s Head near Exeter-Change in the 
 Strand , London ; which are as follow, 
 
 i y?, Three Pair of Compaffes, viz. One Pair of four Inches 
 and half, or fix Inches in Length, with the feveral Points for de- 
 fcribing Arches, with Ink, Black-Lead, &c. A fecond Pair of 
 an Inch and half in Height, with the Pen-Point only, to defcribe 
 very fmall Circles, Arches, &c. And laftly, A third Pair of fix 
 or eight Inches in Length, with their common Points only, to 
 meafure Intervals, draw Occult Lines, Arches, &c. 
 
 idly , A Plain Scale, containing divers Scales of equal Parts, by 
 which Plans and Uprights of Buildings are drawn ; as alfo Scales 
 of Chords for meafuring and laying down their feveral Angles. 
 
 3 dly, A Protra&or, either Semicircular or Oblong, to protraCt 
 or lay down Angles, inftead of ufing the Line of Chords. And 
 here obferve, that the larger the Protractors are, the more exaCt 
 an Angle may be laid down by them. 
 
 4 thfyy A SeCtor, with the 30 and 40 Scales, Line of Lines, 
 and Twelves,' Chords, and Polygons. 
 
 jthly, A Hand-drawing Pen for delineating Right Lines, and 
 a protraCting Pin to fet off any Number of Degrees and Minutes 
 from the Limb of the ProtraCtor. 
 
 6 thly , A Drawing Table made after the manner of a Plain 
 Table, to Ihut on the Paper inftead of leafing it down with Wax, 
 as is ufual ; as alfo, a Te-Square for the ready drawing of Parallel 
 Right Lines, Perpendiculars, &c. without the Aftiftance of Com- 
 pares, which often fcratch and deface the Paper. 
 
 ythly, A Parallel Ruler for drawing Parallel Right Lines on any 
 Paper, or other Drawing, when the Te-Square can’t be us’d. 
 
 And laftly , With good Paper, fuch as Dutch Royal , Imperial ’, 
 &c. Black-Lead Pencils, Squirrel-Tail Pencils, Allum-water, 
 Gum-water, and Indian Ink. 
 
 Being thus provided with Inftruments, the young Student may 
 proceed to Pradice, as follows : 
 
 A 
 
A SURE 
 
 GUIDE to BUILDERS: 
 
 O R, 
 
 The Principle f of Architecture 
 Geometrically Demonfbrated. 
 
 PART I. 
 
 Of GEOMETRY. 
 
 CHAP. I. 
 
 Of Geometrical Definitions, 
 
 DEFINITION I. 
 
 Of a POINf. 
 
 POINT, according to Euclid i. is, that which 
 hath no Part \ but in Practice, 'tis the leaft Su- 
 perficial Appearance that can be made with the 
 Point of a Pin, Pen, Pencil, &c. as this Point pre- 
 fix'd to the Letter 
 
 D E F I N. II. 
 
 Of L INE S. ( Plate I. ) 
 
 A Line, according to EucltdA. Def i. is a Longitude without 
 Latitude, that is, a Length without Breadth or Thick- 
 
 A Line 
 
6 A Sure Guide to Builders. 
 
 A Line is generated by the Motion of a Point, moving from 
 one Place to another. Thus the Point A, ( Fig. i. ) moving 
 dire&ly from A to A, generates the Right Line AB , therefore a 
 Right Line is the neareft Diftance between two Points, which 
 are the Bounds or Limits thereof. 
 
 But had the Point A, in going to B, firft gone to C, thence to 
 D, and afterwards to B y it would by its irregular Motion have 
 defcribed a crooked Line, as ACDB, which being irregular, with- 
 out any refpect to a Center, is therefore called An Irregular Curved 
 Line. 
 
 If the Right Line AB, be fix’d at the Point A , as a Center, 
 and afterwards the End B be moved to E, it will by its Motion 
 generate or trace the crooked Line B E y and becaufe that all the 
 Parts of that crooked Line are at equal Diftances from A y the 
 Center whereon it was defcribed, it is therefore called A Regular 
 Curved Line . 
 
 D E F I N. III. 
 
 Of an AN GL E. - 
 
 AN Angle is confiltuted "by The Congrefiion, or Meeting of 
 ^ any two Lines in any fort, fo that both make not one Right 
 Line. See Problem V. Chap. III. 
 
 When the Lines which contain the Angle are Right Lines, it 
 is called A Plain Right Lined Angle - y as A, ( Fig. II.) But 
 when one Line is a Right Line, and the other a Curved Line, as 
 the Angles BB y it is called A Mix’d Angle. And laftly, When 
 both Lines are curved, as the Angles CC, they are called Spheri- 
 cal, or Curved Andes. 
 
 D E F I N. IV. 
 
 Of SUPERFICIES. 
 
 A Superficies, according to Euclid, is, that which hath only 
 ^ ^ Longitude and Latitude , that is, Length and Breadth with- 
 out Depth or Thicknels. 
 
 As Right Lines are generated by the Motion of Points, fo are 
 Superficies generated by the Motion of Right Lines. 
 
 For, 
 
V 
 
 A Sure Guide to Builders . 
 
 For, i ft, If the Right Line AB , ( Fig. III. ) be fix’d at A, 
 as on a Center, and the Point B moved to C, thence to D, from 
 thence to E, and laftiy to B ; it will by its Revolution defcribe 
 a Superficies, which is called A Circle. 
 
 idly , If the Right Line AD be moved along the Line AG, 
 until AC is equal to AD , that is, in the Pofition CE, it will by 
 its Motion defcribe a Geometrical Square AD EC, and if conti- 
 nued onto FG, it will generate the Parallelogram ADFG. 
 
 Hence it follows , that as Points are the Bounds or Limits of 
 Lines , fo are Lines the Bounds or Limits of Superficies , 
 
 D E F I N. V. 
 
 Of SUPERFICIAL FIGURES. 
 
 CUper fetal Figures are contain’d under one or many T’erms or 
 ^ Limits. As firft, The Circle A, ( Fig. IV. ) is contain’d un- 
 der one Limit or Line, which is called The Circumference , or Peri- 
 phery. The Triangle B under three, the Geometrical Square C, 
 the Oblong, or Parallelogram D , and Trapezian E each under 
 four; the Pentagon F under five; the Hexagon G under fix; 
 the Septagon H under feven ; the Oftogon I under eight ; the 
 Nonagon K under nine ; and the Decagon L under ten, &c. 
 Wherein ’ tis to he obferved, that of tivo Right Lines no Figure can 
 he contain d. 
 
 D E F I N. VI, 
 
 Of a CIRCLE and its Parts. 
 
 i. A Circle is a plain Geometrical Superficies , or Figure con - 
 tabl’d under one Line , ( as before-) call’d T’he Circumfe- 
 rence , and is generated by the Fluxion of a Line, ( by Def. 4. ) 
 whofe Center being exadly in the midft thereof, all Right Lines 
 drawn from thence to the Circumference are therefore equal. So 
 jBD, (Fig. V. ) is equal to BG, and BG to BC ', and BC to 
 B E, &c. - ’’ 
 
 2. All Right limes, which pafs through the Center of a Circle, 
 ns DC or EG, are call’d Diameters, and divide the Superficies 
 thereof into two equal Parts, which are call’d Semicircles , as the 
 Diameter D BC, which dividing the Circle EDGC into two 
 
 equal 
 
1 
 
 B A Sure Guide to Builders. 
 
 equal Parts, do thereby conftitute the two Semicircles EDG, 
 and GCE. Therefore, a Semicircle is a Figure contain'd under 
 the Diameter , and that Part of the Circumference which is cut off 
 by the Diameter. 
 
 3. Half the whole Diameter of a Circle is call'd The Semi- 
 Diameter , or Radius of the Circle ; as EP, DP,G P, CP, &c. 
 
 4. A Segment, Section, or Portion of a Circle, is a plain Figure 
 or Superficies , contain’d under a Right Line, ( which is lefs than 
 the Diameter ) and part of the Circumference either greater or lefs 
 than a Semicircle. As for Example, The Right Line HI, (Fig. V.) 
 
 s cutting off the upper Part of the Circle HD I, does therefore di- 
 vide the whole Circle into two unequal Parts, which are call'd 
 Segments, Sell ions, or Portions ; as HD I, the lefler, contain'd 
 under the Line HI, and part of the Circumference HD I, which 
 is lefs than the Semicircle ADC ; and HCI under the Line 
 HI, and the remaining Part of the Circumference HE Cl, 
 which is greater than the Semicircle ECG. 
 
 j. The fourth Part of a Circle, as EPD, or DBG, &c. 
 
 ( Fig. V. ) is call’d A Quadrant, being contain'd under two Semi- 
 Diameters, ( which are call’d The Sides) and the fourth Pait of 
 the Circumference, which is call’d The Limb of the Quadrant. 
 
 6. A Senior of a Circle is a Figure contain’d under two Semi- 
 Diameters, (as B F and PE) and part oj the Circumference 
 F E contain’d between them. 
 
 y. The Circumference of every Circle is fuppofed to be divided 
 into 360 equal Parts , which are call'd Degrees. Therefore as a 
 Quadrant is one fourth Part of a Circle, the Degrees contain'd 
 therein are Ninety, ( Vide Prob. V. Chap. III. ) and a Semicircle 
 does therefore contain 1 80 Degrees. 
 
 8. Every Degree of a Circle is fuppofed to be fubdivided into 60 
 equal Parts , which are call’d Minutes ; therefore a quarter of a 
 Degree contains 15 Minutes, half a Degree 30 Minutes, three 
 Quarters of a Degree 45 Minutes, &c. 
 
 p. All Right Lines ( lefs then the Diameter ) which divide 
 Circles into Portions, as HI, (Fig. 3.) are call’d Chord Lines, 
 or Subtenle Lines of thofe Arches which they fo fubtend ; be- 
 caufe they fubtend both Segments; that -is, the Line HI, is 
 common as well to the Segment HECGI, as to the Seg-* 
 ment HD I. 
 
 10. Thofe 
 
A Sure Guide to Builders. 9 
 
 1 o. Thofe. Parts of the Circumference of Circles contain’d be- 
 tween the Extremes of Chord-Lines, as HD I, or EDG, are 
 call’d Arches , or Arch-Lines. 
 
 11. The Complement of an Arch , to a Quadrant , or po Degrees, 
 is lb much as an Arch wants of po Degrees : As for Example ; 
 
 The Complement of the Arch GI, is the Arch ID, and the 
 Complement of the Arch HE, is HD; alfo, in Number of 
 Degrees, the Complement of 40 Degrees, is 50 Degrees ; becaufe 
 that 40 Degrees, is lefs than po Degrees, by 50 Degrees : So 
 likewife is 40 Degrees, the Complement of 50 Degrees, and 10 
 Degrees, the Complement of 80 Degrees ; and the like of any 
 other Quantity of Degrees whatever. 
 
 12. 'The Complement of any Number of Degrees and Minutes , 
 to po Degrees , is the Quantity of Degrees and Minutes which 
 are wanting to make their Sum po Degrees complete : As for 
 Example; The Complement of 16 Degrees 17 Minutes, is 63 
 Degrees 43 Minutes : For 2(5 Degrees 17 Minutes being lubftradted 
 from po Degrees, the Remainder is 63 Degrees 43 Minutes ; and 
 the like of any other Quantity. 
 
 13. The Excefs of an Arch, greater than a Quadrant, is fo 
 much as the faid Arch exceeds po Degrees : As for Example. 
 
 The Excefs of the Arch EDI, is the Arch DI ; becaufe whenF/V. V. 
 the Arch ED (which is a Quadrant) is taken from EDI, the 
 Remainder is D I, which is the Excefs more than the Quadrant 
 EHD. 
 
 14. The Complement of an Arch lejs than a Semicircle, is lb 
 much as that Arch wants of a Semicircle, or 180 Degrees : As 
 for Example ; The Arch E H is the Complement of the 
 Arch HDG: So likewile is the Arch CEH the Comple- 
 ment of the Arch HD, and HDG is the Complement of the 
 Arch HE. 
 
 DEFIN. VII. 
 
 Of ANGLES , and their Kinds. 
 
 1. AN Angle, as before proved (Def 111.) is conftituted by 
 the Meeting of two Lines ; and when a Right Line meets, 
 or falls upon another Right Line, making the Angles on either Side 
 equal, each of thofe Angles are called Right Angles, and the 
 
 C Line 
 
IO 
 
 A Sure Guide to Builders . 
 
 Line erefifed, is called a Perpendicular Line thereto : As for 
 Example. 
 
 (Fig. VI.) The Line F C, Handing upon the Line AE, at C, 
 is perpendicular thereto : Becaufe if you defcribe a‘ Semicircle 
 on C, with any Radius, as BHD, the Arch BH will be found 
 to be equal to the Arch HD; and fince that both Arches are 
 equal to each other, and to a Semicircle alfo, being taken toge- 
 ther, it therefore follows that both the Angles, on either Side, 
 are equal ; and are therefore call’d Refit, or Right Angles. 
 
 2. An Angle is fignify’d by three Letters, of which the middle - 
 mo (l always denotes the Angle. So, in this Cafe, ©f the two 
 Right Angles, the one is denoted by the Letters AGF, and the 
 other by the Letters F C E : So alfo is the Angle conftituted by 
 the Lines GC, and CE, denoted by the Letters GCE. 
 
 3. Now feeing that the Semicircle BHD contains 180 De- 
 grees, and is equally divided, in H, by the Perpendicular Line 
 CF ; it therefore follows, that the Angles AC F, and FCE, 
 which are equal to each other, muft each confift of po Degrees: 
 Therefore a Right Angle is that , whofe Arch contains po De- 
 grees precifely. 
 
 4. An Obtufe Angle is that, which is greater than a Right 
 Angle, that is, its Arch, by which it is meafured, confifts of 
 more Degrees than po, and lefs than 180, as the Angle ACG; 
 which conlifting of the Arch H I, more than the Arch of po 
 Degrees B H, is therefore Obtufe, or Blunt-angled. 
 
 5. An Acute Angle is that which is lefs than a Right Angle, 
 that is, its Arch, by which ’tis meafur’d, confifts of fewer De- 
 grees than po, as the Angle GCE, which . is lefs than po De- 
 grees by the Arch HI; and is therefore Acute, or Sharp- 
 angled. 
 
 6. I* he Quantity , or Meafure , of an Angle, is the Arch of a 
 Circle deferib’d on the angular Point, intercepted between the 
 two Sides of that Angle. (Vide Prob. V. Chap. III.) 
 
 7. ‘The Complements of Angles , are the fame as the Comple- 
 ments of Arches: Becaufe their Quantities are meafur’d by 
 Arches of Circles. 
 
 DEFIN, 
 
A Sure Guide to Builders . 
 
 i r 
 
 DEFIN. VIII. 
 
 Of the fever al Kinds of I 3 R IAN G LES. 
 
 f : triangle Is a plain Geometrical Figure , contain'd under three 
 Right Lines ; as ABC. ( Fig. VII.) 
 
 1. Of Triangles there are divers Kinds ; as, firft, thofe whofe 
 Sides being all equal to each other, as ABC, are therefore call’d 
 Equilateral Triangles. 
 
 2. Thofe Triangles, which have two Sides equal to each other, 
 and the third unequal, as the Triangles DEF, H G I, and M K L, 
 are call’d Ifofceles Triangles. 
 
 3. The third Kind of Triangles are thofe, whofe feveral Sides 
 are all unequal, as ABC, DEF, or GHI. (Fig. VIII.) and are 
 therefore call’d Scalena , or Scalenum Triangles. • 
 
 4. Triangles are alfo diftinguifh’d with refpe<ft to their Angles, 
 as well as to their Sides. As, Firft : Thofe Triangles whofe 
 Angles are all acute, as the Equilateral ABC, the Ifofceles 
 MKL (Fig. VII.) and the Scalenum GHI (Fig. VIII.) are call’d 
 Oxigonium , or Acute-angled Triangles. But this Appellation 
 to the Equilateral 'Triangle, / think , is needlefs , fwce the Word 
 Equilateral implies the fame. 
 
 Secondly, Thofe Triangles that have*one of their Angles 
 Right, as DEF (Fig. VII.) and ABC (Fig. VIII.) are call’d 
 Orthigonlum Triangles ; and when they fo happen, that the two 
 Sides, which contain the Right Angle, are equal, as DEF' (Fig. 
 
 VII. ) then fuch Triangles are alio call’d Right-angled Ifofceles 
 Triangles. 
 
 Thirdly, Thofe Triangles that have one of their Angles ob- 
 tufe, as the Ifofceles Triangle HGI (Fig. VIL) and DEF (Fig. 
 
 VIII. ) are call’d Afnbligonium Triangles ; and when any fuch 
 obtufe-angled Triangle happens to have two Sides equal, as 
 
 1 GHI (Fig. VII.) then fuch Triangles are alfo call’d Ohtufe- 
 angled Ifofceles Triangles. 
 
 5. The two Sides of an Orthigonium, or Right-angled Tri- 
 angle, which contain the Angle, as DE and EF of the Triangle 
 DEF (Fig. VIL) are call’d the Legs of the Triangle; and the 
 Slope Line D F, the Hypothenufe ; and iometimes one of the 
 
 C 2 Legs 
 
 z 
 
1 2 
 
 A Sure Guide to Builders. 
 
 Legs is call’d the Bafe of the Triangle, as AC (Fig. VIII.) and 
 the other Leg A B, the Cathetus , or Perpendicular . 
 
 6 . It is to be noted generally, in all Triangles, that in com- 
 panion of any two Sides, the third is called the Bafe : As of the 
 Triangle ABC (Fig. VIII.) in regard of the two Lines BA and 
 BC, the Line AC is the Bafe; in regard to the Lines CB and 
 CA, the Side BA is the Bale; and, laftly, in regard, to the 
 Lines A B and A C, the Line B C is the Bafe. 
 
 7- Th e Perpendicular of a Triangle is always let fall from the 
 angular Point oppofite to the Bafe, down upon the fame ; as the 
 Perpendicular EK, upon DF of the Triangle DEF (Fig. VIII. ) 
 
 8. When a Perpendicular is let fall, from an. Angle, upon the 
 Bafe (as in the preceding) the Bafe is thereby divided into two 
 equal Parts, when the Triangle is Ifofceles, as DF in K ( Fig. 
 VII.) or into two unequal Parts, as D F in K (Fig. VIII.) which 
 Parts of the Bafe, howfoever divided, are feverally call’d, Seg- 
 ments of the Bafe, and are diftinguilh’d according to their Mag- 
 nitudes, by the Names of greater or lelfer. 
 
 DEFIN. IX, 
 
 Of the feveral Kinds of Four fide d Right-lin’d Figures. 
 
 HP H E feveral right-lin’d Figures that are contain’d under four 
 Right Lines ate, the Geometrical Square , A; (Fig. IX.) 
 the Parallelogram , B; the Rhombus , C; the Rhomboides , D; and 
 the Trapezium , E and X. 
 
 i. A Geometrical Souare, or Quadrate, is a quadrilateral 
 Figure, contain’d under four Right Lines, which, in general, 
 are equal to one another; as alio are the Angles : And therefore 
 are all Right-angled, as the Figure A (Fig. IX.) 
 
 The Diagonal of a Square is a Right Line drawn from two 
 oppofite Angles ; as the Diagonal Line i and 8, or 3 and 6 . 
 And the Point where the Diagonals interfed each other, as at A, * 
 rs the Center of the Square. 
 
 The Diameter of a Square is a Right Line drawn through the 
 Center, or Interfedion, of the Diagonals, parallel to any two 
 oppofite Sides ; as the Lines 4 A j, and 1 A 7. 
 
 2. A. 
 
*3 
 
 A Sure Guide to Builders. 
 
 2. A Parallelogram, or Long Square, is a plain Figure 
 contain'd under four Right Lines, whofe Angles are all Right 
 Angles, and oppofite Sides only are equal. As B G (Fig. IX.) 
 is equal to its oppofite Side DE: So likewife is B D, equal to 
 its oppofite Side C E. 
 
 The Diagonals of Parallelograms are equal to one another, as 
 thole of Geometrical Squares : But their Diameters are unequal ; 
 becaule the Length of the Figure is luperior to the Breadth : So 
 a c y the longefi: Diameter, k fuperior to the fhorteft Diameter bd 
 
 3. A Rhombus (or Diamond Form) is a plain Figure, con- 
 tain'd under four equal Sides, as FIGH; whole oppofite Angles 
 only are equal. (Vide Prob. XII. Chap. III. 
 
 4. A Rhomboides, or Diamond-like Figure, is that whole 
 oppofite Sides and oppofite Angles are only equal ; but hath 
 neither equal Sides, nor any Right Angles : As L M K N 
 (Fig. IX.) 
 
 Note, that the Square y Parallelogramy Rhombus , and Rhom — 
 boidesy are commonly call’d Parallelograms : Of which the Square 
 and Oblong are call'd Right-angled Parallelograms, and the 
 other, Oblique-angled Parallelograms; becau an Oblique Angle 
 is an Angle which is either acute or obtufe ; as the Angle LKM, 
 or the Angle F H G. 
 
 5. Trapezia’s, are irregular Figures contain’d under four urn- 
 equal Right Lines, as the Trapezia E, and X. 
 
 D E F I N. X. 
 
 Of Regular POLYGONS. 
 
 P OLYGONS are regular Figures, contain’d under five, fix, 
 &c. equal Sides and equal Angles, as F, GHIKL. (Fig. IV.) 
 
 When a . Regular Polygon confifts of five Sides, as F, ’tis 
 call’d' a Pentagon ; when of fix Sides, as G, a Hexagon ; when 
 offeven,. as H, a Sept agony or Heptagon ; when of eight, as I, an 
 Off agon 'y when of nine, as K, a Non agon ; and when with ten 
 Sides, as L, a Decagon. 
 
 DEFIN. 
 
*4 
 
 A Sure Guide to Builders. 
 
 D E F I N. XI. 
 
 Of Infcribed and Circumfcribed Figures. ( Plate II.) 
 
 i. HTHat Right -lin'd Figure is faid to he Infcribed in another 
 Right -lin'd Figure , which hath every Angle touching every 
 Side of the Figure wherein it is Injcribed . 
 
 So the Triangle CDF (F%. X.) is infcribed in the Triangle 
 ABE; as alfo the Square H K L N, in the Square GIMO: 
 Becaufe all the Angles thereof touch every Side of the Circum- 
 feribing Square GIMO, in the Points KHL N. 
 
 In like Manner, a Figure is faid to be deferib’d, or circum- 
 fcrib’d, about a Figure, when every one of the Sides of the 
 figure circumlcrib’d touch every one of the Angles of the Figure 
 about which it is circumfcrib’d : So the Triangle ABE, is de- 
 ferib’d, or circumfcrib’d, about the Triangle CDE, and the 
 Square GIMO, about the Square HKLN. 
 
 z. .A Right-lind Figure is life rib' d within a Circle , when 
 every Angle of the Infcrib’d Figure touches fome Part of the Circle’s 
 Circumference. (Fig. XI.) 
 
 So the Triangle ABC, and the Square D E F G, are infcrib’d 
 in the Circle ABC, and D E F G ; becaufe every one of their 
 Angles touches the Peripheries, or Circumferences, of both 
 Circles. 
 
 In like Manner, a right-lin’d Figure is faid to be deferib’d 
 about a Circle, when all the Sides of the Figure which is circum- 
 fcrib’d touch the Periphery of the Circle : So the Sides of the 
 Triangle ACE (Fig. XII.) touch the Periphery in the Points 
 B F D, and the Sides of the Square GIMO, in the Points 
 HKLN. 
 
 3. Circles are faid to be deferib' d , or circumfcrib’ d, about right- 
 lin'd Figures , when their Circumferences touch all the Angles of 
 the Figures which they circumjcrihe. 
 
 So the Circles ABC, and DEFG (Fig. XI.) are circum- 
 fcrib’d about the Triangle ABC, and Square DEFG; becaufe 
 their Circumferences touch the Angles of the Triangle at ABC, 
 and the Square at DEFG. And again, 
 
 Circles 
 
A Sure Guide to Builders. 
 
 Circles are faid to be Infcrib'd , when their Circumferences touch 
 all the Sides 'of the Figures in which they are Infcrib'd. 
 
 So the Circles FBD, and KHLN (Fig. XII.) are infcrib’d 
 within the Triangle ACE, and Square GIMO ; becaule their 
 Circumferences touch the Sides of the Triangle in the Points 
 FBD, and the Sides of the Square in the Points KHLN. 
 
 DEFIN. XII. 
 
 Of the POWER, of a LINE . 
 
 i . HTH E Power of a Line y is the Square of the fame Line • or 
 
 * any plain Figure equal to the Square thereof 
 
 So the Power of the Right Line Aj (Fig. XIII.) is the Square 
 A,5,EF. For the Squares of Lines are the fame as the Squares 
 of Numbers : As for Example; Let the Line A j, reprefent the 
 Number^, that is, let it be divided into 5 equal Parts ; as alfb every 
 of the other Sides A E, E F and 5 F : Then I fay, if from every 
 oppolite Divifion Right Lines are drawn, as 1,1; 2, 2 ; 3,3; 4,4;. 
 and a a, bb y cc y dd y they will, by their Interfedions, generate 
 25 Squares, each of which are equal to one whole Integer: 
 Therefore the Power, or Square, of the Line A 5, divided into 
 5 equal Parts, is equal to 5 in Numbers, multiply’d by 5, whofe 
 Produd is 25. 
 
 C o R o L. 
 
 Hence appears the Reafbn of the Multiplication of whole 
 Numbers and Fradions, as of whole Numbers only. For, fup- 
 pofe the given Line was Ae y equal to 4 and -£4 then will the 
 Power of that Line be the Square A elk: For, if from the 
 feveral Divilions, 1, 2, 3, 4, and a y b , c y d y Right Lines are 
 drawn, they will generate 16 complete Squares, as thofe num- 
 bred 1, 2, 3, 4, 5, 6,-7, 8, p, 10, n, 12, 13, 14, 15, 1 6 y which 
 are equal to the Square of the four whole Divilions, fquar’d or 
 multiply'd into themfelves. 
 
 The Quantity produc'd by the Multiplication, or Power of the 
 Fradions, are the Parallelograms 4 elf lfmg y mgni y nidi y 
 equal to stvx y which, taken together, are equal to four 
 
 whole 
 
A Sure Guide to Builders. 
 
 whole Squares, or Integers, and the little Square dip% which 
 is equal to one fourth Part of a whole Integer, caufed by the 
 Power or Multiplication of the Fra&ion into itfelf ; for every 
 Side of the little Square di pk, is equal to the Fra&ion 4^ given. 
 
 This Kind of Multiplication is generally call'd, Crofs Multi- 
 plication ; and ’tis by this Method of multiplying, that the Di- 
 menfions of the feveral Parts of Buildings are generally fquar’d, 
 or call up* 
 
 a. The Diagonal of every Square , is double in Power to the 
 Side of the Square. That is ; that Square, whofe Sides are each 
 equal to the Diagonal of a given Square, is equal to double the 
 Quantity thereof: So the Square GILK (Fig. XIII.) made on 
 the Diagonal GL, of the Square GHML, is equal to double the 
 Quantity thereof. 
 
 For fince that the Triangle GHL is equal to one Half of the 
 Square GHML, and but one Fourth of the Square GILK; 
 therefore the whole Square GHML is equal but to twice GHL, 
 which is but Half the Square GILK: Therefore the Square 
 GILK, made on the Diagonal of the Square GHML, is equal 
 to double the Quantity thereof 
 
 C O R O L. 
 
 Hence it appears , that the Square made of the Diagonal GL, 
 which is the Hypothenufe of the triangle G M L, is equal to the 
 two Squares wade of the two Sides , which contain the Right Angle. 
 For fince that oy Conftru&ion the Squares M L P Q^ and O G N M, 
 are equal to each other, and to double the Triangle GML alfo, 
 that is the Square GHML. And fince that the Triangle X, 
 which is half the Square GHML, is equal to one fourth Part of 
 the Square GILK, made on the Hypothenufe GL; it is alfo 
 equal to the Triangle S, becaufe S is one half of the Rhom- 
 boides GLMQ. And feeing that the Triangle X, which is 
 equal to one fourth of the great Square GILK, is alfo equal 
 to the Triangle S, which is equal to half the Square ML PQj 
 therefore the Triangle R, which is the remaining half of the 
 Square MLPQ, is equal to either of the Triangles ZAY. 
 Therefore the Square MLPQ is equal to half the Square 
 GILK: And as the Square OGNM is equal to the Square 
 MLPQ^, therefore both taken together, are equal to the Square 
 
 GILK, 
 
A Sure Guide to Builders. 17 
 
 * 
 
 <5 ILK, made on the Hypothenufe GL, See more hereof in 
 
 'theorem IV, Chap. II. 
 
 DEFIN. XIII. 
 
 Of SOLID BODIES. 
 
 1. A Solid is that which is contain’d under three Dimenfions, 
 viz. Length , Breadth and Depths or thicknefs. 
 
 2. As Lines are the Bounds or Limits of Superlices, lo are 
 Superfices the Bounds or Limits of Solid Bodies. 
 
 3. The feveral Kinds of Regular Solids, are the Sphere , Cone, 
 Pyramid or tetraedron , Prifm , Cylinder , Cube , Parallelopipedon , 
 Oftaedron , Dodecaedron , and Icofaedron. 
 
 4. ^Sphere is a Solid Body , muofe /v&fc Diameter of a 
 Semicircle abides unmoved , 0#^ revolves about the fame. 
 
 t he Axis of a Sphere , is that fixed Right Line, about which 
 xhe Semicircle revolves j and the Center of a Sphere is the fame 
 Point with that of a Semicircle. 
 
 C o r o L. 
 
 Hence, every Ray or Line drawn from the Center to the Superfices 
 of a Sphere , are equal amongjl themfelves. 
 
 the Diameter of a Sphere is a Right Line drawn through the 
 Center, and terminated on either Side, in the Superficies thereof. 
 
 The Bafe of a Sphere is a Point as M, when 'tis placed on a 
 flat Superficies, as AB. (Fig. XXII. Plate II.) 
 
 5. J Cone is a Solid Body , made when the Bafe or Perpen- 
 dicular of a right-angled plain triangle remaining fix’ d, the tri- 
 angle revolves about to the Place whence it frji mov’d : And when 
 the Bafe and Perpendicular of the Triangle are equal, as AB 
 and BF, (Fig. XIV.) then the Cone is a reft or right-angled 
 Cone ; that is, right-angled at F ; but if the Perpendicular be 
 greater than the Bale, as BC, which is greater than AB, by the 
 Length F C, then it is an acute-angled Cone \ and if leffer, as 
 EB, an obtufe-angled Cone: And thefe are the various Kinds of 
 Cones. • 
 
 the Axis of a Cone is that fix’d Line, as C B, about which it 
 makes its Revolution. 
 
 D the 
 
1 
 
 
 A Sure Guide to Builders. 
 
 The Bafe of a Cone is a Circle, defcrib’d by the Revolution of 
 the Bafe of the Triangle AB. (Fig. XIV.) 
 
 6. ^Pyramid is a Solid Figure, comprehended under divers 
 triangular Planes , fet upon one Plane , (which is the Bafe of the 
 Pyramid) and gathered together to one Point. 
 
 So the four triangular Planes A ah, (Fig. XV.) B be, D dc, 
 and Cda, being fet together upon the Sides of the fquare Plane 
 abed, and gather'd together to one Point, as E, of the Pyrament 
 BC, (Fig. XXIII.) they will form, a fquare Pyramid, whole 
 Bafe is equal to the Square abed. 1 
 
 The Point E form'd by the meeting of the Angles, is call'd 
 the Vertex or vertical Point of the Pyramid, and lornetimes 
 'tis alfa call’d the Apex. 
 
 In like Manner the pentangular Pyramid is fram'd by the 
 feveral Ifofceles Triangles I dh, F ad, G ab, Ube, and YLhe, be- 
 ing gather’d up together in the vertical Point G, and its Bafe will 
 be the Pentagon abdeh : And the like of all others, let their 
 Planes be of any kind whatfoever. 
 
 The Axis of a Pyramid , is the Perpendicular let fall from the 
 vertical Point (as from E, Fig. XXIII.) to the Center of the 
 Bafe G. 
 
 JTetraedron is a Solid Figure , comprehended tinder three 
 equal and equilateral Triangles, fet upon an equal equilateral Tri- 
 angle y and gather'd together , as before was faid of the Pyramid. 
 
 So the equilateral Triangles ABC, (Fig. XVI.) BED, and 
 DFC, being fet upon the equilateral Triangle BCD, and ga- 
 ther’d together, will frame the Tetraedron A. (Fig. XXIII.) 
 
 If the three Sides of every triangular Plane, be divided inta 
 three equal Parts, as at ad, be, and ef and the right Lines a b, 
 de , ef &c. drawn, every Face of the Tetraedron will be di- 
 vided into a Hexagon ; and if the triangular Parts Bab , C de,. 
 cfD, &c. are cut away, the Body will then be contain'd under 
 eight Planes, of which four will be Hexagons, and the other 
 four equilateral Triangles. 
 
 So, A Prism is an equi-t triangular Solid, contain'd under fve 
 Planes , of which two are oppofte equilateral Triangles and the 
 other. Parallelograms, as d f b e. ( Fig. XX.) 
 
 pi. A, Cylinder is a Solid Body, made by the* Revolution of ' 
 
 right-angled P arallelogram, one of the Sides being fix'd until the 
 Mgvolutwn is completed L 
 
 So 
 
 & 
 
A Sure Guide to Builders. ip 
 
 So the Parallelogram ABDE (Fig. XVIII.) having the Side 
 BE fixed, generates the Cylinder A CDE, by its making one 
 compleat Revolution about the fame. The Bafes of a Cylinder 
 are Circles, defcrib’d by the Motion of the two oppofite Sides, 
 as they make their Revolutions with the Parallelogram. 
 
 f he Axis of a Cylinder is a right Line contained between the 
 Centers of the two Bafes, as the Line BE. 
 
 10. A Cube is a Solid Figure contain d under fx equal Squares , 
 of which four are fet perpendicularly upon the Sides of one , and 
 being crown’d or cover’d with the other , compleat s the Cube. 
 
 So (Fig. XIX.) the four Squares CDEF, GEIK, FHLM, 
 and KLNO, being placed upon the Square E FKL, and raifed 
 up fo as to meet together, they will be each perpendicular to 
 the Plane of the Square EFKL ; and if the Square A BCD be 
 laid thereon, fo that its Angles lie exactly over the Angles 
 EFKL, it will compleat the Cube required. 
 
 n. A Parallelopipedon (or Long Cube, Fig. XXI.) 
 is a Solid Figure contained under fx quadrilateral Figures , (as the 
 Cube is of fx Jquare Figures) whereof thoje that are oppofte are 
 parallel. 
 
 For if the oppofite Parallelograms EFBH and DPLM are 
 raifed upon the Lines BH and DP, fo as to be both perpen- 
 dicular unto the Plane B H D P, they will be parallel to each 
 other, becaufe they are both perpendicular to the Plane B H D P. 
 Again, If the two oppofite Ends A B C D and H I P K are raifed 
 upon the Lines BD and HP, fo as to clofe with the other Pa- 
 rallelogram before raifed, they will alfo be perpendicular to the 
 Plane BDPH, and therefore parallel to each other. And laftly, 
 
 If the Parallelogram LMNO be placed upon the Edges of 
 the other Planes, it will compleat the Parallelopipedon, and be 
 parallel to the under Plane BHDP; becaufe the Parallelogram 
 EFBH and DPLM, are of equal Heights above the Plane 
 B H D P : Therefore all the Planes are parallel to each other. 
 
 1 1. An Octaedron is a Solid Figure, contain d under eight 
 equal equilateral friangles : Or otherwife, An Oliaedron is tivo 
 Jquare Pyramids , with one Bafe common to both. 
 
 For if on the Sides of the Squares HIKL, (Fig. III. 
 
 Plate HI.) and MNOP, there be Equilateral Triangles defcrib’d, 
 and each gather’d together, they will form two fquare Pyramids, 
 
 D 2. whofe 
 
20 
 
 A Sure Guide to Builders. 
 
 whofe Bafes, being apply’d together, complete the Oclaedron F. 
 (Fig. XXIII. Plate II.) with its eight equilateral triangular 
 Planes. 
 
 13. A Dodecaedron is a folid Figure , contain'd under twelve 
 equilateral Pentagons , whereof thofe that are oppojite are 
 
 every Side of the Pentagons AK (Fig. VI. Plate III.) 
 equal Pentagons be delineated ( by Prob. XIV. Ch. III.) as B, C, 
 D, F, E, and G HIL K, and being gather’d together (as before 
 has been faid of the Pyramid) they, being apply'd together, 
 will complete the Dodecaedron D. ( Fig. XXIII. Plate II.), 
 
 14. An Icosaedron is a folid Figure contain'd under twenty 
 equal and equilateral triangle s y whereof thofe that are oppofte are 
 
 every Side of the Equilateral Triangles 1, 20 (Fig. II. 
 Plate III.) Equilateral Triangles be defcrib’d, as 2, 3, 4, and 
 17, 18, ip; as alfo others on their Sides, as the Triangles 
 5, 6, p, 10, 7, 8, and 14, 15, 12, 13, 16, n, and be feveraliy 
 gather’d up about the Triangles 1, and 20, and then apply’d 
 together, they will complete the Icofaedron G, (Fig. XXIII. 
 Plate II.) with its twenty equilateral triangular Planes oppolite 
 and parallel to each other.. 
 
 Note, 7 ' hat the tfetraedron, Cube , Otfaedron y Dodecaedron and 
 Icofaedron , are called the fve Regular or Platonick Bodies , 
 in refpeft that they are feveraliy capable of being infcribed 
 within a Sphere . 
 
 A Solid Figure or Body is faid to be infcribed within a Sphere, 
 when all the. Angles of the Figure infcrib’d, are compre- 
 hended m the Superficies of the Sphere wherein it is 
 infcribed* 
 
 parallel. 
 
 If on 
 
 equal and 
 parallel. 
 If on 
 
 DEFIE 
 
11 
 
 A Sure Guide to Builders. 
 
 i ] ~ ' ’ ') • ' »> < I -i 
 
 D E F I N. XIV. 
 
 Of the Altitude of FIGURES. 
 
 T HE Height or Altitude of any plain Figure , is the parallel 
 Difance between the fop of a Figure and the Bafe. 
 
 I ' r ) V v rS . ' C' -!• v? / i • v 
 
 So the Height of the frapezium cefh , (Fig. IX.) is the 
 Perpendicular c d ; becaufe it is the neareft Diftance between the 
 parallel Lines ab the Top, and f dm the Bafe : So alfo the Per- 
 pendiculars ik y and Ivy are the Heights or Altitudes of the 
 fri angle nioy and the Hexagon P qr sox. (Ftg. X. and XI.) 
 
 CHAP. ir. 
 
 Of Geometrical 'Theorems . 
 
 Theorem is, when fomething is propoied to be 
 demonftrated. 
 
 A Corollary is a Confeffary , or fome confe- 
 fequent Truth, gain'd from a precedent Demon- 
 ftration. 
 
 THEOREM L 
 
 / F any two right Lines cut thrd one another , (as A E, Fig. I. 
 
 Plate III. cut by bF or c G) then are the oppofte or vertical 
 Angles equal one to the other. 
 
 For bF cutting AE at right Angles, the Angle aBb 
 and bBd are equal by Def V. fo alfo the Angle bBd is 
 equal to the Angle d Be, and d Be to e B a j therefore 
 they are all equal to one another. And therefore the 
 ©ppofite Angles are allb ecfual j. that is, the Angle bBd 
 
 is 
 
22 
 
 A Sure Guide to Builders . 
 
 is equal to the Angle eB a, and the Angle aBb is equal to the 
 Angle eB d\ becaufe the Arches ab y bd , de , ea , by which they 
 are meafured, are feverally and oppofitely equal. Again, The 
 Angles cBd and aBf conlHtuted by the right Line cG, cut- 
 ting AE in B, are equal ; becaufe the Arch cd being of the 
 fame Radius with the Arch fa, and equal thereto, are therefore 
 equal to one another. So alfo are the oppofite Angles aBc and 
 fB'd • becaufe the Arch ac is equal to the Axdifd. Ch E. D. 
 
 THEOREM IL 
 
 71/ H E AT two parallel right ' Lines are obliquely cut by a right 
 ** Line , it makes the outward Angles on the contrary Sides of the 
 Line equal • and likewife the inward and oppofite Angles on the con- 
 trary Sides of the fame Line • as aljo the outward jungle equal to 
 the inward and oppofite Angle on one and the fame Side of the fall- 
 ing Line ; and the inward Angles on one and the fame Side equal to 
 two right Angles. 
 
 * . ♦ 1 ^ -A 
 
 Let the right Line CG (Fig. XVII.) cut the parallel right 
 Lines AD and FH, and on the Points of Interfedlion B and 
 E, let there be two Circles defcrib’d of equal Radius’s. 
 
 Firfl 3 The outward Angles on contrary Sides of the Line CG, 
 are the Angles ABC and GEH, as alfo CBD and FEG. Now, 
 I fay, that the Angle ABC is equal to the Angle GEH : For 
 fince the Angle G B D is equal to its oppofite ABC, (by the laft 
 Theorem) and F H is parallel to AD; therefore the Angle 
 GEH is equal to the Angle GBD, which is equal to its oppo- 
 fite ABC ; therefore the Angle ABC is equal to the Angle 
 GEH. By the fame Argument is the Angle CBD equal to the 
 Angle FEG. 
 
 Secondly , The inward Angles are firft the Angle CEH, which 
 (by the fir B. ‘Theorem) is equal to its oppofite Angle FEG, and 
 the Angle FEC is equal to GEH, and GBD to ABC, and 
 iaftly, AEG to CBD ; therefore all the inward and oppofite 
 Angles are equal. And fince that the Angles CBD and CEH 
 are equal to each other, as alfo to their Oppofites F E G and 
 ABG; therefore the alternate Angles DEC and FEG are equal ; 
 as alfo the alternate Angles FEC and GBD. 
 
 Lafly , 
 
 r 
 
\ 
 
23 
 
 A Sure Guide to Builders. 
 
 Laftly , The inward Angles FEG and A BG are equal to two 
 right Angles. For fince that the Angles F E C and C E H be- 
 ing taken together, are equal to two right Angles ; fo are the 
 Angles F E C and A B G alfo ; becaufe the Angle A B G is equal 
 to the alternate Angle C E H. E. D. 
 
 The Equality of thefe feveral Angles, may be alfo proved by 
 the Meafures of the feveral Arches of the Circles abed , and 
 e bhgy under which they are feverally contained. 
 
 THEOREM III. 
 
 TT7HEN’ a right Line is divided into -two equal Parts , the 
 Squares made of thofe Parts, are equal but to half the Square 
 made by the whole Line . ( Fig. VIII.) 
 
 This is evident; for the two Squares ABED and B CDF, 
 made by the Squares of the two equal Parts of the Line AC, 
 are equal but to half the Square A CGI, made by the Square of 
 the whole Line AC ; becaufe that the other two Squares DH FI 
 and E D G H are equal unto them. E. D. 
 
 THEOREM IV. 
 
 TI/H EN a right Line is divided by Chance into two imequal c Parts , 
 the Square of the whole Line is equal to both the Squares made 
 of the Parts ; and to two Parallelograms , comprehended under the 
 fame Parts alfo. (Fig. XVI. Plate III.) 
 
 That is, If the right Line B A be accidentally divided in C,. 
 I fay, that the Square A B D E is equal to the Squares made of 
 the Parts, (ACGH and HKFE) and to two Parallelograms 
 CBHK and GHDF alfo, whofe oppolite Sides are equal to the 
 unequal Parts of the divided Line AB ; becaufe that the Whole 
 is equal to all its Parts taken together; which being evident,, 
 needs no further Demonftration, 
 
 C ' ' 
 
 Cor o l. 
 
 Hence it appears, that the Parallelograms cofnprehended under 
 the unequal Parts of the Line A B, are equal to, one another , 
 
 For 
 
2 4 
 
 A Sure Guide to Builders. 
 
 For fince that the Diagonal AHE doth divide the Square into 
 two equal Parts, and thereby the Triangle ABE is made equal 
 to the Triangle ADE ; fo alio is the Triangle ACH equal to 
 the Triangle AGH, and the Triangle HKE to the Triangle 
 HFE. Now, if from the two Triangles ABE and ADE, you 
 fubflrad, or take away the equal Triangles AGH, AGH, 
 HFE, and HKE, the Remains will be equal. For if from 
 equal Quantities you take away equal Quantities, the Quantities 
 remaining will be equal, {Euclid Axiom III. Book I.) and there- 
 fore the Parallelograms GBHK and GHDF are equal. 
 
 Note, That the Squares ACGH and HKFE are generally 
 called the Parallelograms about the Diameter AE; but 
 more properly, in my humble Opinion, the Squares about 
 the Diagonal AE; becaufe they are really Squares, and 
 not Parallelograms; and the Line AE is a Diagonal com- 
 mon to them both, and not a Diameter, as Euclid calls it in 
 the 4th Prop, of his 2d Book. 
 
 The Parallelograms CBHK and GHDF, are called the Sup- 
 plements or Complements of the two Squares ACGH and 
 HKFE, to the whole Square A B D E. 
 
 THEOREM V. 
 
 / N all right-angled plain 'Triangles, the Square made of the Hy - 
 pothenufe , is equal to both the Squares made of the two Legs , 
 which contain the right Angle. 
 
 This has been prov’d already in the ad Corollary of Def XII. 
 Chap-. I. where the two Legs of the right-angled plain Triangle 
 are made equal : But by this Theorem I will prove the fame 
 when the two Legs are unequal, (as Fig. IV. c Tlate III.) 
 
 1. Let the Triangle ABC, right-angled at A, be the given 
 Triangle. 
 
 2. Compleat the Geometrical Squares FGBA, AHCI, and 
 BCDE, and join AD and AE, and draw AM parallel to CE, 
 allb draw F C and BI. 
 
 3. Since all right Angles are equal to one another, therefore 
 the Angle DBG is equal to the Angle FB A ; and as the Angle 
 ABC is common to them both, therefore the Angle ABD is 
 
 equal 
 
A Sure Guide to Builders l 
 
 equal to the Angle FBC ; and as the Side FB of the Triangle 
 
 FBC > ^ eq fV°^ h . e Side B A 0f the Trian S le ABD ; and the 
 S * de BD of the Triangle A B D, is equal to the Side BC of 
 the Triangle P CB • therefore the Triangle FCB is equal to the 
 I nangle ABD, becaufe their obtufe Angles ABD and FBC 
 are equal. For fincc that the Angle DBG and FB A are both 
 right Angles, and equal to one another ; therefore as the Angle 
 ABC is common to them both, and being added to them both 
 leparately, it will make them both equal, becaufe the Addition 
 
 ea 5 h A ls t , he 7 £ ame . : That K if to the right Angle aBb you 
 add the Angle ^ Be, it will be equal to the right Angle cBd 
 with the Addition of the Angle cBb. § ’ 
 
 ^ thls . more P lainer > 1 wil1 prove the Triangles 
 
 L h Y the 4th Propofition of 
 
 tnc nrlt kook. of JLuclid ^ as following • wherc^ fkys he 
 
 !f two 7rjm,gks (as JY> C a„d ABD) have two Sides of the 
 
 ° A f A rT V, T tangle FBC, equal to two Sides If the 
 .f^AB, BD, each to its correfpondent Side , {that is, FB, of 
 thefrumgk FBC, equal to A B, of the friangle^BD andBC, 
 of the Triangle FBC, equal to BD of the Triangle ABD) and 
 have the. Angle ABD equal to the Anile F B C, contain'd under the 
 equal right Lines, they flail have the Bafe FG of the Triable 
 
 a 2 1° ill Bafe i AD f A r ™ n £ /e AB ^{ and the Tri- 
 
 £ e 2ifl t U r he fl Tf *° 2 A BD i and the remain- 
 
 ng f 4 gl 7 B F C / haU be e?ual t0 B A D, and FCB equal to A D B 
 each to each , under which the Sides are fubt ended. " 
 
 D 
 
 E M O N. 
 
 Since the obtrae angular Points of both Triangles, FBC and 
 )D, are in one and the fame at B; therefore if on B, the 
 F laI ^' e A , BD be fo moved, as for the Side BA to lie over the 
 'hen will the Bafe AD cover the Bafe FC, and the 
 Side B D the Side B C ; becaufe the Sides F B and B A are equal 
 Sides o. the Square FG BA, and BC and B D are equal Sides of 
 the Square BCD E, and the obtufe Angles FBC and ABD both 
 equal, as before proy’d. Now feeing that B A is equal to BF 
 
 POT"' * ° f the Triangle ABD will fall on the 
 
 Point ± , when the Side B A is lo mov’d as to lie over BF and 
 
 T the 
 
26 
 
 A Sure Guide to Builders . 
 
 the Point D will fall on the Point C, becaufe BD is equal BC; 
 therefore the right Lines FC and AD, becaufe they have the 
 fame Terms, ftiall agree, and fo confequently are equal ; where- 
 fore the Triangles BBC, ABD, and the Angles BFG, BAD, 
 as alfo the Angles BD A, BCF, do agree, and are equal : Which 
 was to be demon f rated. 
 
 Having thus proved the Equality of the Triangles FBC and 
 ABD, I ftiall now proceed to prove, that the Oblong BP D M 
 is equal to the Square FGBA, and the Oblong P CM E equal 
 to the Square AHC 1 ; and confequently the Square BCDE 
 equal to both the Squares FGBA and A HCI. 
 
 By 41ft Prop, ift Book of Euclid. 
 
 If a Parallelogram B P M D have the fame Bafe BD with the 
 e fnangle ABD, and be between the fame Parallels BD and AM, 
 then is the Parallelogram BPMD, double in Quantity to the Pri- 
 angle ABD. 
 
 1. Draw Q^D parallel to AB, by Prob. VI. Chap. III. hereof, 
 then will the Rhomboides A B QD be equal to the Parallelo- 
 gram BP DM; becaufe the Triangle B A P, which is added to 
 the Parallelogram BPMD, is equal to the Triangle D CfM, 
 which is taken from the Parallelogram B P D M. For as A P is 
 equal to QM, AB to Q^D, and BP to DM, they are therefore 
 equal to each other. 
 
 2. Since the Side BD is equal to its oppofite A as alio B A 
 equal to its oppolite D O^, and the Line AD is common to them 
 both, therefore the Triangle ABD is equal to the Triangle 
 A ; and therefore as the Rhomboides BAD Q^ is equal to 
 the Parallelogram B P D M, it is therefore double in Quantity to 
 the Triangle ABD, which is equal but to half the Rhomboides. 
 Again, Draw FR parallel to B C, and conftitute the Rhomboides 
 FRBC, which will be equal to the Square FGBA ; becaufe 
 the Triangle ABC, taken in to cornpleat the Rhomboides, is 
 equal to the Triangle F G R, which is left out. Now as the 
 oppolite Sides of the Rhomboides are equal, therefore the Tri- 
 angle FBC, which is one half of the Rhomboides, is alfo equal 
 to half the Square FGBA. 
 
A Sure Guide to Builders . 
 
 And fince that the Triangle FBC is equal to half the Square 
 FGBA, and to the Triangle ABD alfo, which is alfo equal to 
 half the Parallelogram BP DM; therefore the Parallelogram 
 BPDM is double in Quantity to the Triangle ABD or FBC, 
 ■Which being each equal to half the Square FGBA, therefore 
 the Parallelogram BPDM is equal to the Square FGBA. 
 
 By the fame Way of Argument, is the Parallelogram PCME 
 equal to the Square AH Cl; therefore is the whole Square 
 BCDE equal to the Squares FGBA and AHCI : Which was 
 to he demo nfl rated. 
 
 This Theorem was firft difcover’d by Pythagoras , which, for 
 its many excellent Ufes, truly deferves to be wrote in Capitals of 
 Gold, in Memory of that famous Geometrician, as will appear in 
 the third Chapter hereof. 
 
 THEOREM VI. 
 
 r T' HE fuperfcial Content of every right-angled plain T’r tangle , 
 is equal to half that right-angled Parallelogram , which hath its 
 Length and Breadth equal to the containing Sides of the right 
 Angle : Or whofe Length is equal to the fuhtending Side, and 
 Breadth to the Perpendicular drawn from the right Angle to the 
 fame Side. 
 
 Let AEF (Fig. XIX.) be the right-angled Triangle given, 
 right-angled at E, and let AB be drawn parallel to EF, and 
 F B parallel to A E, by Prop. IV. Chap. III. Now, I fay, that 
 the fuperficial Content of this Triangle is equal to half the Pa- 
 rallelogram ABEF. For as the Angles A, B, E, F, are all 
 right-angled, every oppofite Side mull be equal ; and therefore 
 AB is equal to EF, and BF to AE, and AF is common to 
 both Triangles; therefore the right-angled Triangle AEF, is 
 equal to half the Parallelogram ABEF: Which was to he de- 
 monf rated. 
 
 Again, by Proh. II. Chap. III. let fall the Perpendicular EC, 
 and by Proh. I. Chap. III. at the Points A and F, raiie the two 
 perpendicular Lines A D and F G perpendicular to the Bale of 
 the Triangle A F, making each of them equal to the Perpen- 
 dicular EC, and drawing DG thro’ E parallel to AF, you’ll 
 
 E 2 compleat 
 
A Sure Guide to Builders. 
 
 compleat the Parallelogram AFDG, whofe Length is equal to 
 the fubtending Side of the right Angle of the Triangle, and 
 Breadth to the Perpendicular drawn from the right Angle to the 
 fame Side. 
 
 Now, I fay, that the Triangle AEF is equal to half the 
 Parallelogram AFD G For as the Triangle AD E is equal to 
 the Triangle A E C, and the Triangle CEF equal to the Tri- 
 angle EFG; therefore the two Triangles EGA and CEF, 
 which compofe the Triangle AEF, are equal to half the Paral- 
 lelogram ADFG, which is compofed of the two Triangles 
 A D E and EFG : Which was to. he demonji rated. 
 
 T H E O R E M VI L 
 
 TT 1 HE Area or fuperfcial Content of every equilateral Triangle, 
 is equal to half that Parallelogram, whofe Length and Breadth 
 is equal to one of the Sides and the Perpendicular. (Fig. 
 XV.) 
 
 Let BDF be an equilateral Triangle., and BE the Perpendi- 
 cular thereof. Now, I fay, that the Area, of that Triangle is 
 equal to half the Parallelogram ACDF. 
 
 For as the Triangle is equilateral,, therefore the Perpendicular 
 A E will divide the Parallelogram into two equal Parts : And 
 lince that the Side D F is parallel to AB, and DA and FC pa- 
 rallel to the Perpendicular A E ; therefore the Sides BF and BD, 
 of the Triangle BDF, will divide each half of the Parallelo- 
 gram D A B E and B C F E into two equal Parts. Now his 
 evident, that as the right-angled Triangle BEF is equal to the 
 right-angled. Triangle BCF, and the' right-angled Triangle 
 BDE equal to the Triangle ABD,- and the right-angled Tri- 
 angle BDE equal to the right-angled Triangle BEF; therefore 
 the right-angled Triangles BDE and BEF are equal to the 
 right-angled Triangles ABD and BCF, which are equal to half 
 the Parallelogram ACDF : Which was to he demonflrated. 
 
 Hence it follows, that half the Bare of any Triangle being 
 multipiy’d into the Perpendicular, the Product is the Area*. For 
 if D F be ccnlider’d as the Bale, and BE the Perpendicular, 
 then the Oblong or Parallelogram ABD E, made by DE the 
 half Bafe, and BE the Perpendicular,, will be equal to the, Area 
 
A Sure Guide to Builders . 
 
 of the Triangle BDF; becaufe the Triangle A BD, which is 
 added to the half of the Triangle B D E, is equal to the other 
 half of the Triangle BEF, which is left out of the Parallelo- 
 gram A B D E. 
 
 THEOREM VIII. 
 
 T H F, Diagonal Lint of every Geometrical Square , is double in 
 ‘Lower to the Side of the fame Square . 
 
 D E M O N* 
 
 Let the Diagonal AC of the Square ABDC, (Fig. XII.) 
 be given. I fay, that its Power is double to any of its Sides : 
 That is, the Square thereof AEFC, is equal to the Squares 
 made by any two of the Sides- See the cth Theorem hereof 
 Q-E.D- 
 
 H /•.’ ' ! • ; T \ j : ; r; ' Jf. I ’.'VU' i. . • ( •• f < \ \ I 
 
 THEOREM IX. 
 
 yd Square, whofe Side is equal to' the Diagonal of any other Square, 
 double in fuperficial Quantity to the other Square . 
 
 This is manifeft by the taft Theorem : For the Square AEFC 
 having its Side.AC, the Diagonal of the Square ABDC, is 
 double in Quantity. For the Triangle ABC being equal but to 
 the^Triangle A ED, there remains the two Triangles EDF, and 
 D r* C, which are alio equal to the two Triangles ADC and 
 ABC, which compofe the Square ABDC, whole Diagonal A C„ 
 is one Side of the Square A E F C. E. D. 
 
 THEOREM X., 
 
 P arallelograms , which confift on one and the fame Bafe, or on 
 
 equal Bafes , and in the fame ^Parallels, are equal the one to the 
 other . 
 
 Let B CD E (fig. XVIII.) and ADBE be two Paralleled 
 grams, which confift on one and the fame BafeDE, (or on 
 
 equal 
 
 29 
 
A Sure Guide to Builders. 
 
 eqpal: Bafes, which is the very lame Thing) and in the fame 
 Parallels, 
 
 Now, I fay, that thofe two Parallelograms are equal. For 
 as A B is equal and parallel to DE, BE equal and parallel to 
 AD, BD equal and parallel to GE, and BC equal and parallel 
 to DE; therefore the Triangles ABD and BDE, which com- 
 pofe the Parallelogram A BDE, are equal to the Triangles 
 BDE and BCE, which compofe the Parallelogram B C D E 5 
 therefore the Parallelogram ABD E is equal to the Parallelo- 
 gram B CD E : hVhich was to be demonstrated. 
 
 S C H O L. 
 
 Hence it appears, that every Rhombus or Rhomboides is 
 equal to a Parallelogram, whofe Length is equal to the parallel 
 Diftance between the Ends, and the Breadth to the Length of 
 one of the. Ends. For the Parallelogram BCD E hath its Length 
 equal to BD, the parallel Diftance between the Ends AB and 
 D E ; and its Breadth equal to D E, one of the Ends : And 
 the like of the Rhombus ABCEDF. (Fig. XXXVI.) 
 
 Now from hence is the Reafon, why the End DE of the 
 Rhomboides ABDE being multiply'd into the Length, or per- 
 pendicular Diftance of the Ends BD, the Product is the fuper- 
 hcial Content. And fince that the oblique-angled Parallelogram 
 ABDE is equal to the right-angled Parallelogram BCDE, the 
 Reafon is alfo fhewn, why the Breadth or Power of the Line 
 DE, being infolded or multiply’d into the Length or Power of 
 D B, produceth the Area or fuperftcial Content of the lame. See 
 Dej. XII. Chap. I. 
 
 THEOREM XI. 
 
 £ VER.T Eolygon is equal to a Parallelogram, whofe Length Is 
 equal to half the Perimeter or Clrcumjerence thereof and 
 Breadth to a Perpendicular drawn from the Center to the Middle 
 of any Side of the fame. 
 
 D.E MON. 
 
A Sure Guide to Builders • 
 
 Demon. 
 
 . i. Let the Hexagon {Fig. XIV.) idhlop be the given 
 Polygon, and en a Perpendicular, drawn from the Center n to 
 the Middle of the Side dh. 
 
 i. Draw right Lines from the Center n to the Angles i, d, h, /, o,p • 
 alfo continue ed to a, making ea equal to half the Perimeter of 
 the Polygon : That is, m^ke dc equal t o hi, cb equal to lo, and 
 ba equal to eh ; then compleat the Parallelogram aekn by ^Prob. 
 II. Chap. III. and make im and fak each equal to in. Now* I 
 lay, that the Parallelogram aekn, whofe Length ae is equal to 
 half thp Circumference of the Polygon, and Breadth to the Per- 
 pendicular en , is equal to the Polygon dhlopi. For as the 
 Triangles i, a, 3, 4, 5, and 6 are all equal to one another j 
 fo alfo are the Triangles 7, 8, 9,- and 10 equal thereto alfo ; 
 becaufe they are all of equal Bafes^ and between the fame 
 Parallels, a h and kl. 
 
 Now feeing that the Triangles dne and din are already com- 
 prized within the Parallelogram aekn , it only remains to prove, 
 that the Triangles 7, 8, 9, 10, and abk, are equal to the re- 
 maining Triangles of the Polygon enh , a, 3, 4, and 5. 
 
 It has been already proved, that all the feveral Triangles 1, 
 1, 3> 4? 5 -> 7, 8, 9, 10, are equal to one another ; there- 
 
 fore the Triangle 7 may be faid to be equal to the Triangle 5 ; 
 the Triangle 8, to the Triangle 4 ; the Triangle 9, to the Tri- 
 angle .3 ; the Triangle 10, to the Triangle 1 ; and laftly, the 
 Triangle a bk, to the Triangle enh • therefore is the Parallelo- 
 
 t he Polygon idhlop'. Which was to be 
 
 S C H O L. 
 
 Hence appears the Reafon of the General Rule for the Men- 
 furation of Polygons, To multiply half the Circumference by a 
 (perpendicular let fall from the Center upon one of the Sides , 
 
 gram aekn equal to 
 demonf rated. 
 
 THEOREM 
 
A Sure Guide to Builders v 
 
 THEOREM XII. 
 
 PA E E * ^' mie ls f ear ty ei l ual t0 a Parallelogram, whofe Length 
 is equal to half its Circumference, and Breadth to the Semi- 
 diameter : Or every Circle is equal to the Parallelogram, whofe 
 Length is equal to the Diameter , and Breadth to jj thereof. 
 
 Suppofe the Circle ABI (Fig. V.) to be 14 Feet Di- 
 ameter, and its Circumference 44 Feet: Then, I fay, that the 
 Oblong BHIM, whofe Length BH is equal to 22, the half of 
 the Circumference of the Circle A El, and Breadth HM to the 
 Semi-diameter BI, is equal to the Parallelogram AC IK 
 whofe Length C K is equal to the Diameter A I, and Breadth to 
 tt thereof. • . , / 
 
 For HM, which is equal to 7 Feet, being multiply^ into B H 
 22 Feet, the Produd or Area thereof is 154 Feet. And again > 
 A I the Diameter, 14 Feet, being multiply^ into AC, ii 
 thereof, viz. 1 1 Feet, the Produd or Area thereof is 1 54 Feet*, 
 as before. Therefore thofe two Parallelograms are equal, and 
 either of them nearly equal to the Area of the Circle ABI. 
 
 C. ' . c c r.; , vU 5 iK' ; s ■ J i'j.V ' . ! j ./i 
 
 \ ... * ‘ * fc . . - ^ ' 
 
 C O R O L. Xi 
 
 _ Hence appears the Reafn of the general Rule for the Met fur a- 
 tion of Circles. To multiply half the Circumference by haljf 
 the Diameter. .or 
 
 f T . j v f .JA'- Vu;i {V 
 
 C O R o l, 2. ' 
 
 Hence every Semi-circle is nearly equal to the Oblong or F a talkie- 
 gi am, whofe Length is equal to half the Curve or ylrch and 
 Breadth to the Radius or Semi-diameter. 
 
 That is, the Semi-circle A El is nearly equal to the Paralle- 
 logram BHIM, whofe Length IM is nearly equal to half the 
 Arch Line A El, and Breadth HM to the Semi-diameter B I. 
 For the Parallelogram AC BF is equal to half the Parallelo- 
 gram A Cl K. 
 
 COROL, 
 
A Sure Guide to Builders. 
 
 33 
 
 C O R O L. 3. 
 
 Hence it appears, that every Circle is nearly equal to that right- 
 angled triangle, whofe Baje is equal to its Circumference , and ^Per- 
 pendicular to the Semi-diameter thereof. 
 
 For if the Side AO^of the Parallelogram AQ^BH be conti- 
 nued to X, and made equal to the whole Circumference AEZI, 
 and the Hypothenufe BX being drawn; I fay that the Triangle 
 BAX is equal to the Parallelogram AQjBH. For as AX is 
 equal to twice AQ^, and AB is perpendicular to AX ; therefore 
 QX, the Side continued, will be equal to BH, which is parallel 
 to ACf , and confequently CfH will be bifeded in P by the Hy- 
 pothenufe BX. Now feeing that QJX is equal to A Cf, PX to 
 P B, and the Angles XOP and BHP both right-angled; 
 therefore the Triangle AXB is equal to the Parallelogram 
 AQBH, becaufe the Triangle QXP is equal to the Triangle 
 BPH. 
 
 THEOREM XIII. 
 
 E VERT Serf or of a Circle is nearly equal to a Parallelogram , 
 whofe Length is equal to the Semi-diameter of the Circle , and 
 Breadth to half the Curve or Arch Line thereof : Or whofe Length 
 is equal to half the Semi-diameter , and Breadth to the whole Curve 
 or Arch Line thereof. (Fig. XIII.) 
 
 Let nmx be the Se&or of a Circle, whofe Arch Line nx is 
 equal to 5 Feet, and Semi-diameter nm to 7 Feet: I fay that 
 the Oblong ann m, whofe Length is equal to the Semi-diameter 
 nm , and Breadth to half the Arch nx , is equal to the Oblong 
 hhvm , whofe Length vm is equal to the whole Curve nx^ 'and 
 Breadth to half the Semi-diameter h m. For an, which is equal 
 to half the curved Line nx, viz. 1 Feet one half, being muiti- 
 piy’d into 7 Feet, the Semi-diameter, the Area or Produd is 17 
 one half : So likevvife hb, which is equal to the whole Curve 
 nx, viz. 5 Feet, being multiply’d into half the Semi-diameter 
 hm, 3 Feet one half, the Area or Product is alfo 17 one half, 
 as before. For as nx is equal to hb, and hv equal to bm', fo 
 alfo is a r equal to n m, and a n to half n x ; and as all the Angles of 
 
 F the 
 
A Sure Guide to Builders. 
 
 the three Parallelograms anrm , obrm, and hov r, are all right 
 Angles, and their refpedive oppofite Sides equal ; therefore the 
 two Parallelograms anob and obrm , which compofe the Pa- 
 rallelogram anrm , made by the half Arch multiply’d into the 
 whole Semi- diameter, is equal to the two Parallelograms obrm 
 and hovr , which compofe the Parallelogram hbvm , made by the 
 whole Arch multiply’d into half the Semi-diameter : Which was 
 to be dcmonjirated. 
 
 C O R O L. 
 
 Hence ’tis evident , that the Area of any Circle , Semi-circle , Qua- 
 drant, or Seel or, may be found by this one general Rule , viz. ' 
 Multiply half the Curve or Arch Line by the Semi-diameter ; 
 or, multiply half the Semi-diameter by the whole Curve or Arch 
 Line, and the Product will be the Area requir’d. 
 
 THEOREM XIV. 
 
 / F the Proportion that the Diameter of a Circle hath to its Cir- 
 cumference , be allow’ d to be as 7 is to 22, then the Square made 
 of the Diameter of any Circle , is in Proportion to that Circle y 
 (as 14 is to 1 1 ) and therefore every inferih’d Circle within a Square 
 is thereof 
 
 Let the Circle AZEI be infcnVd within the Square NORS; 
 I fay that the Area of that Circle is equal to of the Square. 
 Suppofe the Diameter of the Circle A I, or Side of the Square 
 NR, to be equal to 14 Feet, and the Circumference to 44 Feet: 
 For as 7 is to 22, lb is 14, the Diameter given, to 44, the 
 Circumference given. 
 
 Demon. 
 
 1. Multiply half the Diameter 7 Feet, by half the Circum- 
 ference aa, and the Produd is 154 Feet, the Area of the Circle. 
 
 2. Multiply one of the Sides of the Square, as NR, into 
 itfelf, viz . 14 by 14, and the Produd is the Area of the 
 
 Square. 
 
 Now 
 
A Sure Guide to Builders. 
 
 35 
 
 Now by the Rale of Proportion , 
 
 As 154, the Area of the Circle, is to ip6, the Area of the 
 Square ; fo is 1 1 to 1 4. 
 
 154 : 1 96 : : 11 : 14 
 1 1 
 
 1 96 
 196 
 
 __ — i 
 
 154)215^(14 
 
 *54 
 
 616 
 
 616 
 
 000 remains. 
 
 “ 1 ■ ■ ■ ; ■ ■ * * • t ~ 
 
 Therefore the Proportion that a Circle hath to a Square, whole 
 Diameter and Sides are equal, is as 1 1 to 1 4. 
 
 C o r o L. 
 
 Hence arlfes the fated Numbers and Rule by which the Area of 
 Circles are found , when the Diameters only are given , viz. 
 
 Square the Diameter given, multiply the Product by 1 1 , and 
 divide the laft Produd by 14, the Quotient is the Area re- 
 quired. 
 
3 6 
 
 A Sure Guide to Builders. 
 
 As for EXAMPLE : 
 
 Let the Diameter of a given Circle be 14 Feet, as before. 
 14 
 
 14 ! 1 
 
 56 
 
 14 ", l t 
 
 Product 1 the Diameter fquared. 
 
 Multiply'd by 1 1 5 { '! 
 
 i$6 
 
 1 96 
 
 34) 2156 (154, the Area of the Circle, as be- 
 14 fore, when half the Cir- 
 
 — — cumference was multiply ’d 
 
 75 into the Semi - diameter. 
 
 70 Vide theorem XII. 
 
 & 
 
 00 remains, ; 
 
 CHAP. 
 
*•> 
 
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 . - X. 
 
 A : 
 
 r 
 
 
 
 
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 \ 
 
 / 
 
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A Sure Guide to Builders. 
 
 37 
 
 CHAP. III. 
 
 Of fuch Geometrical Problems, that are abfolutely necejfary 
 in Drawing, Setting out, Framing, Meafuring, 
 
 PROBLEM I. (Plate IV.) 
 
 raife a Perpendicular from a given Point, at the 
 '.nd of a right Line . 
 
 Note, This, Problem may be perform’d by feven 
 different Methods, as follow : 
 
 * A 
 
 Method i. 
 
 By Help of the Te-Square and Drawing- 7 ’able. 
 
 P radii ce. Let 1234 (Fig. I.) reprefent your Drawing- 
 Table, and kl the Te-Square, which apply to any Side of 
 your Table, and by its Edge draw a Line at Pleafure, as c d 3 
 and let the Point c be the given Point. 
 
 Then applying the Head of your Ruler to the Side 4, 2, Hide 
 its Edge until it lies over the given Point c ; and then drawing 
 the Line, it will be perpendicular to c d, as requir'd. 
 
 But here note , That if your Drawing-Table is not truly fqnare 
 at its Angles, the Sides as truly freight as can be, and the 
 Te-Square truly fix’d at right Angles, the Work will be 
 falfe.. But that you may not be deceiv’d, it will be bed to 
 examine them as following. 
 
 Fir ft, A perpendicular Line is that, which, when rais’d, cr 
 Handing up on another right Line, makes equal Angles on each 
 Side : As for Example, (Fig. III.) Where he is perpendicular to 
 
 a v \ 
 
38 A Sure Guide to Builders, 
 
 ay: For if on e, with any Opening of your Compaffes, you de- 
 fcribe a Semi-circle, as cig , you will find that the Arch cl is 
 equal to ig , and therefore is perpendicular to ay. 
 
 Now, when right Lines are thus perpendicular to each other, 
 they form fquare Angles, and are therefore call’d right Angles : 
 But when a right Line falls upon another right, a szi or wl, 
 inclining from the perpendicular lx , thereby making unequal 
 Angles on each Side, then fuch Lines conftitute other kind of 
 Angles, which are called acute or obtufe. 
 
 An acute Angle is that Angle which is lefs than a Square or 
 right Angle, as mlo, ormiw , or wla, &c . 
 
 And here note, That an Angle is always denoted by three 
 Letters, of which the middlemoft always denotes the angular 
 Point. -» 
 
 So here, when I fay the Angle nix or xi.m, the Letter i de- 
 notes the angular Point. And the like of all other Angles. 
 
 An obtule Angle, is that which is more than a right Angled 
 as the Angle nlm or niw. (Fig. III.) - — 
 
 Both acute and obtufe Angles, are call’d oblique Angles ; 
 •therefore all Angles that are not right Angles, are oblique Angles : 
 Such as thofe of Triangles, Pentagons, Hexagons, &c. 
 
 Now feeing that a perpendicular Line doth conftitute equal 
 Angles on each Side, you may eafily difcover the Truth of your 
 Drawing-Table and Te-Square, by applying their Edges to a 
 perpendicular Line rais’d Geometrically, by either of the follow- 
 ing Methods. 
 
 Method 1. 
 
 1. Draw a right Line e x , (Fig. I.) at Pleafure, and on the End 
 e y with any Opening of your Compaffes, defcribe the ArchyV. 
 
 1. Mak efi equal to ef\ and on /, as a Center, defcribe the 
 Arch fghm. 
 
 3. Set off the Diftance ef three times, from f to g , from g 
 to h , and from h to m. 
 
 4. Draw em, and ’tis the Perpendicular requir’d. 
 
 Method 
 
A Sure Guide to Builders . 
 
 Method 3. 
 
 Let mn ( Fig. I.) be given, to raife the Perpendicular nt from 
 the Point n. 
 
 1. With any Opening of your CompafTes on n , defcribe an 
 Arch as nipo ; make ip and po each equal to in', then on o, 
 with the fame Opening, defcribe the Arch pc, and on p the Arch 
 0 y, interfering the Arch pc in t. 
 
 2. Draw the Line tn , and ’tis the Perpendicular requir'd,. 
 
 Method 4. 
 
 Let y b be a given Line, and v the given Point. (Fig. I.) 
 
 Open your CompafTes to any Diftance ; fet one Foot in 
 v, and pitch down the other at random, as at 7 ; then turning 
 the other Point about, interfed the given Line in x, and 
 then on 7 defcribe the Arch wz : This being done, lay a Ruler 
 from x to 7, and it will cut the Arch yy in z ; then from v thro’ 
 z draw v e, the Perpendicular requir’d. 
 
 Method 5. (Fig. II.) 
 
 Let ic be the given Line , and c the given Point. 
 
 1. From a Scale of equal Parts, (as Parts of Inches, Inches s 
 Feet, &c.) fet off 8 from c to b. 
 
 1. Take ten of thofe Parts in your CompafTes, and on b , over 
 the Point c, defcribe the Arch dd. 
 
 3. On the Point c, with fix of the fame equal Parts, defcribe 
 the Arch ee , cutting dd in f. 
 
 4. Draw the right Line/* c, and ’tis the Perpendicular requir’d. 
 
 Method 6 . (Fig. lit) 
 
 By the P ROfRJCfO R. 
 
 Let gh be your given Lane, and h the given Point . 
 
 Apply the Center of the Protrador to the given Point h, and 
 its Diameter clofe to the given Line^^, as in the Figure ", then 
 with your protrading Pin, make a Mark or Point againft 90 De- 
 grees , 
 
40 
 
 A Sure Guide to Builders, 
 
 grees at i then from h y through i, draw the Perpendicular re- 
 quir’d. 
 
 Now obferve, That fince the Protractor, which is a Semi- 
 circle, does contain twice po, or 1 80 Degrees, ’tis evident that 
 one half thereof is po Degrees : Therefore when d right Line 
 hands upon a right Line, and makes equal Angles on each Side 
 thereof, Tis 'plain that each of thofe Angles niuft contain po De- 
 grees, and both taken together 1 80. 
 
 Thefe Degrees on the Limb of the Protra&or, are transferr’d 
 into a right Line, (as I fhall fhew you hereafter) and are call’d 
 Chords, or the Line of Chords ; by which Perpendiculars may 
 be rais’d by the following 
 
 Method 7. 
 
 Xet 1 n be the given Lhie y and n the given Point . (Fig. II.) 
 
 With do Degrees of your Scale of Chords (taken from a plain 
 Scale, &c.) on//, deferibe the Arch mop y then taking po De^- 
 grees (the whole Length of the Scale) in your Compaffes, fet it 
 from m to 0 ; and drawing qn through 0, it will be the Perpen- 
 dicular requir’d. 
 
 Now from thefe various Methods, you may be always able to 
 xaife perpendicular Lines at your Pleafure : But the moft ready 
 Method in fetting out the fquare Angles of the Foundation of 
 Buildings, is Method 5 ; for being prepar’d with three Rods, the 
 one fix, the other eight, and the longeft ten Feet in Length, and 
 being apply’d together in a right-angled Triangle, as ABC, 
 ( Fig. III.) the two Ihorteft Rods AB and CB, will make the 
 . fquare Angle requir’d. Vide 47th Prop, of the frit Book of 
 Euclid. 
 
 By this Method you may alfo know, when the inward Angles 
 of Rooms are fquare by the Help of a ten Foot Rod only : For 
 if from the Angle you meafure off fix Feet one way, and eight 
 Feet the other, th^ ten Foot Rod will exa&ly reach between 
 both Meafures : But if the Angle is lefs than a Square, then the 
 Diftance between the fix and the eight Feet, will be lefs than 
 ien Feet \ and if greater, it will be more than ten Feet. 
 
 The other Methods are ipore ufeful on Paper, when you are 
 drawing, and in Works where Compaffes can be ufed, as Carpen- 
 ters, Joiners, Mafons, &c. than in fetting out Buildings, .when, 
 
 inftead 
 
A Sure Guide to Builders. 
 
 inftead of Compafles, we make Ufe of Lines, which, by un- 
 equal Stretchings, become very erroneous, and caufe great 
 Miftakes. 
 
 Thefe are the various Methods of railing Perpendiculars ; I 
 will, in the next Place, inform you of the Nature of letting fall 
 perpendicular Lines, from given Points upon given right Lines. 
 
 PROBLEM II. 
 
 0 let fall perpendicular Lines, from 
 right Lines. 
 
 given Points 
 
 upon given 
 
 To let fall perpendicular Lines from given Points, there are 
 two Cafes ; the one js, when the given Point is, or nearly, over 
 the Middle of a Line y and the other, when the given Point 
 is, or nearly, over the End of a Line. 
 
 Case i. (Fig. IY.) 
 
 Let it he requir d to let fall the Perpendicular h i, from the 
 Point h on the right Line ad. 
 
 i. With any Opening of your CompafTes on h , defcribe an 
 Arch cb } then on c y with the Diftance cb y defcribe g; and 
 on h , the Arch, f interfering g in e \ lay a Ruler from e to 
 h y and draw ih y the Perpendicular requir’d. 
 
 Case a. (Fig. IV.) 
 
 Let it he requir d to let fall the Perpendicular mp, from the 
 Point m on the right Line qr. • 
 
 i. From m draw a right Line, as onrriy at random, which di- 
 vide into two equal Parts in n. 
 
 . 2 * Gn with the Diftance nm y defcribe the Arch mpo. cut- 
 ting the Line qr\n p. 
 
 3 . Draw mp, and ’tis the Perpendicular requir’d. 
 
 L All thefe J ever al Methods I under (land : Put how mull I 
 raife a Perpendicular from a Point given , which is in or near the 
 Middle of a Line ? 
 
 M. Very eafily. Suppofe the given Point, (Fig. IV.) fet 
 off on each Side thereof any Diftance, as ic and ib. both equal: 
 
 G ' then 
 
4 2 
 
 A Sure Guide to Builders. 
 
 then with any Diftance on b defcribe an Arch, as //, over the 
 Point #, and with the fame Diftance on c the Arch kk, interfer- 
 ing 1 1 in h j then draw hi, and ’tis the Perpendicular requir’d. 
 
 N. B. That when a Point is given on your Drawing- Table, to 
 let fall a perpendicular Line from it , to any Line that is 
 parallel to the Table s Side , you have nothing more to do , than 
 to Jlide up the -Edge of your Ruler to the given Point, and 
 draw the Line requir'd. Suppofe the Point 6 (Fig. I.) to be 
 given , then Jliding up the Edge of your Te-Square , draw the 
 Line 6 8 perpendicular to d c, as requir'd. 
 
 PROBLEM III. 
 
 O divide a right Line and an Angle into two equal Parts by & ■ 
 Perpendicular. 
 
 Firft, to divide a right Line (ab) into two equal Parts , by a 
 Perpendicular. (Fig. V.) 
 
 Open your Compafles to any Diftance greater than half,' ab , 
 and on b defcribe an Arch, as dd ; then with the fame Opening 
 on a, defcribe the Arch cc , interfering dd in ei ; draw the right 
 Line ie , and it will divide ab in h, viz. into two equal Parts, 
 as requir’d. . 
 
 Secondly, To divide any given Angle, as lfk, into two equal 
 Parts , by the Perpendicular, f o. . 
 
 1. On f with any Opening, defcribe an Arch 1 , zs aa. 
 
 2 . With any Opening on a a defcribe the Arches nn and mm, 
 interfering each other in o. 
 
 3. Draw fo, and it- wilLdivide the Angle lfk into two equal 
 Parts, as requir’d. 
 
 Note, This. Problem is very ferviceable to the Carpenter' and 
 Joiner., in fading out the Mitre of an Angle given, be it 
 acute, right , or obtufe ; for half the Quantity of any Angle 
 is. its. true Mitre thereof ... 
 
 PRO B L.E Mr 
 
43 
 
 A Sure Guide to Builders. 
 
 PROBLEM IV. 
 
 J^O draw parallel Lines • both Right-lhid and Circular. 
 
 I. Right-lin’d Parallels are drawn, either at the Diftance of a 
 given Line, or Point. 
 
 Firft, At the Difance of a given Line. (Fig. VI.) 
 
 Let it be requir'd to draw ab parallel to fh, at the Dijlance- 
 of ik. 
 
 i . Take in your Compaffes the given Diftance i k, and Petting 
 one Foot of your Compaffes on any Part of the given Line, as 
 at e, with the other defcribe the occult Arch cc , then towards 
 h, as at g , with the fame Opening, defcribe the Arch d d. 
 
 i. Lay a Ruler to the Convexity of both Arches, and draw 
 the Parallel ab requir’d. 
 
 Secondly, At the Dijlance of a given Point. (Fig. VI.) 
 
 Let it be required to draw lz through the Point m, and parallel 
 
 to q r. 
 
 1. Set one Foot of your Compaffes in m, the given Point, and 
 with the other take the neareft Diftance to the Line qr. 
 
 2. With that Diftance towards r , on the Line q r, place one 
 Foot of your Compaffes, (as at p) and with the other defcribe 
 an Arch, as oo. 
 
 3. Lay a Ruler from the given Point m to the Convexity of the 
 Arch oo, and draw the right Line lz, which will pafs through 
 the Point m, and be parallel to qr, as requir’d. 
 
 II. Circular Parallels, or Concentrick Circles, (as the Circles 
 ABC, Fig. VIII.) are defcrib’d by the Revolution of one Point 
 of your Compaffes being open’d to any Diftance requir’d, whilft 
 the other refts upon the Center D. 
 
 You may from hence difcover the Nature of parallel Lines, 
 which tho’ they be continu’d ad Infinitum, yet will never meet ; 
 becaufe that all Perpendiculars that are drawn between them, as 
 the Lines 12, 34, j < 5 , 7 8, p o, and zz , are equal, and 
 
 G a confequentiy 
 
 1 
 
A Sure Guide to Builders. 
 
 confequently the Line ab (Fig. VIII.) is parallel to cd\ for if it 
 had any Inclination, the Perpendiculars would be unequal in 
 their Heights. 
 
 PROBLEM V.. 
 
 /V F Angles , and the Manner of meafuring their Arches , by the 
 Protractor , Line of Chords , &Cc. 
 
 An Angle (as has . been before hinted) is conftituted by the 
 Meeting of two Lines, and the Point of Meeting is call'd the 
 angular Point. Thus the right Line CB (Figi. IX.) haying an 
 Inclination towards the Line D E, do, by being continu’d from 
 C to A and from D to A, conftitute the Angle B AE : But had 
 B C been parallel to D E, they would have never met, tho’ con- 
 tinu’d ad Infinitum. 
 
 All kinds of Angles are me^fur’d by the Arch of a Circle, 
 and the feveral Degrees and Minutes contain’d in them, is call’d 
 their Quantity. 
 
 As for Inftance ; Apply the Center of your Protra&or to the 
 Angles, (Fig. X.) and its Diameter to the Line agy then will 
 the other Line ae cut the Degrees and Minutes which are con- 
 tain’d in the Angle. 
 
 And here note, I 3 hat in dll ProtraBors, which are in themfelves 
 Semi-circles , be them great or finally there's the very fame 
 Number of Degrees in the one as in the other : For were the 
 Degrees of the Protractor BEG (Fig. XI.) to be continued 
 out , and a larger Protractor, with its Center in the fame 
 < Place of C f laid down over them , they would divide the Cir- 
 cumference thereof in the very fame Proportion as BEG; 
 but the larger that ProtraBors are , the larger their Degrees 
 will be ; and therefore may be the more nicely divided into 
 Minutes , and Angles more truly known. 
 
 Now feeing that Protra&ors are divided into 1 80 Degrees, it 
 therefore follows, that a Circle mult contain 3 do Degrees. 
 
 Every Degree is fuppos’d to be divided into do equal Parts, 
 which are call’d Minutes ; and therefore, when the Degrees on 
 the Limbs of Protractors are fubdivided into two equal Parts, 
 then, each reprefents 30. Minutes ; if into four, 15 Minutes, &c. 
 
 The 
 
A Sure Guide to Builders. 
 
 The Quantity of an Angle may be meafured by the Scale of 
 Chords without the Protractor : But before I fhew that Ope- 
 ration, it will not be amifs to fhew the ConftruCtion thereof, 
 which is as follows : 
 
 fo make a Line of Chords to the Radius of any Circle requir'd. 
 
 Note y That the Radius of a Circle is the Semi-diameter thereof 
 
 Let it he requir'd to make a Line of Chords to the Radius C D. 
 
 (Fig. XII.) 
 
 1. Make AD equal to twice CD, and on C ereCt the Perpen- 
 dicular CB. 
 
 2. On C, with the Radius CD, defcribe the Semi-circle 
 ABD, then will the Perpendicular BC divide the Semi-circle 
 ABD into two equal Parts, each of which are called a Quadrant, 
 or fourth Part of a Circle. 
 
 3. If you fet the Radius CD from D to 60, (on the Arch 
 DB) and from B to 30, you will have divided the Arch BD of 
 5>o Degrees into three equal Parts, each containing 30 Degrees. 
 
 Now here obferve, fhat the Semi -diameter is equal to 60 De- 
 grees exatdly ; and 'tis therefore that you muf when you ufe 
 your Line of Chords , firf defcribe an Arch of 60 Degrees , 
 and afterwards meafure or fet off the Quantity of the Angle 
 requir'd. 
 
 4. Divide by Elfays made with your Compares, D, 30 ; 30, 
 60 ; and 60 , po ; each into three equal Parts, then will every 
 one reprefent 10 Degrees. And laftly, If in like Manner you 
 divide every Divifion into 10 equal Parts, you will have divided 
 the Arch D B into po Degrees. 
 
 5. Set one Foot of your Compares in D, and extend the other 
 to 10 Degrees, and fet off that Diftance from D to 10 on the 
 Diameter DA ; then take the Diftance D 20 on the Arch, and 
 fet it from D to 20 on the Diameter : And fb in like Manner all 
 the other Degrees contain'd in the Arch DB, whereby the Line 
 of Chords will be compleated, as requir’d. 
 
 Th* 
 
 45 
 
A Sure Guide to Builders. 
 
 The Conftru&ion of the Scale of Chords being thus under- 
 ftood, we’ll now proceed to their Ufe in meafuring the Quan- 
 tity of Angles. 
 
 Let it be requir’d to 
 (Fig. X.) 
 
 Open your Compalfes to do Degrees of your Scale of Chords, 
 (where is generally plac'd a Brals Point) and on the angular 
 Point a defcribe the Arch b c , then taking the Extent of the 
 Arch be in your Compalfes, apply one Foot to the Beginning of 
 your Line of Chords, and the other will reach to the Number of 
 Degrees and Minutes contain’d in the Angle, which are equal to 
 thole before found by the Protractor. And the like of any other 
 Angle whatfoever. 
 
 Having thus taught the Nature of Lines and Angles, I will 
 in the next Place inform you how to apply them to Practice, in 
 the GonftruCtion of fuch Geometrical Figures, that are ufefui in 
 the Art of Building. 
 
 The feveral Geometrical Figures necelfary for this Purpofo, 
 are the Ellipfs , Triangle , Square , Oblong , or Parallelogram , Pen- 
 tagon, Hexagon , Septagon , OAagon, Nonagon, Decagon , SCc. 
 
 PROBLEM VI. 
 
 /V F ELLI*PSfS’s , and the various Ways of deferibing 
 them. 
 
 N. B. When Builders make mention of an Ellipfs, they generally 
 mean an Oval , compounded of divers Arches of Circles , of 
 which an attual Ellipfs has no Part. 
 
 An aCtual Elliplis is generated by an oblique SeCtion of a Cone, 
 and is thus deferibed to any Length and Breadth given. 
 
 Let the right Lines a and b (Fig. XIII.) be two given right 
 Lines to defcribe an Elliplis, whofe tranfverfe and conjugate 
 Diameters fhall be equal thereto. 
 
 Note, That the forte ft Diameter of an Ellipfs , is call’d the 
 Conjugate Diameter \ and the longed the Axis, or Tranfverfe 
 Diameter . 
 
 meafure the Quantity of the Angle ead. 
 
 i. Draw 
 
A Sure Guide' to Builders. 
 
 i. Draw cf equal to b y which divide into two equal Parts by 
 the Perpendicular da. 
 
 i. Make de and ea each equal to half the given Line a, then 
 will da be equal to a. 
 
 3. With the Diftance of half the longeft Diameter, as ef or 
 ec on a, defcribe the Arches mm and //, and on d the Arches kk 
 and nn , which will interfe<ft the Diameter cf in the Points h and 
 i , which are the Centers or Focus Points of the Ellipfis. 
 
 4. In the Points h and i fix two Pins, Nails, &c. then with a 
 Thread, Chalk Line, &c. fallen the Ends thereof to the two 
 Nails, in fuch a Manner, that the double Part thereof, when 
 extended moderately tight, may reach to the End of the longeft 
 Diameter c ox f : This done, apply a black Lead Pencil, &c. to 
 the Line, and moving the lame about from c to d , thence to f, 
 a and c , you will defcribe the Ellipfis requir’d. 
 
 ‘The other Elliptical or Ovallar Figures, compounded of divers 
 Arches of Circles , are defcrib’d by divers Methods , as frfl to any 
 given Length , without regard to Breadth . (Fig. XIV.) 
 
 Let v x be the given Length. 
 
 1. Make yz equal to v x, and' divide it into three equal Parts 
 at a and b. 
 
 1. On by with the Radius bz , defcribe the Circle zicano \ 
 and on <2, the Circle yecbnm. 
 
 3. Lay a Ruler from n to b r and draw bp at Pleafure ; alio 
 from c to by and draw bk at Pleafure. Again, from n to a draw 
 ady and from c to a draw ah. 
 
 4. On iiy with the Radius niy defcribe the Arch ie-y and on c 
 the Arch 0 m j which compleats the Oval requir’d. 
 
 Now feeing that oftentimes the Conjugate Diameter is limitted 
 as well as the Tranfverfe r I will therefore fhew you 
 
 How to defcribe an Oval to any Length or Breadth requir’d. 
 
 Let it be requir’d to defcribe the Oval endo, (Fig.YLV. PlateY.) 
 whofe longeft Diameter e d fhall be equal to the given Line y, and 
 fborteji to the given Line 2. 
 
 1. Make ed equal to yy and no to z y cutting ed at- right 
 Angles in A 
 
 x. Make- 
 
 47 
 
4.8 A Sure Guide to Builders. 
 
 2. Make dc equal to bo or hn\ divide be into three equal' 
 Parts, and make cp equal to one of thofe Parts. 
 
 3. Make b a equal to bp , and then Petting your Compafles in 
 p, extend the other Foot to a, and wich that Opening deferibe 
 the Arches mm and vv\ and on a, with the fame Radius, the 
 
 ' Arches kk and ww, interfering the former E and X in l and *. 
 
 4. Lay a Ruler from x top, and draw the Line ps at Plea- 
 fure ; as alfo from X to a, and draw at at Pleafure. Again, Lay 
 your Ruler from E top, and draw pt at Pleafure j and from E to 
 a draw ag at Pleafure. 
 
 .5. On p, with the Radius pd, deferibe the Arch q dr ; .and on 
 a the Arch feh. Laftly, On X, with the Opening X^, deferibe 
 the Arch h nr ; and on E the Arch foq } which will compleat the 
 Oval requir’d. 
 
 Note, 7 * his Method of deferibing an Oval , is of all others the 
 bejl for Bufinefs , not only in refpett to its being the mofl 
 ready , but the mof exaid Method ; and whereas the Car- 
 penter, Bricklayer , Mof on, S-Cc. is oftentimes oblig’d to work 
 an Architrave, &c. about Windows, Stc. of this kind, he 
 may, by the Help of the four Centers p, a, E, X, and the Lines 
 of Direction ps, pt, ag, and ai, deferibe any Moulding very 
 exailly about them, that will be parallel, or truly concentrick 
 thereto, at any Difance requir’d. 
 
 As for Example : 
 
 Let it be requir’d to deferibe the Oval D ECF, concentrick to 
 e n d o, at the Di fiance of A B. 
 
 1. Make eD equal to AB; then on a and p, the former Cen- 
 ters, with the Radius a D, deferibe the Arches D and C ; and on 
 E and X, with the Radius X 1 or X 2, deferibe the Arches 1 E 2 
 and 3F4; which will compleat the concentrick Oval requir’d. 
 And in like Manner you may deferibe as many others as you 
 pleafe. 
 
 Oval-like Figures of all kinds may be deferib’d by the Inter- 
 fedion of right Lines, according to the long pradis’d Method of 
 Ship-Builders, who lay down all their various curved Lines by 
 the following Method, without having refped to any Center. 
 
 Let 
 
■oz -oV-oP-off D ■ o^OKot? 
 '■ <>\9 ; 
 
 o 
 
 gb toff jr far rnp M/d ' * HU " 
 


A Sure Guide to Builders. 
 
 Let the Length of the longef Diameter he HI, and the 
 forte /l KL. (Fig. XVI. Plate V.) 
 
 i. Make CE equal to Hi, and on E ered the Perpendicular 
 EB, which make equal to KL. 
 
 i. Draw AC parallel to BE and equal to KL, and join AB 
 which will compleat the Parallelogram ABCE. 
 
 3. Divide each Side of the Parallelogram into two equal Parts 
 in DdG and F, and then every of thofe Semi-fides, as A d, d B, 
 BG, GE, EF, FC, CD and DA, into any Number of equal 
 Parts, the more the better. But in this Example, each Semi- 
 fide is divided but into eight, that you may the better conceive 
 the Reafons thereof, without being confus’d by a Multitude of 
 Lines. 
 
 4. From the Divifions in each Semi-llde, draw right Lines to 
 the refpedive Divifions in the next adjacent Semi-fide, as from d to 
 4, from 7 to 5, from 6 to 7, and from 5 to 1, &c . ; fo will their 
 exterior Interfedions form a curv’d like Line, that will form one 
 quarter Part of the Oval : Then performing the like Operations 
 at the three other Angles, you will compleat the Oval requir’d. 
 But ’tis to be remember’d, that altho’ thefe Interfedions do ge- 
 nerate an Appearance very like unto an Oval, yet in Fad it is 
 not, it being no more than an ovallar Polygon, confining of a 
 great Number of Sides, which being in themfelves very fhort, 
 and their Angles very obtufe, do therefore nearly refemble the 
 fame Curve, as an Oval of the fame Diameters would do. 
 
 By this Method Mr. Halfpenny and Mr. Hoar pretend to de- 
 fcribe all Sorts of Arches and Curves ufed in Houfe-building, 
 Ship-building, Gardening, &c> in their Art of Sound Building , 
 and Builders Pocket Companion j when all the while they are 
 doing no more than defcribing of Polygons, or Segments of Po- 
 lygons, inftead of Ellipfis’s, Circles, and Segments of Circles, 
 &c. as they imagin’d : But had they known how to dcmonftrate 
 the Properties of thofe Lines, which they pretend to have firft 
 invented, (tho’ well known to Ship Builders and others for more 
 than a hundred Years paft) they muft have certainly difcover’d 
 and known, that the Interfedion of right Lines can no more form 
 Curves of any kind, than a Point, when its Motion is made in a 
 right Line, can form an Arch. 
 
 As I have thus laid down the various Methods of defcrib- 
 ing Ellipfis’s and Circles, I fhall now proceed to fhcw the 
 
 H Geometrical 
 
A Sure Guide to Builders. 
 
 Geometrical Confbrudion of Triangles, and other regular iright- 
 lin’d Figures. 
 
 PROBLEM VII. 
 
 T° delineate an Equilateral Triangle. 
 
 An Equilateral Triangle is that, whofe Sides are all equal to 
 each other, as a be. (Fig. XVII.) 
 
 Let it be requir’d to deferibe the Equilateral Triangle a b e, with 
 each Side equal to the given Line f. 
 
 i. Make be equal to f and on b and c, with the Radius be , 
 deferibe the Arches ee and dd y interfering each other in a\ join 
 ac and ab y and they compleat the Triangle requir'd. 
 
 PROBLEM VIII. 
 
 r O delineate an Ifofceles Triangle , whofe Sides J, ball be refpeflively 
 equal to two given right Lines. 
 
 An Ifofceles Triangle hath two Sides equal, and the third un- 
 equal, as abc. (Fig. XVIII.) 
 
 Let d e be the given Lines. 
 
 i. Make ac equal to d\ then on a and with the Radius 
 deferibe the Arches ff and hh y interfering each other in b. 
 
 2. Join ba and be , and they compleat the Ifofceles Triangle 
 requir'd. 
 
 PROBLEM IX. 
 
 fTO delineate any Scalenum Triangle , whofe three Sides fhall be 
 equal to three given right Lines of unequal Lengths. 
 
 Let the given Lines be fgh. (Fig. XIX.) 
 i. Make ab equal to^ then on b , with the Radius g y de- 
 feribe the Arch dd ; and on a , with the Radius h , the Arch ee y 
 interfering the other in c. 
 
 2. Join cb and c and they compleat the Triangle requir'd, 
 Thefe are the various Conftrurions of right-lin'd Triangles ; 
 now I proceed to four-fid ed Figures. 
 
 PROBLEM 
 
A Sure Guide to Builders. 
 
 5 l 
 
 PROBLEM X. 
 
 noff" to delineate a Geometrical Square. 
 
 Let it be requir'd to delineate the Geometrical Square abed, 
 (Fig. XX.) with its Sides each equal to the given Line zz. 
 
 1. Make c d equal to z z, and on d ered the Perpendicular d b. 
 
 2. With the Radius zz on c deferibe the Arch ff and on b 
 the Arch ee , interfeding the other in a. 
 
 3. Join a b and a c, and they will compleat the Geometrical 
 Square requir'd. 
 
 Note, ’That the Diagonal of a Geometrical Square , is that Line 
 which is drawn from one Angle to another , as the Diagonal 
 Lines h n and k g ; and the Diameter or Diameters are i r and 
 1 o, which fafs thro ' the Center of the Square where the Di- 
 agonals interfeB , and cut both themfelves and the Sides of the 
 Square at right Angles. 
 
 PROBLEM XI. 
 
 O delineate an Oblong or Parallelogram to any Length and Breadth 
 requir'd. 
 
 Let it be requir'd to draw the Oblong , Parallelogram , or Long 
 Square (which is all one and the fame Figure ) acbd, (Fig. XXL) 
 with its Length equal to the given Line z, and Breadth to the 
 Line y. 
 
 1. Make b d equal to z y and on d ered the Perpendicular dc ? 
 making dc equal to y. 
 
 2. On c , with the Diftance b d , deferibe the Arch i i \ and on 
 b , with the Opening dc , the Arch nn , interfeding the other in a. 
 
 3. Join ac and ab , and they will compleat the Oblong re- 
 quir’d. 
 
 Note, That the Diagonals k h and ei of the Parallelogram e hik, 
 are the fame as of the Geometrical Square j as alfo are the 
 Diameters 1 g and f o. 
 
 H a 
 
 PROBLEM 
 
6 2 
 
 A Sure Guide to Builders . 
 
 PROBLEM XII. 
 
 Hf O delineate a Rhombus , whofe Sides jhall be each equal to a given 
 •L Line , as ab. (Fig. XXII.) 
 
 i. Make dc equal to ab', then on c, with the Radius dc, de- 
 fcribe the Arch def and make de and ef equal to dc. 
 
 i. Join de, ef, and jc, and the Rhombus is compleated as 
 requir'd. 
 
 Note, 'That as the Angles of this Figure are all oblique, viz. 
 the Angles Ih acute , and ki obtufe , therefore their Di- 
 agonals Ih and ki are unequal, viz. lh is longer than ki, 
 notwithstanding that the Sides are all equal, as in the Geome- 
 trical Square abed (Fig. XX.) therefore, if a Geometri- 
 cal Square hath any two of its oppofte Sides put out of a per- 
 pendicularPoftion, fo as to alter their right Angles, it inf ant ly 
 becomes a Rhombus, or Diamond Form. 
 
 PROBLEM XIII. 
 
 HTO delineate a Rhomboides , or long Diamond Form, whofe op - 
 ** pofte Sides jhall be equal to two given Lines, and each oppofte 
 acute Angle equal to an Angle given. 
 
 Let the right Lines hi, (Fig. XXIII.) and the Angle mys be 
 given. 
 
 1. Make equal to h ; then open your Compafles to any 
 moderate Diftance, and on the angular Point v of the given 
 Angle mvs, deferibe the Arch fd ; then take the Diftance os 
 between your Compafles, and fet it from to e, and fromg thro' 
 e draw a right Line, which make equal to i. 
 
 2. With the Diftance of i on b deferibe the Arch zz, and on 
 c, with the Diftance g b, the Arch tin. 
 
 3. Join c a and ab, and the Rhomboides will be compleated 
 as requir'd. 
 
 PROBLEM 
 
A Sure Guide to Builders, 
 
 S3 
 
 PROBLEM XIV. 
 
 r T'0 defer the any regular Polygon , having a Side given. 
 
 1 
 
 Firft, Draw a right line, as YX, (Fig. XXIV.) reprefenting 
 the Diameter, and in any Part thereof, as at M, ered the Per- 
 pendicular M S. 
 
 2. Let AB be the given Side, which divide into two 
 equal Parts in P: Make MO, MN, each equal to half the 
 given Line AB, and from the Points N and O draw the right 
 Lines N h and OQ^ parallel to the Perpendicular MS. This 
 being done, you may deferibe any Polygon, from five to five 
 hundred, or a thoufand Sides, in the following Manner. 
 
 1. Divide 360, the Degrees contain'd in a Circle, by the Num- 
 ber of Sides contain'd in the given Polygon, and the Quotient will 
 be the Quantity of the vertical Angle, that every Ifofceles Tri- 
 angle of the Polygon makes at the Center of the Polygon. For 
 if the Semi-diameters of a Polygon are confider’d with the Sides 
 of the Polygon, they conftitute as many Ifofceles Triangles, as 
 there are Sides contain’d in the Polygon. 
 
 2. On M deferibe the Semi-circle hnl of any Radius, and 
 thereon fet off half the Quantity of the vertical Angle before 
 found, from n to fc, and from 11 to /, and thro' the Points k and l 
 draw right Lines, until they cut the parallel Lines and OQ_ 
 in h and Q^ 
 
 3. On M, with the Radius MQ or Mh y deferibe the Circle 
 y^QjTV, &c. and then taking the Extent of the J_dne^Q_in 
 your Compaffes, and turning it about upon the Circumference, 
 you will fet off the feveral angular Points of the Polygon, to 
 which right Lines being drawn, will compleat the Polygon as 
 requir'd. 
 
 Example. 
 
 Let the Line A B he the given Side of an 0 Si agon. 
 
 1. As an Odagon confifts of S Sides, divide 360 by 8, and : 
 the Quotient is 45, which is the Quantity of the Angle that muff 
 be fet off at the Center. 
 
 2. As before direded make the Angle kMl equal to* 
 22 Degrees 30 Minutes, and then drawing the Lines OQ 
 
 and? 
 
A Sure Guide to Builders. 
 
 and N h parallel to M S, at the Diftance of half the given 
 Line AB, they will interfed the Lines MR and Mf'mh 
 and Q. 
 
 3. On M, with the Radius MQ_, defcribe the Circle 
 T V W, &c. and taking ^QQn your Compaffes, let that Extent 
 from Q_ to T, from T to V, from V to W, &c. and they will be 
 the angular Points of the Octagon. Laftly, Draw the feveral 
 "Lines h Q_ , Q_T, T V, V W, & c. and they will compleat the 
 Odagon requir’d. 
 
 Now feeing that the Polygons moft in ufe are the Pentagon, 
 Hexagon, Septagon, Odagon, Nonagon, and Decagon, I will 
 therefore give you the Quantity of their Angles feverally, that 
 the Trouble of Divifion may be fav’d, when ’tis requir’d to de- 
 lineate either or all of them, according to the Rule before 
 delivered. 
 
 "Pentagon,' 
 
 Hexagon, 
 
 is a plain Ge- 
 
 ''five > 
 fix 
 
 Sides andAngles, 
 
 / 
 
 0 
 
 V 
 
 Septagon, 
 
 ometrical Fi- 
 gure, confifM 
 
 feven 
 
 whofe Quantity 
 at the Center are 
 
 JIfl 
 
 ] Odagon, 
 
 eight 
 
 4J ( 
 
 Nonagon, 
 
 ing of 
 
 nine 
 
 feverally 
 
 40 
 
 ^Decagon, > 
 
 
 ten 
 
 
 3 6 J 
 
 PROBLEM XV. 
 
 nrO defcribe any regular Polygon , having the Diameter thereof 
 given . 
 
 Let the given Diameter be KL. ( Fig'. -XXV.) 
 
 Rule. 
 
 1. Defcribe a Circle, whofe Diameter is equal to the Diameter 
 given, as ABC, and through its Center draw the Diameter 
 ABC; then making the whole Diameter Radius, fet one Foot 
 on C, and with the other defcribe the Arch A f and on A the 
 Arch C e interfering the other in D. 
 
 1, Divide the Diameter of the Circle into as many equal Parts 
 as the Polygon is to confift of Sides, and then laying a Ruler 
 from D to the fecond of thofe Divifions on the Diameter, it 
 
 will 
 
A Sure Guide to Builders. 
 
 will cut the Circumference in the Point H, from which a right 
 Line being drawn to the Extream of the Diameter A, it will be 
 one Side of the Polygon requir’d. 
 
 Example. 
 
 Let it be requir'd to defcribe the Off agon AHINCZML. 
 (Fig. XXV.) 
 
 i. Defcribe a Circle equal in Diameter to the given Diameter 
 K L, and divide its Diameter into eight equal Parts, as at i , a, 
 3> 7 , C. 
 
 i. On C and A, with the Radius AC, defcribe the Arches eC 
 and Af, interfering in D. 
 
 3. Lay a Ruler from D to 2, the fecond Divifion on the Di- 
 ameter, and it will cut the Circumference in H. 
 
 4. Draw A H, and it will be the Side of the Odagon, which 
 being fet from H to I, from I to N, from N to C, from C 
 to Z, from Z to M, from M to L, and from L to A, and right 
 Lines being drawn, they will compleat the Octagon requir’d. 
 
 Having thus Ihewn the Nature and Dodrine of Lines and 
 Angles, and their Ufe in the Conffcrudion of fuch Geometrical 
 Figures that are ufeful to the young Student in Architedure, I 
 will, in the next Chapter, exhibit their Ufe in the Menfuratiori 
 and drawing of the Plans and Uprights of Buildings. 
 
 CHAP. 
 
0 
 
 A Sure Guide to Builders. 
 
 CHAP. IV. 
 
 Of the Manner of Meafuring and ‘Delineating Blans 
 and Uprights of Buildings . 
 
 PROBLEM I. 
 
 I ^ ' " ■ ; ' : i . ; • A;L i; 
 
 0 make Decimal and Duodecimal Scales for delineating 
 oj Plans and Uprights of Buildings. 
 
 The Inftrument requifite for thefe Purpoles is a 
 plain Scale, (commonly call'd the Surveying Scale) 
 whereon are graduated feveral Scales of equal Parts, which are 
 feverally divided, as well Duodecimally into Twelves, as Deci- 
 mally into Tenths. 
 
 The Reafon why thefe Scales are divided into Tenths and 
 Twelfths are twofold. Firft, The Decimal Divifions are fuffi- 
 cient, and moft ready for taking off and numbering, when in 
 Measuring or Drawing we have refpeft to whole Feet, &c. only, 
 without regard to Inches, or any other Parts of a Foot, &c. but 
 when our Dimenfions are taken in Feet and Inches, then we are 
 oblig’d to the Duodecimal Divifion of Twelves, becaufe we can 
 then take off the odd Inches, when any happen, with great Ex- 
 aclnefs, which were we to endeavour to do in a Decimal Divifion, 
 we could not, being oblig’d to eftimate the odd Parts. 
 
 Let ABCDEFG {Pig. XXX. ) reprefent one of thele double- 
 divided Scales of four Inches in Length, divided into four prin- 
 cipal Divifions of an Inch each, at D E F and G at Bottom, and 
 imno at the Top. 
 
 The Decimal Divifion thereof is the Line BG, where the- firft 
 Inch B D is divided into ten equal Parts, and therefore is call’d 
 the Decimal Divifion. Now, as DE is equal to BD, it is there- 
 fore number’d with io ; lo alfo is F with 20, and G with 30 ; 
 and fo on to whatever Length you defire your Scale to be. 
 
 If 
 
 % 
 
A Sure Guide to Builders . 
 
 If you imagine every tenth Divifion of BD to reprefent one 
 Foot, then BD contains io Feet, and confequently BG repre- 
 ients 40 Feet. When you are to takeoff in your Compaffes any 
 Number of Feet under 10, you muft place one Foot of your 
 Compaffes in D, and extend the other to the Number of Feet 
 requir’d, as 1, 2, 3, &c. 
 
 But when you are to take off any Number of Feet more than 
 10, and lefs than 20, then you muftfirft place one Foot of your 
 Compaffes in E, and extend the other to the odd beet above 10, 
 as fuppofe 15 Feet, then extend them from E to C ; and the like 
 of any other Number of Feet requir’d. 
 
 Now it remains to fpeak a Word or two of the Scale of 
 Twelves, wherein obferve, that as BD in the Decimal Divifion 
 lepiefents 10 Feet , the fame Diftance duodecimally divided as 
 above, reprefents but one Foot, and every Sub-divifion an Inch • 
 therefore A h reprefents three Inches, A i fix Inches, Ak nine 
 Inches, and A / one Foot : The Divifions Irn , mn , and no , are 
 each equal to A/, viz. one Foot, being number’d 1, 2, 3’ &c. 
 and may be continu’d to any Length further, as requir’d. 5 
 
 When you are to take from your Scale any Number of Inches 
 only, you muft place one Foot of your Compaffes in /, and ex- 
 tend the other to the Inches requir’d, as fuppofe three Inches ; 
 then fet one Foot in /, extend the other to £; and the like of 
 any other Number of Inches requir’d. 
 
 But when you are to take off any Number of Feet and Inches, 
 as two Feet and nine Inches, then fet one Foot of your Com- 
 pafles in w, the Number of Feet, and extend the other to h, the 
 odd Inches, and that fhall be the Extent requir’d ; and the like 
 of any other Length requir’d. 
 
 I will illuftrate their Ufe in the following Problems : 
 
 PROBLEM II. 
 
 TO delineate a right-lin'd Fri angle by the Decimal Scale of Feet 
 1 BG.. (Fig. XXX.) 
 
 The three given Sides are in Length as following, viz. the one 
 20 Feet, the fecond 18 Feet, and the third 15 Feet. 
 
 C P raff ice. 1. Make AC (Fig. XXXIII. Plate VI.) equal to 
 20 Feet of BG, and with 18 Feet (taken in your CompaiTes) on 
 
 I ' " A. 
 
 57 
 
 
A Sure Guide to Builders. 
 
 A, defcribe the Arch ee\ alfo on C, with 15 Feet in jour Com- 
 pares, defcribe the Arch dd, interfering the former in B. 
 
 Join BA and BG, and they compleat the triangular Plan as 
 
 requir’d. 
 
 PROBLEM III. 
 
 T O delineate a right -lin’d triangle hy the Duodecimal Scale of 
 Feet and Inches. 
 
 The three Sides are in Length as following, viz. the Bafe 
 (which is always the longeft Side) two Feet nine Inches, the 
 other longeft Side two Feet fix Inches, and the fnorteft two Feet 
 
 three Inches. _ 
 
 Frattice. Make AC (Fig. XXXIV.) equal to two Feet nine 
 Inches, and on A, with the Extent of two Feet fix Inches, de- 
 fcribe the Arch gg ; alfo on C, with the Opening of two Feet 
 three Inches, defcribe the Arch ff interfering the former in B. 
 Laftly, Join BA and BG, and the triangular Plan is compleated 
 
 as requir’d. 
 
 PROBLEM IV. 
 
 J O meafure divers given Lengths hy the Decimal and Duodecimal 
 Scales. 
 
 There is a Geometrical Square ABCD, (Fig. XXXV.) and 
 an Oblong EFGH, already defcrib’d ; I demand the Length oi 
 the Side of the Square BD in Feet, by the Decimal Scale ot 
 Feet Meafure, and the Length and Breadth of the Oblong Eh G H 
 in Feet and Inches, by the Duodecimal Scale of Feet and Inch 
 
 Meafure. ~ 
 
 lattice. 1. Take the Side of the Square CD in your Com- 
 pares, and applying it to the Scale BD, you will find it to con- 
 tain nine Feet exariy, which is the Side of the Square according 
 
 to that Scale. , 
 
 a. Take E F in your Compares, and applying that Lengtp to 
 
 the Scale AP, it will be found to contain one Foot and eight 
 Inches. 
 
 3. Take 
 
59 
 
 A Sure Guide to Builders. 
 
 3. Take F H in your Compalfes, (as before) and applying 
 that Length to the Scale A /, it will be found to contain fix Inches ; 
 therefore the Length of the Oblong is one Foot eight Inches, 
 and Breadth fix Inches : Which is what was requir'd. 
 
 Now from thefe Examples you may fee, how very eafy ’tis to 
 delineate Geometrical Figures by any Scale of Feet, or Feet and 
 Inches, as it may be requir’d ; as alfo how to mealure the Sides 
 of any Figure by a given Scale. 
 
 Note, 7 * he ufual Scales of equal Tarts on the common furveying 
 plain Scales , fold by mo(l Mathematical Inf rument -makers, are 
 fix, viz. an Inch divided into 30, 35, 40, 45, 50 and < 5 o 
 Parts ; but they may be divided into 10, 15, 2.0, 25, &c. 
 alfo , as the young Student likes bef , or as the Nature of his 
 Drawings require : For where much Space is to be reprefente.d 
 in a fmall Compajs , he muf make nfe of a fmall Scale ; but 
 when a J'mall Space is to be reprefented in a large Drawing , 
 then he muf make ufe of a larger Scale , as will befl fuit his 
 Purpoje ; Jo as to Jill out his intended Magnitude of Paper. 
 
 N. B. 7 muf alfo inform you , that there is another kind of Scale 
 of Feet and Inches befdes the preceding , which is very com- 
 monly placed upon the better Sort of two Feet Rules , Juch as 
 Cogeeflhairj-, &c. in a Diagonal Manner , as reprefented in 
 Fig. XXXI. Plate V. 
 
 Thefe Diagonal Scales of Twelves reprefent the Foot or 12 
 Inches, firfl, in an Inch, as ABE ; lecondly, in three Quarters 
 of an Inch, as P X W thirdly, in half an Inch, as GIL ; and 
 laflly, in a Quarter of an Inch, as B S Z. 
 
 The Divifion of an Inch AB<r being equally divided in B, and 
 the Diagonals B d and BE being drawn thro’ the fix Parallels 
 ddd, &c. which are all at equal Diftances, they are thereby each 
 divided into fix equal Parts, each reprefcnting an Inch, ,and are 
 therefore number'd from E upwards, with 1, 2, 3, 4, 5, 6 , and 
 then downwards from B to d , with 7, 8, p, 10, n, 12, equal to 
 the Inches in a Foot. 
 
 Now as the Foot is here reprefented in an Inch, therefore the 
 Numbers of Feet belonging to this Scale, are prefix’d at every 
 
 I 2 Inch 
 
6o 
 
 A Sure Guide to Builders. 
 
 Inch forward towards the right or left Hand, according to which 
 End of the Rule the Divifion of Inches are plac’d. 
 
 When you are to take off any Number of Feet and Inches, 
 place one Foot of your Compaffes on the Line of the Foot given, 
 and on the fame parallel as the Inch Hands on alfb : As for Ex- 
 ample ; Take off the Length of one Feet nine Inches : Set one 
 Foot on the Line nY F at V, and extend the other Foot to the 
 Point p of the Diagonal B d, and it will be the Length requir’d. 
 Again, If you was to take off three Feet and four Inches ; fet one 
 Foot in W, as before, and extend the other to the Point 4, where 
 the Diagonal BE cut the Line W 4 : And the like of any other 
 Feet and Inches requir’d. 
 
 As you are now taught how to take off any Number of Feet 
 and Inches from this Scale of one Foot in an Inch, you are to 
 underftand the fame of the other Scales, that are in three quarters, 
 half^ and one fourth of an Inch, reprefented by XPWCf, 
 KLI, and RT6; and as all their feveral Ufes are exa&ly 
 the fame as the Scale of Twelves, before defcrib’d and explain’d 
 ( Fig. XXX.) therefore I need not fay any more on this Head, 
 but proceed to further Inftru&ions : But before I proceed thereto, 
 I muft inftruT you in a few other Geometrical Problems , which 
 often happen in Praffice. 
 
 PROBLEM V. * 
 
 'J” O make an Angle equal to an Angle given. 
 
 Let it be requir'd to make the Angle mG I equal to the Angle 
 CFD. (Fig. XXXVI. Plate VI.) 
 
 1. Draw GI at Pleafure ; then opening your Compaffes to any 
 Radius, let one Foot on F, and defcribe an Arch, as EB, and 
 with the fame Opening on G, the Arch H K. 
 
 1. Make H / equal to E B, and drawing the Line G m through 
 /, it will make the Angle mGl equal to the Angle CFD, as 
 requir’d. 
 
 PROBLEM 
 
A Sure Guide to Builders . 
 
 PROBLEM VI. 
 
 r J~ O meafure the Quantity of an Angle hy a common jive or ten 
 Foot Rod , or for want of them a common two Foot Rule ; and 
 to delineate the fame on Paper. 
 
 Let the Angle CAE ( Fig. XXXVII.) he the Angle of a Wall , 
 and ’tis requir'd to plan the fame. 
 
 Firft make a Sketch thereof on the Leaf of your Pocket- 
 Book or other Paper, as at Z ; then from the inward Quoin or 
 Angle A, meafure off any Number of Feet towards E and C, 
 fuppofe fix Feet, as at B and D, which Points reprefent in your 
 Sketch at a and h : Then with a Line, or rather two five Foot 
 Rods, meafure the exa 61 Diftance in Inches and Parts of Inches 
 from B to D, which we here fuppofe to be eight Feet, which fet 
 down in your Sketch by the prick’d Line ah. 
 
 Having thus taken the Meafure of the Angle, which is call’d 
 taking the Dimenfion thereof, I will, in the next Place, fhew 
 you how to delineate the fame upon Paper. 
 
 i. Draw a right Line at Pleafure, as FL ; then with a Scale 
 of Feet, (the larger the better) open your Compalfes to fix Feet 
 thereof, (the Diftances fet on each Side from the Angle) and fet- 
 ing one Foot on F, with the other deferibe the Arch K G. 
 
 i. Make K I equal to eight Feet of your Scale; and then 
 drawing H F through I, it will compleat the Angle requir’d. 
 
 P. But fuppofe that I am to take the Dimenfon of an Angle , as 
 ABC, (Fig. XXXVIII.) and I cannot hy any means get within - 
 fde to take the Dimenfon s ; pray how mu ft I proceed then ? 
 
 M. When you cannot meafure an Angle within, you mufl 
 meafure it without, which is a little more Trouble, but very 
 eafily perform’d : As thus ; Continue the Out-lines of the Angle, 
 as KI towards E, and NI towards D ; then will the Angle 
 EID be equal to the inward Angle ABC, becaufe oppofite 
 Angles are always equal ; therefore proceed to take the Dimen- 
 fions of the Angle EID, as you did the Angle CAE. (Fig. 
 XXXVII.) 
 
 6 1 
 
 PROBLE M 
 
A Sure Guide to Builders, 
 
 PROBLEM VII. 
 
 A 2 V 7 three Points being given , fo that they are not in a right 
 7 * Line, to jind the Center of a Circle , whofe Circumference 
 fall pajs through them . 
 
 Suppofe the three given Points are ABC. ( Fig . XXXIX.) 
 
 Practice, i . Imagine that right Lines were drawn from A to 
 B, from B to C, and from C to A, fo as to form a right-lin’d 
 Triangle. 
 
 2. Then if you divide any two of them into two equal Parts, 
 (as fuppofe AC and BC) by the Perpendiculars FE and DD, 
 the Point of their interfering one another at E, will be the Center 
 of a Circle, whofe Circumference will pafs through all the 
 given Points, as requir’d. 
 
 PROBLEM VIII. 
 
 O IV to take the Plan of any irregular curved Line , which is 
 no Part of an EllipJjs , Circle , £Cc. 
 
 Let ACB (Fig. XL.) be the given Curve. 
 
 1. Make a Sketch thereof, as A ZB, drawing the Line A B 
 from one Extream to the other. 
 
 2. Meafure any fmall Diftance from A towards B on the Line 
 AB, fuppofe 5 Feet, as from A to d ; and there raife a Perpen- 
 dicular dp, or by the Help of a Square meafure off, at right 
 Angles, from d to the Curve p, which fuppofe to be io Feet ; 
 then fet thefe two Meafurements down in your Table H in this 
 Manner, Ad 5 Feet, OfF-fet 10 Feet; then go 5 Feet for- 
 warder from d to e, (or further, if the Curve differs very little) 
 and in like Manner, meafure off from e to the Curve a, which 
 fuppofe to be 11 Feet; then place them down in your Table 
 thus, at Af 10 Feet, Off-fet 1 1 Feet, as in the Table ; and fo in 
 like manner take as many other Off-fets as the Nature of the 
 Curve requires, but the more, the exacter your Work will be. 
 The other Off-fets in this Example are at flog i, as exprefs’d in 
 the Table H, wherein you are to obferve, that the Stationary 
 Difiances of the Off-fets are in general accounted from A, and 
 
 t not 
 
A Sure Guide to Builders . 
 
 not from one another ; therefore, altho* they are in this Example 
 each at 5 Feet apart, yet they are all fet off from the Beginning 
 A, as AiyFeet, Ae 10 Feet, A f 15, A h 20 Feet, Ag 25 
 Feet, A i 30, and AB 40, againft which in the Table Hands &, 
 fignifying that the Curve terminates there without any OfF-fet. 
 
 Having thus taken the Dimenfions, I will now proceed to the 
 Delineation thereof Geometrically. 
 
 1. Draw a right Line at Pleafure, and therein, with any Scale 
 of equal Parts, fet off 40 Feet, reprefenting the whole Spand of 
 the Curve AB ; then having recourfe to your Table, you lee 
 that the firft Scation Ad is at 5 Feet, therefore from your Scale 
 of Feet, fet off 5 Feet from A to d on the Line A B, and on d 
 raife the Perpendicular dp„ which make equal to 1 1 Feet, as ex- 
 prefs’d in the Table. 
 
 2. The next Stationary Diftance in the Table is Ae, 10 Feet, 
 which take from your Scale and fet on the Line A B, from A to 
 e, and there raife the Perpendicular ea, which make equal to 1 1 
 Feet, as exprefs’d in the Table. 
 
 3. Proceed to the third Station A f which make equal to 15 
 Feet, and the Off-let equal to 1 2, as before ; and fo in like Man- 
 ner the other Off-fets hn^ gl , and ib 
 
 Laftly, If you apply a Bow, or thin Ruler, that is pliable, to 
 the leveral Points A, />, a, m, n, /, £, B, you may defcribe the 
 curved Line as requir’d. 
 
 P. But fuppofe that I cannot get to meafure the Stationary De- 
 fiances between A and B, and am confi rain’d to be without as at C, 
 • pray how mu ft I proceed then ? 
 
 M. Why fuch Cafes as this happens very often in Praftice ^ 
 but ’tis very eafily perform’d, as following : 
 
 Being without the Curve, make Choice of any two Stations on 
 the Ground, as D E, where ’tis belt to drive down two Stakes, 
 and ftrain a Line from the one to the other ; which Line may be 
 continued beyond D and E, as occalion requires. This done, 
 raife a Perpendicular from the Beginning of the Curve at A to 
 the Line D E, which we fuppofe to be A D • alfo raife a Perpen- 
 dicular from the other Extream of the Curve, as B7, and mea- 
 llire the Interval between the two perpendicular Points D and 7, 
 which fuppofe to be 42 Feet. This being done, meafure off 
 
 any 
 
64 A Sure Guide to Builders. 
 
 any Stationary Diftance on the Line DE, asDi, and at i mea- 
 fure off the Off-fet i /, which note down in a Table as before 
 direffed. 
 
 Then proceed forward to the next convenient Station, fuppofe 
 at 2, which let be 1 1 Feet 4 Inches from D, and there meafure 
 off the Off-fet 2 a, which note down as the firft ; and fo in like 
 Manner proceed, and take as many Off-fet s, as the feveral fudden 
 Windings or Turnings of the Curve ^require, until the whole 
 arc taken. 
 
 When all thefe feveral Dimenfions are thus taken in your Eye- 
 Draught or Pocket-Book, you may delineate them on Paper, as 
 before directed, for the other Off-lets taken within : For if you 
 fuff draw a right Line at Pleafure, and from a Scale of equal 
 Parts fet on the Number of Feet, as the Diftance of the perpen- 
 dicular Points were found to be, viz. 42 Feet, and then from 
 the Ends thereof, as from D and 7, raife the Perpendiculars DA 
 and 7 B, making DA equal to 15 Feet 6 Inches, the before mea- 
 fur’d Length, and 7B equal to 8 Feet 6 Inches, as exprefs’d in 
 your Table, you will have got the Extreams of the Curve. And 
 laftly, If from D to 1,2, and 3, &c. you fet off the feveral 
 Stationary Diftances, and their feveral refpective Off-fets, (as be- 
 fore directed in the fetting off the Off-fets taken within Side) 
 you may, through their feveral Terminations, draw the Curve 
 Line ABC, as requir'd. 
 
 PROBLEM IX. 
 
 r O take the Plan of 
 (Fig. 1 . Plate VII.) 
 
 the Out-Lines of Buildings in general. 
 
 The firft Work to be done, is to make a rough Sketch or Form 
 of the fame on Paper, which miff always be made as large as 
 you can, that the feveral Meafures of the Sides being placed 
 thereon, as you take them, may not interfere or crowd one ano- 
 ther, and caufe a Confufion. Your rough Draught thus pre- 
 par'd, is call’d an Eye-Draught, and its Ufe is as following : 
 
 Firf Beginning at any Angle of the Building, as at E, begin 
 to take the Dimenfions of the Front ED, mealiiring firft the 
 Length E a, 14 Foot, which write down on the refpective Line 
 of your Eye-Draught, then the Return ah , 3 Feet, which place 
 
 parallel 
 
St 
 
 W / <?&. 
 
 £71 I os 
 
 Fig.-XXXV' 
 
 ^ Ki 
 
 S> ^ 
 
 ^ ^ 
 
 3*?/ 
 

A Sure Guide to Builders. 
 
 parallel againft that Line reprefented in your Eye-Draught, as 
 in the Figure. This done, proceed to meafure from b to d , 
 which being 1 6 Feet, write down 1 6 Feet againft the refpective 
 Line in the Eye-Draught ; and lb in like Manner meafure the 
 Length of every Side of the Building, and note them down in 
 their refpe<ftive Places. 
 
 When all your Meafures of the Sides are thus taken, and 
 enter'd in your Eye-Draught, the next Work is, to examine into 
 the Nature of the feveral Angles, as before dire&ed ; but in 
 this Example all the feveral Angles are fuppos'd to be fquare, or 
 right-angled. 
 
 To make a Geometrical Plan from this Eye-Draught , proceed 
 
 as following : 
 
 i. Draw a right Line at Pleafure, as AB, and through any 
 Part thereof, as at H, draw a right Line cutting it at right 
 Angles, as D D. 
 
 i. Since eg contains 17 Feet, take 8 Feet one half in your 
 Compafles, and fet that Diftance from H to g, and from H to e. 
 
 3. As the exterior Breaks of the Front E a, cf hi , and mF, 
 are all in a right Line, and parallel to DD, at 3 Feet Diftance ; 
 therefore at that Diftance draw the parallel right Line EF at 
 Pleafure, making zh and zf each equal to Hg and He, f c and 
 hi each equal to 10 Feet, ca and im each equal to 16 Feet, and 
 laftly mF and E a each equal to 14 Feet. 
 
 4. The Breaks b d and kl being each 3 Feet deep, therefore 
 at 3 Feet Diftance from am , draw the right Lin ebdkh, then 
 making yd and yk equal to zc and zi , alfo kl and db equal to 
 ca and im, and then drawing the Returns of the Breaks a b, c cl, 
 ef gh , ik, and ml, the whole Front ED will be delineated 
 as requir'd. 
 
 Now for the delineating of the End Front E G. 
 
 1. On E ere<ft the Perpendicular EG, making EG equal to 
 the whole Depth, viz. 52 Feet : And fince that the Breaks no 
 and zy are 3 Feet deep, therefore at the parallel Diftance of 3 
 Feet, draw the right Line oy. 
 
 1 
 
 K 
 
66 
 
 A Sure Guide to Builders. 
 
 2. Make E n and ho each equal to p Feet, and draw the Re- 
 turn no \ alio make nr and op each equal to 7 Feet, and draw 
 the Return rp.' Again, Make r s equal to 3 Feet, sv equal to 
 p Feet, and vx equal to 3 Feet ; then dividing vs into two 
 equal Parts in H, on H, with the Diftance Hr, defcribe the 
 Semi-circle stv. 
 
 And here note, T hat if inf e ad of this Semi-circle .the Curve had 
 been more or lefs than a Semi-circle , you mufl have meafured 
 the Off-fet Ht, taken from the Middle of sv , at H, whofe 
 ext ream (Part t being taken with the Points s and v, would 
 be three given Points , through which you might have defcrib’d 
 the Curve % as before dire bled in Problem III. 
 
 3. Make pw equal to rx y alfo xz and wy each equal to 7 
 Feet ; and then drawing the Returns x w and zy, you will eom- 
 pleat the End Front as requir’d j and by the fame Method de- 
 lineate the Front FY. Now feeing that the Front GY only re- 
 mains to clofe up the Body of the grand Building, therefore at 
 G draw the right Line GY parallel to EF, and make GH and 
 X Y each equal to i 3 Feet ; and feeing that the Returns H I and 
 ~Xh are at 3 Feet Diftance, draw the right Line Ih at the parallel 
 Diftance of 3 Feet. 
 
 4 From the Points HX, draw the Lines HI and ~Kh per- 
 pendicular to GH and YX, making each of them equal to 3 
 Feet, the Depth of the Returns HI and Xi> ; then drawing the 
 right Line I h , fet off 3 Feet from h to W and from I to K. 
 
 5. As the Quoins (or Angles) L and T are each 12 Feet 
 diftant from the Points P and V, where the Sides ML and ST 
 interfed the right Line K W ; and fince that thofe two Points are 
 each 1 2 Feet diftant from K and W, therefore on your Paper 
 fet off on the Line K W 1 2 Feet, from K to P and from W to V, 
 and from thence ered two perpendicular Lines PM and VS. 
 
 6 . Make YT and PL each equal to 12 Feet, and on P and Y, 
 with the Radius KP or VW, defcribe the Arches or Quadrants 
 KL and TW ; alfo, make LM and TS each equal to 5 Feet, 
 and draw the Lines LM and TS. 
 
 7. Draw the right Line MS, and make MN and RS each 
 equal to 10 Feet, as alfo LO and QT, 
 
 Laftly, 
 
A Sure Guide to Builders. 
 
 Laftly, Draw the right Lines MN, NO, OQ^, QJR, and 
 RS, and they will compleat the Plan of the grand Building ED, 
 GY, as requir’d. 
 
 It now only remains to Jhewhow the Out-Offices X Y are to be 
 delineated ; to which I proceed. 
 
 i. Since that the ranging or front Line AD of the right Hand 
 Wing of the Building X, hath its End A 5 Feet Diftance from 
 G, and is perpendicular to AY, therefore continue the Line YG 
 to A, and at A ered the Perpendicular A D. 
 
 a. Continue the Line DA towards C, making AC equal to 2 
 Feet, .and on C raife the Perpendicular CB, which make equal 
 to 10 Feet. 
 
 3. At the parallel Diftance of CB from B, draw the right 
 Line BPPTXW, and from thence fet off the feveral Parts of 
 the Building, as following : 
 
 Firjt, Make BZ equal to 2 Feet, and draw the Line BZ. 
 
 Secondly , Make AK equal to p Feet, KO equal to 13 Feet, 
 as alfo O V and VY ; likewife make YD equal to p Feet, and 
 Dn equal to 2 Feet. Again, make ZI equal to 12 Feet, IP 
 equal to 10 Feet, PT equal to 13 Feet, TX equal to 10 Feet, 
 X W equal to 1 2 Feet, W m equal to 2 Feet, and draw the right 
 Lines KO, VY, D« ; and IP, TX, and W m. 
 
 i thirdly , Continue the right Line GA from Z to E, making 
 ZE equal to 10 Feet; then from the Angle K, at the parallel 
 Diftance of AK, draw the right Line KF parallel to EG ; 
 make PF equal to ZE, and draw the right Line EF. 
 
 Fourthly , Since KL and MN, taken together, are equal to 8 
 Feet, therefore draw ^N parallel to AK, at the Diftance of 8 
 Feet, and make ^ N equal to 1 1 Feet, as in your Eye-Draught : 
 Continue FK to L, making KL equal to 5 Feet; alfo draw 
 MN parallel to FK, making it equal to 3 Feet, and join ML, 
 Make F G equal to 5 Feet ; and becaufe that FI I is at the pa- 
 rallel Diftance of 3 Feet from GP, therefore fet off 3 Feet from 
 G to H, and draw' IH parallel to GP, and making it equal to 5 
 Feet, join GH. , 
 
 Fifthly , Lay a Ruler from P to O, and from T to V, making 
 QJP, OR, ST, and VW, each equal to 2 Feet, and draw the 
 right Lines QP, Q^S, ST, and OR, RW, WV. At Y ered 
 
 K 2 the 
 
63 
 
 A Sure Guide to Builders. 
 
 the Perpendicular YZ, which make equal to 5 Feet, and con- 
 tinue ZY to S at Pleafure. Make xS equal to 10 Feet, the 
 Sum of AX and SM taken together, and let 5 Feet back from 
 S to M, and there raife the Perpendicular M A, which make equal 
 to 3 Feet, and join AX. 
 
 Laftly, Set off 2 Feet from m to W, and from n to D, and 
 laying a Ruler from W to D, make GW equal to 10 Feet, and 
 DB equal to 5 Feet ; and then drawing the right Lines SG, 
 GW, DB, and ZB, you will compleat the Plan X as requir’d. 
 
 Note, The other Side-Building or Wing is to be deli- 
 neated after the very fame Method , and therefore needs no 
 Repetition. 
 
 Now feeing that this Example is fully fufficient to inform you 
 in the Method of Planing the Out-Lines of Buildings, I will, in 
 the next Place, fhew how to take the Dimenfions of the Thick- 
 neffes of the Walls, Partitions, &c. and to delineate them in 
 like Manner. 
 
 PROBLEM X. 
 
 r J~ O take Dimenfons of the Walls and Partitions of Buildings , 
 and delineate the fame in a Plan by the Duodecimal Scale of 
 Feet and Inches. 
 
 To make the young Student underftand the Methods of deli- 
 neating the Plans of Solid Bodies with Eafe and Delight, I will 
 illuftrate the fame by four Examples, which will enable him to 
 perform every thing that can be demanded of this Nature. 
 
 Example i. 
 
 SFo take the Dimenfons of the triangular Building CAB, (Fig. 
 
 XLL Plate VI.) and delineate the fame. 
 
 Praftce. Ftrf , On Paper, &c. make a Sketch or Eye- 
 Draught thereof, as FDE, wherein reprefent the Number of 
 Doors and Windows that are contain’d in each Side, as in the 
 Figure. This being done, begin to meafure the Dimenfions of 
 
 * the 
 
A Sure Guide to Builders . 69 
 
 the feveral Parts, beginning always at an Angle, as at A, and 
 meafuring the Diftance from the Angle or Quoin A to the Jaumb 
 i of the Window /£, denote the ftime in the refpeftive Place of 
 the Eye-Draught Dp. 
 
 Then meafure the Breadth of the Window ih, which being 8 
 Feet, write down the fame between po in your Eye-Draught. 
 
 And laftly, meafuring the Diftance from the Window Jaumb 
 h to the Quoin or Angle G, denote down the fame between o and 
 F in the Eye-Draught. 
 
 Secondly , Proceed to the Menfuration of the Dimenfions con- 
 tain’d in the other Sides GB and BA, placing them refpectively 
 in your Eye-Draught as they are taken ; then will your Eye- 
 Draught appear as DFE. 
 
 'to defcribe a Plan of this Building , proceed as follows : 
 
 1. Draw a right Line, as AB, which make equal to 40 F eet 
 by any Scale of Feet Meafure. 
 
 2. From the fame Scale of Feet take off 47 Feet, and on the 
 Point B defcribe the Arch a a, and on the Point A, with the Ex- 
 tent of 52 Feet, defcribe the Arch bb, interfe&ing the other in 
 C ; then joining CB and GA, you’ll have plann’d the Out-Lines 
 thereof. 
 
 3. Since the Side AB of the Building is reprefented by D E 
 in the Eye-Draught, make Ah equal to Dm, 17 Feet; hi equal 
 to mn , 6 Feet ; and i B equal to ;zE, 17 Feet. 
 
 4. Since the Side BC of the Building is reprefented by EF, 
 make Bk equal to Ey, 21 Feet ; k l equal to yr, 7 Feet, and 
 /C equal to rF, 15 Feet. 
 
 5. Since the Side A G of the Building is reprefented by D F in 
 the Plan, therefore make A i equal to Dp, 20 Feet ; ih equal to 
 p<?, 8 Feet ; and h C equal to oF, 24 P'eet. 
 
 Laftly, Since the Thicknefs of the Walls is two Bricks thick, 
 viz. 18 Inches, equal to one Foot and half, draw the right Lines 
 H K, K I, and I H, at the parallel Diftance of one Foot and 
 half ; then drawing the Skew-back or Jaumbs of the Windows 
 hz y iz y lz y kz, hz, i z, according to the Angles thereof found 
 in' the Building, you will have compleated the triangular Plan, 
 as requir’d. 
 
 E X A M P I. F 
 
70 
 
 A Sure Guide to Builders. 
 
 Example 2. 
 
 To take DimenJjons of the Geometrical Square Building A BCD, 
 (Fig. XLII.) and delineate the fame. 
 
 Brattice. 1. Make an Eye-Draught or Sketch thereof, as 
 EFGH, and therein place down the Meafure of every Part in 
 its refpe&ive Place, as before in the foregoing Example ; which 
 being done, draw a right Line, as C D, which make equal to 40 
 Feet, the Side GH of the Eye-Draught ; and as the whole Plan 
 is a Geometrical Square, therefore compleat the fame by Prob . X. 
 Chap. III. 
 
 2. Make £D equal to vH, 2S Feet; ik equal to tv , 5 Feet; 
 and C i equal to Gt, 7 Feet. 
 
 3. Proceed in like Manner to make the Parts of the other Sides 
 proportionable to the Meafures in the refpe&ive Parts of the Eye- 
 Draught, and fo doing you will compleat the Geometrical Square 
 Plan as requir’d. 
 
 Now feeing that the Thickneffes of Walls in Buildings, differ 
 very much in their Thickneffes and Forms, I will therefore in 
 the firffc Place fhew how to plan the Foundations of Buildings, 
 and afterwards their other Stories, as they arife above Ground. 
 Admit that the Plan (Fig. I. Plate VIII.) be the given Plan of 
 the Foundation of a Houfe, which has many Returns and Angles, 
 occafion’d by the feveral Breaks therein ; and as the whole con- 
 fifts of five feveral Parts, including the Stair-cafe, N° V, I have 
 therefore number’d every Part with I, II, III, IV, and V, that 
 you may at firft Sight difcover the Parts which I am treating 
 about, becaufe very often I have been oblig’d to make ufe of 
 alike Letters for References, which I could not avoid, in refpeft 
 to the many Angles contain’d therein. 
 
 Your firft Work, at coming on the Premifes, is (as I faid be- 
 fore) to make an Eye-Draught of the Building, wherein you 
 rnuft firft carefully reprefent every Return and Angle contain’d 
 therein ; and then meafure the Length of every refpecfive Side 
 in Feet and Inches, which place againft every refpe&ive Side, as 
 in the Plan. 
 
 When the Length of any Side or Part confifts of even Feet, 
 as 5, io, 1 j, &c. you need write down no other Figures againft 
 
 thofe 
 

 
 
 ■ 
 
 
 t • 
 > 
 
 
 
 ■ 
 
 . 
 
 
 
 
 ' 
 
 
 . 
 
 
 
 
 
 
 
 
 
 
 
 ■v 
 
 
 
PlaU.tf 
 

 * 
 
 
 . m 
 
 •• ' . 
 
 
 
 
 
 . 
 
 
 
 
 i ' - 
 
 l 
 
 
 
 
 
 
 
 
 ■ 
 
 
 
 
 
 
 
 
 
 - 
 
 ^ ; ' " 
 
 
 
 
 
 
 
 ' 
 
 
 
 
 
 
 
 
 
 
 
 
 I v 
 
 
 
 
 
 
 . 
 

71 
 
 A Sure Guide to Builders. 
 
 thofe Sides, than fuch as reprefent the Quantity of Feet ; but 
 when Lengths contain Feet and odd Inches, as 5 Feet p Inches, 
 then they muft be written thus , 3 : p, as Shillings and Pence 
 are in common Accounts. 
 
 Note, It often happens , that the Figure p is taken for the 
 Figure 6, after Dimer f on s are taken , being read the inverted 
 Way ; & Contra, the Figure 6 for the Figure p : But that 
 you may be never miftaken therein , befure that you place a 
 Point or Dot behind thofe Figures , as thus , 6 . p. For if 
 you invert thefe Figures , by turning this Page Bottom up- 
 wards, to caufe the Figure p. to appear as Figure 6. and 
 Figure 6. as Figure p. then will thofe Points fand before 
 them in (lead of behind , which is J'ujfcient to prove that their 
 Numbers are falfe , and therefore muft be read the contrary 
 Way. F hefe Cautions being obferv’d , as you pafs through the 
 feveral Meafures , you will very cor re lily place down all your 
 feveral Dimenfons as they are taken. 
 
 N^ B. <r the proper Inftruments for meafuring of Dimenfons , are 
 a ten Feet Rod , two fve Feet Rods , and a comjnon two Feet 
 Rule. 
 
 Now to the Matter in Hand. 
 
 i. Draw a right Line, as AY, reprefenting theOuthde of the 
 Building, which make equal to 80 Feet 6 Inches ; then on the 
 Point Y ered the Perpendicular YX, which make equal to 65 
 Feet 6 Inches. 
 
 1. From the Point X, draw the right Line XC parallel to 
 AY, which make equal to 82 Feet 6 Inches. 
 
 3. On the point A ered the Perpendicular AB, and continue 
 it to abik and r, making AB equal to 33 Feet, B a equal to 6, 
 ai equal to 5 Feet 6 Inches, ik equal to p Feet 6 Inches, and 
 kr equal to 1 Foot 6 Inches : Draw / C at right Angles to CX 
 and parallel to Ar, and make 1 C equal to 10 Feet ; then join- 
 ing Ir , you will compleat the Out-lines of the whole Plan. 
 
 N, 
 
 ow 
 
A Sure Guide to Builders . 
 
 Now for the Divifons jVithin-fde. 
 
 1. Since M L {Numb. III.) andXZ ( Numb . II.) are 7 Feet each, 
 and M n 2 Feet 6 Inches, and their Sum p Feet 6 Inches, there- 
 fore draw the right Line ZLO OS WZG, at the parallel Di- 
 stance of p Feet 6 Inches. 
 
 2. Make ZK and K L (Numb. III.) each equal to five Feet, as 
 exhibited in the Plan, alfo make LO equal to p Feet 6 Inches, 
 Off equal to 15 Feet, QS equal to 12 Feet, SW equal to 14 
 Feet 6 Inches, WZ equal to 10 Feet, and Z n equal to j Feet 
 6 Inches. 
 
 3. At the Points L, O, Cf , S, W, Z, draw the right Lines 
 ML, NO, Pff , RS, YW, XZ, at right Angles to the Line 
 ZOWG, making each of them equal to 7 Feet, as in the Eye- 
 Draught ; and drawing the Lines K L, MN, PR, and VX, 
 you will compleat that Side of the Plan. 
 
 From the Point n (Numb. II.) draw the Line no x elm, at the 
 parallel Diftance of 7 Feet from the Line YX, and make no 
 equal to 4 Feet, ox equal to 10 Feet, xc equal to qe, eg, and 
 g i, (viz. 26 Feet 6 Inches) cl equal to 10 Feet, and Im equal 
 to 2 Feet. 
 
 Likewife, make Y p equal to 11 Feet 6 Inches, pq equal to 
 sr, and vt (viz. 11 Feet p Inches) qe , equal to p Feet 3 Inches, 
 eg equal to df (viz. 8 Feet), gi equal to p Feet 3 Inches, ik 
 equal to p Feet, and laftly, &X will be equal to p Feet. Then 
 from the Points 0 , x, c, and /, draw the right Lines ov, xt , ch , 
 and Is, at right Angles to the Line nx cm, making the Lines ov 
 and xt each equal to 3 Feet, and the Lines ch and Is each equal 
 to 4 Feet, and join vt and hs j and in like Manner fet off at 
 right Angles the Lines ih, fg, de , and qt , each equal to 4 Feet, 
 as alio the Returns j>s and rv. Laftly, Join ps , sr, and rv, 
 as alfo d% f which will compleat that Part or Gable End of the 
 Plan. 
 
 The Side XC being the next in Order, 
 
 i. Make Xy equal to xo Feet, qy equal to id Feet, yl equal 
 to 10 Feet, lb equal to 17 Feet, bi equal to 9 Feet p Inches, 
 iq equal to 15 Feet, and q C will be equal to p Feet pinches. 
 
 2. From 
 
73 
 
 A Sure Guide to Builders. 
 
 2. From the Points q,y, /, b, l, g, draw the right Lines qp, 
 yz, Ik, bi , iJ, and gp, at right Angles to the Line CX, and 
 each equal to 2 Feet, as exprefs’d in your Eye-Draught. 
 
 3. Laying a Ruler to the extream Parts of the laft fet-off 
 Lines, make pr and iz each equal to 3 Feet; alfo draw the 
 Line ki, and make dt equal to 2 Feet, and tp equal to 3 
 Feet. 
 
 4. From the Points r , /, /, and t, draw the fmall Returns to , 
 t e, i n, and r 6 , at right Angies to the Line prizkldetp, and 
 each equal to 2 Feet, and join oe and eo. 
 
 j. Since the inward Line of the Wall mngdmaz x vn m is at 
 3 Feet 6 Inches diftant from the laft Line, therefore draw it at 
 the parallel Diftance of 3 Feet 6 Inches, and make mn (Numb, I.) 
 equal to 3. Feet 6 Inches, ng equal to 1 1 Feet, gm equal to gd 
 and dm (viz. 13 Feet), ma equal to 1 1 Feet 6 Inches, az equal 
 to 4 Feet 6 Inches, zx equal to 6 Feet 6 Inches, xv equal to 3 
 Feet 6 Inches, vn equal to 11 Feet, and nm equal to 5 Feet; 
 alfo makeg^ equal to 10 Feet, and draw the Lines .mn, gd, az, 
 xv, and nm. 
 
 6 . From the Points n , g, m , a, z, x, v, and n, draw the right 
 Lines no,ge, mn, ah, zy, xw, ve, and no, at right Angles to 
 •the Line mngdmazxvnm , until they meet the Line onnheo ; 
 fo will the third Side of the Plan be compleated. 
 
 Again, on G ereft the Perpendicular Cl, making it equal to 
 10 Feet, and on l erect the Perpendicular Ir, or draw Ir parallel 
 to Cg, and equal to 2 Feet, as in the Eye-Draught. 
 
 Lay a Ruler from the End of this laft Line r to A, where 
 you firft began, and draw the Line AZBrt/£r; alfo from 
 K to m, draw the inward Line ¥LGT)Cc dom. . Make rk equal 
 to 1 Foot 6 Inches, and mo equal to 4 Feet, and join ko. 
 
 Make kl and od equal to p Feet 6 Inches, alio la and dc 
 equal to 5 Feet 6 Inches, and draw ac. 
 
 Make a B and c G ! each equal to 6 Feet, and draw BC; then 
 fet off 3 Feet from C to D, and ered the Perpendicular DF 
 equal to J Feet. From the Point F draw the right Line 
 FHELM parallel to A ZB. Make FI equal to 2 Feet and a 
 half, I H equal to 3 Feet, HE equal to 11 Feet, EL equal to 
 7 Feet, and LM equal to 7 Feet. Then from the Point E fet 
 off the Line EG at right Angles to EHF, and equal to 5 Feet. 
 Join KG, and you will compleat the fourth Side of the Plan. 
 
 L Now 
 
74 
 
 A Sure Guide to Builders. 
 
 Now there only remains the inward Partitions . 
 
 1. From the Point FI {Numb. III.) draw the right Line H fh 
 parallel to LOQ^S ; alio, at the parallel Diftance of 3 Feet draw 
 the right Line Iglk, and making HZ' and Ig each equal to 25 
 Feet, draw the Return fg • likewife, ma k.tfh and gl equal, to 
 1 1 Feet, and draw hi. 
 
 2. Continue the right Line id {Numb. V.) tog and f making 
 dg equal to 1 8 Feet 6 Inches, and gf equal to 1 1 Feet 6 Inches ; 
 alfo de parallel to if ahd join ef And lince that the Stairs 
 ikgh are p Feet 6 Inches in Breadth, equal to ik y therefore 
 draw kh parallel to ig, and make kh equal to ig. Then divid- 
 ing gi and hk ? each into 13 equal Parts, the Number of Steps 
 contain’d within the Plan, and drawing right Lines from every 
 refpc&ive or oppolrte Divilion, you will compleat the Stair- 
 cafe. 
 
 3. From the Point a by S, in the right Line ZLOQST 
 {Numb. III.) draw the Line abdram to the Point m y for one 
 Side of the middle Partition, and parallel to NTT&aik. Make 
 ma {Numb.V.) equal to 3 Feet, ar equal top Feet, ra, includ- 
 ing the End of the Partition a, equal to 3 Feet 2 Inches, ak 
 equal to 17 Feet, ki equal to 3 Feet, id equal to 4 Feet 6 
 Inches, .db equal to p Feet, and b S equal to 5 Feet. Make a T 
 equal to 2 Feet, and from the Point T draw Teem parallel to 
 Sbdl, making T c equal to Sb y viz. 5. Feet, and join bc\ alfo 
 make ce equal to bd y and join de. Make em equal to 13 Feet, 
 and from the Point m y draw mqzy parallel to T WZ n r making 
 mq equal to 2 Feet, qz equal to 8 Feet, and zy equal to 8 Feet. 
 Then joining xy, you compleat Numb. II. . . : ,ni • 
 
 4. Make mh {Numb. I.) equal to 4 jF.eet, and from h draw 
 
 hiab parallel to mqzy. Make hi equal to 1 Foot, ia equal 
 to 8 Feet, and ab equal to 8 Feet ; and join be, which will 
 be equal to 14 Feet. r 
 
 Laftly, Join hd y {Numb. I.) and make hg equal to p Feet 6 
 Inches, gb equal to p Feet, and bd equal to 3 Feet ; then joining 
 rgj abj q i , and za y you will compleat the whole Plan as requir’d. 
 
 Note, That when you make any Drawings , either of Plans or 
 Upright s y they are be (l done when firji drawn in Black Lead , 
 
 becauje 
 
A Sure Guide to Builders. 
 
 becaufe that thofe Parts of Vines which in the Example are 
 pricked or dotted , mud not appear in a real Drawing , there- 
 fore having frfl made the Drawing in Black Lead Lines , you 
 may with Pleafure draw every Line in Ink over them , as is 
 requir’d j and afterwards , with clean Bread , rub off the re- 
 maining Lines entirely clean , as if they had never been drawn. 
 
 The other Plan (Fig. II.) is a Plan of the firft Floor of the 
 farpe Building, wherein the Thicknefles of the Walls are reduc’d, 
 and the Windows, Doors, Chimneys, and Clofets fet out in their 
 proper Places, as therein exhibited. 
 
 And as the feveral Operations of taking and delineating this 
 Plan, are of the very fame Nature as thofe in the preceding Ex- 
 amples, it is needlefs to go through the feveral Operations there- 
 of, and therefore recommend it for the young Practitioner’s 
 PraCtice. 
 
 'fir 
 
 PROBLEM XI. 
 
 : ) 
 
 If O delineate Geometrical Elevations or Uprights of Buildings in 
 **■ general. 
 
 o 
 
 As the Plans of Buildings confift of the Thicknefles of Walls, 
 Partitions, &c. Uprights contain all that is beautiful and noble, 
 as Windows, Doors, Columns, Pediments, Rufticks, and other 
 Ornaments, which confift of great Variety of Proportions, that 
 makes the Delineation thereof truly entertaining to the Mind. 
 
 It is very eafy to delineate the principal Parts of Buildings in 
 Grofs, as Doors, Windows, &c. but when you come to delineate 
 their feveral Parts or Members of which they are compos’d, you 
 will find fomething of more Difficulty therein, not but they are 
 alfo very eafily perform’d, as will appear hereafter. 
 
 And that you may have a clear Underftanding therein, I will 
 begin with Examples of the principal Parts in Grofs, and after- 
 wards advance to their feveral Parts, of which they are com- 
 pofed. 
 
 As I before directed you in the drawing of Plans, to make an 
 Eye-Draught of the Building before you began to take the Di- 
 menfions thereof, fo I muft alfo advife herein. 
 
 L a 
 
 Admit 
 
A Sure Guide to Builders. 
 
 Admit that you are to draw the Elevation of the Banquetting- 
 Houje. (Fig. I. Plate IX.) 
 
 1. Make your Eye-Draught, wherein reprefent the Windows, 
 Door, Piers, &c. and then beginning at any Angle, as at AL; 
 meafure the Breadth from the Quoin to the Window, which fup- 
 pofe to be i Feet, which note down as at a. 
 
 2. Meafure the Breadth of the Window, (fJurnb. I.) which 
 note down as before ; and fo in like Manner meafure the Breadths 
 of the Pier he , the Door c d y the Pier de , the Window, (Numb. 
 III.) and the Pier^i Having thus taken all the Dimenfions of 
 Breadth, the next are thofe of Height, which firft is the fetting 
 off in the Brick at N O, which fiippofe to be 2 Feet 3 Inches, 
 which note down, placing the Figures to be read upwards, as 
 in the Figure. That being done, meafure the Height from N 
 to the Ceil of the Windows PQ^, as alio the Height of the 
 Windows R a , the Height of the Cornice a B, and the Height of 
 the Parapet or Balls of the Dome B i, and place all their feveral 
 Meafures in their relpedive Places. 
 
 Tour Dimenfions being thus taken , proceed to the Delineation 
 thereof as following ; 
 
 1. Draw a Horizontal or Bafe Line, as LM, which make 
 equal to 21 Feet 6 Inches, the whole Breadth of the Front 
 LGM. 
 
 2. Divide L G into two equal Parts in G, and from the Point 
 G ered the Perpendicular G m; alfo draw AL and MK parallel 
 to Gm , and each equal to 21 Feet, and join AK. 
 
 3. Draw dx and cn parallel to Gm, each at 3 Feet Diftance 
 from Gm; alfo draw eY and Z»X parallel to cn and dx, each at 
 2 Feet Diftance ; and laftly, draw /Z and a W parallel to 
 and eY , fo will all the Limits of your Dimenfions in Breadth 
 foe determin'd. 
 
77 
 
 • # * , ,-v. > 
 
 A Sure Guide to Builders. 
 
 7 * he next Work is to interfeff thofe perpendicular Lines with others 
 
 parallel to the Horizo?i> which Jhall divide the feveral Parts , 
 
 as requir’d. ■ / • 
 
 < ' ' * V* f M rr r. ^ \ 
 
 • i t - , ■ • 
 
 1 . Make B a and HZ' each equal to i Foot, and draw nabcdefm 
 for the Depth of the Cornice, and Tops of the Windows and 
 Door. 
 
 2. Make ^R and/'V each equal to n Feet 6 Inches, and 
 draw the right Line PO , cutting £X in S, and eY in T, and 
 join RS and TV. 
 
 3. Draw hg above the Cornice, at the parallel Diftance of 2 
 Feet 6 Inches, and make AB and KI each equal to 1 Foot ; 
 then from the Points B and I ered the Perpendiculars BC and I g, 
 cutting hg in the Points C and g. 
 
 4. Becaufe the Center of the Dome is fix Inches above the 
 Line hg, therefore at that Diftance draw iZ,k parallel to hg , 
 and where the right Line ik cuts the right Line MZG, is the 
 Center of the Dome. 
 
 Therefore extend your Compafles from Z to i or k y defcribe 
 the Dome imk\ and thus will you have laid down all the grand 
 Parts of the Building, as requir'd. 
 
 Fig. II. Plate IX. is the Geometrical Elevation of two Houfes, 
 whofe Dimenfions being prefix'd thereto, and the feveral Lines 
 drawn, their Interfedions forming the Windows, Doors, Piers, &c. 
 needs no more to be faid on the Manner of delineating them, 
 the Method being exadly the fame with the preceding, (Fig. I.j 
 and therefore are only plac'd for further Exercife therein. 
 
 It now remains to Ihew, hew to delineate the particular Parts 
 of Buildings, as Columns, Pillafters, Architraves, Freezes, Cor- 
 nices, Impofts, Pediments, Rufticks, &c. and by the Way, I 
 believe that it mayn't be improper, as I go on, to give the Ety- 
 mology of every Part, that you may know from, whence their 
 Name derives, and thereby diftinguifh their true Place and 
 Signification. 
 
 / 
 
 I. Of 
 
 I 
 
A Sure Guide to Builders . 
 
 
 1 Of a COLUMN. . , 
 
 < Column,, ( Cvlomne , French , of Column a, Lathi) .a Support 
 or Pillar, fupporting an Entablature, viz . an .Architrave, Freeze, 
 atjd t Cornice, or oilier Parts of Buildings, requir’d. 
 
 ■ 'Moft Author^ define a Column to be a round long Cylinder, 
 which it is not, becaufe that" the upper Part or a Column has a 
 lefs Diameter than at its Bafe, caufed by thp Diminution which 
 begins- from one third Part of the Plcight $ whereas a . Cylinder 
 (which is generated by a Parallelogram making a Revolution 
 about one pf its longed: , Sides) hath the Diameters at each End 
 equal, which, a Column hath not. 
 
 When Archite&ure was in its Infancy, the firft Columns were 
 made of young Trees, which then ferv’d as Props or Supports 
 to crofs Pieces laid from one another in the Manner , of Archi- 
 traves ; and as yo'ung Trees are naturally Ids in Diameter -at 
 their Tops than at their Bottoms, therefore to rcprclcnt their 
 Growths and Statures, Columns were firft diminifh’di The firft 
 Perfon that regulated the Forms of artificial Columns, made of 
 Brick, Stone, &c. was King' 'Ddrus, who built a Temple in Ho- 
 nour of the Goddefs in the City of Argos j wherein ho 
 
 plac’d Pillars of Stone, refembli'ng thole which were before made 
 of young Tre'es, giving to them a beautiful Proportiop, which 
 he eftarolUh'd, and 'Was afterwards, practis’d in moft other Build- 
 ings of that Country } and from hence came the very Original 
 of Orders, which, from the Name of Dorus , was call’d the 
 Corick Order : And as the City of Srgos, wherein it was firft 
 built, (as afordaid) is in Greece , it is therefore alfo call’d the 
 Primitive Greek Order. r. . . .. ^ 
 
 Columns are two-fold, viz. round and lquare ; which laft are 
 generally plac’d at the Angles or Quoins of Buildings, and the 
 former in the intermediate Spaces between. 
 
 There are Five Kinds of Columns, viz/. the L’ufcan , the Do- 
 rick, the Muck , the Corinthian , and the Compofite. The Tufcap 
 and CompoJjte are* call’d Latin Orders ; and the Dortik, Muck, 
 and Corinthian , Greek Orders. 
 
 ( Plate XII.) A Column, be it of what Kind foever, is com- 
 pos’d of three principal Parts, viz. the Bafe P, the Shaft O, and 
 
 the 
 
A Sure Guide to Builders . 
 
 the Capital N, and each of thefe of divers other lefier Parts, 
 whofe Names I fhall give you, as 1 come to them in Pradice. 
 
 Now as a Column is compos’d of three principal Parts, fo alfb 
 is the Entablature which it fiipports, and the Pedeftal whereon 
 it ftands. The principal Parts of an Entablature are an Archi- 
 trave H, a Freeze R, and a Cornice S. Likewife the Parts of a 
 Pedeftal are the Bafe W, the Die ,or Trunk V, and the Cornice T. 
 {Fide Fig . VIII. Plate XII.) 
 
 When a Column ftands on a Pedeftal, and fupports an Enta- 
 blature, (as Fig . VIII. Plate XII.) they being in general taken 
 together, compote an entire Order of Architedure ; therefore when 
 a Column is plac’d without its Pedeftal or Entablature, it cannot 
 be faid to be an entire or compleat Order ; excepting the Dortch 
 Column, which originally was made without a Pedeftal, nay 
 even without a Bafe to the Shaft, as may be feen by the Dortch 
 Columns of the Theatre of Marcellas , and many- other antient 
 Buildings of Rome . 
 
 The fevers.} Part$Oof a Goluirin are meafured and delineated 
 by a Scale of Modules and Minutes. A Module is always a 
 Length equal to the- Diameter of the Shaft of the Column at 
 the Bafe, as XZ, {Plate XII.) which is always divided (or fup- 
 pos’d to be divided) into 60 equal Parts, and are call’d Minutes. 
 
 It is 'with tbele Parts, that the Proportions of all the Members 
 of the five Orders, of Columns > are laid down and determin’d, as 
 will immediately appear, d! ... in , * ?i ' 
 
 The centeral Line of a Column, is that which paftes from the 
 Center of the Bafe diredly through the midft of -the Shaft, Ca- 
 pital, and Entablature, making an Angle of po Degrees with 
 the Bate,, as -..the Line A PL {Fig. I.) It is on the centeral Line 
 of a Column, that thei Height of all the feveral Members are 
 adjufted, and ’tis from thence- that all their Projedures ate 
 determined. 
 
 PROBl e M XII. 
 
 TO deferibe the feveral Moldings , which compofe the Ornaments 
 
 4 with which Buildings at re adorn'd. - 
 
 d 1 -• 1 - • uj •• M 
 
 ' The feveral Moldings which compote and enrich ah the beau- 
 tiful Parts of a Structure, are the Plinth, the Torus, the 1 'Fillet, 
 the Scotia, the Aftragal, the Ovolo, the Caveto, the Cima 
 
 * a ' • Reda, 
 
80 A Sure Guide to Builders . 
 
 Reda, and Cima Reverfa ; which two laftare vulgarly 1 calfd by 
 Workmen the Fore and Back Ogees. 
 
 I will begin with thofe Moldings which compoie the Bafes of 
 Columns, and then proceed to the others' contain’d in their fe- 
 veral Capitals and Entablatures. j\« • , 
 
 Tt *"1 fi t i I 3Y*»'iS 
 <{} 3 '■> kjAtTI 
 
 Fir [l then, The Plinth A, the Fillets CE, and Cindure G, be- 
 ing all Parallelograms, are defcrib’d by Pr,ob. . Chap. III. 
 
 Secondly , The Torus’s B and F, having their centeral Lines ba 
 and FK drawn, and their : Radius’s being fet back thereon from 
 a, to 0, and from K to H, H and o will be their Centers whereon 
 they are delcrib’d. 
 
 Thirdly , To defcribe the hollow Molding or Scotia D, there 
 are divers Methods, as following : 
 
 . W. d :: lifvTl 
 
 Method i. (Fig. VIII. Plate XI.) 
 
 . : v , ir '.oM ..V. .zz ij r.'' T i ■ - a ;>. •• T i; yd 
 
 i. From the lower Angle of the upper Fillet D, draw the 
 right Line D B to the upper Angle of the lower Fillet. 
 i. Divide DB into four equal Parts, as at ae and i. 
 
 3. On D, with two of thofe four equal Parts, defcribe the 
 Arch #«, and on B, with three of thofe Parts, the Arch m m , 
 and draw the right Lines A D and A B. 
 
 4. Compleat the Equilateral Triangle ACB, fo will C be the 
 Center of BDA, the lower Part of the Scotia. 
 
 5. Bifed DA in F, and on F raife the Perpendicular FE, 
 which continue until it interfed AC, the Side of the Equilateral 
 Triangle, in E, which is the Center of the Arch AGD, which 
 compleats the whole as requir’d. 
 
 Method 1. (Ftg. IX.) 
 
 1 . Draw the right Line G H, and divide it into five equal Pgrts 
 
 in abed. 
 
 2. On H, with four of thofe Parts, defcribe the 'Arch jf and 
 on G, with two of thofe Parts, interfed the Arch // in the 
 Point I. 
 
 t . 
 
 i ’ . ■' \ ‘ . 
 
 3. Com- 
 
 ' i n 
 
 (Fig. XIV. Plate X 
 
A Sure Guide to Builders. 
 
 3. Compleat the Equilateral Triangle IKH, and on the angu- 
 lar Point K, defcribe the lower Part of the Scotia HLI. 
 
 4. Bifed I G in 2, and ere# the Perpendicular 2 M, continu- 
 ing it until it interfed the Side IK of the Equilateral Triangle 
 I K H in M, which is the Center of the upper Part of the Scotia, 
 and compleats the whole, as requir’d. 
 
 Method 3. 
 
 1. Draw the right Line BD, and divide it into fix equal 
 Parts. 
 
 2. Make Be equal to one fixth Part of BD, and on D de- 
 fcribe the Arch en. 
 
 3. On B, with the Opening of two Sixths or one Third of 
 BD, defcribe the Arch dm, interfeding the other in C, and draw 
 the right Lines CD and CB. 
 
 3. Divide CD into four equal Parts, and compleat thelfofceles 
 Triangle CGD; make each of the Sides C G and G D equal to 
 three Fourths of C D, and on the angular Point G defcribe the 
 Arch DZC. 
 
 4. Biffed CB in/, and on i raife the Perpendicular /F, which 
 continue until it interfed the Side of the Triangle CG in F, 
 which is the Center of the Arch CHB, and compleats the 
 Scotia as requir’d. 
 
 Method 4. 
 
 1. Draw the right Line j 1, and divide it into fix equal Parts. 
 
 2. Make 1 c and 1 e each equal to two fixth Parts of 5 1 ; and 
 from e , through c , draw the right Line e ca, making ca equal to 
 ce ; and then compleating the Equilateral Triangle hae, a will 
 be the Center of the Arch ef h. 
 
 3. Draw the right Line h j, which bifed in n, and on n 
 ered the Perpendicular ttl, continuing it until it meet the Side of 
 the Triangle ha in /, which is the Center of the Arch hk$, and 
 compleats the Scotia requir’d. 
 
 M Fourthly, 
 
82 
 
 A Sure Guide to Builders. 
 
 Fourthly , Ovolo’s (or quarter Rounds, as term'd by Work- 
 men) are defcrib’d, either on the angular Point of an Equila- 
 teral Triangle, (as Fig. VI. and VII. Plate X.) or on the an- 
 gular Point of an Ifofceles Triangle, (as Fig. V.) where the 
 two equal Sides AyandAp each contains four Fifths of py, 
 
 • the fubtending Side. 
 
 But oftentimes an Ovolo is defcrib'd as the fourth Part of a 
 Circle, when their Heights and Proje&ions are equal y and then 
 it is that they are real quarter Rounds, as Workmen call them. 
 See Fig. IV. and VII. Plate XII. where is exhibited the three 
 feveral Methods in one Figure, which fhews the different 
 Swellings thereof. ( {' 
 
 Fifthly, Ca veto's' are defcrib'd by the very fame Rules as Ovo- 
 lo’s. As for Example ; Fig. XIII. Plate X. is defcrib'd on the 
 angular Point E of the Equilateral Triangle EFH, and Fig. X. 
 and XI. on the angular Points O and B of the Ifofceles Triangles 
 XOY and ACB, whole equal Sides in each Triangle are each 
 equal to three Fourths of the fubtending Sides XY and AC. 
 And laftly, The Caveto is alfo defcrib’d by the Arch of a Qua- 
 drant, or fourth Part of a Circle, as BDA. (Fig. XI.) 
 
 Sixthly , The Cima Re£ta (Fig. I. II. VIII.) and Cirna Reverfa, 
 (Fig. III. and IV.) are defcrib’d either on the angular Points of 
 Equilateral Triangles, as is fhewn at large in the next Problem 
 of the Example of delineating the Fufcan Entablature, (Fig. II. 
 and III. Plate XII.) or on the angular Points of Ifofceles Tri- 
 angles, (as Fig. I. II. and IV. Plate X.) in Manner following. 
 
 Example. (Fig. II.) 
 
 1. Draw the light Line 2 1 from the lower Angle of the 
 upper Fillet A, to the upper Angle of the lower Fillet B, and 
 bifeft it in V. 
 
 2. Divide IV and V a each into {even equal Parts, and com- 
 pleat the Ifofceles Triangles I 3 V and V 4 2, making each of 
 the equal Sides I 3, 3 V, and V 4,. 2 4, equal to fix Sevenths of 
 IV or V 2 ; then will the angular Points 3 and 4 be the Centers 
 of the two Arches, which together form, the Cima Re&a re- 
 quir'd. 
 
 ■t 
 
A Sure Guide to Builders. 
 
 quir’d. And fo in like Manner ‘any other requir’d, as the feve- 
 ral Figures here exhibits. 
 
 But fometimes the Cima Reverfa is defcrib’d as following, 
 (Fig. III. Plate X.) 
 
 1. From its utmoft Projedion, as at A, draw the right Line 
 A I, which bifed in D. 
 
 2. Bifed AD in L, and DI in K, and at the Points L and K 
 ered the Perpendiculars LH and KB, continuing them until 
 they touch or interfed the Extreams of the Cima in the Points 
 H and B, which are the two Centers, on which you may de- 
 fcribe the two Arches that compofe the Molding requir'd. 
 
 Seventhly , The curved or hollow Parts of the Bafes of the 
 Shafts of Columns, which reft upon the Cindures, (as Fig. XIV. 
 Plate X.) are defcrib’d as following : 
 
 1 . Let A C be the Upright of the lower Part of the Shaft, 
 refting upon the Cindure E D j and let C D reprefent the Pro- 
 cedure of the Cindure beyond the Upright of the Column. 
 
 2. Divide C D into three equal Parts, and make C A equal to 
 four of thofe Parts ; then by the 47th of the ift of Euclid , the 
 Hypothenufe AD will be equal to five of thofe Parts. 
 
 3. Bifed AD in 5, and on 3 raife the Perpendicular 5B, con- 
 tinuing it out at Pleafure, until it cut AB (which muft be drawn 
 parallel to C D at the Diftance of A C) in the Point B, which is 
 the Center of the Curve AGD, as requir’d. 
 
 The curved or hollow Part of the Shaft, under the Fillet of 
 the Aftragal, may be defcrib’d as the preceding, or as follow- 
 ing. (Fig. XV.) 
 
 Let CF reprefent the Fillet under the Aftragal Z, and El 
 the Upright of the Shaft. Make E C equal to E F, and on F, 
 w r ith the Diftance F C, interfed E I in H. Bifed F H in N, 
 and on N raife the Perpendicular N G, which continue until it 
 cut HG (which muft be drawn parallel to EF, at the Diftance 
 of EH) in G, which is the Center of the Curve requir’d. 
 
 INI 2 
 
 But 
 
8 4 
 
 A Sure Guide to Builders.. 
 
 But fome Archite£ts make both thefe preceding Curves the 
 fourth Part of a Circle, (as Fig. V. Plate XII.) where, making 
 BG equal to BE, and drawing EH parallel to BG, and GH 
 parallel to B E, their Point of Interfe&ion H is the Center of the 
 Curve requir'd. 
 
 PROBLEM XIII. 
 
 Hr O delineate the Tufcan Column, with its Entablature , accord - 
 ing to the Proportions of Andrew Palladio. ( Plate XII. 
 Fig. L) 
 
 Thofe Numbers written againft every Member at their Ex- 
 treams, denote the Quantity of their Projedure from the cen- 
 teral Line, and the others written againft the centcral Line, to 
 be read upwards, denotes the Height of each Member. 
 
 Now to the Matter in HancT. 
 
 1. Draw a right Line at Pleafure, asgBfz, and in any Part 
 thereof, as at B, ered the Perpendicular Y A. 
 
 2. Make Y h and Y i each equal to 40 Minutes, as prefix'd 
 againft the right Line ie, and draw e i and fh perpendicular to 
 h i, and each equal to 15 Minutes ; then joining f e, which will be 
 parallel to hi , you will compleat the Plinth fehi. 
 
 3. Make XZ equal to 12 Minutes and a half, and thro’ the 
 point Z draw ec parallel to f e •, alfo make Xr and Xg equal to 
 33 Minutes |, as alfo Z<? and Z c, and draw the occult Lines cdg 
 and ear ; then dividing er and eg in x and a, on the Points x 
 and a describe the Semi-circles cdg and ehr , which compleats- 
 the Torus ZX. 
 
 4. Make W Z equal to 2 Minutes and a half, and draw db 
 thro’ W, parallel and equal to ec, then joining.^ and de, you 
 compleat the Cin&ure W Z. Theft three Members being taken 
 together, compofe the Baft of the Column, whoft Height, is 
 always equal to half the Diameter, or 30. Minutes.. 
 
 But you muft here note, Phat althd the Cinlture W Z is here 
 included in this Bafe, yet in all other Bafes } tis excluded , and 
 is a Part of the Shaft, as will appear 2 when I come to fhew 
 you the Proportions thereof. 
 
 The 
 

 
 j ; 
 
 
 
 
 - 
 
 
 
 
 ■ 
 
 - 
 
 ■-vf04< 
 
 
 ' ' 
 
 
 
 fC ( , 
 
 >w." I' 
 
 I , •- ' s 
 
 • • ■ . 
 
 ' ' 
 
A Sure Guide to Builders. 85 
 
 The Etymology of thefe three Members which compofe this 
 Bafe, viz. the Plinth , the Torus, and the Cindure, are as 
 following : 
 
 Fir ft , Of the Plinth Y X, from the Greek. and Latin 
 
 Plinthus , a fquare Brick or Tile, being always plac’d at the 
 Bottom of every Pedeftal, Column, &c. and by fome 'tis call'd 
 Orlo. 
 
 Secondly , The Thorns XZ, from the Greek Word Toros , a 
 Cable, which its Curvature reprefents j or otherwife, from the 
 Latin Word Torus, a Bed, becaufe that the Bafe of the Shaft, 
 viz. the Cincture W Z is beded or placed thereon. And as Co- 
 lumns are generally Supports of great Weights, it is fuppofed 
 that the Swelling or Curvature of the Torus is caufed by the 
 great Preffure of Weight thereon. 
 
 i 'Thirdly , The CinBure WZ, from the Latin Word CinBura , 
 and Italian LifleUo , a Girdle or Bond, binding about the lower 
 Part of the Shaft, to prevent its fplitting or burfting by the great 
 Weight laid thereon. 
 
 This Part of the Shaft was originally made of Iron, when 
 wooden Columns were firft ufed, in the Manner of a Feril or 
 Ring, driven on to preferve their Bottoms from fplitting ; fince 
 which they have been imitated in Columns of Stone, as now 
 practis’d in all Buildings where Columns are ufed. 
 
 Having thus given the Etymology of the Plinth, Torus,, 
 and Cindure, which compofe the Bafe, I will, in the next 
 Place, proceed to the Drawing of the Shaft of the Column, with 
 its Capital. 
 
 1. Make WO equal to 6 Modules and a half, and draw wOq 
 through the Point O, and parallel to ^DWIA, for the upper 
 Part of the Capital. 
 
 2. Make OP equal to 10 Minutes, and draw xVr parallel to 
 O P. Make O w, O y, P x, and P r, each equal to 30 Minutes, as 
 prefix'd between y and r 3 and joining wx and qr , you com- 
 pleat the Abacus (5 P» 
 
 3. Make PH equal to to Minutes, and draw t parallel 
 xJlr. Make H y and Ht each equal to 24 Minutes and 
 
 a half. 
 
A Sure Guide to Builders . 
 
 a half. Then on the Points h and i, with the Opening ha y de« 
 fcribe the Arches z a and t s y which will compleat the Ovolo 
 PH. 
 
 4. Make HQ_ equal to 1 Minute and a half, and draw jQjy 
 parallel to aHt y and equal to at ; then drawing ay and tv> the 
 Annulet P H is compleated. 
 
 Laftly, Draw aKx at the parallel Diftance of 8 Minutes and 
 a half, and make Qy?, Cfw, and Ka y K#, each equal to 22, 
 Minutes and a half ; then joining za and xw y you compleat the 
 Freeze Q_K, which does alfo compleat the whole Capital. 
 
 The Etymology of the Capital and its Parts, is as follows : 
 
 The Capital of a Column, takes its Name from the Latin Word 
 Cafitellum , the Head or Top : 'His alfo call’d Chapiter , from the 
 French Word Chapiteau , the Crown or upper Part of a Pillar. 
 Now for the Members feverally. 
 
 1. The Abacas OP comes from the Greek Word a/Saf, Abax y 
 which fignifies a fquare Trencher. In French ’tis call’d Tailloir y 
 and by the Italians Credenza. In Architecture ’tis the upper Part 
 of a Capital, whereon the Architrave refts. Palladio ealls it a 
 Plinth , from its fquare Form, being in the Fufc an Order of the 
 fame Form with the Plinth of the Bafe. 
 
 But the Abacus in the Dorlck , Ionick , Corinthian and Compo- 
 se Orders, is different in tits Figure : As frf y In the Dorlck 
 Order, "tis compos’d of a fquare Body, as in the Fufcan y but 
 crown’d with a Cima Reverfa or Back Ogee, and a Fillet, as 
 in Plate XIX. and XX. 
 
 Secondly , In the Ionick Order, ’tis compos’d of a Cima Reverfa 
 and Fillet only, as in Plate XXI. and XXII. 
 
 Thirdly , In the Corinthian and Compofite Orders, ’tis compos’d 
 of an Ovolo, a Fillet, and a Caveto, as Fig . I. and II. Plate 
 XXIII. and XXIV. 
 
 It is to be noted, Float the Capitals of the Tufcan and Doricfc 
 Orders , are call'd Capitals with Moldings , becaufe they are 
 feldom enrich'd with any Ornaments of Carving , Sec. and as 
 the Ionick, Corinthian, and Compofite are wholly compos’d 
 
A Sure Guide to Builders. 
 
 of carved Ornaments , they are therefore call'd Capitals with 
 Sculptures , from the Latin Word Sculptura, to carve in 
 Wood, Stone , &Cc. 
 
 • i. The Ovolo PH, call'd by fome Workmen Boultin, and 
 in general Quarter Round ; and as this Member is often- 
 times carved in* the Dorick , Ionick, and Corinthian Orders, 
 with what Workmen call Eggs and Anchors, (as Fig. II. Plate- 
 XXXIX.) it is therefore call'd Ovolo , from Ovum an Egg. But 
 thefe Ornaments were originally made to reprefent a Chefnut 
 when 'tis ripe, and burfting out of the Husk ; and as the out- 
 ward Husk or Shell of a Chefnut is full of fmall Prickles, like 
 unto the Prickles of a Hedgehog’s Back, it was therefore call’d 
 Echinus , from the Greek onto tS i yjva, a Hedgehog. 
 
 3. The Annulet H , from the Latin Word Annulus,. a Ring. 
 ’Tis a Iquare Member plac’d under the Ovolo PH, ferving as a 
 Bond to the Top of the Freeze QJC. In the Dorick Order 
 (Plate XIX.) the Capital contains three Annulets plac’d 
 under the Ovolo ; but Palladio calls this Member Lifella , from 
 the Italian Word Lifla , a Lift or Selvage, and fometimes Cincture, 
 for in Fa& there is no Difference in their Forms. 'Tis alfo call’d 
 a FiUet, ■ from the French Word Filet , of Filum , Latin , a Hair- 
 lace to bind up Hair, which is not improper, as being a Part of 
 the Head or Capital of the Column : But as ’tis generally plac’d 
 under the Ovolo’s of the Vufcan and Dorick Capitals,. I cannot 
 fee any Reafbn why it fhould be call’d Super cilium , Latin , the 
 Brow or Eye-brow, as many Authors do : For as the Eye-brow 
 hath a Projecture over the Eye, as the Corona of a Cornice hath,, 
 over all the lower Parts of the Order, 'tis my humble Opinion, 
 that the Corona may more properly be call’d Super cilium than, 
 the Annulet HQ. 
 
 4. The Part of the Capital Q^K is call’d the Freeze of the 
 Capital, becaufe it divides the upper Members from the Aftragal 
 KS, as the Freeze of the Entablature I£L divides the Cornice 
 from the Architrave. Vitruvius calls it the Gorge , or Gule or 
 Neck. 'Tis alfo call’d Hypotrachelium , from the Greek 
 %p\10v, the Top or Neck of a Pillar. 
 
 The Freezes of the I’ufcan Capital and Entablature are always 
 plain; but thofe of the Dorick Capital and Entablature are 
 
 oftentimes 
 
83 
 
 A Sure Guide to Builders ; 
 
 oftentimes enrich’d with carved Ornaments ; a§ alfo are the 
 Freezes of the Ionick , Corinthian , and Composite Entablatures. 
 
 The Enrichments of thefe laft mention’d Freezes, were ori- 
 ginally compos’d of the Reprefentation of divers Animals, and 
 therefore the Freeze is oftentimes call’d Zoophorus , or Zophorus , 
 from the Greek Zaopop's, Animal-bearing : But the ^ord Freeze 
 comes from the Latin Phrygio , an Embroiderer ; or rather from 
 the Italian Word Freggio , a fring’d or embroider’d Belt. 
 
 Having thus done with the Delineation of the Capital, and the 
 Etymology of its Parts, I will now proceed to the Delineation of 
 the Aftragal KST, and the Shaft TBDFVW. 
 
 j. Continue out the Line aYLx, the upper Part of the Aftragal 
 as to g and z, and draw o S b parallel to a Kx, at the Di- 
 ftance of 4 Minutes ; then making K# and K# each equal to Sb 
 and Sz y defcribe the Semi- circles gy, making their Projedure 
 equal to 27 Minutes. 
 
 1. Draw cF a parallel to oSh y at the Diftance of 1 Minute 
 and a half ; then making S h So y and TtT^, each equal to 24 
 Minutes and a half, join ha and oc y and fo will you have com- 
 pleated the Aftragal K S, with its Fillet S T, as requir’d. Now 
 for the Shaft. 
 
 It has been already mention’d, that the Diminution of Columns 
 were originally taken from the taper Growth of young Trees, 
 whofe Bodies diminifh thro’ their feveral Degrees of Height, and 
 therefore I fhall proceed to the Diminution thereof. 
 
 The Diminution of the 7 * \ifcan Order at its Aftragal, is one 
 fourth Part of its Diameter at the Bafe, viz . 15 Minutes, and 
 therefore the Diameter at the Top is but 45 Minutes, whofe half 
 is 22 Minutes and a half, as above prefix’d. The Diminution of 
 Columns does always begin from one third Part of their Height, 
 excluding Bafe and Capital, as at the Line iVk , and therefore 
 the firft third Part of the Shaft is a Cylinder. 
 
 1. Divide the whole Height WS into three equal Parts, and 
 make W V equal to one of thofe Parts. Draw i V \ thro’ V, and 
 parallel to DWI, and make WI, W D, and Vi, V£, each 
 equal to 30 Minutes, and draw the Lines Di and Ifc, the Out- 
 lines 
 t 
 
A Sure Guide to Builders . 
 
 lines of the firft third Part of the Shaft. Imagine B E D F (Fig.Y.) 
 to be Part of the Cincture dbec , (Fig. I.) and the perpendicular 
 Line BG A, part of the Out-line of the Shaft IK ; then making 
 BG equal to BE, and EH equal to BG, and parallel thereto all'o, 
 with the Opening H G on H defcribe the Arch G Z E. Likewife 
 at dD perform the fame Operation, and the lower Part of the 
 Shaft will be compleated : Or otherwife, defcribe thofe curved 
 Parts of the Shafts according to the 7th of the Tenth * Problem 
 hereof. 
 
 2. On V defcribe the Semi-circle imnr stvolk. Take the 
 Diameter of the Column at the Top, 45 Minutes, in your Com- 
 palfes, and make st in the Semi-circle equal thereto, which is 
 very eafily done with your Te-Square, and that Opening apply ’d 
 thereto. 
 
 3. Divide V T, the upper Part of the Shaft, into four (or more) 
 equal Parts, at the Points F, D, B, and thro' them draw the right 
 Lines ^F^, eD f and cBd ; alio divide the Segments of the Semi- 
 circle is and tk each into as many equal. Parts as VT is divided 
 into, (which in this Example is four) as at the Points mnr- and vol. 
 
 4. Draw the right Lines sa and bt parallel to VT, at the 
 Diftance of xt and xs\ alfo from the Points r and v draw right 
 Lines parallel to TV, until they cut the Line cBd in c and d ; 
 alfo from the Points n and 0 draw right Lines, until they cut the 
 Line eT>f in the Points e and and laftly, from the Points m 
 and l draw the right Lines mg and /£, cutting the right Line 
 g F h in g and h. 
 
 Then if Lines are drawn from m to g y from g to e , from e to 
 c 7 from c to N, alfo from k to h y from h to f from f to d y 
 and from d to O, they will truly form the upper Part of the 
 Shaft as requir’d. 
 
 The Etymologies of the Aftragal K T, and the Shaft 
 NODI, are as follow : 
 
 The Aflragal KT comes from the Greek little 
 
 Joints in the Neck or Heel, and therefore the French call it Falon, 
 or the Heel itfelf ; but the Italians call it Fondino , in refped to 
 its -Swelling being like that of a Finger Ring. 
 
 1. The Shaft NODI, alfo call’d Fuji, from the Latin , 
 Fuji is a Club, and by fome Arc hi teds Scaptts , of which Vitruvius 
 was the firft that call’d it by that Name. 
 
 N 
 
 It 
 
po A' Sure Guide to Builders. 
 
 It now remains to fhew the Delineation of the Entablature, 
 by which is underftood the Architrave, Freeze, and Cornice of 
 any Order. But the Word Entablature comes from the Latin, 
 fabulatum, fignifying a Ceiling or Flooring ; and as the Freezes 
 of Entablatures were' originally compos’d of the Ends of Joifts, 
 which are what is call’d naked Flooring, it leems that the Word 
 is not fo much mifapply’d as fome imagine. ’Tis alfo call’d 
 Entablement and 7 'rabeation , French of Latin. 
 
 The Architrave is compos’d of a Fillet LM, and two Fafcia’s 
 MN and NO, which are thus delineated. 
 
 r. Draw jN o parallel to uOp, at the Diftance of 12 Minutes 
 and a half, and make N t, N 0 , and O v, Op, each equal to 22 
 Minutes and a half, and draw tv and vp for the firft Fafcia 
 NO. 
 
 2. Draw qUn parallel to jNo, at the parallel Diftance of 17 
 Minutes. Make Mr, Us, and N s, N 0, each equal to 24 Mi- 
 nutes, and draw r s and so. Continue Mr to q, and Ms to n, 
 making each equal to 27 Minutes and a half. Make rn equal 
 to qr, and gm equal to qr, and parallel to rn, then will m be 
 the Center on which you may defcribe the Arch qn. Perform 
 the like Operation at sn, and you’ll compleat the fecond crupper 
 Fafcia MN. 
 
 3. Draw pEm parallel to qMn, at the Diftance of 5 Minutes. 
 Make L p and L m each equal to Mn and M q, viz. 2 7 Minutes 
 and a half, and joining pq and mn, you compleat the Tenia 
 
 1 or Fillet LM, which finifties the whole Architrave as requir’d. 
 
 By the Word Architrave is underftood, the firft Member of 
 an Entablature, that bears upon the Capital of a Column, as 
 LO, taken together. The Word comes from the Greek Archos, 
 Chief, and the Latin I’rabs, a Beam ; and as it refts immediately 
 upon the Heads or Capitals of Columns, ’tis therefore likewife 
 call'd Epifiyle , from the Greek Epi, upon, and Stylos, a Co- 
 lumn. 
 
 But befides the Architraves that help to compofe Entabla- 
 tures, there are others which are Ornaments to Doors, Windows, 
 and Chimney-pieces, as the Architraves BB, &c. (Fig. II. and 
 111. Plate XLII.) and A A, &c. (Fig. I. and III. Plate 
 XLIII.) 
 
 y All 
 
A Sure Guide to Builders. pr 
 
 All kinds of Architraves finifh either with a Teniae or Fillet 
 only, as in Plate XVII. XVIII. &c. or with an Ovolo or Caveto 
 and Fillet, (as Fig. V. VII. X. and XI. Plate XXXI.) or 
 with a Cima Reverfa and Fillet, ( Plate XXI. and XXII.) 
 
 The Fafcia MN or NO, are fo call’d from the Latin Word 
 Fafcia , a large Turban ; but, in my humble Opinion, they arc 
 more properly large Lifts or Fillets ; but as Cuftom has fo long 
 prevail'd among Workmen, 'tis very reafonable to believe, that 
 they will never be induced to call them by any other Name than 
 Fafcia , Facia, or Fafce. 
 
 Now for the finilhing Stroke, which is to delineate the Cor- 
 nice AK. 
 
 1. Set up the Height of the Freeze LK equal to 26 Minutes, 
 
 and thro' the Point K draw the right Line and make Kn 
 
 and Kg each equal to 24 Minutes; alio make Km, K / and 
 Lo, L l, each equal to a a Minutes and a half, and joining mo 
 and fl, you compleat the Freeze KL. 
 
 2. Set up 7 Minutes and a half from K to I, and thro’ I 
 draw the right Line kin , and make I&, In, each equal to 32 
 Minutes. Continue K m to /, making K / equal to I k, fo ftiall 
 1 be the Center of the Arch K m. Perform the like Operation at 
 g n , and you'll compleat the Caveto I K. 
 
 3. Make IH equal to 1 Minute and a half, and thro' the 
 Point H draw the Line iH& equal to Ik and In ; then join i k 
 and kn, and you’ll compleat the Lift: or Fillet IH. 
 
 4. Set up p Minutes from H to G, and thro’ the Point G, 
 draw the right Line g h G m ie parallel to /Hi Make Gh, Gi 
 each equal to 40 Minutes ; alfo make G n, G m, each equal to 
 Hi and Hi ; then on n , with the Radius ni, defcribe the Arch 
 ih , and on m the Arch ki, fo will you compleat the Ovolo or 
 Echinus GH. 
 
 5. Set up from G to F 10 Minutes, and thro’ the Point F 
 draw efFdi parallel to gGe. Make F e and Fi each equal to 
 54 Minutes 1 quarter ; alfo make F f and Fd equal to 52 Mi- 
 nutes 1 quarter ; then continuing Gh tog, and Gi to e, mak- 
 ing each of them equal to^F and F d, and joining fg and de, 
 you compleat the Corona or Supercilium FG. 
 
 N 2 6 . Set 
 
 7 
 
2 
 
 A Sure Guide to Builders . 
 
 6 . Set up from F to C i Minutes, and thro’ C, draw dCb 
 parallel to eF i. Make dC , Cb, each equal to*?F and Fi j then 
 join de and bi, you compleat the Fillet CF. 
 
 7. Set up from C to E 10 Minutes, and thro’ the Point E 
 draw the right Line rEc, and make Eq E c, each equal to 66 
 Minutes. Set up from E to D 3 Minutes and a half, and thro’ 
 the Point D draw the right Line b A a. Make b A and A a each 
 equal to cE and Et\ and joining be and ae, you compleat the 
 upper Fillet D E. 
 
 Laftly, Imagine abed (Fig. II.) to be the Fillet laft deferib’d, 
 and let the Fillet nr op reprefent the Fillet deCFbi of Fig. I. 
 Then to deferibe the Cima Recta or Ogee bhn, draw the 
 Line bn , which bifeft in lo. Open your Compaffes to the Ra- 
 dius nh , and on n deferibe the Arch hrn , alfo on h the 
 Arch In and^A; then moving them from h to b, on b deferibe 
 the Arch eh, interfering the Arch bf in i, as the Arch nl in- 
 terfered the Arch hm in k. Now if on k you deferibe the 
 Arch hzn , and on i the Arch bszh, you’ll compleat the Cima 
 Rera or Ogee b zh zn, which does alfo compleat the whole 
 Cornice as. requir’d. 
 
 But note, ‘That the Cima Reft a may be deferib’d by the 6 th of 
 Problem X. hereof 
 
 Now feeing that the Cornice is compos’d of three Fillets, 
 (DE, CF, and HI) the Cima Rera EC, the Corona FG, the 
 Ovolo G H, and the Caveto I K, whofe Etymologies are not yet 
 in general given, I will therefore proceed thereto, that thereby 
 this Order may be compleated. 
 
 1. The Fillets being of the fame Derivation with thofe pre- 
 ceding, I need not repeat the fame again. 
 
 1. The Cima Reft a or Ogee EC, alfo call’d Cymaife , Gimaife , 
 and Cy mat turn , from the Greek xvjuctror, Kymatian,, which fig- 
 nifies a rowling Wave. 
 
 There are two kinds of Cymatiums , the one call’d Cima Re£ia y 
 as the above EC, (Fig. I.) whofe upper Part is concave, and 
 lower Part convex, call’d by the French Gola > or Throat,, or the 
 
 Doucire . 
 
A Sure Guide to Builders . 
 
 The other kind of Cymatium is call'd the Back Ogee , or Cima 
 Reverfa , or Invert a, {Fig. III.) whofe upper Part is convex, and 
 lower Part Concave, call’d by the French Falon, or Heel. 
 
 3. The Corona F G, or Coronis , Latin, a Crown, call’d by the 
 French Larmier , and by the Englijh Super cilium, the Brow of the 
 Cornice, and fometimes Stillicidium , Drip, becaufe its extraor- 
 dinary Projection defends the reft of the Work from Wind and 
 Weather. And as this Member has in all the Orders a greater 
 Projection than either of the others, it therefore has a large Ceil- 
 ing, call’d by Architects Plancere , and by the Italians Soffito, 
 Soffit a, Sqffiita , or Soffit, from the Latin Word Subjixum, a CieL- 
 ing. Thefe Cielings or Soflita’s are enrich’d with different Orna- 
 ments, according to the Will of the Architect ; but the moft 
 ufual are thofe reprefented in Hate XLVII. 
 
 4. The Ovolo or Echinus GH being before defbrib’d in the 
 Ovolo of the Capital, I fhall therefore proceed to the Caveto 
 IK, which comes from the Latin Cavus , a Hollow, and is gene- 
 rally made by the fourth Part of a Circle, as before directed. It 
 is alfo deferib’d as the Ovolo, {Fig. VII.) where you firft draw 
 the right Line h n, and divide it into five equal Parts ; then on h 
 and/, with the Opening iaothn , deferibe the Arches n x and 
 ax, interfeCting each other in x , which is the Center on which, 
 with the Radius xh, you may deferibe the Ovolo hgi, whofe 
 Curvature will be left fweliing, than that before deferib’d in the 
 Capital at zha and 1 st. 
 
 The Cima Reverfa , ( Fig. III. and VI.) may be deferib’d as 
 directed for the Cima ReCta, as reprefented in Fig. II. or as 
 following in Fig. VI. wherein ’tis always to be remember’d, 
 that the Height and ProjeCture muft be always equal to each 
 other, for therein conlifts the whole Beauty of this Molding. 
 
 Let the ProjeCture hy be equal to the Height zy. Divide hy 
 into 7 equal Parts, and make in and xr each equal to one of the 
 feven Parts. Draw nx , and divide it into two equal Parts in e, 
 and divide ex into 7 equal Parts. This done, fet your Compaffes 
 in x, and open them to /, and with that Diftance deferibe the 
 Arch ih , and on e, with the fame Opening, defcribe the Arch 
 nt, interfeCting the former in In the lame Manner deferibe 
 the Arches ak, bk , and on k and ^ deferibe the Arches nme 
 and ehx, which compleats the Cima ReCta as requir’d. . 
 
 From. 
 
94 
 
 A Sure Guide to Builders . 
 
 From thefe leveral Operations preceding, you may very eafily 
 delineate any of the five Orders of Columns, according to any 
 Proportions laid down, and therefore more Examples of this 
 Nature would be needlefs. But as this Example has been made 
 on a Column, which has a little Difference from a Pillafter, and 
 is oftentimes placed in the Head of a Column, and very often 
 behind Columns, as in Frontifpieces, &c. it will not be amifs to 
 fhew the Difference between a Pillafter and a Column, and what 
 is to be obferv’d in drawing of their Entablatures. 
 
 i . A Pillafter is a fquare Pillar, of the fame Height in all the 
 Orders as a Column, and differs only in its Breadth, which is 
 the fame at the Top, next the Aftragal KT, as CD, as it is at 
 the Bottom DI, whereas a Column diminifhes at the Top, as 
 N O , which Diminution, as has been before noted, does always 
 begin from one third Part of the Height, as at i V k. 
 
 Now as Pillafters are of the fame Diameters at the Tops of 
 their Shafts as at Bottom, you muft therefore, when you draw 
 their Capitals and Entablatures, add to the Projedture of every 
 Member as much as the Column of the Order is diminifh’d at 
 the Top: As for Inftance ; The Fillet of the Aftragal ST, 
 which in the Column has but 24 Minutes and a half Projedture 
 at ca, muft have 7 Minutes and half more added to it for as 
 the Semi-diameter of the Shaft at Top is but 22 Minutes and a 
 half, which is 7 Minutes and a half lefs than 30, the Semi- 
 diameter at the Bafe ; therefore you muft add 7 Minutes and a 
 half to the Projedture of every Member in the Pillafter ; and 
 the Fillet of the Aftragal, which in the Column has but 24 
 Minutes and a half Projecture, muft have in the Pillafter 32 
 Minutes Projedture ; and the like of all others contain’d in the 
 Capital and Entablature. 
 
 PROBLEM XIV. 
 
 r O defcribe the Ornament of the Ovolo , commonly call’d Eggs 
 and Anchors. ( Fig. III. Plate XL) 
 
 Frail ice. 1. Let CD {Fig. I.) be the given Height, which 
 divide into three equal Parts at E and G, and thro’ E draw HI 
 at right Angles to C D, continuing it on both Sides infinitely. 
 
 2. On 
 
A Sure Guide to Builders. 
 
 2. On E, with the Radius EC, defcribe the Semi-circle 
 ACB. 
 
 3. Bifed the Semi-diameter AE in F, and make HA, and 
 BI, each equal to FB. 
 
 4. On E defcribe the Semi-circle A G B, and from H and I, 
 thro’ the Point G, draw the right Lines L G I and HGK; and 
 on H and I, with the Radius H B, defcribe the Arches B K and 
 AL. 
 
 5. Bifed G D in M, and from the Points N and O (where the 
 Lines LI and HK interfed the Semi-circle AGB) draw the 
 right Lines O Q__ and N P thro’ the Point M. 
 
 6 . On O and N, with the Opening O L or N K, defcribe the 
 Arches KP and LQ. 
 
 Laftly, On M, with the Radius MQ, defcribe the Arch 
 QJ)P, which will compleat the Egg, or Egg ovallar Figure as 
 requir’d. 
 
 Now to defcribe the Side Ornaments , which reprefents the Shell of 
 the Chefnyt. {Fig. II.) 
 
 1 . Let the Line B 2 be drawn, and A H be the given Height 
 of the Ovolo. 
 
 2. Make 0 H equal to one lixteenth Part of A H, and then 
 between A and 0 compleat the Egg Oval as before taught. 
 
 3. Make AB equal to live Eighths of AH, and draw the 
 right Line 2 3 parallel to AH, at the Diftance of half AH. 
 
 4. Divide A / into three equal Parts at n and h , alio divide 
 the Line 2 3 into four equal Parts at 1 a, n 2 ; and then from n } 
 thro’ h , draw the right Line nh D, and on nD compleat the 
 Equilateral Triangle dJ)n ; then will n be the Center of the 
 Arch DG J, and the Point r will be the Center of the Curve 
 d o. 
 
 5. Divide DB into three equal Parts at EZ, and from E, 
 thro’ h , draw the right Line JLhm, making hm equal to ir ; 
 then on E m compleat the Equilateral Triangle TLem, and fo 
 will m become the Center of the Arch EF^ ; and the Point s 0 
 where the Side m e cuts the Perpendicular A. H, is the Center of 
 the Curve e H, . 
 
 Proceed . 
 
A Sure Guide to Builders. 
 
 Proceed in like Manner to defcribe the other Arches on the 
 right Hand Side, and you'll compleat the whole as ( Fig. III.) 
 as requir’d. 
 
 Sometimes inftead of a Dart, which is commonly call’d an 
 Anchor, as B, {Fig. III.) there’s plac’d a Leaf, as A, between 
 each Egg, which, I think, is more natural to the Egg or Chef- 
 nut than a Dart, excepting when they are plac’d to reprefent 
 Symbols of Love, &c. 
 
 PROBLEM XV. 
 
 T° delineate the wreathed Shaft of the Dorick Order. 
 
 Twilled or waved Columns, are call’d wreath’d Columns, from 
 the Saxon Word ppeo ^ean, to twill or twine about. 
 
 There are three feveral Methods, by which the Shafts of Co- 
 lumns are wreath’d ; of which the firfl- is the moll proper for 
 the Dorick Order, the fecond for the lonick , and the third for the 
 Corinthian and Compofte. , 
 
 N. B. rfhe Tufcan Order being ufed more for Strength than 
 Beauty , is never wreath’d as the others often are. 
 
 {Fig. II. Plate XIII.) 
 
 i . Since the Shaft of the Dorick Order is 7 Diameters in Height, 
 exclulive of its Bafe and Capital, you mull therefore divide the 
 Height of the Shaft contain’d between the Cin&ure GI, and the 
 Lift of the Aftragal S T, into 7 equal Parts, as at A B C D E F G. 
 
 1. Draw the Out-lines of the Shaft SGTI, as dire&ed for the 
 Diminution thereof in Page 8p ; and then through the feveral 
 Points A B C D E F G, draw right Lines parallel to G I, as HAK, 
 LBM, nCi, mDh , IFg, and kF f 
 
 3. Draw the Diagonals of the Square HKGI, viz. Hn I and 
 G;;K, continuing it to w, making Kw equal to n K. 
 
 4. Draw the Diagonal K u L, continuing it to c , alfo draw the 
 Diagonal M u H, continuing it to m, making the Continuations 
 H m and L c equal to half of one of the Diagonals Lu or Hu. 
 
 5. On m, with the Radius m H, defcribe the Arch H G, and 
 on n the Arch K I } alfo on w, with the Radius ^K, defcribe 
 
 the 
 
J^late ■ JJ. 
 
 Qj'Wtnr TTletAoi 
 
 Scofias, II gg s, Anchor &,kc : 
 
i 
 
• 1 
 
 1 . 
 
- ' 
 
 
 * ' 
 
 . 
 
 ; 
 
 
 
 
mm , 
 
 A Sure Guide to Builders . 
 
 the Arch K M, and on u the Arch H L. Then beginning again, 
 draw the Diagonals of the Square ni L M, continuing them on 
 each Side as before direded, and on their Extreams defcribe the 
 Arches «L and iM. 
 
 Laftly, If you perform the fame Operations in the other re- 
 maining Squares, you’ll compleat the whole Shalt as requir’d. 
 
 PROBLEM XVI. 
 
 0 delineate the wreathed Shaft of the Ionick Order . (Fig. III.) 
 
 1. Delineate the Out-lines of the Shaft F RPCk, and continue 
 the upper Part of the Cindure PQ^to E, making EP equal to 
 one third Part of the Height PF. 
 
 2. Draw the Line EF, and with that Radius on F, defcribe 
 the Arch E V, and on E the Arch F V, alfo on X the Arch E F. 
 
 3. Divide the Arch EF into 1 2 equal Parts, at the Points 
 1, 2, 3, 4, 5, 6, 7, 8, p, 10, 11, and 12, and from thole Points 
 draw right Lines parallel to EPQ^, thro’ the Shaft of the Co- 
 lumn, cutting the Side F P in the Points nn,&c. and the Side 
 Q^R in the Points 0, 0 , 0, &c. 
 
 Thefe parallel Lines will divide the Shaft into 12 unequal 
 Parts, whofe Curves are defcrib’d as follow. 
 
 Divide n P into four equal Parts, and on P, with three of thofe 
 Parts, defcribe the Arch ar , and on n the Arch hr y lo will the 
 Point of Interfedion r be the Center of the Arch n P. Perform 
 the like Operation at 0Q_, and defcribe the Arch Divide 
 
 all the other Parts of the Out-lines in the fame Manner, and 
 then deferibing Arches of three fourths Radius of every Divi- 
 fion, you’ll have the Centers on which you may defcribe the 
 feveral Arches that compofe the Twills contain’d in the wreathed 
 Shaft, as requir’d. 
 
 PROBLEM XVII. 
 
 O delineate the Shaft of the Corinthian 
 (Fig. IV.) 
 
 or Compolite Order . 
 
 1. Delineate the Out-lines of the Shaft BDON, and continue 
 the Fillet of the Aftragal OB out to A, making BA equal to 
 BD, the Height of the Shaft, and draw the right Line AD. . 
 
 O 2. With 
 
 97 
 
A Sure Guide to Builders . 
 
 2. With any Opening of your Compares, as AZ, defcribe 
 the Arch ZC, which divide into 12 equal Parts, at the Points 
 
 3. Lay a Ruler from the Point A, to the feveral Points in the 
 Arch, i, 2, 3, &c. and draw the right Lines 1 n, 2 n, 3?;, 4^, 
 57/, < 5 ;/, 7«, 8®, p?;, io», 1 1 //, which will divide the Out- 
 line of the Shaft BD unequally in the Points //, n, n r &c„ 
 
 4. Draw the right Lines nm , nm, &c. from the feveral Points 
 n, n, n, &c. parallel to the Bale DN ; then opening your Com- 
 pares from N to m, on m defcribe the Arch Ni, and on N the 
 Arch m /, fo will the Interfedion i be the Center of the Arch 
 
 then in like Manner on D defcribe the Arch ni and D /, 
 and on i defcribe the Curve ng D. 
 
 Laftly, Proceed in like Manner with the other Divifions, and 
 you’ll compleat the Shaft as requir’d. 
 
 PROBLEM XVIII. 
 
 yO divide the Rujiicks contain'd in the Tufcan, Dorick, and 
 S Ionick Columns . 
 
 The Shafts of the 'Tufcan, Dorick, and Ionick Columns are 
 oftentimes made with Rufticks, (as Fig . V. VI. VII. VIII. and 
 IX. Plate XIII.) 
 
 Since thefe Rufticks in Columns are plac’d as fo many 
 Cindures, to bind the Parts of the Shaft together, and pre- 
 ferve it from burfting by the great Weight which they are 
 fuppos’d to fuftain, they Ihould be never ufed but in ftrong and 
 maffy Buildings. 
 
 The feveral Kinds and Proportions of Rufticks are generally 
 at the Pleafure of the Archited ; fome making them very thick 
 let, with fmall Gutters between, (as Fig. IX. Plate VIII.) and 
 others much thinner, as AB, (Fig. VIII.) BDFHK, (Fig. VII.). 
 and thofe of (Fig. V. and VI.) 
 
 When Rufticks are to be placed at lome large Diftances from 
 each other, as thofe laft mention’d, their Heights and Number 
 mull be lo proportion’d, as to have the fame Diftance between 
 the upper Ruftick and Capital, as is between the lower Ruftick 
 and Cindure of the Bafe. 
 
 The Height of the Tufcan Shaft is 6 Diameters, exclufive of 
 the Bafe and Capital ; and fince that each Ruftick Ihould be 45 
 
 Minutes 
 
A Sure Guide to Builders. 
 
 Minutes in Height, and the Diftance of the Shaft between 
 each Ruftick 30 Minutes, (as in Fig. V.) therefore it fol- 
 lows, that that Column can have but five Rufticks ; and the 
 Intervals between the Capital and upper Ruftick, and Bafe and 
 lower Ruftick, each one Eighth of a Module, viz. 7 Minutes 
 and a half. 
 
 Mod. Min. 
 
 The Height of five Rufticks is equal to - - - 03 45 
 
 The Height of the four Intervals of the Shaft be-i 
 
 tween them, is equal to ------- J 02 00 
 
 The Diftance from the Bafe to the firft Ruftick - 00 07 i 
 
 The Diftance from the Capital to the upper Ruftick 00 07 1 
 
 Sum Total 06 00 
 
 which is equal to the whole Height of the T'ufcan Shaft. 
 
 The Dorick Shaft, exclufive of its Bafe and Capital, hath 7 
 Diameters or Modules, which may be divided into Rufticks, as 
 exprefs’d in Fig . VI. 
 
 The Height of each Ruftick and Intervals of the Shaft be^ 
 tween being equal to each other, viz. 45 Degrees each, it there- 
 fore follows, that there can be but five Rufticks ; for if you 
 reduce the whole Height, 7 Modules, into Minutes, and divide 
 them by 45, the Height of each Ruftick ; the Quotient will 
 be p, and the Remains 15. 
 
 See the Operation. 
 
 One Module is equal to - 60 Minutes. 
 
 Which multiply ’d by - 7 
 
 The Shaft’s Height in Min. 420, which divide by 45 Min. the 
 Height of one Ruftick. 
 
 45)4*o(p 
 
 405 
 
 15 Remains. 
 
 Now as nine is the Quotient, and 1 j the Remains, therefore 
 ftye Rufticks and four Intervals is equal to the Quotient : and if 
 
 O 1 you 
 
1 OO 
 
 A Sure Guide to Builders . 
 
 you divide 15 the Remains by 2, the Quotient is 7 and half, 
 which is theDiftance that the lower Ruftick muft be placed above 
 the Bale, as alfo the Diftance that the Capital muft be above the 
 upper Ruftick. 
 
 The Height of the lonich Shaft, exclufive of the Bafe and 
 Capita], is S Diameters; and as the Ionick Order is in itfelf 
 feminine, it therefore muft have its Pmfticks lefs robuft, as thofe 
 of Fig. VII. and VIII. 
 
 The Height of the Interval contain’d between the Cindurc 
 and the lower Ruftick is 40 Minutes, as alfo is the Height of the 
 Capital above the uppermoft Ruftick. 
 
 Each Ruftick contains 20 Minutes in Height, and each Inter- 
 val between 40 Minutes ; fo that every Interval and the next 
 above Ruftick contains 1 Module compleat : And fince that the 
 firft Interval contain’d between the Cindure and lower Ruftick; 
 the upper Ruftick and Interval next above it under the Capital, 
 are each equal to 20 Minutes, and their Sums to one Module, 
 it therefore follows, that the Remains of the Shalt is equal to 6 
 Modules ; and fince that every Module contains 1 Ruftick and its 
 Interval, it therefore follows, that the whole Shaft muft contain 
 7 Rufticks and 6 Intervals, exclufive of the firft and uppermoft 
 of 20 Minutes each. 
 
 Fluted Columns are oftentimes bound with Cindures or Rufticks, 
 (as Fig. VIII.) but I cannot recommend the Pradice thereof ; 
 For as Flutes are made to reprefent a feminine Drefs and Slen° 
 dernels, their Beauty is deftroy’d, when they are broken into 
 many Parts by the Rufticks. ’Tis true that the Flutings of Co- 
 lumns do in fome meafure weaken the Shaft, and therefore 
 Rufticks may with lome Reafon be ufed, as a Means to help, 
 fortify or bind their Parts together; but confidering the ill Effed 
 that their Flutes have when fo often broken thereby, they are not 
 to be introduc’d in fluted Columns, where good Architedure is 
 intended. 
 
 The Projedure of Rufticks beyond the Upright of the Shaft, 
 fhould never be greater than the Projedure of the Cindure at the 
 Bafe, as the Ruftick EFGH,. (Fig. VI.) whole Projedure is 
 equal to the Projedure of the Cindure IK, viz. 3 Minutes 3 
 Quarters in the Fafcan , 3 Minutes and a half in the Dorick and 
 Corinthian , 3 Minutes in the Ionick y and 4 Minutes in the Com - 
 pfit.e.. And as the Shaft of Columns diminilh, fo will the 
 
 Rufticks 
 
lor 
 
 A Sure Guide to Builders, 
 
 Paifticks alio, by giving every Ruftick, as they advance in 
 Height, an equal Projedure. 
 
 There are but two Kinds of Rufb'cks, the one call’d Rabbet 
 Ruftick, as thofe of Fig. IX. whofe Channels are cut exactly 
 fquare, and the other call’d Miter Ruftick s, as thofe of Fig. IX. 
 Plate XII. whofe Channels are cut with an Angle of 45 Degrees, 
 which by Carpenters, Joiners, &c. is call’d a Miter, and indeed 
 fo is the half Quantity of any Angle, be it either acute, right, 
 or obtufe. 
 
 The next Thing to be conftder’d in relation to the Shafts of 
 Columns and Pillafters, is the Manner of delineating their Flutes 
 and Fillets, which were originally made by the Ionians to repre- 
 fent the Folds and Plaits of Womens Garments, when they built 
 a Temple in Honour of Diana. 
 
 The French call them Cannelures , Channellings, and are ufed 
 in the Dorick Order without Fillets, (as Fig. III. Plate XIV.) 
 but in the Ionick , Corinthian , and Co mg oft e Columns, they have 
 Fillets between them, (as Fig. I.) 
 
 The Number of Flutes in the Dorick Shaft is twenty, “ but in 
 the other Orders there are twenty-four. 
 
 To delineate the Flutes of Columns as they appear in the 
 Shafts, proceed as following : 
 
 PROBLEM XIX. 
 
 O divide and delineate the Flutes of the 
 
 (Fig. III. Plate XIV.) 
 
 Dorick Column. 
 
 1. Let AEZF reprefent the lower Part of the Shaft, and 
 A D the Diameter. Bifed AD in B, and with the Radius A B 
 defcribe the Semi-circle A CD, and divide the Circumference 
 thereof into 10 equal Parts, at the Points a , b , c , d y &c„. 
 Bifed each Part in the Points 1, a, 3, 4, 5, &c. and from the 
 Center, thro’ each of them, draw right Lines, as Bi, Ba ? 
 B3, Bj, &c. which will divide the Semi-circle into ten 
 
 equal Parts, and prepare it ready for to defcribe the Flutes 
 requir’d. 
 
 The Depth of Flutes are according to the Will of the Archi- 
 ted ; feme defcribe them on the oppolite Angle of an Equilateral 
 Triangle, as on the angular Point q of the Triangle zqa, and 
 
 others 
 
i 02 
 
 A Sure Guide to Builders . 
 
 others on the Center of a Geometrical Square, whofe Side is 
 equal to the Breadth of a Flute, as on the Center x of the Square 
 x y ozv. 
 
 To deferibe them on the angular Point of an Equilateral Tri- 
 angle, take za in your Compafles, and make zq and aq each 
 equal thereto, fo will q be the Center of the Flute za. With 
 the Radius By deferibe the Quadrant qrstvl , which will cut 
 the Lines Br, B j, B t y Be/, and B/ in the Points r, r, t y v y /, 
 which are the Centers on which you may deferibe the Flutes ab y 
 b c y c d , d e y and e y &c. But 
 
 To deferibe them on the Centers of Geometrical Squares, 
 •com pleat one Square, as zyow y and draw the Diagonals zw y 
 o y, in t effecting each other in x y which is the Center of the 
 Flute zo. 
 
 Then with the Radius Bx on B deferibe the Arch xponmk y 
 ■interfering the Lines Bp, B o, B n y B m, and Bk in the Points k y 
 m y n, o y p y which are the Centers whereon you may deferibe 
 the Flutes on y ni y ih y and hf 
 
 The Difference of the Depths of thefe Flutes are not very 
 confiderable, as may be feen in Fig. V. where the Flute f il is 
 deferib’d on the Geometrical Square, and the Flutey’ i / on the 
 triangular Point z j but when they are deferib’d on the Centers, 
 the Point of Interle&ion of the Circumference of the Column 
 with the Line B they are almoft Semi-circular, and much 
 deeper than either of the other two Kinds. This laft Kind of 
 Fluting is moft proper for the Ionick and Corinthian Shafts, when 
 they are tiled more for Beauty than Strength, than for the Dorick y 
 which being robuft and Herculean, would appear too much 
 weaken’d by thofe deep Channellings therein. 
 
 When you have deferib’d your Flutings on the Bafe of the 
 Shaft, whofe half Part is here reprefented by the Semi-circle 
 ACD, draw right Lines from the Angles of the Flutes parallel 
 to the upright Sides of the Shaft, as al y b¥L y cL y d M, <?N, fO y 
 hPy iQ, n R, and oS, which will truly reprefent the Several 
 flutes, as they appear diminilh’d in their Breadths from the 
 Middle to the Extreams thereof. 
 
 The Method of delcribing the Flutes and Fillets of Columns, 
 differs very little from the preceding, as will appear by the fol- 
 lowing (Problem . 
 
 PROBLEM 
 
 \ 
 
A Sure Guide to Builders , 
 
 IG 3 
 
 PROBLEM XIX. 
 
 HTO divide or defer ibe the Flutes and Fillets of the Ionick Shaft, 
 1 (Fig. I.) 
 
 i. Delineate part of the Ionick Shaft, asXXDF, with the 
 Aftragal XX. Bifed DF in E, and thereon, with the Radius 
 ED, deferibe the Semi-circle DGF. Divide the Circumference 
 DGE into two equal Parts in G ; alfo divide DG into fix equal 
 Parts at the Points HIKLM, and draw the Lines HE, IE, 
 KE, LE, and ME. 
 
 Imagine that an (Fig, II.) to be one of the fix Divifions of 
 the Semi-circle DGF as MG, then will the Lines dza 
 and kxn reprefent the Lines EG and EM, of Fig. I. then 
 divide an (Fig. II.) into eight equal Parts, as at 1, a, 3, 4, 5, 6 y 
 7, 8, and on a and with the Radius of ar or i/7, (that is, 
 three of thole Parts) deferibe the Flutes y z r and i x A, fo will 
 every Flute contain fix, and every Fillet two Parts j that is,, 
 every Fillet will become one third of a Flute. 
 
 Laftly, If from the feveral Divifions of the Flutes and Fillets 
 in the Circumference, you draw right Lines parallel to the Side 
 AD, and terminate them with Semi-circles at the Line AC, 
 where the Curvature of the Shaft ends, they will truly repre- 
 fent the Flutes and Fillets of one fourth Part of the Shaft as 
 requir’d. 
 
 The French oftentimes make fmall fquare Flutes between the 
 large circular ones, (as Pig. Y.) The Manner of delineating 
 them are the fame as thofe preceding, which is plainly exhibited 
 by the feveral parallel Lines, drawn from the Divifions of the 
 femi-circular Plan A D C to the Cincture H H. 
 
 The Flutings of Columns are generally fill’d from their lower 
 Parts up one third Part Qf their Height with Cables, or rather 
 cylindrical Bodies, as the lower Part CDEF of the Shaft 
 ABEF, (Fig. IX. Plate XLVIII.) call’d by the French 
 Sta/fs. Thefe Cableings are oftentimes enrich’d with curi- 
 ous carved Work, as reprefented by Fig. I. IV. Y. VI. VII. and' 
 their upper Parts are moftly finifh’d with the Curvature of a 
 Circle, (as Fig. VIII.) or a fmall Feftoon, (as Fig. II.) 
 
 P R O B L EM 
 
A Sure Guide to Builders. 
 
 PROBLEM XX. 
 
 divide and delineate the Flutes and Fillets of Pillafers. 
 
 The Flutes of Pi 11 afters are of equal Magnitudes, as alio are 
 their Fillets among themfelves. Every Pillafter ought to con- 
 fift of feven Flutes and eight Fillets, (as Fig. VIII. Plate XIV.) 
 wherein the Breadth of every Flute muft contain the Breadth of 
 three Fillets; and as every Fillet is equal to one third of a Flute, 
 we will therefore call every Fillet one, and every Flute three : 
 Now eight Fillets is equal to eight, and feven Flutes to 21, and 
 confeqnently the whole taken together equal to 2p. 
 
 The Method for readily dividing the Flutes and Fillets of 
 Piilafters, is as following : 
 
 1. Since every Pillafter contains 19 equal Parts, as before 
 proved, therefore draw a right Line at Pleafure, as AB, (Fig. 
 VI.) and with any final 1 Opening of your Compaffes fet off 
 25) Divifions, as 1,2, 3,4 ,5, 6, &c. 
 
 2. Take the Extent of the 25) Divifions in your Compaffes, 
 and with that Opening on A defcribe the Arch BL, alfo on B 
 the Arch A M, interfering the former in N, and compleat the 
 Equilateral Triangle ABN. 
 
 3. Continue out the Lines NB, NA at Pleafure, as to C 
 and D, and from the Angle N, thro' every Divifion of the Line 
 A B, draw right Lines out at Pleafure. 
 
 4. Take the Diameter of the Pillafter AB, (Fig. VIII.) and fet 
 it from N to C and from N to D, in Fig. VI. and as the Triangle 
 ABN is Equilateral, therefore the Triangle CDN is alfo Equi- 
 lateral, becaufe the Angle CND is the fame as the Angle AN B, 
 and confequently the right Line CD will be divided into 2p 
 equal Parts by the feveral dotted Lines, as the Line AB. 
 
 If you make Bo and Fv, (Fig. VIII.) as alfo A a and 
 E ", (Fig. VIII.) each equal to C a or r D, (Fig. VI.) and 
 draw the Lines ag and ov, they wilt determine the Breadth 
 of the two outmoft Fillets ; then make at, on y and gh> 
 a h. of Fig. VIII. each equal to ah or tjr } of Fig. VI. 
 
A Sure Guide to Builders . 
 
 and draw the right Lines nt and bh parallel to ov and ag y and 
 they will determine the Breadth of the two outmoft Flutes. This 
 done, fet off in like Manner the Breadths of the remaining Fillets 
 and Flutes, as exhibited in Fig. VI. and VIII. The lower Parts of 
 the Flutes muft terminate where the Curvature of the CinCture 
 begins, as at the Line E F ; and as the Flutes of Pillafters are 
 generally funk in the whole Radius of the Semi-circle, therefore 
 their Ends muft terminate with a Semi-circle, as in the Figure. 
 
 It has been the Practice of fome Architects to divide the 
 Diameters of Pillafters into 22 Parts, giving one Part to each 
 Fillet, and two to every Flute, as exhibited by Fig. IV. but I 
 cannot recommend the Practice thereof, they being nothing near 
 lb beautiful as thofe of Fig. VIII. whofe Fillets are one third of 
 the Flutes. There are alio many Workmen, who divide the 
 Face' of a Pillafter into five, fix, and fometimes nine Flutes, 
 which is entirely wrong, and contrary to the beautiful Rules of 
 found Architecture, and therefore not to be practis'd. 
 
 It is the Practice of fome Architects, to make the Shafts of 
 their Columns iii the Form of an OCtagon, or fome other Poly- 
 gon, (as Fig. VII.) which I cannot but recommend, for their 
 feveral regular Angles have a very agreeable EffeCt. 
 
 Having thus Ihew’d the various Methods of delineating the 
 feveral Orders of Columns and Pillafters, I lhall fpeak a Word 
 or two of fome other Devices, which have been introduc’d for 
 the Support of Entablatures inftead of Columns. 
 
 Thefe Devices are of three Kinds : The firft is Captives or 
 Slaves, (as Fig. XII. Plate XLIX.) which the ancient Greeks firft 
 introduc’d, to perpetuate the Memory of their Victories that 
 they had obtain’d over the rebellious Carians . 
 
 This PraCtice was alfo obferv’d by the Lacedemonians, who 
 vanquifh’d the ferjtans at Plat tea. 
 
 When an Entablature is fupported by a Male Captive, ’tis 
 call’d the Perjtau Order, and when by a Female Captive, ’tis 
 call’d the Cariatides Order, from the Greek Kariatydes , a People 
 of Caria. 
 
 But fometimes inftead of Captives, Angels, fabulous Deities, 
 as Hercules , Mars , &c. are introduc’d, denoting Strength, Va- 
 loifir, err. (as Fig . XIV. and XV. Plate XLIX.) 
 
 
 P 
 
 CHAP. 
 
A Sure Guide to Builders. 
 
 106 
 
 CHAP. V. 
 
 Of the General ‘Proportions incident to the Five Orders 
 of Columns in Architecture, according to the Propor- 
 tions laid down by Vitruvius, Palladio, Scamozzi, 
 Vignola, Serlio, Perault, BofTe, and M. Angelo. 
 
 HE feveral Orders of Columns, after whofe Pro- 
 portions we lhould form all our Buildings, were 
 originally given to ns by the Antients, and are five 
 in Number, viz. the Tttfcan, JDorick^ Jonick , Corin- 
 thian , and Compojitc. The moft ancient Order of 
 the five is the Dorick , which, as has been before obferv’d, was 
 firft modef d by Dorns King of AchaJjs , who built a magnificent 
 Temple of this Order in the City of Argos , and dedicated it to 
 the Goddefs Juno. Soon after the Building of this Temple, the 
 Ionians built another Temple in Honour of the Goddefs Diana , 
 wherein they plac’d great Number of Columns, which they 
 made fomething higher than thofe of the Dorick in the Temple 
 of Juno , in refped to their better reprelenting the airy Stature 
 of that Goddefs j and that this Rcprefentation might be the 
 more perfed, they therefore contriv’d its Capital with Volutes or 
 Scrolls, to reprefent thole beautiful Locks of Hair, which the 
 fair Sex of that Time were adorn’d with in their Head Attire. 
 
 They alfo fluted the Shafts of their Columns, to reprefent the 
 Folds and Plaits of her Garments, and added a Bafe thereto, to 
 reprefent the buskin’d Ornaments of her Legs and Feet. 
 
 For as the Dorick Order was made to reprefent both Strength 
 and Beauty, it was therefore originally made without any Bafe ; 
 fo that from hence we are taught, that the firft Bafe was the 
 Jonick , and that the Ionick Order is fo call’d from the Ionians , 
 who firft compos’d it, or rather copy’d and improv’d it fronvthat 
 originally built by King Dorns \ 
 
 The 
 

••• 'V . w 
 
 
 
 
 r 
 
 
 
 
 i 
 
 
 
 
 
 
 
I 
 
 A Sure Guide to Builders. 
 
 The Corinthian Order, being the next, was firft defign’d at 
 Athens, -and afterwards executed in the City of Corinth , and 
 therefore call’d the Corinthian Order. This Order is, of all 
 others, the moft noble and delicate, when truly perform’d. Its 
 Capital confifts of Acanthus Leaves, Volutes, &c . richly carved, 
 which originally were invented by' Calimachus , an Athenian Sta- 
 tuary, from a Hint that he receiv'd from a Basket, which was 
 plac’d on the Grave of a young Corinthian Lady, wherein her 
 Play-things, which fhe in her Life-time ufed to divert herfelf 
 with, were put, and cover’d over with a Tile, about which there 
 grew a Thiftle, or fome other-like Vegetable, (fome f Acan- 
 thus, or Branca Urjlna , Bearsfoot) whofe Leaves fomfd a very 
 near Appearance of that beautiful Figure in which the Corinthian 
 Capital now appears : And as the Growth of fome of the Leaves 
 were fuperior to others, and having grown to the full Height of 
 the Basket, were oblig’d, when the perpendicular Growth of 
 their Tops were hopp’d, by the over- hanging of the Tile, to 
 direct themfelves in a new and curved Direction, from thence 
 he took the firft Hint of the Volutes or Scrolls. The Abacus he 
 form’d from the Tile, and the Vafe or Vambour from the Basket. 
 And thus, fays Vitruvius , was the Corinthian Capital invented. 
 Thefe three Orders here mention’d, viz. the Dorick , lonick, and 
 Corinthian , are call’d Greek Orders, from their being firft made 
 in Greece ; and the others, viz. the Vufcan and Compojlte , Latin 
 Orders, for the fame Reafon. 
 
 The tfufean Order was originally taken or borrow’d from the 
 Dorick Order by the AJiatick, Lidyans, who, ’tis faid, were the 
 firft People that inhabited Italy, in that Part call’d Tufcany , 
 where they built divers Buildings after this plain and fimple 
 Order, and was therefore call’d the Tufcan Order. Vitruvius 
 makes mention of the Vufcan Column and Entablature, but don’t 
 fpeak one Word of a Pedeftal, or of any Gates or Doors built 
 of this Order ; and I believe that therefore Palladio did not 
 make any more than a Zoccolo or fquare Die for a Pedeftal to 
 this Order, that thereby its native Plainefs and Simplicity might 
 be truly preferv’d and maintain’d. 
 
 The Compofite Order, call’d by fome the Roman Order, and 
 by others the Italian Order, is compos’d of the lonick and Corin- 
 thian, having Voluta’s, as thofe of the lonick, and a double 
 Row of Leaves underneath, as in the Corinthian Capital : And, 
 
 P 2 indeed, 
 
io8 
 
 A Sure Guide to Builders. 
 
 indeed, I may further add, that the Compofite Capital has a Part 
 of the Dorick Capital in it ; for the Echinus or Ovolo of the 
 Dortch Capital, is alfo in the Compofite Capital, plac’d diredly 
 under the Abacus ; but as that of the Dorick is generally plain,, 
 this is enrich’d with carved Eggs and Anchors, as term’d by 
 Workmen. Vitruvius makes no mention of this Order as diftind 
 from the .Corinthian, but fays, that oftentimes the Shaft of the 
 Corinthian Column had a Capital plac’d thereon, which was com- 
 pos’d of feveral Parts taken from the Dorick , Jonick , and Corin- 
 thian Capitals, as before obferv’d. 
 
 Having taken this general View of the five Orders, I will now 
 proceed to explain them particularly ; and altho’ the Dorick was 
 the Original of all others, yet, according to Cuftom, I will be- 
 gin with the fiufcan, and afterwards the Dorick , Ionick , Corin- 
 thian , and Compofite , as they are generally underftood, according 
 to their feveral Degrees of Stature. 
 
 L Of the TUSCAN ORDER. 
 
 1. As this Order is of all others the moft plain and rural, k 
 has been therefore chiefly ufed in fuch Buildings where Strength 
 and Solidity were requir’d, <• as City Gates, Magazines, Bridges, 
 Prilbns, &c. nay even in the Portico’s of Churches, as that grand 
 Portico of St. fiauT s Covent-Garden , built by that celebrated 
 Archited Inigo Jones , and for illuftrious Decorations, as the 
 Columns of fir a] an and Antoninus , now Handing in Rome , and 
 that of fiheodofius at Confiantimple : In brief, this Order, with 
 refped to its Simplicity, is truly grand, when judicioufly plac’d 
 in Portico’s, &c. and the lower Storks of magnificent Buildings. 
 
 2. The Height of the fiufcan Shaft, including its Safe and 
 Capital, is 7 of its Diameters at the Bafe ; and the Dimi- 
 nution thereof at the Aftragal, one quarter of its Diameter. 
 The Height of its Bafe, including the Cindure, is always equal 
 to half its Diameter at the Bafe, as alfo is the Height of the 
 Capital, exclufive of the Aftragal, at the Top of the Shaft. 
 The Height of the Entablature fhould be exadly one fourth 
 Part of the Column’s Height, viz. one Diameter and three 
 Fourths. 
 
 Now 
 
A Sure Guide to Builders. 
 
 Now feeing that the Height of the Shaft contains 7 Modules 
 or Diameters, which being multiply’d by 4, (the Quarters in a 
 Module) the Product is 28 ; and as the Height of the Entabla- 
 ture is equal to one Diameter 3 quarters, which are equal to 7 
 quarters ; therefore the whole Height of the Order, accounted 
 in Quarters of a Module, is equal to 35. And fince that the 
 whole Height of the entire Order is equal to 35, therefore when 
 you are to proportion this Column with its Entablature to any 
 given Height, divide the Height given into 35 equal Parts, of 
 which give 7 to the Height of the Entablature, and the Re- 
 mainder 28 will be the Height of the Column. 
 
 The Module or Diameter of the Column at its Bafe, will be 
 equal to 4 of the 35 Parts ; which being divided into 60 equal 
 Parts, will be Minutes, by which you may proportion the Height 
 and Projedure of every Member as requir’d. 
 
 The Pedeftal, when any is uied, fhould be plain, as 
 before obferv’d ; for in Fad it Ihould be no more than 
 a Subplinth, as in Palladio’s Tufcan Order, having its Height 
 equal to the Diameter of the Column at its Shaft, and 
 Projedure 3 Minutes more than that of the Plinth. When 
 you are to ered this Column on a Pedeftal with its Entablature, 
 divide the given Height into 35) equal Parts, of which the 
 lowermoft 4 will be the Height of the Pedeftal, the next 28 the 
 Height of the Column, and the remaining 7 for the Height of 
 the Entablature.. 
 
 3. The Intercolumnation of this Order, that is, the Diftance 
 that the Columns fhould be plac'd from each other, is greater in 
 this than in all other of the Orders ; becaufb its Architrave is 
 generally made of Wood, and therefore hath an Intercolumna- 
 tion of 4 Diameters, as the Columns IF, {Fig. V. Plate 
 XXXII.) or 4 Diameters 45 Minutes, as AB, {Fig. IV. Plate 
 XXXIV.) 
 
 This Intercolumnation Vitruvius calls Arceoflyle, from the 
 Greek Aracos y thin-fet or rare, and Stylos , a Column. 
 
 Note, Vhe Intercolumnation of Columns , is accounted from the 
 centeral Lines of the Columns , and not from their Uprights , 
 as fome imagine , 
 
 iop 
 
 When 
 
no 
 
 A Sure Guide to Builders. 
 
 When you are to introduce Arches between the Columns, as 
 FB, (Fig. IV. Plate XXXII.) the Intercolumnation may be 4 Di- 
 ameters and a half, as there exhibited, or 5 Diameters 15 Minutes, 
 (as Fig. III. Plate XXXIV.) The Aperture or Opening K 
 ( Fig.V . Plate XXXII.) mull be 3 Diameters and 10 Minutes 
 in Breadth, and 4 Diameters in Height, to the lower Part of the 
 Impoft. 
 
 Now fince the Breadth of the Aperture K is 3 Diameters 10 
 Minutes, and the two Semi-diameters of the Columns make one 
 Diameter more, their Sum is equal to 4 Diameters 1 o Minutes, 
 which being fubftradled from the whole Intercolumnation 4 Di- 
 ameters and a half, the Remains are 20 Minutes, one half of 
 which is 10 Minutes, for the Breadth of each Pied-roit CE. 
 
 For the Form and Proportions of the i'll] can Impofts and Ar- 
 chitraves, Vide Plates XXX. and XXXI. 
 
 Some Archite&s allow an Intercolumnation of 6 Diameters 
 40 Minutes, becaufe the Crown of the Arch is a Support to 
 the Architrave ; and at fuch Times the Breadth of the Aperture 
 Ihould be 4 Diameters 40 Minutes, and each Pied-roit or Pil- 
 lafter 30 Minutes. But 'tis reafonable in thefe great Interco- 
 lumnations to place the Columns in Pairs, as here exhibited. 
 
 II. Of the DORICK ORDER. 
 
 s. The folid Beauty and Herculean Afpect of this moft antient 
 Order, has introduc’d it into the moft grand and majeftick Build- 
 ings, both abroad and at home ; for as the Beauty of an Order 
 conftfts in having its principal Parts well proportion’d to one 
 another, which is in this illuftrated, ’tis therefore that this 
 Order has been fo highly efteem’d in many Parts of the World, 
 as to be call’d the very Order of Orders. 
 
 When the feveral Members which compofe the principal Parts 
 of an Order, are many and ftnall, or few and large, they either 
 divide and fcatter, or prefs together the feveral Rays of Sight in 
 fuch a Manner, that the whole appears either in a Confufion, or 
 a heavy lumpy Mals of Stone, &c. 
 
 But 
 
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A Sure Guide to Builders. 1 1 1 
 
 But to the great Advantage of this Order, it hath its principal 
 Parts and feveral Members beautifully proportion'd, and in fuch a 
 Manner, that when entirely plain, they have a very graceful 
 and majeftick Afped, and no lefs mafculine when adorn’d with 
 the Enrichments of carved Ornaments. 
 
 n. This Column was at firft but 6 Diameters in Height, being 
 taken from the Proportion of human Bodies, whofe Heights are 
 generally equal to fix Times the Length of the Foot ; but this 
 Height being diflik’d, they added another Diameter to its Height, 
 which was no fmall Addition to its Stature. This additional 
 Beauty encourag’d them to make further Trials, and add one 
 Diameter more to its Height, which gave it that agreeable and 
 folid Alped with which it now appears. But this additional 
 Diameter was always added difcretionally, i. e. when fet alone, 
 for in Portico’s, &c. they never gave them any more than 7 
 Diameters. 
 
 This Order Waa originally made Avithout any Bale, which 
 might probably be done with refped to its robuft Alped, which 
 being like that of Hercules , was therefore, like him, reprefented 
 on his bare Feet. 
 
 But as a Bafe adds a Grace to a Column, and ftrengthens its 
 ftanding alfo, therefore modern Architeds do oftentimes give it 
 that Bafe which Vitruvius calls Httic, whole Proportions are as 
 follow : 
 
 The Height of the Attic Bafe is equal to the Se mi-diameter of 
 the Shaft at its Bafe, viz. equal to 30 Minutes. The feveral 
 Members which compole this Bafe are fix in Number, viz. a 
 Plinth A, (Ftg. XVIII. Plate X.) two Torus’s B and F, a Scotise 
 D, and two Fillets E and C. The Height of the Plinth is equal 
 to one third Part of the whole Height, viz. 10 Minutes, and 
 the remaining Part 20 Minutes being divided into four Parts, one 
 fourth Part thereof, viz. 5 Minutes, is the Height of the upper 
 Torus F, and half the remaining 1 5 Minutes, viz. 7 Minutes: 
 and a half, is the Height of the lower Torus B ; the Remains 
 left for the two Fillets E and C, and Scotias D, being 7 Minutes 
 and a half, give 1 Minute to each Fillet, and the remaining 5 
 Minutes and a half to the Scotias D j and thus are the Heights of 
 the feveral Members determin’d, 
 
 Thgr 
 
ii2 A Sure Guide to Builders . 
 
 The Proje&ure of the Plinth and lower Toms, was originally 
 one fourth of the Diameter at the Bafe, beyond the Upright of 
 the Column, being 45 Minutes from the Axis or centeral Line, 
 which being rather too great, Vitruvius did afterwards make it 
 with lefs Projecture, and ’ris now fettled at 40 Minutes from the 
 centeral Line, which is one fixth Part of the Diameter from the 
 Upright of the Column. 
 
 P. But before you proceed any further , pray let me know the 
 Etymology of the Word Scotia ? 
 
 M, I will. The Word Scotia comes from the Greek Skotos y 
 Darknefs, as being plac'd under the Torus F, where ’tis fome- 
 thing darken’d thereby. ’Tis alfo Call’d tfrochilos, or 7 *rochilus y 
 from the Greek , a Fully, which its Curvature was fiippos’d to 
 refemble. 
 
 I will now proceed to the other Parts of this Order. 
 
 And firft of its Capital, whofe Height is always equal to the 
 Semi-diameter of the Column at its Bafe, viz. 30 Minutes, con- 
 futing of three Parts, viz . an Abacus, an Ovolo, and Freeze, 
 which Vitruvius made equal to each other, viz. 10 Minutes 
 each, including the Annulets with the Ovolo or Echinus. See 
 Plate XVII. 
 
 The Architrave of this Order was antiently made with one 
 Facia only, as that of Vitruvius and Vignola in Plate XVIII. but 
 modern Archite&s have divided it into two, as may be feen in 
 the Orders of Palladio , Scamozzi , &Cc. 
 
 The upper Part of the Architrave being bound with its Tenia 
 or Fillet H, which Vitruvius calls Platte~band y hath its pendant 
 Drops or Gutta’s nmop plac’d dire&ly under the extream Parts 
 of the Channels in the Triglyph y and altho’ thofe Drops are 
 a Part of the Architrave, yet, by their Pofition, they appear 
 as if they had flow’d from the Channels of the Triglyph, thro’ 
 the Tenia and fmall Fillet under it. 
 
 It oftentimes happens that the Triglyphs cannot be introduc’d 
 in the Freeze, (as will appear when I come to the Intercolumna- 
 tion of this Order) and then, at all fuch Times, thefe Gutta’s or 
 Drops are left out. 
 
 The 
 
A Sure Guide to Builders . 
 
 The Triglyphs of this Order being Ornaments of the Freeze, 
 are always plac’d exadly over the Column, and their Breadths 
 are always equal to half the Diameter of the Column at its Bafe : 
 Their Heights are always determin’d by the Height of the 
 Freeze, which fhould be never more than three fourths of a 
 Diameter, or 45 Minutes. 
 
 *The Breadths of the Channels, which Vitruvius calls Graveurs y 
 are each one lixth Part of the whole Breadth, as alfo are each 
 of the intermediate Spaces between them, and the Demi-graveurs 
 or Semi-calicula’s, that is, the two angular Hollows, are each 
 equal to one twelfth Part of the whole Breadth. Now fince 
 that the three Spaces, and the two Channels, are each equal to 
 one fixth Part of the whole Breadth, therefore divide the whole 
 Breadth into 1 1 equal Parts, and then giving the two outward 
 angular Channels, each one Twelfth, and the others each one 
 Sixth, you will divide the Triglyph into its proper Channels, as 
 requir’d. 
 
 The Word Triglyph comes from the Greek fignify- 
 
 ing a three fculptur’d Piece, quajt tres hahens Glyphas , call’d by 
 the French < Triglyphe y and by the Latin Vriglyphus. This Orna- 
 ment was firft ufed in the Delphic Temple, and was there plac’d 
 as a Reprefentation of an Antick Lyre y which, ’twas faid, Apollo 
 invented. 
 
 The Diftance from one Triglyph to the next adjacent, are 
 generally equal to then Height, and thereby the Spaces between 
 them will become exadly fquare, as W, (Fig. I. Plate XV.) 
 For the next Triglyph ;s conftitutes a Geometrical Square ; but 
 the Diftance /from the outward Part of the Triglyph F, to the 
 utmoft Projedure of the Freeze A y is never any more than one 
 third Part of the Triglyph’s Breadth. 
 
 Thefe fquare Spaces between the Triglyphs, as the Square 
 W, are call’d Metops y from the Greek ju.irev 5 At fxenv 6 tm, and 
 for amen , Interval 1 um y fignifying the Front ; or |xsto7w, a Space 
 or Interval between every Triglyph in the Freeze of the Dorick 
 Order. 
 
 Now altho’ that the Beauty of thefe Metops confifts in being 
 truly fquare, yet when we Hand very near to the Building, they 
 do not appear fo ; for excepting that the Eye is placed level with 
 the Line A, exa&ly level with the upper Part of the Tenia B, ’tis 
 impoflible that they can appear fquare, becaufe the Projedure of 
 
 Q_ the 
 
ji Sure Guide to Builders. 
 
 the Tenia B interpofes between. But this I will demonftrate : 
 Suppofe CD to be the Ground Line, and Handing at C, you 
 view the Tenia B, which projefting before the Face of the 
 Freeze, caufes the Ray of Sight CB to cut the Freeze in A, 
 therefore all that Part of the Freeze below the Line A, will be 
 eclips’d by the Tenia B, and therefore the Height of the Freeze 
 or Metop will appear to be no more than AK ; but if you 
 move further back, as to D, then the Ray of Sight DI palling 
 by the Tenia B, will cut the Metop in the Point I, and then 
 the Height of the Freeze will appear equal to IK. Now fince 
 that the more remote a Building is view’d, the higher the Freeze 
 appears, ’tis therefore impoffible to ailign any additional Height 
 to them, as Monf. le Clerc advifes, excepting that a particulai 
 
 Point of View be affign’d. , . . . . . 
 
 The Ornaments that were firft ufed by the Antients in their 
 Metops, were the Sculls of Beafts, Bafons, Vafes, and other 
 Inftruments ufed in facriflring, and even to this Day they, are 
 ufed in many Buildings of Note, tho’ (in my humble Opinion) 
 very improperly; and if I might be permitted, I would, inftead 
 thereof recommend, for a Nobleman’s Villa, the feveral Parts of 
 his Family’s Arms, Creft, &c. ; for Banquetting-Houfes, Fruits, 
 Flowers, &c . ; for Forts, Caftles, &c. Trophies of War : And in 
 Portico’s of Churches with human Skulls, Thigh-bones, Bibles,, 
 Hour-glalfes, Lamps not extinguilh’d, and the Hieroglyphick 
 Serpent of the Egyptians , and other Emblems of Mortality ; but 
 within Churches, and other Places of Worlhip, Cherubims, 
 Glories Doves, and other Emblems of Divine Worihip. 
 
 The’ Cornice, which is plac’d over the Capital of the Tri- 
 glyphs, is made after three feveral Manners ; as firft . plain, with- 
 out any Ornaments, as thole of Vitruvius and Palladio . Secondly , 
 With Dentils, as that of Scamozzi and Fignola. Thirdly and 
 laftly With the Ornament of Modilions or Mutils only, as 
 A A which is one and the fame Ornament; but indeed 
 the ’ Modilions are more properly belonging to the Corin- 
 thian Order, where they are richly adorn’d with carved Work, 
 and are there oftentimes call’d Cantalivers , whereas in the Dorich 
 they Ihould be plain, and when ufed in the Ionick or Compoftte , 
 a {ingle Leaf underneath at the moft. Nor are Dentils an origi- 
 nal Ornament of this Order, being never ufed by the Antients, 
 
 but borrow’d from the Ionick^ to whom they more properly be- 
 long; 
 

 I . ■ ■ 
 
A Sure Guide to Builders. 1 1 $ 
 
 long ; but, however, I can’t but recommend them, jf they are 
 perform’d after a Workman-like Manner. 
 
 The Word Dentil comes from Dens , a Tooth, and therefore 
 Vitruvius calls them a Gang of Teeth. The fquare Facia or 
 Member wherein they are cut, is call’d the Denticule y from the 
 Latin Denticulus. 
 
 When this Cornice is enrich’d with Modilions, they are to be 
 plac’d direCtly over the Triglyphs, and of the fame Breadth ; 
 
 And as the Architrave under each Triglyph is enrich’d with 6 
 Gutta’s or Drops, fo likewife are the Soffita’s of the Modilions 
 with 3 <5 Drops, (as Fig. VI. Plate XLVII.) whofe Vertex’s 
 or Points are a Tittle funk, or let into the Cieling or under 
 Surfaces thereof The intermediate Spaces between each Mo- 
 dilion may be enrich’d with Trophies, and fiich-like Ornaments, 
 as were recommended for the Triglyphs • but the antient Orna- 
 ments for thofe Spaces were Thunderbolts, herein exhibited, and 
 Vitruvius exprefly fays, “ Nothing muft be cut unlefs it be 
 u Thunderbolts.” A very proper Ornament for Temples, Ca- 
 thedrals, &c. but, in my humble Opinion, for no other Edifice 
 whatfoever. 
 
 The Diminution of the Shaft at its Aftragal, according to the 
 general Pra&ice of Architects, is one Fifth of the Shaft’s Di- 
 ameter at its Bafe, viz. 11 Minutes, which is a good Proportion 
 of Diminution, when the Column Hands on the Ground y but 
 when elevated in the fecond, third, or fourth, &c. Stories, the 
 Diminution of one Fifth will be found to be more, and indeed 
 too much, as it advances in Height. 
 
 Vitruvius takes fome Notice of this, faying, that great Pillars, 
 which have their higheft Part further from the Eye, muft have 
 their Diminutions leffer than thofe that are nearer, according to 
 the ordinary EffeCt of Perfpe&ive ; but he has not laid down 
 any pofitive Rule of Perfpective to determine fuch Diminu- 
 tions. 
 
 The Rule which he has deliver’d is abfolute, without any 
 Mathematical Reafon, as following : 'That a Pillar of 15 Feet 
 Height , . ought to have in the Upper Part 5 Parts op 6, into which 
 the Diameter of the Bafe of the Pillar is divided {viz. 10 Minutes). 
 that which is prom 1 5 to 20 Feet y ought to have 5 and a half of 
 the 6 and an half of the Diameter ; that which is from 30 to 
 
 ( v ' . ; , - . ■ ■ < a «- ... 
 
n 6 A Sure Guide to Builders 
 
 40, mu ft have 6 and an half of 7 and an half of the Diameter • 
 that which is from 40 to 50, mufl have 7 or 8 of the Diameter . * 
 
 ’Tis a common Saying among moft People, that ObjeCts 
 view'd on high appear lefs than they really are , becaufe (fay they) 
 the Rays of Sight are contracted : Which is true ; but why they 
 are, very few knows, and none that I know of has ever yetmado 
 publick. 
 
 Now feeing that the Diminution of the Shafts of Columns 
 wholly depends upon the Height of their Situation, I will here 
 demonftrate the Reafon, why their upper Parts appear to be 
 contra&ed or inclining to one another. 
 
 1. Let G1PR (Fig. II. Plate XV.) reprefent a Cylinder, 
 Handing perpendicular upon the Horizon FR ; alfo let E repre- 
 fent the Height of the Eye plac’d at an affignM Point of Yiew, 
 from which draw the horizontal Ray E N, parallel to the Hori- 
 zon, unto the centeral Line of the Column QH in N ; likewife 
 draw the vilual Ray EH. 
 
 2. Draw a right Line at PKalhre, as Sa, (Fig TV.) making Set 
 equal to the Ray EH, (Fig. II.) and Sb equal to the Horizontal 
 Ray EN. 
 
 3. Make a Y, aZ, and ^T, 6 X, each equal to the Semi- 
 diameter of the Cylinder, as MN or NO, and draw the right 
 Lines SY, SZ, and ST, SX; then will the right Lines SY 
 and SZ reprefent the two Rays of Sight, under which the Di- 
 ameter of the Cylinder GI is feen ; and the right Lines ST and 
 S X will reprefent the horizontal Rays of Sight, under which 
 the Diameter M O is feen. 
 
 4. On S, with the Radius of any Circle, defcribe an Arch, as 
 d f and join T Y and XZ, which will be parallel to each other. 
 
 5. Now lince that the right Line YZ is equal to the Diameter 
 G I, and at the fame Diftance from S, as the Eye E is from H 
 and is feen under the Angle cSe, which is lefs than the Angle 
 dSf which is the Angle under which TX is feen, (which is 
 equal to the Diameter MO) therefore YZ will appear equal in 
 Diameter to Y W, as being feen under the fame Angle, and 
 confequently lefs than T X, which is equal to the Cylinder’s 
 Diameter at MO. 
 
 6 . Now lince that VW, being feen at S, (which is equal to 
 the Diftance of the Eye E from the Cylinder N) appears equal 
 to YZ j therefore making KH and HL equal to b V and bW, 
 
 and 
 
A Sure Guide to Builders. 
 
 and drawing the right Lines KR and LP, they will reprefent 
 the true Appearance of the Cylinder, with its gradual Diminu- 
 tion, as it feems to have being view’d at E ; and fo in like 
 Manner being view’d at any other Place. 
 
 Now feeing that equal Objeds view’d on high, appear di- 
 mmilhd when they really are not, it therefore follows, that 
 Columns which are diminilh’d at their Aftragals, mull appear as 
 much more contraded than they really are, according to the 
 Quantity of their real Diminution : Hence ’tis evident that the 
 Columns . are the lefs they ought to be diminifh’d. 
 
 . The ^ lmln ution aflign’d by Architeds for the Dorick Order 
 is one Fifth of the Diameter at theBafe, for the Ionick one Sixth' 
 tor the Corinthian one Seventh, and for the Compose one Eighth : 
 But thefe are in general confider’d as when Handing on the 
 Ground in the firft Story. And fince that Columns in the fecond 
 Story are double the Height of the firft, therefore make them in 
 their Diminution proportionably lefs, viz. if the Dorick Order 
 
 C- t ?u bC P i. ac ^ e lec0 !? d St0f y> let its Diminution be but one 
 Sixth, liiftead of one Fifth, as when in the firft Story • and 
 
 if t0 be P lac ’d in the third Story, its Diminution 
 ftould be but one Seventh, and when in the fourth Story one 
 
 The bell proportion’d Height for the Entablature is one 
 quarter of the Column’s Height, viz. two Diameters ; and if 
 
 you confider every Diameter contain'd in the Height to be di 
 
 vided into three equal Parts, as the 7 ufcan Order was before into 
 four equal Parts, then the Height of the Column alone will be 
 a 4 , and with its Entablature 30.- And altho’ the Antients made 
 no ufe of a Bafe to this Order, yet the Moderns have added not 
 only a Bale, as has been before obferv’d, but a Pedeftal alfo • 
 whofe Height, (as Fignola oblerves) including its Bafe and Ca- 
 pital, mould be equal to one third Part of the Height of the 
 Coiumn, including its Bafe and Capital, viz. two Diameters and 
 two Thirds, which is equal to 8 third Parts. 
 
 u If u^ U -n add 8 thi f dParts > the Height of the Pedeftal, to so 
 the third Parts contain’d in the Column and Entablature, their Sum 
 
 • S e 5 U 4 al «. t0 i 38 j therefore whe ' n y° u are to erect a Column, with 
 its Pedeftal and Entablature, divide the given Height into 3 8 
 
 and a / a f ItS fh° f T? Vhl m glVC 8 f ° the Pedefta1 ’ 2 4 to the Column, 
 and 6 to the Entablature. Again, If you are to proportion 
 
 the 
 
 n 7 
 
A Sure Guide to Builders . 
 
 the Column with its Entablature, without a Pedeftal, divide the 
 given Height into 30 equal Parts, of which give 24 to the 
 Height of the Column, and 6 to the Entablature. And laftly, 
 With the Column and Pedeftal, without the . Entablature, divide 
 the given Height into 32 Parts, of which giveS to the Pedeftal, 
 and the Remainder 24 to the Column, with its Bale and Capital; 
 The feveral Heights and Projedures of the Members are to be 
 fet off from the Minutes of the Diameter, which is equal to 3 of 
 the aforefaid Parts, by which you proportion d the Pedeftal, 
 Column, and Entablature. 
 
 3. The Intercolumnation of this Order is always regulated by 
 the Number of Triglyphs in the Freeze : As frfl, It may. be of 
 2 Diameters and 20 Minutes, where there is but one Triglyph 
 between thofe over the Columns. Secondly , It may be of 3 
 Diameters and 18 Minutes, as AB, {Fig. VIII. Plate XXXII.) 
 where there are two Triglyphs between thofe over the Co- 
 lumns. And liijlly y It may be of 4 Diameters and 24 Minutes, 
 as B C, where 'there are three TrigLyphs between thofe over 
 the Columns. Thefe are the feveral Intercolumnations when 
 the Freeze is enrich’d with the Triglyphs ; but when they 
 are not regarded, the Intercolumnation is three Diameters 
 precifely. 
 
 When the Dorick Arch is to be made, the Intercolumnation 
 muft be greater than either of the preceding, and may be either 
 5 Diameters and a half, (as Fig. II. Plate XXXII.) where there 
 are four Triglyphs between the Columns ; or 7 Diameters, 
 (as Fig. IV.) where there are five Triglyphs over the Arch. 
 For the Impofts of this Order, fee Fig. XII. and XIII. Plate 
 XXX. and XXXI. 
 
 III. Of the IO NICK ORDER. 
 
 As the Dorick Order was firft form’d to reprefent the robuft 
 Afped of a well-proportion’d Man, fo likewife was this Ionick 
 Order made to reprefent the airy Stature or feminine Slendernefs 
 of a well-made Woman ; and in order thereto, the Iomdm gave 
 it 8 Diameters in Height, at the Time when the Dorick had but 
 y •_ gut the Antients loon after added half a Diameter more, and 
 fince them, the Moderns have added another , lo that now the 
 
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A Sure Guide to Builders. 
 
 Height of the Shaft isp Diameters, which gives it an elegant 
 and ftately Stature. 
 
 And to compleat the Beauty of this Order, the Antients con- 
 triv’d a Bafe, which was the very firft that was made ; for the 
 Dorick Order* which was then the only Order extant, had not 
 any. 
 
 To offer a Profile of this firlt contriv’d Bafe would be an I'm-* 
 pofition, fince no two of our antient Archite&s can agree therein ; 
 •but however I will give you the Proportions of the Bafe, which 
 Vitruvius aflign’d for it, as following : 
 
 The Breadth of the Ionick Baje (faith he) is the Diameter of 
 the Pillar , to which is added a \th and an 8 th Part , viz. 1 5 
 Minutes^ and J Minutes and a half ; whofe Sum is 22 Minutes 
 and a half, and the whole Breadth equal to one Module 22 Mi- 
 nutes and a half, and its half Sum 41 Minutes and a quarter, 
 which is the Proje&ure from the centeral Line or Axis of the 
 Column. The Height is equal to the Semi-diameter of the 
 Shaft of the Bale, viz. 30 Minutes, of which he allowed one 
 Third, viz. in Minutes, for the Height of the Plinth 3 the 
 other tw r o third Parts remaining he divided into feven equal Parts, 
 of which he gave three to the Torus, and plac’d it at the upper 
 Part next to the Cin&ure of the Shaft ; the remaining 4 Sevenths 
 he divided into two equal Parts, and made the upper Scotia with 
 its Aftragal equal to one Part, and the lower Scotia with its 
 Aftragal equal to the other Part ; the Height of each Aftragal 
 muft be one eighth Part of the Scotia, whofe Proje&ure muft be 
 the eighth Part of the whole Bafe added to the fixth Part of the 
 whole Diameter. Thus far our Father Vitruvius. 
 
 The Shaft of this Order is generally fluted with Fillets be- 
 tween them, (as Fig. I; Plate YL. IV.) containing 24 in Number. 
 The common Diminution of the Shaft at the Aftragal, is one 
 Sixth of the Diameter at the Bafe ; but when ’tis plac’d in a ad 
 Story to be view’d from the Ground, it fhould diminilh but one 
 Seventh ; and when in a 3d Story one Eighth, as before was faid 
 of the Dorick Column. 
 
 The Capital is compos’d of an Abacas, (which Vitru- 
 vius fays) muft have in its Square the Diameter of the Bot- 
 tom of the Pillar , and one eighteenth Part , which is 1 Di- 
 ameter 3 Minutes 7 Twelfths) a Volute, and an Ovolo. The 
 Voluta’s which firft adorn’d this Capital, were plac’d dire&ly 
 
 parallel 
 
120 
 
 A Sure Guide to Builders . 
 
 parallel to the Front of the Column, as . reprefented in the Ca« 
 pital after the Manner of the Antients, ( Plate XLIX.) after 
 which Scamozzi contriv'd to place the Voluta’s in an angular 
 Pofition with the Front of the Column, making an Angle of 45 
 Degrees ; by which means every Side of a Column has the very 
 fame Effed, as the Fronts and Rears of thofe plac’d after the 
 •antient Manner. 
 
 The moll expeditious and corred Method for deferibing the 
 Voluta of this Capital is by 25 Centers, as following. (Fig. 
 VI. Plate XV.) * 
 
 1. Having delineated the Heights and Proje&ures of the 
 feveral Members which compofe the Capital, let fall the perpen- 
 dicular Line AD from A, the under Part of the Abacus, and 
 thro’ the Middle of the Aftragal draw the centeral Line EC, 
 interfeding the Cathetus or Perpendicular N D in B. 
 
 2. On B, with the half Breadth of the Aftragal, deferibe the 
 Circle WM, wherein inferibe a Square, as A BCD. (Fig. 
 VI.) 
 
 3. Divide AB into two equal Parts in 1, as alfo AC in 2, 
 BD in 4, and CD in 3, and draw the Diameters 1 3 and 2 4. 
 
 4. Divide each Semi-diameter into 3 equal Parts, at the Points 
 3 p, 6 10, 128, 11 7 ; alio make 1 a 9 2 b 9 4^, 3 c, each equal 
 to one Fourth of 15, 5 p, &c. alfo make je, pg, 6f iok, 
 7 b, 1 1 /, 8 h, and 1 2 0, each equal to 1 a or 2 £, &c. and thus 
 will you have fix’d your 24 Centers, on which you may deferibe 
 the Voluta truly diminifh’d, as following : 
 
 1. Set one Foot of your Compafles in the Point 1, and ex- 
 tending the other to A, deferibe the Arch A B, and on the Point 
 a the Arch N O. 
 
 2. On the Point 2, with the Radius 2B, deferibe the Arch 
 BD, and on with the Radius bO, the Arch OP. 
 
 3. On the Point 3, with the Radius 3D, deferibe the Arch 
 DE, and on c the Arch PQ^ 
 
 4. On the Point 4, with the Radius 4E, deferibe the Arch 
 E F, and on d the Arch QJR. 
 
 5. On the Point 5, with the Radius jF, deferibe the Arch 
 F G, and on e the Arch RS. 
 
 6 . On 
 t 
 
121 
 
 A Sure Guide to Builders . 
 
 6 . On the Point 6, with the Radius 6G, defcribe the Arch 
 OH, and on f the Arch ST. 
 
 7. On the Point 7, with the Radius 7 H, defcribe the Arch 
 H I, and on h the Arch T V. 
 
 8. On the Point 8, with the Radius 8 1 , defcribe the Arch IK, 
 and on i the Arch V W ; and then performing the like Opera- 
 tions on the Points yg and 10 k, you will compleat the Thiclc- 
 nefs of the Lift of the Volute with its true Diminution, as 
 requir’d. 
 
 The Eye ‘of the Volute fhould be always made equal in Di- 
 ameter to the Height of the Abacus, exclulive of its Fillet or 
 Lift, and the Center of the Eye fhould alfo be on the ccnteral 
 or middle Line of the Aftragal \ but very often le Clerc and 
 fome others place the Center of the Eye againft the lower Line 
 of the Echinus or Ovolo, as in Fig. V. which, in my humble 
 Opinion, is nothing near fo graceful as that of Fig. VI nor is 
 the Curvature of the Lift fo pleafant. 
 
 The Eye of the Volute is oftentimes carved, and very often 
 they have Feftoons of Fruit or Flowers hanging therefrom, 
 according to the Cuftom of the Antients, when they ufed this 
 Order in Banquetting Houles, &c. 
 
 The Height of this Capital is arbitrary, as alfo its Comp'ofition, 
 for even the Antients themfelves vary’d very much therein, as 
 may be fceu by the Capitals of the Antients, (in Plate XL.) 
 where they have introduced the Addition of a fquare Fafcia in 
 the Abacus, more than now practis’d, and a Freeze under the 
 Ovolo, after the manner of the Dorick Capital, which they 
 enrich’d with Roles, &c. 
 
 And as the lonick Column was taken from the Dorick, whofe 
 Capital conlifts of a Freeze or Neck above the Aftragal, ’tis very 
 reafonable to believe, that the preceding Capital is after the firft 
 Model that was made from, the Dorick Capital ; for the Diffe- 
 rence is no more than the Volutes, which the Ionians introduced 
 to reprefent the Head Attire of the Fair Sex, under whofe Sta- 
 ture this Column was originally reprefented. 
 
 The Architrave of this Order is divided into 3 Fafcia’s, which 
 are crown’d with a Cymatium next to the Freeze. The Propor- 
 tions of thefe Fafcia’s are various, as may be feen by the Archi- 
 traves laid down by Vitruvius, Palladio , Scamozzi , and Vignola , 
 Sertio, Perault , Bojje , and Angelo , in Plates XX. and XXI. but 
 
 R Vitruvius 
 
2 
 
 A Sure Guide to Builders. 
 
 Vitruvius fays, that the Height of the Cymatium fhould be one 
 twelfth Part of the whole Architrave, and then dividing the 
 other 1 1 Parts into i a equal Parts, he allows 3 to the lower 
 Fafcia, 4 to the fecond, and 3 to the upper Fafcia, upon which 
 refts the Cymatium. 
 
 The Freeze of this Order is generally enrich’d with Feftoons 
 and other Carvings, and is therefore made much higher than 
 when ’tis wholly plain. 
 
 Vitruvius makes its Height one Fourth lefs than the Archi- 
 trave when plain, and one Fourth greater when enrich’d. Upon 
 the Freeze he places a Cymatium revers’d, whofe Height he 
 makes equal to one Seventh Part of the Freeze, and its Pro- 
 jefture fhould always be equal to its Height, for therein the 
 Beauty of this Member confifts. Next above this Member is 
 placed the Dentils which I lpoke of in the Dorick Order, whofe 
 Breadths may be 5 Minutes and a half, and Intervals between 3 
 Minutes and a half, (as Fig. VI. Plate XXXVII.) or each Dentil 
 may be 6 Minutes in Breadth, and Interval 4 Minutes, (Fig. VII.) 
 
 The Height of the Entablature fhould be equal to one fifth 
 Part of the Height of the Column. 
 
 To proportion this Column with its Entablature to any given 
 Height, divide the Height into fix Parts ; then will the upper 
 fixth Part be the Height of the Entablature, and the remaining 
 or lower five the Height of the Column ; and if you divide the 
 Height of the Column into nine equal Parts, one of them will 
 be equal to its Diameter. 
 
 To proportion this Column on its Pedeflal, with its Entabla- 
 ture, to a given Height, divide the Height into 1 5 equal Parts, 
 of which give the upper 1 to the Entablature, 10 to the Height 
 of the Column, and the remaining 3 to the Height of the Pe- 
 
 deftal. 
 
 To proportion this Column with its Pedeflal, exclufive of its- 
 Entablature, divide the given Height into 13 equal Parts,,, 
 whereof give the upper jo to the Height of the Column, and 
 the Remainder 3 to the Height of the Pedeftal. And laftly, If 
 in this and the preceding you divide the 10 Parts, which con- 
 tains the Height of the Column, into p equal Parts, one Part 
 thereof will be the Diameter of the Column, which being- 
 divided into < 5 o Minutes, you may from thence proportion the 
 feveral Members requir’d,.. 
 
 The. 
 
Geometrical Elevations ^ tfe Join c ' k Order a^coi'diny ft? /die Ji in? / i andw n? /aid do/im l> 
 
'z'z 
 
A Sure Guide to Builders . 123 
 
 The Irttercolumnation of this Order depends upon the Num- 
 ber of Dentils between Column and Column : For fince that 
 over every centeral Line of a Column there is placed a Dentil, 
 as the Triglyphs of the Dortch Order are, it therefore follows, 
 that the Number of Dentils in every Intercolumnation will be 
 odd. The firrt Variety of thefe Intercolumnations is that of 
 Columns in Pairs, as C and A, (Fig. I. Plate XXXVII.) of one 
 Diameter 30 Minutes, confining of p Dentils, as noted in the 
 Freeze. The fecond Variety is of 4 Diameters 3 Minutes, 
 confifting of 27 Dentils. And thirdly, of j Diameters 15 Mi- 
 nutes, confining of 35 Dentils, as noted in the Freeze. 
 
 Thefe are the various Intercolumnations of Columns alone, 
 but when they have Arches between they may be fomething 
 larger, as AB, {Fig. I.) of 5 Diameters 33 Minutes and 37 
 Dentils, and BC, which hath 5 Diameters 51 Minutes and 3p 
 Dentils ; and when Pedertals are ufed, (as Fig. II. Plate XXXIII.) 
 the Intercolumnation may be 7 Diameters 40 Minutes, with 4 6 
 Dentils. 
 
 For the Imports of this Order lee Plates XXXI. and XXXII. 
 
 N. B. That the mofl common Intercolumnation is two Diameters 
 and one Fourth , which Vitruvius calls Eurtillos, being (as he 
 lays) the bejl kind of Intercolumnation. 
 
 IV. Of the CORINTHIAN ORDER. 
 
 As the lonick Order was originally ufed in Temples, and is 
 now a-days in Churches, Courts of Judicature, &c. where Soli- 
 tude and Beauty are requifite, fo is this mort noble, rich, and 
 delicate Order to be ufed in the mort rtately and magnificent 
 Buildings we have, particularly in thofe that are not to be 
 view’d at a great Dirtance, and therefore mort proper for infidc 
 Works. 
 
 The Height of this Column is p Diameters and a half, and 
 oftentimes nine and 3 quarters, or ten Diameters, but never more, 
 including Bafe and Capital. 
 
 Vitruvius makes no Difference in the Height of this Column 
 from the lonick , excepting in the Capital, whofe Height (fays he) 
 makes them appear Jlenderer and higher j but our modern Archi- 
 
 R 1 teds 
 
i 24. A Sure Guide to Builders. 
 
 teds have augmented its Height, which renders it much more 
 beautiful and ftately. 
 
 The Bale of this Order is varioufly compos’d by Architeds ; 
 fome make it to confift of a Plinth, two Torus’s, two Scotia’s, 
 and a double Aftragal,. as thofe of Vitruvius and Vignola , and 
 others, who, I fuppofe, took them from the Rotunda , and other 
 antient Buildings of Rome , that have the Corinthian Bafe of that 
 Compofition ; and, on the contrary, Palladio and Scamozzi , and 
 others, compofe them much after the fame Manner as the Attick 
 Bafe, as may be feen in Plate XXIII. which ’tis very probable 
 they took from the Arch of Lyons at Verona , the Frontifpiece 
 of Neron at Rome , &c. which confifts of two Torus’s, a Scotia, 
 and Plinth. 
 
 The Shaft of this Column is generally fluted with 24 Flutes, 
 and as many Fillets. The Height of the Capital was originally 
 but 60 Minutes, or 1 Diameter, which Vitruvius pradis’d ; for 
 (fays he) the Capital, comprizing the. Abacus , hath for its Height 
 the Breadth of the Bottom of the Pillar. But our modem Archi- 
 teds have added 10 Minutes more to its Height j lo that now 
 its Height is 1 Diameter and 10 Minutes. 
 
 The Height of the Abacus is one feventh Part of the whole 
 Height, viz. 10 Minutes, and the remaining 60 Minutes, as 
 exhibited in Plate XXVIII. 
 
 In the Abacuo, dire&ly nvpr thf» T.tnf* of the Column, 
 
 is placed a Rofe Pomegranate or Tail of a Fifh,. as at A,, 
 whofe Diameter muft be always equal to the Height of the. 
 Abacus., 
 
 N. B. The Curvature of the Capital, is defcrib’d on the 
 angular Point of an Equilateral 'Triangle, as the angular 
 Point Z. 
 
 The Diminution of the Shaft at its Aftragal is one Seventh of 
 the Diameter of the Bafe, if in the firft or fecond Story ; but in 
 a third or fourth Story, it Ihould be one Eighth at the leaft. 
 
 The Architrave of this Order (as Vitruvius obferyes) is of the 
 fame Compound as the lonick, as alio is the Freeze and Cornice, 
 excepting in its Cantalivers or Modilions, which are generally 
 richly carv’d, which in the lonick they are notq and indeed lb 
 
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 are all its Members, efpecially the Freeze, which is very fre- 
 quently adorn’d with rich Foliage, Peftoons, &c. 
 
 The Height of the Entablature is equal to one fifth Part 01 
 the Column's Height, and its Pedeftal to one Fourth, according 
 to Palladio. 
 
 To proportion this Column with its Entablature to any given- 
 Height } divide the Height into fix equal Parts, the uppermoft 
 will be the Height of the Entablature in Grofs, and the remain- 
 ing five the Height of .the entire Column ; and if the Height of 
 the Column is 10 Diameters, then one half of either of the fix 
 Parts will be the Diameter ; but if the Height of the Column 
 be but p Diameters and a half, divide the five Parts before found 
 for the Column’s Height into ip equal Parts, and two thereof 
 fhall be equal to the Diameter of the Column. 
 
 If you make the Column’s Height equal to 10 Diameters, the 
 Height of the Pedeftal will be equal to 2 Diameters and a half, 
 viz. one fourth Part thereof ; and if to their Sum you add z 
 Diameters, the one fifth Part of the Column’s Height, the Sum 
 will be equal to 14 Diameters and a half, which is the whole 
 Height of the entire Order,. 
 
 To proportion this Order entire to any given Height, divide 
 the Height into 2p equal Parts, of which give 4 to the Height 
 of the Entablature, 20 to the Column, and the remaining 5 to 
 the Pedeftal. 
 
 And laftly, To proportion this Column with its Pedeftal, ex- 
 clufive of its Entablature,. to any given Height, divide the 
 Height into 25 equal Parts, and then giving 20 to the Height 
 of the Column, the remaining 5 will be the Height of the 
 Pedeftal. 
 
 For the Ornaments of the Soffita of the Corona of the Cor- 
 nice, fee Plate XLVII. 
 
 The Intercolumnation of this Order may be the fame as the 
 Jpnick , viz. 2 Diameters and a quarter ; but if we have Re- 
 courfe to the Modilions in the Cornice, the Intercolumnation 
 maybe 4 Diameters 22 Minutes and a half, or 5 Diameters 37 
 Minutes and a half, as in Plate XXXV.) where the firft con- 
 fills of 7 Modilions, and the latter of p, as number’d oyer theft 
 Entablatures.. 
 
 The, 
 
s 26 
 
 A Sure Guide to Builders. 
 
 The Tntercolumnation may yet be greater, where the Arch of 
 this Order is to come between ; as firft, it may be of 7 Diame- 
 ters 40 Minutes, (as Fig. II. Plate XXXIV.) or of 8 Diameters 
 26 Minutes, (as Fig. I.) or of 8 Diameters only, (as Fig. III. 
 Plate XXXVI.) where the firft Arch contains 11 Modilions, 
 and the fecond Arch 1 2 Modilions. 
 
 For the Impofts and Architraves of this Order fee Plates 
 XXX. and XXXI. 
 
 V. Of the ROMAN or COMPOSITE ORDER. 
 
 Altho’ this Order is not pure and diftind in itfelf, as the others 
 are, yet ’tis not to be defpifed or rejected, as fome young fcrib- 
 ling Pretenders to Archite&ure have endeavour’d to do, tho’ to 
 no PurpofF ; for this, like Truth, clears itfelf at all Times. 
 
 This Order may be introduc’d in all Kinds of Buildings, 
 where Richnels, Beauty, and Strength ftiould be in Con- 
 junction. 
 
 For as ’tis a Compofition of the Dorick, Ionick and Corinthian 
 Orders, 1 believe I may venture to fay, that it receives its 
 Strength from the Dorick , its Beauty from the Ionick , and its 
 Richnefs from the Corinthian , which being well confider’d, will 
 Be found to be truly magnificent in all its Parts, and well deferv- 
 ing the Notice of the mo ft curious. 
 
 The Height of the Column is the fame as of the Corinthian , 
 viz. 10 Diameters, and therefore (as Vitruvius obferves) differs 
 in its Capital: only. See Plate XXV. and XXVI. For (fays he) 
 fometimes upon the Corinthian Pillar was placed a Capital compo/d 
 of Jeveral Parts, which were taken from the Corinthian, the 
 Ionick, and Dorick Orders. 
 
 ' The Bafe to this Column is generally the Attick before de- 
 fer it; ’d, and fometimes a Compofition of the Attick and Ionick. 
 See the feveral Bafes given to it by Palladio , Scamozzi , Le Clerc , 
 Per a alt, Serlio , and Vignola , in Plates XXV. and XXVI. 
 
 The Shaft of this Column is fluted with Flutes and Fillets, as 
 the Corinthian Shaft, and its Capital hath the fame Height alfo, 
 excepting that of Sebajiian Serlio s, which hath but 1 Diameter, 
 or 60 Minutes. 
 
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A Sure Guide to Builders. 
 
 The Height of the Entablature is a fourth or a fifth Part of 
 the Column's Height, according to the Will of the Architect. 
 See the Compojite Entablatures of Palladio , Scamozzi , Vignola^ 
 6 ic, in Plate's XXV. and XXVI. 
 
 The Diminution of the Shaft is the fame as that of the Corin- 
 thian , viz. one Seventh or one Eighth, according to its Si- 
 tuation. 
 
 To proportion this Column of io Diameters high, with its 
 .Entablature, to any Height requir'd, divide the Height into 1 2 
 equal Parts, and then giving 2 to the Height of the Entabla- 
 ture, the remaining 10 will be the Height of the Column, and 
 one will be equal to the Diameter of the Shaft at its Bafe. 
 
 The Height of the Pedeftal is equal to one third Part of the 
 Height of the Column, viz. 3 Diameters one Third, which 
 being added to 10 Diameters, the Height of the Column, and 
 1 Diameters, the Height of the Entablature, the Sum will be 
 equal to ij Diameters one Third; and if you imagine each 
 Diameter divided into three Parts, then the whole Height will be 
 4 6 Parts ; then giving 10 of thofe Parts to the Pedeftal, and 30 
 to the Height of the Column, the remaining 6 will be the Height 
 of the Entablature. 
 
 Again, To proportion this Column, with its Pedeftal, exclu- 
 five of its Entablature, divide the given Height into 40 equal 
 Parts, and giving 30 to the Height of the Column, the remain- 
 ing 1 o will be the Height of the Pedeftal. 
 
 The Intercolumnation of this Order is 1 Diameter and 30 
 Minutes, when plac’d in Pairs, but when fingle it is of 4. 
 Diameters, or 5 Diameters 30 Minutes, as in Plate XXXV. 
 
 The Intercolumnation may yet be larger, when an Arch is 
 compris’d between them, and may be either of 6 or 8 -Di- 
 ameters. 
 
 The Intercolumnation of this Order is alfo regulated by the 
 Number of Modilions contain’d therein ; as firft, Columns placed 
 in Pairs and the Interfpace between them, may confift either of 
 8, 11, or 16 Modilions, 
 
 For the Impoft of this Order, fee Plates XXX. and-XXXL 
 
 Having thus laid down the general Proportions of the five 
 Orders of Columns, I now recommend to you the Perulal of 
 Plates XVEXVIL XVIII. XIX. XX. XXII, XXIIL XXIV, 
 
 XXV. , 
 
 1 27 
 
 / 
 
A Sure Guide to Builders „ 
 
 XXV. and XXVI wherein are exhibited their various Proporti- 
 ons, according to Vitruvius, Palladio, Scamozzi , Vignola , Serin 
 •Per ault, BoJJe, and jtf. Angelo. 1 
 
 The next Work to be confider’d, is the placing of Columns 
 over one another, in fuch Manner, that the Diameters of thofe 
 in the fecond Story may be proportionable to the Diameters of 
 them in the hrft, and the third to the fecond, ©V. But before 
 we proceed thereto, Vis neceffary to determine, whether we lhall 
 
 ^■ aCe ,r° U n? ' UmnS agamft the Wall > Partly in the Wall fas 
 ivg. V. Plate XLV.) or clear from the fame, (as Fig IV ) If 
 
 we determine to place our Columns as Fig. V. then one quarter 
 Part of the Diameter of the Column mnft be plac’d in the Wall 
 as exhibited by the Plan dHa , where dH, which is equal 
 to one Qiiarter of the Diameter, Hands within the Wall ^and 
 
 are calBd S^Work ^ 5 and ' tis therefore that fuch Columns 
 are call d by Workmen Three-quarter Columns 
 
 thfwaT/T TrTf VV ° Ur C ° 1UmnS t0 ftand 
 
 W ‘ ? r A A fk' IV ) We muft P W * PiUa/lcr with 
 them agamft the Wall, to appear as a fquare Column, having a 
 
 fmall Prpjedure from the Face of the Wail, to fupport that 
 
 wall's the EntablatUre that runs from the Capital P A to the 
 
 The Projefture of Pillafters from the Face of the Wall 
 ihould be never more than one quarter Part of their Diameter 
 but one Fifth is much better. The Plinth of the Column muft 
 •be placed at a convenient Diftance from the Plinth of the Pil- 
 lafter, viz. about 8 or io Minutes, as exprefs’d in the Plan at 
 
 v\U- I? nd th n re i by thc Sha ^ o f the Column, and that of the 
 i ulafter, will have a free Diftance. 
 
 When Columns are thus placed, you may (when Occafirm 
 requires) give their Heights fomething more than what has been 
 before laid down, becaufe the Pillafters themfelves fupport aPart 
 of the Weight with the Columns. PP aU 
 
 The Manner of placing your Columns againft the Wall or 
 free from it, being determin'd, you muft make the Diamete? of 
 ..he Column in the fecond Story at its Bafe, equal to the Diame- 
 ter of the Column in the hrft Story at its Aftragal : that is 
 
 XXX vn’T ft , n C ° 1Umn HA > HI- PlSe 
 
 J, J X V L > muft n ) ade equal to the Diameter B of theColumn 
 BLj io alio muft the Diameter B of the Column BA, be 
 
 equal 
 
V 
 
flak’ XXW 
 
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 (reorne27~icat 2E ' Leimtumo of the Ccnrvjur-rUe Order ft/ 
 
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A Sure Guide to Builders. 1 2 9 
 
 equal to the Diameter B of the Column BK. And again, If 
 a third Story of Columns were to be placed over the Columns 
 HA and BA, their Diameters mull be equal to the Diameter 
 B A ; and the like of all others requir’d. 
 
 # 
 
 And as I have now deliver’d the Manner of proportioning 
 Columns over each other, I will, in the next Place, Ihew how 
 to proportion the Height of a Statue on any Edifice, fo as to 
 appear of the fame Stature as a Man on the Ground. 
 
 Let ZX {Fig. IV.) be the common Height of a Man, (fup- 
 pofe 5 Feet 10 Inches) and ’tis requir’d to place a Statue on 
 the Cornice O, that fhall appear equal in Height to ZX. 
 
 <P R A C f ICE. 
 
 it. Draw out the Line XID at Pleafure, and at right Angles 
 to the Axis ZO. 
 
 a. In any Part thereof affume a Point, as at D, and from 
 the Height Z draw the right Line Z D \ alfo from the Point 
 O, whereon the Statue is to be placed, draw the right Line 
 OD. 
 
 3. On D, with any Radius, defcribe the Arch El, and make 
 GF equal to HI, and from the Center D, through the Point 
 F, draw the right LineDFQ^, interfering the Line XO be- 
 ing continu’d in P, which is the Height of the Statue re- 
 quir’d. For fince that equal Objects are feen under equal 
 Angles, therefore the Height PO will appear equal to the 
 Height ZX, becaufe the Angle IDH is equal to the Angle 
 GDF. ChE. D. 
 
 s 
 
 CHAP 
 
130 
 
 A Sure Guide to Builders. 
 
 CHAP. VI. 
 
 Of Pedestals and their Ornaments. 
 
 EDESTALS (as has been before obferv’d, are 
 compos'd of three Parts, viz. a Bafe, a Die, and a 
 Capital, fee F/g. VIII. Flate XII. ; and every of thofe 
 Parts (the Die or Cube excepted) of divers Mem- 
 bers, as Plinth, Cima’s, Torus’s, Facia’s, Aftra- 
 
 gals, &c. 
 
 The Kinds of Pedeftals are two, viz. the one broken, and 
 the other continu’d. Broken Pedeftals arc thole which break 
 out or project before the Wall or Face of the Building, as AB, 
 (Fig. V. of the preceding Flate) and continu’d Pedeftals are 
 thole which run through the whole Building without any fuch 
 Projetfture, as D (Fig. I.) 
 
 When ’tis requisite to place Pedeftals to Columns of any Order, 
 their juft Heights are to be firft confider’d and determin’d, and 
 then their principal Parts to be proportion’d thereto. 
 
 And altho’ ’tis abfolutely necelfary to determine the Heights 
 of Pedeftals throughout the five Orders of Columns, yet none 
 of the Antients are known to have fettled them, as appears by 
 the following Table. 
 
 A TABLE 
 
A Sure Guide to Builders. 
 
 A TABLE exhibiting the different Heights of Pedejlals } as 
 f rabbis d by the Antients. 
 
 Height of the Tufcan Pedeftal. 
 
 Diam. Min. 
 
 Palladio - - i 30 
 
 Scamozzi - - - 1 42 
 
 Vignola - - - - 2 30 
 
 Serlio - - 2 1 5 
 
 Height of the Dorick Pedeftal. 
 
 Height of the Corinthian 
 . Pedeftal. 
 
 Diam. Min. 
 
 Altar of the Pantheon 3 58 
 
 Colifeum - - - 2 02 
 
 Palladio ----231 
 Scamozzi - - - 3 1 1 
 
 Vignola - - - - 3 3 ° 
 
 Serlio - 3*5 
 
 Diam. Min. 
 
 Palladio 
 
 — ‘Z 
 
 
 Scamozzi 
 
 2 
 
 08 
 
 Vignola - - 
 
 - 2 
 
 34 
 
 Serlio - 
 
 - 3 
 
 00 
 
 Height of the Ionick Pedeftal. 
 
 Diam. Min. 
 Temp. For tuna Viril'ts 3 42 
 
 Temple of Marcellas 1 38 
 
 Collifeum ~ - 2 22 
 
 Palladio ----- 2 34 
 
 Scamozzi - - - 2 30 
 
 Vignola 3 00 
 
 <5Vr//0 - - - - 3 00 
 
 Height of the Compofte 
 Pedeftal. 
 
 Diam. Min. 
 
 Goldfmiths Arch - 3 38 
 
 Palladio - - 5 07 
 
 Scamozzi - - - 3 02 
 
 Vignola - - 3 30 
 
 6Vr//o •• - - - 3 42 
 
 Now to fettle a juft Proportion for their feveral Heights, I 
 humbly conceive, that if a Mean be taken between the Extreams, 
 that Mean fo taken may be generally receiv’d and eftablifh’d as a 
 determin’d Height : As for Example \ 
 
 Firf , In the 1 ’ufcan Order, the lelfer Extream is that of Pal- 
 ladio’s , 1 Diameter 30 Minutes ; and the greater that of Vignola , 
 
 S 2 2 Diameters 
 
A Sure Guide to Builders. 
 
 a Diameters 30 Minutes, whofe half Sum being taken, may be 
 well receiv’d for a determin'd Height of the Fufcan Pedeftah 
 
 Diam. Min. 
 The greater Extream 2 30 
 
 The idfer Extream 1 30 
 
 • Their Sum 4 00 
 
 Their half Sum 2 00 
 
 Height for the T’uJ'can Pedeftah 
 
 the 
 
 determined 
 
 Secondly , In the Derick Order, the leffer Extream is that of 
 Palladio , 2, Diameters 5 Minutes • and the greater that of Serlio y 
 3 Diameters, which being added together, and the half Sum taken, 
 their mean Height may be eftablifh’d at 2 Diameters 30 Minutes. 
 
 Diam. 
 
 Min. 
 
 The greater Extream 
 
 3 
 
 00 
 
 The lelfer 
 
 a 
 
 05 
 
 Their Sum 
 
 5 
 
 05 
 
 Their half Sum 
 
 a 
 
 32 ± 
 ** 2 
 
 But fmee odd fractional Parts are inconvenient in Pra&ice, we 
 will therefore rejeCt the odd 2 Minutes and half, and fettle the 
 determin’d Height at a Diameters 30 Minutes. 
 
 7 hirdly , In the Ionick Order, the greateft Extream is the Temple 
 of Fortuna virilis , 3 Diameters 4a Minutes; and the Idler the 
 Temple of Marcellas , 1 Diameter 38 Minutes, which being added 
 together, and the half Sum taken, the mean Height will be a Di- 
 ameters 40 Minutes. 
 
 Dlam. Min . 
 
 The greater Extream 3 4a 
 
 The Idler 1 38 
 
 Their Sum 5 20 
 
 Their half Sum a 40 the determined 
 
 Height for the Ionick Pedeftah 
 
 Fourthly , 
 
A Sure Guide to Builders . 1 33 
 
 Fourthly , In the Corinthian Order, the greateft Extream is the 
 Altar of the Pantheon , 3 Diameters 38 Minutes ; and the Coli- 
 Jeum 2 Diameters 2 Minutes, which being added together, and 
 their half Sum taken, the mean Height will be 3 Diameters, 
 
 Diam. Min. 
 
 The greateft Extream 
 
 3 58 
 
 The leffer 
 
 2 02 
 
 Their Sum 
 
 6 00 
 
 • ^ 
 
 Their half Sum 
 
 3 00 the determined 
 
 Height for the Corinthian Pedeftal. 
 
 
 Fifthly , In the Compojite Order, the greateft Extream is the 
 Goldlmiths Arch 3 Diameters 38 Minutes, and the leffer is that 
 of Scamozzi 3 Diameters 2 Minutes ; which being added toge- 
 ther, and their half Sum taken together, the mean Height will 
 be 3 Diameters 20 Minutes. 
 
 Dlam. Min. 
 
 The greateft Extream 3 38 
 
 The leffer 3 02 
 
 Their Sum 6 40 
 
 Their half Sum 3 20 the determined 
 
 Height of the Compojite Order. 
 
 Hence -it appears, that the mean Heights of the feveral Pe- 
 deftals are as following, viz. the T if can of 2 Diameters, the 
 JDorick of 2 Diameters 30 Minutes, the lonick of 2 Diameters 40 
 Minutes, the Corinthian of 3 Diameters, and the Compojite of 3 
 Diameters 20 Minutes. 
 
 Note, Phat the Diameter by which the Heights of PedeflaJs 
 are determin'd , is the Diameter of the Column which is always 
 fuppofed to be placed upon them. 
 
 But fince that by this Method of taking the Mean between 
 the Extreams, the Height of the Dorick Pedeftal is 2 Diameters 
 
 30 Minutes, 
 
1 34 - 
 
 A Sure Guide to Builders. 
 
 30 Minutes, which I think is 10 Minutes too high, therefore let 
 the Height of that Pedeftal be eftablilh'd at 2 Diameters 20 
 Minutes, and then the Difference of all their feveral Heights 
 will be alike proportionable, of 20 Minutes each. 
 
 The fecond Confideration is to proportion the Heights of the 
 feveral Parts of Pedeftals, as the Bafe, Die, and Capital, which, 
 as well as the entire Heights of Pedeftals, is left undetermin’d by 
 both Ancients and Moderns, as appears by the following Table : 
 
 ^ TABLE exhibiting the Proportions of the principal Parts 
 of ‘Pedeftals , viz. their Bafes , Dies, and Capitals , as practis'd 
 by ant lent and modern Ar chit efts. 
 
 
 Height of 
 rheZoccolo 
 
 Height of 
 theMolding 
 of the Bale. 
 
 Height of 
 the Die. 
 
 Height of 
 the Cornice 
 
 Dorlck 
 
 Pedeftal 
 
 0, f Palladia 
 
 5 y\Scamozzi 
 
 24 
 
 28 
 
 I 2 
 
 14 
 
 66 
 
 57 
 
 l8 
 
 21 
 
 lonkk 
 
 Pedeftal 
 
 ( Temple of Manly 0 
 rat j Fortune ft 
 
 ) C Colifeum 
 ) ^ c Palladio 
 ^ tScamozzl 
 
 30 
 
 28 
 
 22 
 
 25 
 
 I 2 
 
 , 8 
 
 I I 
 
 1 2 
 
 59 
 
 73 
 
 70 
 
 6 5 
 
 1 9 
 
 I I 
 
 17 
 
 18 ■ 
 
 Corinth. 
 
 Pedeftal 
 
 c Conftantlne’s Arch 
 V kt \Collfeum 
 j ^ Palladio 
 \Scamozzl 
 
 IO 
 
 24 
 
 20 
 
 l8 
 
 14 
 
 1 1 
 
 10 
 
 1 1 
 
 79 
 
 73 
 
 75 
 
 77 . 
 
 1 7 
 
 12 
 
 15 
 
 14 
 
 Compof 
 
 Pedeftal 
 
 s- Titus’s Arch 
 \G0ldfn1iths Arch 
 
 J Palladio 
 ) Scamozzl 
 ^ Septlmius’s Arch 
 
 2 6 
 
 1 9 
 
 20 
 
 2 1 
 
 15 
 
 14 
 
 P 
 
 10 
 
 10 
 
 14 
 
 67 
 
 81 
 
 75 
 
 74 
 
 76 
 
 1 3 
 
 1 1 
 
 *5 
 
 15 
 
 14 
 
 Note, A hat the Parts exprefs’d In the feveral Columns of this 
 ft able, are 1 10 th Parts of the whole ftlelght of every Pedeftal ; 
 that is, the Height of every Pedeftal is ft up pos’d to be divided 
 Into 120 equal Parts, and of thufe Parts the Bafe, Die, and 
 Cornice of every Pedefal confifs, as exprefs’d in the ft able. 
 
 It 
 
A Sure Guide to Builders . 
 
 It appears by this Table, that the antique Proportions of the 
 Bafe are greater than thofe of the Cornice, and the Zoccolo or 
 Plinth of the Bafe greater than the Mouldings thereof. 
 
 Serlio and Vignola make the Zoccolo lefs than the Mouldings, 
 which is entirely wrong ; for the mOft heavy Parts fhould always 
 fuftain the next leaf! heavy Part, and not the inferior to be over- 
 loaded with the fuperior, like the Ionick Bafe of Vitruvius , 
 where he has placed a monllrous large Torus over two fmall 
 Aftragals and their Scotia’s, which feem fufficient to crulh them 
 to Pieces. 
 
 Palladio and Scamozzi come very near the antique Proportions, 
 wherein they feem to be very regular ; for that they always 
 make the Zoccolo with its Moldings equal, or nearly equal, to 
 twice the Height of the Cornice, excepting in the Dorick y 
 Ionick , and Compofite Orders ; Scamozzi makes the Zoccolo equal 
 to twice the Height of the Mouldings of the Bafe, as in the pre- 
 ceding Table. 
 
 Now feeing that a determin’d Proportion of their Parts is 
 abfolutely neceflary, therefore the Corinthian Pedeftal of Palla- 
 dio’s feems to be the very thing ; for he (as Perault has alfo 
 done) gives to the Height of the Zoccolo and Bafe one quarter 
 Part of the whole Height of the Pedeftal, of which the Zoccolo 
 contains two Thirds, that is, one fixth Part of the Height of 
 the whole Pedeftal : Then to the Height of the Cornice he gives 
 one eighth Part of the whole Height, and the Remainder to the 
 Height of the Die, which will always confift of three eighth 
 Parts of the whole. 
 
 And here note, I 3 hat the Proje flare of the Die or Drunk of 
 every Pedeflal , muf he always equal to the ‘Proje hi are of the 
 Bafe of the Column that is faced thereon , 
 
 From thefe Proportions of Palladio , the following Rule is 
 deduced for Pedeftals in general, be they either Dufcan , Doricf 
 Ionicky Corinthian y or Compofte. 
 
 * 3 $ 
 
 A General 
 
i3 6 
 
 A Sure Guide to Builders . 
 
 A General RULE. 
 
 Divide the given Height of the Pedeftal into 1 20 equal Parts , 
 (as before Jdid) and of thofe Parts give to the ■ Zoccolo 20, to the 
 Mouldings of the Bafe 10, to the Die 75, and to the Cornice 15. 
 
 Now to compleat our Pedeftals, we muft confider how to pro- 
 portion the Projedture of the feveral Parts contain’d in the Bafe 
 and Capitals thereof 
 
 The Projedtures of thefe Parts, as practis’d by the antique 
 Architedts, were much greater than they are now made by Mo- 
 derns ; and indeed fome of them were very great, as the follow- 
 ing Table exhibits : and, on the other Hand, many of our 
 Moderns have given them much too little a Projedture, whereby 
 they have a very mean Afpedt, as well as feemingly incapable 
 to fupport and protect the cover’d Parts from the Injuries of 
 Weather. 
 
 Both antient and modern Architedts agree in their Projedtures 
 of the Cornices of Pedeftals, making them fomething greater 
 than that of their Bafes, thereby to cover and preferve them 
 dry from their Drip, which is the whole End and Defign of a 
 Cornice. 
 
 Monf. Berault, confidering the Beauty of well-proportion’d 
 Cornices, affign’d that their Projedtures fhould be equal to their 
 Heights, as alio the Projedtures of the Mouldings of the Bafe : 
 For as the Heights of thofe Mouldings are differently propor- 
 tionable in every Order, fo will their Projedtures be proportion- 
 ably different, nearly the fame as practis’d by the Antients. 
 
 M TABLE 
 
A Sure Guide to Builders . 
 
 A TABLE exhibiting the ProjeCtures of the Bafe and Cornice 
 of Pedefals , as practis'd by antient and modern Architects. 
 
 
 Projedture of 
 the Bafe. 
 
 Min. 
 
 1 6 
 
 1 1 
 
 Projedture of 
 the Cornice, 
 
 Height of the en- 
 tire Pedeftal. 
 
 r, . T c Palladio 
 
 Donck < rr 1 
 
 Le ignola 
 
 Min. 
 
 1 6 
 
 1 1 
 
 Diam. Min. 
 
 2 20 
 
 2 40 
 
 C Temple of Manly y 
 
 T - i j Fortune • . - \ 
 
 Iomck \ n 77 j- J 
 
 j Palladio 
 
 C Vignola 
 
 26 \ 
 
 14 
 
 14 
 
 1 3 
 
 14 
 
 16 
 
 3 34 
 
 2 35 
 
 3 00 
 
 f Temple of Vefa ato 
 
 Corinth ) 7 ' ivoli “ “ J 
 
 C orintto. < p a ]j n ^- in 
 
 C Vignola 
 
 24 s 
 
 I 
 
 l 3 
 
 24 
 
 T t) 
 
 l 3 
 
 3 ©7 
 
 2 30 
 
 3 06 
 
 C Titus's Arch 
 
 ^ ^ jSeptimius’s Arch 
 
 Compof. W alladi0 _ . 
 
 t Vignola 
 
 28 
 
 24 I 
 
 14 
 
 13 
 
 25 f 
 
 14 
 
 1 3 
 
 2 15 
 
 3 co 
 
 3 co 
 
 3 3 C 
 
 Mean Project ares reduced by Perault, the heft approved of 
 
 for Practice. 
 
 Dorick - - - 
 
 12 
 
 14 
 
 2 20 
 
 Ionick - - - 
 
 14 
 
 17 
 
 2 40 
 
 Corinthian - 
 
 15 
 
 
 3 00 
 
 Compof te - 
 
 16 
 
 22 
 
 3 40 
 
 Note, T he ProjeCiures fpecifed in this Table, are to be fet from 
 the Upright or Face of the Die or Cube of the Pedejtal. 
 
 1 37 
 
 T 
 
 CHAP. 
 
138 
 
 A Sure Guide to Builders. 
 
 CHAP. VII. 
 
 Of Co lumns, and their Ornaments . 
 
 T has been already faid, that a Column is compos’d 
 of three Parts, viz. the Bafe, the Shaft, and the 
 Capital, which we will now confider feverally \ and • 
 firft of their Bafes. 
 
 The Bafes of Columns is an Ornament added to them fince 
 their firft Inftitution ; for originally the Dorick Order, which is 
 the very firft that was made, was without any Bale more than, 
 the Cindure. 
 
 But afterwards modern Architeds (as before hinted) contriv’d 
 Bafes of divers Kinds, of which the young Student has great 
 Variety exhibited in <Plate XXXVIII. 
 
 And ’tis to be obferv’d, that as moft Authors have agreed to 
 make the Height of the Bafes of Columns in general equal to 
 30 Minutes, or the Semi-diameter of the Column ; fo do they 
 alfo very nearly agree in the Projedures of their Bafes, as 
 by the following Table appears, wherein the Projedures are 
 exhibited, as were pradis’d by both antient and modern 
 Architeds, 
 
 A TABLE 
 
BASE'S and JMPOSTS after t/ie odd Grecian. ^ Koman inamier 
 Plaits 3 8 . 
 
 Plaxs t/iu cujP 
 'd'ct- 138, 
 
. .. . ; . . 
 
 ■ • • •. v.'-. < : t ‘ > ■ 
 
 ' ' ' 
 
 ‘ • 
 
 ° y ‘ x '■ • ^ 
 
 ■ ■ \ 
 
 
 u 1 
 
 - 
 
 - \ 
 
 - 
 

A Sure Guide to Builders. 
 
 ^ TABLE of the antient and modern Procures of the 
 
 Bafes of Columns . 
 
 
 Tufcan. 
 
 Dorick. 
 
 Ionick . 
 
 Corinth. 
 
 Compof. 
 
 Min. 
 
 Min. 
 
 Min. 
 
 Min. 
 
 Min. 
 
 Trajan’s Column - 
 
 40 
 
 
 
 
 
 Palladio 
 
 40 
 
 40 
 
 40 
 
 4i 
 
 42 
 
 42 
 
 Scamozzi 
 
 42 
 
 41 
 
 40 
 
 4i 
 
 Vignola 
 
 41 
 
 4i 
 
 42 
 
 42 
 
 42 
 
 Serlio • 
 
 42 
 
 44 
 
 4i 
 
 40 
 
 41 
 
 Colifeum 
 
 
 40 
 
 40 
 
 40 
 
 — 
 
 Portico of th zPantheon 
 
 
 
 
 4i 
 
 Three Columns of 
 
 the Campo VaccinoS 
 
 
 
 
 42 
 
 
 Pillafters of the Por-^ 
 tico of the Pan-\ 
 theon - - J 
 
 
 
 
 43 
 
 
 Bath of Dioclefan 
 
 
 
 
 42 
 
 43 
 
 Temple of Bacchus 
 
 
 
 
 
 41 
 
 Vitus’s Arch 
 
 
 
 
 
 44 
 
 Septimius's Arch 
 
 
 
 
 
 4i 
 
 By this Table it appears, that the leaft Proje&ure is 40 Mi 
 nutes, and the greateft 44. 
 
 T 2 
 
 139 
 
 The 
 
140 
 
 A Sure Guide to. Builders. 
 
 The neareft mean Proportion, in whole Numbers, between 
 thefe Extre.ams is 42, which is the Proje&ure now generally .ufed 
 by modern Architeds. 
 
 Secondly , Of their "Shafts ; whofe Lengths or Heights w r ere 
 antiently undetermin’d, as well as their other Parts. Vitruvius 
 made his Dorick Shafts in Temples fhorter than thofe in Porches, 
 to give them more Majefty ; becaufe (fays he) ’tis there that 
 Majefty is required more than in any other Structure whatfoever. 
 Palladio follow’d Vitruvius in the fame Path, excepting when 
 he placed Columns on Pedeftals, and then he allow’d them a 
 greater Height • which, in my humble Opinion, is a Miftake, 
 becaufe a Pedeftal is a kind of Lengthening or Addition to the 
 ffender View of a Column and therefore Columns Ihould not 
 be lengthen’d, particularly on fuch Occafions ; but. rather 
 fhorten’d, if any Alteration be made. 
 
 Serllo alfo made his Columns of different Heights, as thole 
 that were detach'd lie made uuc iniij lowci than thole that 
 were not detach’d ; which, in my humble Opinion, was need- 
 lefs, lince the Order might have been preferv’d with equal or 
 greater Strength, by giving it a lefs Intercolumnation. 
 
 But notwithftanding that Authors have thus difagreed about 
 the Height of Columns in the lame Order, yet they ftill keep 
 a like Proportion in the feveral Orders compared together, by 
 which their Increafe of Heights are proportionable in every 
 Order. 
 
 The Increafe of Height in the antique Architedure, confifts 
 of two Diameters and a half, beginning with the Vufcan at 7 
 Diameters and a half, and ending with the Compojite in 10 Di- 
 ameters ; and the Increafe of Vitruvius is the fame, but then he 
 allows the Tufcan but 7 Diameters, and ends in the Compojite 
 with p Diameters and a half. 
 
 Modem Architeds have made the Increafe greater ; for Sea* 
 mozzi makes the Increale of 2 Diameters and three Fourths, and 
 Palladio and Serllo of 3 Diameters : But more of this at larg;p 
 fee in the following Table : 
 
 Tufcan, 
 
A Sure Guide to Builders. 
 
 141 
 
 I’ufcan. 
 
 Dorick. 
 
 Ionick. 
 
 Corinthian. 
 
 Diam. 
 
 Vitruvius 7 
 
 Diam. 
 
 Vitruvi - ^ 
 z/j within/ 7 
 Temples ) 
 
 — inPor-) 
 tico’s of >7 -L 
 Temples ) 
 
 Biam. 
 Vitruvius 8 •§ 
 
 Diam. 
 
 Vitruvius 9 ~ 
 
 Palladio 7 
 
 8 
 
 Sf 
 
 P 1 
 
 Scamozzi 7 | 
 
 8 4 
 
 P 
 
 P T 
 
 Vignola 7 
 
 8 
 
 P 
 
 P 
 
 Serlio 6 
 
 
 8 1 
 
 P 
 
 Vrajan’s 7 g 
 Golumn J 
 
 
 
 
 Colijeum 
 
 9 i 
 
 8 1 
 
 8 47 
 
 
 Theatre 7 
 of Mar-( 
 cellus atT ' 
 
 Rome. ) 
 
 8 f 
 
 
 
 Corinthian . 
 
 Biam. Min. 
 
 Porch of the Pantheon 9 36 
 
 Temple of Vejla - 9 39 
 
 Temple of Sybil - 816 
 
 Temple of Peace - 9 32 
 
 Three Columns in 7 ✓ 
 
 ^ * • fio °6 
 
 Carnpo vaccina - J 
 
 Temple of Fauflina - p 30 
 
 Bafiiick of Jntoniuf 10 00 
 
 Porch of Septimius - p 38 
 
 Arch of Confiantine 8 37 
 
 Composite 
 
 Biam Min. 
 
 Arch of Vitus - 10 00 
 
 Temple of Bacchus 9 45 
 
 Scamozzi - - p 45 
 
 Arch of Septimius - 9 39 
 
 ’Palladio - - 10 00 
 
 From 
 
H 2 
 
 vf Sure Guide to Builders. 
 
 From thefe Varieties of Increafe MonC Perault has laid down 
 the following, which feems to be a Mean between the Extreams 
 and is now generally practis'd by modern Architects, viz. 
 
 To the Pufcan he allows 7 Diameters, the Dorick 8, the Iunick 
 8 Diameters 40 Minutes, the Corinthian 9 Diameters 20 Minutes, 
 and the Compojlte of 10 Diameters. 
 
 So that his Increafe of Height from xhetfufcan to the Compose 
 eonfifts of 3 Diameters precifely, which is the very fame Increafe 
 that was practis'd by Palladio. 
 
 Thus much with refpeCt to the Height of Columns ; now we’ll 
 proceed to fpeak fomething of their Diminution. 
 
 Columns have been diminifh'd in three different Manners ; as 
 hrft, from the Bafe,^ and continu’d to the Capital : Secondly, 
 From one Third of the Height above the Bafe unto the Capital, 
 which is after the Antique, (as taught at Page 88.) and the 
 third Manner was to make the Column thickeft in the Middle, 
 dimimfhing as well towards the Bale as the Capital, which the 
 Antients call’d Szvell'mg • But as the Forms of Columns were 
 originally taken from the taper Growth of Trees, this laft Me- 
 thod is net to be follow’d, for no fuch Example was ever feen 
 in Nature : Nor, indeed, is the firft to be follow’d, fince the 
 fecond is the moft noble and beautiful, as well as ftrongeft, and 
 11 ear eft to Nature herfelf ; who, if obferv’d, makes the lower 
 Parts of the Bodies of Trees, for fome Height above Ground, 
 of an equal Thicknefs, which is reprefented in the lowermoft 
 third Part of the Column’s Height. 
 
 As to the Quantity of their Diminutions at their Aftragals, 
 it has not yet been determin'd with refpeCl to Situation, as hath 
 been before obferv’d in Page 1 15, &e. 
 
 And that we may the better attain the Knowledge thereof, I 
 will here add a Table of the Diminution of Columns, as 
 practis'd by the Antients, which may help young Students at 
 fuch Times, when the common Rules before laid down will 
 not. 
 
 A TABLE 
 
A Sure Guide to Builders. 
 
 A TABLE of the Diminution of Columns , taken from 
 
 the Antients. 
 
 
 
 Height of the Co- 
 
 
 
 
 
 
 
 
 luma, exchlfive of 
 
 Diameter of the 
 
 Diminution of 
 
 
 
 the Bale and Capital 
 
 Column at its Bafe. 
 
 the Capital. 
 
 
 
 Feet. 
 
 Inch. 
 
 Pcs. 
 
 Feet. 
 
 Inch. 
 
 Pts. 
 
 Min. 
 
 of Diam. 
 
 
 r Theatre of Mar-~\ 
 
 
 
 
 
 OO 
 
 00 
 
 
 
 •g 
 
 c cell us - - S 
 
 20 
 
 00 
 
 00 
 
 3 
 
 I 2 
 
 OO 
 
 <3 
 
 [ Colijeum - 
 
 22 
 
 10 
 
 1 
 
 2 
 
 2 
 
 08 
 
 I 
 
 4 
 
 4 
 
 jr^ 
 
 2 
 
 lonick. 
 
 . . ^ i 
 
 ^Temple of Concord 
 
 36 
 
 OO 
 
 00 
 
 4 
 
 02 
 
 1 
 
 2 
 
 10 
 
 1 
 
 2 
 
 ) Temple of Manly y 
 ) Fortune - f 
 
 22 
 
 10 
 
 OO 
 
 2 
 
 I I 
 
 00 
 
 7 
 
 1 
 
 7 
 
 Colifeum 
 
 *3 
 
 OO 
 
 OO 
 
 2 
 
 08 
 
 3 
 
 10 
 
 00 
 
 
 Temple of Peace - 
 
 4V 
 
 °3 
 
 OO 
 
 5 
 
 08 
 
 00 
 
 6 
 
 2 
 
 
 Portico of Pantheon 
 
 *6 
 
 07 
 
 no 
 
 4 
 
 06 
 
 00 
 
 6 
 
 8 
 
 
 Altars of Pantheon 
 
 10 
 
 10 
 
 OO 
 
 1 
 
 04 
 
 1 
 
 8 
 
 00 
 
 
 Temple of Fefla 
 
 2 7 
 
 05 
 
 OO 
 
 2 
 
 I I 
 
 00 
 
 6 
 
 JP 
 
 2 
 
 §5 
 
 Temple of Sybil 
 
 
 00 
 
 OO 
 
 2 
 
 04 
 
 00 
 
 8 
 
 OO- 
 
 * ^ 
 
 5s 
 
 a 
 
 Temple of Fan/lina 
 
 36 
 
 00 
 
 OO 
 
 4 
 
 0(5 
 
 00 
 
 8 
 
 00 
 
 Three Columns of 1 
 
 Campo vaccina 3 
 
 37 
 
 06 
 
 OO 
 
 4 
 
 0 6 
 
 1 
 
 7 
 
 5 
 
 I 
 
 7 
 
 Balilick of Antoninus 
 
 37 
 
 00 
 
 OO 
 
 4 
 
 °5 
 
 1 
 
 6 
 
 * 
 
 8 
 
 
 Cunflantine’s Arch 
 
 21 
 
 08 
 
 OO 
 
 2 
 
 08 
 
 "3 
 
 7 
 
 00 
 
 
 In fide of the Pantheon 
 
 28 
 
 06 
 
 00 
 
 3 
 
 °5 
 
 OO 
 
 7 
 
 00 
 
 
 ^Portico of Septimius 
 
 37 
 
 00 
 
 00 
 
 3 
 
 °4 
 
 00 
 
 7 
 
 JL 
 
 2 
 
 ^ / 
 
 .■K V 
 
 - Bath of Dio clef an 
 
 35 
 
 00 
 
 00 
 
 4 
 
 04 
 
 00 
 
 1 1 
 
 1 
 
 3 
 
 V 
 
 ) Temple of Bacchus 
 
 10 
 
 08 
 
 00 
 
 1 
 
 04 
 
 I 
 
 4 
 
 d 
 
 ii i 
 
 
 1 Titus’s Arch 
 
 1 6 
 
 00 
 
 00 
 
 1 
 
 1 1 
 
 2 
 
 7 
 
 1 
 
 7 
 
 00 
 
 
 S'eptimius’s Arch - 
 
 21 
 
 01 
 
 00 1 
 
 2 
 
 08 
 
 7 
 
 00 
 
 'Thirdly, Of their Capitals. 
 
 The Capitals of Columns are of two Kinds, the one plain,, 
 compos’d of Mouldings only, as the TuJ'can and Dorick , and 
 the others enrich’d with Volutes, carved Leaves, Foliages, &c. 
 of which great Variety are exhibited in Plates XXXIX. XL 
 and'XLI. which being after the antient and antique, as well as; 
 
 tlxe 
 
V - • V# - §■ V . .; ■■■>; 
 
 i 44 . A Sure Guide to Builders . 
 
 the modern Manner now in pra&ice, are here placed, not only 
 to fhe-w how variouily they have been compos’d in the feyeral 
 Ages, from the Infancy of Architecture to this prefent Time ; but 
 to give the young Student fuch Hints as may improve him in 
 designing, ornamenting, &c. 
 
 But altho’ Capitals have been thus variouily compos’d, as ex- 
 hibited in the aforefaid Plates, ' yet their Heights have always 
 been contain’d under three Varieties: As \fl. The Tufcan and 
 .. Dorick , whole Capitals a-moft ail Authors have agreed to make 
 30 Minutes or a Semi-diameter in Height, notwithstanding the 
 Capital of that famous Column of Trajan has but 20 Minutes 
 Altitude, which is 10 Minutes lefs j and the Capitals of the Do- 
 rick Columns in the Theatre of Marcellas almoft 33 Minutes, 
 which arc near three Minutes more ; and thofe of the Colifeum 
 near 38 Minutes, which are 8 Minutes more.’ 
 
 I will not here take upon me to give the Reafons why the Ca- 
 pitals of thefe famous Structures were lefs or more in Height 
 than the Semi-diameter of their Bales, lince all our celebrated 
 Architects has pals’d over the lame with oilcncc, and liavc efta- 
 blilh’d their own Heights at 30 Minutes each. 
 
 2 Jly y The Height of the Ionick Capital generally confifts of 
 the Semi-diameter and one eighteenth Part thereof, enrich’d with 
 Volutes, which are plac’d either parallel to the Face of the Co- 
 lumn, according to the antient Manner, or making an Angle of 45 
 Degrees, as firft invented by Scamozzi , which laft of the two- is 
 the moft graceful. 
 
 Laftly , The third Kind of Heights is that of the Corinthian 
 and Comfojite Capitals, which are generally of an entire Diame- 
 ter and a Sixth, viz. 70 Minutes high : But our Father Vitruvius 
 allow’d the Height of the Corinthian Capital but 50 Minutes, 
 and in the Temple of Sybil at Tivoli they contain 37 Minutes, 
 and the Goldfmith’s Arch, and that of Septimius , (58 and a half, 
 which is one Minute and a half lefs. And on the other Hand, 
 the Capitals of the Frontifpiece of Nero are 76 Minutes high, 
 thofe of the Temple of Vejia at Rome 77 Minutes, and the Com- 
 pojite Capitals of the Temple of Bacchus 76 Minutes, which in 
 general exceed the now approv’d Height of 70 Minutes. 
 
 CHAP. 
 
CAPITALS after t/ie ttieL 'Grecian a^ui TtermaJi ftlanfi&r Patu>. im . T htej.-yg 
 

 i:; 
 
 
$ 
 
 * 
 
 
 
 * 
 
 
 
 
 r 
 
 
 / 
 
 
'nticnl-'.tlnkque ^ ( Mo rlem Capital's oft/ie £o?'int/uan and Cainpir/Zte Orders 
 
I 
 
 
A Sure Guide to Builders. 
 
 CHAP. VIII. 
 
 O/Entablatures, and their Ornaments . 
 
 HE Entablature of an Order, (as before has been 
 Paid) confifts of an Architrave, Freeze, and Cor- 
 nice, which Monf. Per emit , throughout all the five 
 Orders, makes equal to two Diameters ; but other 
 Archite&s have not confin’d themlelves fo ftri&ly, 
 fome making their Heights more, and others lefs, as the follow- 
 ing Table exhibits. 
 
 I muft confefs, that 'tis very neceflary to determine the Height, 
 as well as the Proje&ures of Entablatures ; for when they are 
 well proportion’d to their Columns, they have a very fine Effect ; 
 and on the contrary, when they are difproportion’d, nothing 
 looks worfe : As for Example ; a very mafly Entablature laid 
 upon tall and llender Coloumrfs, or a very fmall Entablature 
 upon Pnort and ftrong Columns, as thofe of Bullant and De Lor me, 
 whole Entablatures are mean and pitiful, are horrid Objects to 
 behold. 
 
 The Height of Entablatures Ihould be always proportionable 
 to the Length or Height of the Columns that fupport them * 
 therefore very tall and Fender Columns fhould have fmall Enta- 
 blatures, becaufe their extraordinary Height is a weakening to 
 them ; and on the contrary, fhort and ftrong Columns may be 
 loaded with larger Entablatures, provided that they are not ftu- 
 pendoufly large. 
 
 'Tis true, that there is a very great Variety of Heights con- 
 tain’d in the following Table ; but if I may be permitted to 
 fpeak my Opinion, 1 think that the Entablatures of Palladio are 
 the very beft proportion'd among all thole which are laid down 
 by thofe great Matters, whofe Proportions I have here very accu- 
 rately laid down, that every one may make Choice as pleafes 
 beft. 
 
 U 
 
 A TABLE 
 
A Sure Guide to Builders . 
 
 ^ TABLE of Entablatures , as prafisd by antient and modern 
 Mr chit efts, exhibiting their different Heights more or lejs than 
 two Diameters , as ajfgnd by Monf. Perault. 
 
 Height of the fufcan Entabla- 
 
 ture 
 
 Vitruvius 
 Palladio • 
 ■Scamozzi 
 Vignola 
 Serlio - 
 
 lefs than 
 2 Diam. 
 
 Height of the Dorick Enta- 
 blature, by 
 Min. 
 
 Theat. of Marcellas 7 \ 
 
 Vitruvius - - 15 
 
 Palladio - - ; 12 
 
 Vignola - - - iq l lefs than 
 
 Serlio - - 13/ 2 Diam. 
 
 Bull ant - - 15 
 
 Be Lorme. - - 5 
 
 Barbaro - - 
 
 The Colifeum 
 Scamozzi 
 
 26 \ more than 
 27 J 2 Diam. 
 
 Height of the lonick Enta- 
 blature, by 
 Min. 
 
 Palladio - - 11 lefs. 
 
 Temp, of For tun a\ 
 
 'Thefof Munellus zj/Tniam" 
 aUfeum - - tfiC 2 Diam - 
 
 Vignola - - - 1 8 J 
 
 ,■ Serlio - - - 13'^ 
 
 - - ijf Iefsthan 
 
 " 1 Y 2 Diam. 
 
 Vitruvius - - 19V 
 
 Bullant “ - - 37 J 
 
 Height of the Corinthian 
 Entablature, at 
 
 Afm. 
 
 TheTemp. of Pe^cc 8 A 
 P. of Septimus - 12Q 
 3 Columns of theT 
 
 3 columns 01 cnc c 2< cy 
 Forum Komanum 5 * \ 
 P: de Lorme - io-> 
 
 more than 
 2 Diam. 
 
 Frontifp. of Nero 
 Temple of Sybil 
 Palladio - - 
 Scamozzi 
 Vitruvius - - 
 
 Vignola - - - 
 
 »5Vn?/0 “ - 
 
 19 
 
 47 
 
 21 
 
 6 
 
 o 
 
 !9 
 
 12 
 
 14 
 
 lefs than 
 2 Diam. 
 
 Height of the Compojite 
 Entablature, at 
 
 Min. 
 
 The Arch of Lions 34 mores 
 The Arch Septimius 19 lefs 
 The Arch of Fitus 19 lefs 
 Vignola - - - 30 lefs 
 
 Serlio - - 30 more 
 
 Temple of Bacchus 2 lefs 
 Palladio - - - o 
 
 Scamozzi 3 Ids ^ 
 
 The 
 
 * 
 
 than 2 Diameters. 
 
A Sure Guide to Builders. 
 
 The Proje&ures of the Cornices of Entablatures is the next 
 Thing to be confider’d. Vitruvius (as aforelaid) has laid 
 down this Rule, that their Projethires he equal to their Height : 
 But this has not been exactly obferv’d either by the antique or 
 modern Archite&s ; for in the Antique they are fomewhat lefs, 
 and the Moderns for the Generality are lomewhat more, as the 
 following Table exhibits. 
 
 And fince that a determin’d Mean is abfolutely necelfary to be 
 fettled, for the young Student to work after, be the following 
 ProjeCtures therefore eftablilh’d, viz. Make their ProjeCtures 
 equal to their Heights in all the Orders, the Dorick excepted 
 when ’tis made with Mutiles, (which fhould be plain, without 
 any Scroll or Foliage) whofe Lengths require the entire Cornice 
 to have more ProjeCture than Height : But when ti e Dorick 
 Cornice is made without Mutiles, as it is in the Colifeum , then its 
 Proje&ure fhould be equal to its Height, as the Projectures of the 
 other Orders. 
 
 A TABLE exhibiting the different frojeffures of Entablatures , 
 according to the Proportions of antique and modern Architects. 
 
 <L> 
 
 x 
 
 w 
 
 <4H 
 
 o 
 
 <u 
 
 •s 
 
 G 
 
 <D 
 
 X 
 
 /“Temple of Vefla at Pivoli 
 lonick of the Colfeum 
 Dorick of the Colifeum 
 Arch of Confantine 
 Porch of Septimius 
 Infide of the Pantheon 
 <2 \ Temple of Concord 
 Temple of Fauflina 
 lonick of Scamozzi 
 Corinthian of Palladio 
 Corinthian of Vignola 
 Compofte of Palladio 
 ACompofte of Scamozzi 
 
 G 
 
 ci 
 
 jG 
 
 OJ 
 
 4-* 
 
 ri 
 
 <U 
 
 on 
 
 
 v-T 
 
 U X i 
 
 && 
 
 5-h 00 
 
 PM .tS 
 
 CO 
 
 JS 
 
 S 
 
 Min. 
 
 r 4 
 
 1 
 
 o - 
 o 
 
 2 
 
 o , 
 
 16 
 
 o - 
 
 3 
 
 0 - 
 
 4 
 
 1 
 
 v I A 
 
 U 2 
 
 »47 
 
 But 
 
The Entablature of the 
 
 A Sure Guide to Builders. 
 
 But the following have their Heights greater than their 
 
 Projectures. 
 
 /'Goldfmiths Arch ------ 
 
 <* 
 
 Altars of the Pantheon - 
 
 C ! 
 
 03 ! 
 
 Arch of I’itus ------ 
 
 4-> 
 
 lonick of the Theatre of Marcellus 
 
 u 
 
 Si 
 
 Temple of Bacchus - - - 
 
 rO 
 
 <U 
 
 Corinthian of the Colifeum - - 
 
 
 ( Temple of Manly Fortune - - 
 
 II 
 
 v 'o' 
 
 Arch of Septimius ----- 
 
 Portico of the Pantheon - - - - 
 
 ^ & 
 
 The three Columns of Campo vaccino 
 
 60 
 
 .•H co 
 
 r-i 
 
 Temple of Peace - 
 
 4-* 
 
 lonick of Palladio - - 
 
 S 
 
 V. 
 
 k lonick of Vignola - -- -- - - 
 
 Min. 
 
 6 
 
 7 
 
 0 
 
 5 > 
 
 5 
 
 3 
 
 I 2 
 
 i3 ■ 
 2 
 
 1 
 
 7 
 
 7 
 
 i 
 
 CHAP. IX. 
 
 Of Pillasters, and their Flutings. 
 
 |ILLASTERS (as has been before obferv*d) are 
 a Kind of fquare Columns, which appear to be in 
 Part funk within the Wall againft which they ftand, 
 and that Part of them which appears before the 
 Face of the Wall, is call’d their ProjeCture. 
 
 The Projectures of Pillafters are to be confider’d with refpeCt 
 to the Order they are of : As frjl y The ProjeCture of Fujcan 
 and Derick Pillafters need not be more than one fifth, or one 
 fixth Part of their Diameter, excepting when they are to receive 
 Imports againft them, and then they mu ft project more, as one 
 Fourth, &c. that the Projection of the Import may not project 
 before the Face of the Pillafter, 
 
 Secondly , 
 
A Sure Guide to Builders . 
 
 Secondly , PiilaHers of the Ionlck , Corinthian , and Compojite 
 Orders, Ihould have a Projection always equal to half their Di- 
 ameters, that the Returns of their Capitals may terminate exactly 
 in their Middles, whereby they have the molt noble Effe&. 
 
 And as Pillafters have but one Face clear of the Wall, they 
 are therefore feldom diminifh’d, but when Handing with Co- 
 lumns, with the Entablature continu’d equally over both with- 
 out any Break ; and at fuch Times, they Ihould be equally di- 
 minilh’d in Front with the Columns, leaving the return’d Sides 
 to the Wall perpendicular : But when a Pillafler Hands at an 
 Angle, with two Faces clear of the Walls, they are fometimes 
 diminifh’d both Ways, tho’, I think, ’tis an improper Practice ; 
 for as the Angles of a Building Ihould be made firm, and Hronger 
 than any other Part, they ihould not be weaken’d by being 
 diminifh’d, but left entire and perpendicular. 
 
 PiilaHers are either fluted or plain, and are fometimes fluted, 
 tho’ the Columns they accompany are not, as in the Porch of 
 the Pantheon , which perhaps might be omitted by the Columns 
 being made of Marble that is of divers Colours, which, in fome 
 Meafure, deflroy the Beauty of Flutings. 
 
 And contrarily, there are alfo Columns that are fluted which 
 accompany PiilaHers that are plain, as in the Temple of Mars 
 Ultor , and the Porch of Septimius. 
 
 There Ihould be no Flutings made on the Return of PiilaHers, 
 when they have lefs Proje&ure than half their Diameter, not- 
 withHanding ’tis now ufually pra&is’d to introduce two Flutes 
 on each Return. 
 
 The Number of Flutes after the antique Manner were diffe- 
 rent, as 7 and p ; as in the Porch of the Pantheon , the Arch of 
 Septimius , and that of Conflantine , there are but 7, and within 
 the Pantheon they have p, altho’ the Columns have but 24. 
 
 The Flutings of PiilaHers Ihould be always odd in their Num- 
 ber, unlefs in Semi-pillaflers Handing in Angles, where they 
 fhould each confiH of 4 Flutes inflead of 3 and a half, and 5 
 inflead of 4 and a half, when the whole has but 7 or p. 
 
 But ’tis to be underflood, that in confideration of making 
 each half Pillafler with 4 Flutes, they muH therefore be made 
 fomething more than 30 Minutes in Breadth, that the carved 
 Parts of Capitals may be fo placed, as for none of their Leaves, 
 
 &c> 
 
 149 
 
icjo A Sure Guide to Builders. 
 
 &c. to interfere with one another, or to render them lharp- 
 pointed, with their middle Volutes too clofe together. 
 
 The Capitals of Pillafters are of the fame Height as thofe of 
 Columns, but their Breadths are greater when they are not dimi- 
 niftfd at their Aftragals, and their Number of Leaves are gene- 
 rally the fame, which are 8 in Number, on the four Faces of 
 the Capital ; but there are fome Capitals of Pillafters that have 
 1 2 Leaves, viz. 3 on every Face, as in the Ftontilpiece of Nero, 
 and the Baths of DiocJeJtan. 
 
 'Tis ulual to place the Leaves of the Capitals of Pillafters in 
 fuch Manner, that thofe in the lower Row, where the lelfer 
 Leaves are, conftft of two on each Face, and in the upper Row 
 one entire, in the Middle with two half Leaves on the Sides, 
 which are equal to half of one of the great Leaves folded back 
 upon the Angle. 
 
 The upper Parts of the Tambour or Vafe of the Capitals are 
 ufually made fomething circular and prominent, as that of the 
 Bafilick of Antoninus , which advances the 8th Part of the Di- 
 ameter at the Bafe, that in the Porch of Septimius one Tenth, 
 and in the Portico of the Pantheon one Twelfth. See the 
 Capital of Plate XXVIII. 
 
 CHAP. 
 
A Sure Guide to Builders. 151 
 
 C H A P. X. 
 
 On divers Errors committed by fome Architects 3 in their 
 Manner of placing Columns and Eillajiers at the 
 Angles of Buildings , See. 
 
 LTHO’ Pillafters, or rather fquare Columns, are 
 the moft proper Supports of Entablatures at the 
 Quoins of a Building, yet fometimes Columns are 
 placed in their Stead, as at D and AB, Fig. L 
 Plate XLII. 
 
 Where ’tis to be obferv’d, that the double Columns AB are 
 entirely falfe and erroneous ; for where two Bodies cut into 
 each other as they do, it cannot be faid that they are perfed 
 Bodies ; for by their Interfedion they conftitute one irregular 
 Body, which is nothing near fo beautiful as the lingle Column 
 D which fupports the Entablature, as well from itfelf to E as 
 to A, and is abfolute alfo, as well as much more natural \ but 
 in Fad, neither the double Column A B, or fingle Column D, 
 are near fo agreeable in an Angle as the Pillafter C, whofe two 
 Faces do as well refped the Angle itfelf, as it does the other 
 Pillafters F and G. 
 
 The fecond Error is, the placing of half Pillafters on tha 
 Sides of a whole Pillafter, as 1 and E on each Side of K ; 
 whereas if two entire Pillafters were fo placed, as for their 
 Capitals and Bafes to be clear of each other, as GH, they 
 would perform the fame Office, and have a much grander 
 Afped, than when cut into Halves, as I and E. This laft is a 
 very common Error, and may be feen in a great Number of 
 Frontifpieces of Doors in both City and Country, to the no fmall 
 Difcredit of their Makers or Surveyors, who direded their 
 PofitionSo. 
 
 The 
 
i £2 A Sure Guide to Builders. 
 
 The third Error is, the placing of half Pillallers in the in- 
 terior Angles of Buildings, as LF, which has a very dif- 
 agreeable Effe£l, when we confider how the Body of one muft 
 cut into the Body of the other • and that the Angle Pillafter 
 C, which performs the very fame Office of fupporting, does not 
 only take up much lefs Space, but is agreeable and natural, 
 as well to the Angle itfelf wherein it Hands, as to the Pillallers 
 G F, &c. with which it ranges. 
 
 It was the Practice of the Antients, to divide the Fronts of 
 their Buildings into as many Heights of Orders, as they con- 
 fifted of Stories in Height ; as the Banquetting-Room at 
 Whitehall , which being divided into two Stories, is therefore 
 adorn’d with two different Orders of Columns that are truly 
 grand and noble. 
 
 Therefore it is to be remember’d, that one Order of Columns 
 muft never run through two grand Stories, except in Churches, 
 grand and magnificent Palaces, &c. where Views being very 
 extenfive, every Part muft therefore have a grand and noble 
 Afpeft, and nothing mean and little. 
 
 The fourth Error is, the breaking or flopping of the Bed- 
 Mouldings of Pediments, for the Sake of introducing fome trifling 
 Ornament, as in the Pediments over the Windows of St. Mary 
 Je Strand ; or for the Sake of continuing up fome prepoflerous 
 Rufticks, &c. as in the Pediments over the Windows of the 
 Chancel End of St. Georges Church, Hanover- Square. The 
 Defign of Pediments placed over Doors or Windows, was origi- 
 nally intended for Shelter more than Ornament, and therefore 
 their upper Parts were laid with fuch an agreeable Reclination, 
 as to call off Rains, &c. as the Roofs of Dwelling-Houfes do. 
 
 The Ufe of the continu’d Bed-Moulding and Corona in a Pe- 
 diment, is to tye in the Thruft of the reclining Cornice, as 
 Girders, &c. do, which tye in the raffing Plates whereon the 
 Feet of Rafters Hand; which, for want thereof, might, by their 
 Weight and Pufh, thruft out the perpendjcular Walls whereon 
 they Hand, and come down. 
 
 CHAP. 
 
A Sure Guide to Builders. 
 
 J 53 
 
 CHAP. XI. 
 
 Of PEDIMENTS. 
 
 H E various Rules by which the Pitches or Heights 
 of Pediments are determin'd, are the following, viz. 
 
 Rule I. (Fig. IX. Plate XL VI.) 
 
 i. Bifed the Cima Reverfa AD in B, and divide BD into fix 
 equal Parts. 
 
 a. On B raife the Perpendicular B C, which make equal to 
 B E, that is, to two fixth Parts and one half Part of BD; fo 
 fhall G be the Height of the Pitch requir'd. 
 
 Rule II. (Fig. X.) 
 
 i . Bifed the Cima Reverfa E C in D, and E D in G. 
 
 a. On D ered the Perpendicular DA, making DA equal to 
 G D ; fo fhall A be the Height of the Pitch requir'd. 
 
 Rule III. (Fig. VI.) 
 
 i. Bifed the Cima Reverfa Alin H, and on H ered the Per- 
 pendicular HG, continuing it downwards towards K. 
 
 a. Make HK equal to IH, and KG equal to KI ; fo fhall 
 G be the Height of the Pitch requir'd. 
 
 Rule IV. (Eg. I.) 
 
 i . Bifed B 3 in F, and divide B 3 into three equal Parts at the 
 Points 1 and a. 
 
 a. Make AF equal to one Third of B3, and GA equal to 
 Ae ; fo will G be the Height of the Pitch requir’d. 
 
 X 
 
 Rule 
 
i$4 
 
 A Sure Guide to Builders. 
 
 Rule V. {Fig. II.) 
 
 1. Bifed Ip in K, and divide 1 51 into nine Parts. 
 
 2. Make KH equal to live of thole equal Parts, and HN 
 equal to HC ; fo will N be the Height of the Pitch requir’d. 
 And thefe are the various Rules by which the Pitch of Pedi- 
 ments are determin’d, according to the Will of the Architect. 
 
 The feverai Sections or Parts of Pediments, Fig. III. IV. 
 V. VIII. XI. and XII. exhibit an erroneous Method often 
 nfed by many Builders in the Heights of Raking Cornices in 
 Pediments, w r ho believing them to be equal to a Level Cornice, 
 do therefore make an Angle in the upper Moulding, where there 
 Ihould be none : As for Example, Fig. IV. the upper Mould- 
 ing is an Ovolo ; which, inftead of being work’d at its full 
 proper Height BC, its upper Part HB is continu’d on to A, 
 where it meets DA, which is the. fame Height above FE, as 
 BH is above EG in A, and forms the Angle DAB, where there 
 Ihould not be any ; for the Spring or Rile of the Raking Cor- 
 nice Ihould begin at B, whereby it is fo much higher, as is pro- 
 portionable to its extraordinary Height above the Level Cornice ; 
 wherefore its Afped becomes truly grand and noble, to what 
 the others do, as herein exhibited, which are poor and mean in 
 Afped. The like is to be feen in all the others, which muft 
 ever be avoided in Pradice. 
 
 CHAP, 
 
I 
 
 A Sure Guide to Builders* 
 
 CHAP. XII. 
 
 Of the ‘Proportion s of Halls, Antichambers, Chambers, 
 Galleries, Gates, Doors, Windows, &c. according to 
 Andrea Palladio. 
 
 ALLS fhould have fuch Proportions, that their 
 Lengths fhould not be lefs than twice their Breadth, 
 nor more than three times. 
 
 That their Heights with flat Cielings be not lefs 
 than two Thirds of their Breadth, nor more than 
 three Fourths. 
 
 That their Heights with arched or coved Cielings be not lefs 
 than five Sixths, nor more than eleven Twelfths of their Breadth. 
 
 i . Antichambers fhould have fuch Proportions, that 
 their Lengths be always equal to the Diagonal of a Square, 
 whofe Side is equal to the Breadth of the Room ; which Breadth 
 muft be proportion’d to the whole Building by the Difcretion of 
 the Architect 
 
 That their Heights are not lefs than two Thirds of their Breadth, 
 nor more than three Fourths of their Length, when with flat 
 Cielings ; and when arched, not lefs than five Sixths, nor more 
 than eleven Twelfths of their Breadth. 
 
 3. Chambers fhould have fuch Proportions, that their 
 Lengths never exceed the Breadths more than one Fifth ; that 
 their Height in the firft Story be not lels than two Thirds of 
 their Breadth, nor more than three Fourths of their Length ; the 
 Height in the fecond Story to be eleven Twelfths of the Height 
 of the firfl: ; and the third three Fourths of the fecond. 
 
 The Eafl: Expofition being generally the pleafanteft, and 
 cooleft, in Summer, we fhould fo contrive the Situation of our 
 Chambers of Delight, as to have the Advantage of that Afped; 
 but when fine Profpefts, &c. happen that are otherwife fituated, 
 
 X 1 we 
 
A Sure Guide to Builders. 
 
 we fhould always be fure of preferving them, fince they contri- 
 bute greatly to the Pleafure of a Country Seat. 
 
 4. Galleries fhould have fuch Proportions, that their 
 Lengths are not lefs than five Times, nor more than 8 Times 
 their Breadths : That their Breadths in grand Buildings be not 
 lefs than 16 Feet, nor more than 24. 
 
 That their Heights be equal to their Breadths when with flat 
 Cielings ; and when arched one Fifth, one Fourth, or.one Third. 
 Their Situation is beft when towards the North, becaufe they 
 are generally adorn’d with good Pi&ures, which have the beft 
 Effed in a North Light. 
 
 5. Gates fhould have fuch Breadths that fhould not be lefs 
 than 7 Feet, nor more than 12 Feet; and their Heights to be 
 never lefs than their Breadth and a half, nor more than twice 
 their Breadth, which is allow’d to be the beft Proportion of all 
 others. 
 
 6. Doors fhould have fuch Proportions, that their Heights 
 be always equal to double their Breadths. 
 
 That their Breadths be not lefs than 2 Feet and a half, nor 
 more than 6 Feet : That thole of the fecond Story be placed 
 directly over them of the firft, with Semi-circular Arches to dis- 
 charge the Weight from their Heads. For Doors, and their 
 Ornaments, fee Plates 'KL.llI. XLVII. XLVIII. XLIX. L. LI. 
 LIL LIII. LlV. LV. LVI. 
 
 7. Windows fhould be proportion’d to the Rooms they are 
 to illuminate, not only in Magnitude, but Number alfo. 
 
 Windows of the firft or Ground Story, fhould have their 
 Heights equal to the Diagonal of a Square, whofe Side is equal 
 to the Breadth of the Window. 
 
 Windows of the fecond Story fhould have their Heights equal 
 to double their Breadths ; and thole of the third or Attick Story 
 fhould be exa&ly lquare, if we would follow the Proportions of 
 the Antients. 
 
 But Palladio makes the Height of thofe of the firft Story equal 
 to twice their Breadths, with the Addition of one Fourth, one 
 Third, or one Half: Thofe of the fecond eleven Twelfths ol 
 
 the 
 
A Sure Guide to Builders. 
 
 the Height of the firft ; and the third or Attick Story three 
 Fourths of the Height of the fecond. 
 
 The Breadth of Windows fhould be fo proportion’d, as not to 
 exceed the Breadth of the Peers between them ; nor fhould they 
 be plac’d near the Angles or Quoins of the Building, left the 
 Structure be weaken’d thereby. For the feveral Ornaments of 
 Windows, fee ty/ate XLIII. 
 
 CHAP. XIII. 
 
 Of Floors, Pavements, Chimneys, Staircafes, &c. 
 
 LOORS are of divers Kinds, as Earthen, Stone, 
 Brick, and Boarded, which laft being the warm- 
 eft, is therefore rnoftly ufed in this Kingdom. 
 
 The chief Things to be obfery’d herein, are 
 firft, that they be level throughout every Story, 
 without going up and down Stairs out of one Room into ano- 
 ther : That the Height of the firft or Ground Floor be never 
 lefs than i Foot, nor more than 4 Feet, above the Surface : 
 That Ground Joifts be of Oak, of fuch Lengths and Scantlings 
 as exhibited in the Ad of 1 9 Car. II. 
 
 That let the Manner of finishing be either with folding Joints, 
 ftraight Joints, &c. be fure that they are perfedly dry, and the 
 Sap clean lifted out, before they arc laid, and afterwards remain 
 a full Year before they are nail’d down } that being fully 
 fhrink’d, they may be laid clofe together, without having large 
 Crevices between them, which always happen when laid green,, 
 and nail’d down at the fame Time. 
 
 2. Pavements are of divers Kinds, as firft of Purbeck 
 Stone, moft proper for Kitchens, Cellars, &c» Secondly, of 
 Portland Stone, proper for Hails, Veftibles, <5 Y,. : And thirdly, 
 
 « of 
 
 *57 
 
A Sure Guide to Builders . 
 
 of Marble, which is as often ufed with Portland Paving, as by 5 
 itfelf alone. 
 
 The moft beautiful Pavements of Marble that 1 ever faw, are 
 that admirable Floor of the Grotto of the Honourable Mr. 
 Scawen at Carjhalton in Surrey , and that of the Cold Bath of the 
 Honourable 'John Roberts at Twickenham in Middlefex y which, 
 with other Ornaments of abfolute Ufe to Workmen, I {hall 
 fpeedily communicate in a fecond Part. 
 
 Thefe Pavements are each compos’d of three different Kinds 
 of Marble, as white, black, and Dove-colour’d, which are fo 
 difpos’d of, that in the Dusk of an Evening, they both appear 
 as if they confifted of a Number of long Cubes, lying with 
 their Angles upwards, forming of Ridges like the Roofs of 
 Houfes, that appear dangerous to walk upon, and therefore 
 Strangers are naturally apt to forbear going thereon, left they 
 fall by the feeming Unevennefs thereof 
 
 3. Chimnies are of divers Kinds, as firft, Kitchen Chim- 
 nies, which fhoijld be light and fpacious, and their Depth not 
 lefs than a Feet and a half, or 3 Feet. Hall Chimnies fhould 
 have the fame Depth ; their Breadths between Jaumb and Jaumb 
 not lefs than 6 Feet, nor more than 8 ; and their Heights from 
 the Floor to the under Part of the Mantle Tree from 4 Feet and 
 a half to 5 Feet. 
 
 Chamber Chimnies may have their Breadths from 4 Feet to 7 
 Feet, and their Heights 4 Feet and a half. Chimnies in Studies 
 may be in Breadth from 18 Inches to 4 Feet, and their Heights 
 the fame as thofe of Chambers of the fame Story. 
 
 The Depth of Chimnies fhould be never lefs than 1 Feet and 
 a half, nor the Thicknefs of the Jaumbs ever lefs than 18 
 Inches. 
 
 Great Care fhould be taken to give the Bread: of every Chim- 
 ney a fufficient Breadth ; for when they are choak’d in that Part, 
 they never fail of fmoaking the Rooms whereunto they belong y 
 nor is there any Cure for fuch Chimnies, but pulling them down, 
 and rebuilding them again larger. 
 
 The Funnels muft be proportion’d to the Chimnies, fo as not 
 to be too narrow for the Smoak to pafs freely, nor too large for 
 the Winds to drive it down into the Rooms. 
 
 
 When 
 
A Sure Guide to Builders. 
 
 When the Funnels of Chimnies are not carry’d above the 
 Level of the Roof, the reflex Winds will oftentimes drive down 
 the Smoak with great Force ; therefore due Care muft be taken 
 to carry them above the Height of fuch reflecting Powers. 
 
 That no Timber be laid within the Funnel of any Chimney, 
 on Penalty as the Ad of 22 Caw II. cap. 1 1. 
 
 4. Staircases fhould be fo contriv’d and fituated, as to be 
 fpacious, eafy in Afcent, and with good Light : Their Breadth 
 fhould not be lefs than 3 Feet and a half, nor more than 10 Feet 
 or 1 2 Feet in the moft magnificent Buildings : The Height of 
 Steps fhould not be lefs than 4 Inches, nor more than 6 Inches, 
 or 7 at the moft • and their Breadths not lefs than 10, nor more 
 than 1 8 Inches. 
 
 5. Laftly , The Kitchen fhould be fpacious and light, and as 
 far remote from the Parlour as poffible ; and, indeed, this, as 
 well as other Offices, are beft when fituated under Ground, where 
 Springs lie deep enough to allow thereof. 
 
 FINIS , 
 
 159 
 

0OQ3OQ COQ Q OQ3OQOOQ 5O5 6Q05OQQQ9 SQQ3Q0 
 
 A N 
 
 APPENDIX. 
 
 WHEREIN 
 
 The feveral Acts of Parliament, 
 
 now in Force , relating to Builders, Building, and 
 Materials, are explain d y for the Service of Surveyors , 
 Mafier Builders , Workmen y and Proprietors of 
 Houfes i See. 
 
 i fl y With refpefi to Foundations. 
 
 Stat. 22 Car,. II. Cap. u. 
 
 O Builder fhill lay Foundations, until that proper Sur-FoundatL 
 veyors (appoimed by the Lord Mayor, Aldermen, and 
 Common Council) have view’d the fame, and- feen 
 the Party Walls and Peers equally fet out. But before 
 fuch Survey is taken, the Builders (hall go to the Cham- 
 berlain and enter their Names, and the Places where their Buildings 
 are to be creeled, and at the fame time pay Six Shillings and Eight 
 Pence, taking an Acquittance for the fame : And upon the Builders 
 exhibiting the faid Rcce ; pt unto the proper Surveyors, or any of 
 them, they (hall furvey and let out the Foundation within three 
 Days after fuch R. quell : And in Default of Payment, the Cham- 
 berlain may fue for it before the Mayor and Aldermen, 
 
 Y 
 
 N. B. It 
 
162 jn APPENDIX. 
 
 N. B. It is very convenient to add one Brick in Thicknefs to 
 the Foundation of every Party- Wall, more than is appointed by 
 the following Ads, to be fet off in three Courfes, equally on 
 both Sides. 
 
 idly y With refpetf to Party- Walls. 
 
 19 Car. II. 
 
 Hp H E better to prevent Fire from having a free Paffage from 
 *■* Houfe to Houle, ’tis Ena&ed, That between every two Houfes 
 there fhall be one Party- Wall of Brick or Stone, and of fuch 
 Thicknefs, as deliver’d in Page 163. 
 
 And to prevent Difputes between Landlord and Landlord, in re- 
 fped to the Expences thereof, it is hereby Enaded, That there fhall 
 be Party- Walls and Party-Peers fet out equally on each Builder’s 
 Ground, and whoever firft builds his Houfe, fhall be oblig'd to 
 Tooth- leave a convenienr Toothing In the Exrreams of his Front and 
 j" t | stobe Rear Walls, that when his Neighbour or Neighbours is, or are dif- 
 pos’d to build up his or their Houfe or Houfes, the Walls thereof 
 may be incorporated, and firmly bound together. 
 
 O B $ E R V A T 1 O N. 
 
 But ’tis to be obferv’d, that if the firft Houfe be built any eonfi- 
 derableTime before thefccond, and is wholly fettled in its Courfes, 
 1 can’t fee how the other Buildings, afterwards built into the 
 Toothings of the firft, can be incorporated and firm j for fince that 
 every Building of Brick doth fettle very much as the Work be- 
 comes dry, the fettling of the laft Buildings muft caufe a Fradure at 
 the Toothings of the firft, which being then fettled, refills the 
 Settlement of the laft, and therefore cannot be firm and found. 
 Hence ’tis much the belt Way to build all together, if Time and 
 Conveniency permits. 
 
 Expence To return. Nor fhall the fecond Perfon build againft the faid 
 of Party- Party- Walls, or on their own contiguous Grounds, until they have 
 beequaiiy P a id ^ firft Builder the Moiety of the Charge of fuch Party- Walls, 
 paid, with with Intereft at 6 per Cent . from beginning of firft Building : And 
 imereft. p rov id ec [ that any Differences arife concerning the Value of fuch 
 
 W alls. 
 
An APPENDIX. 163 
 
 Walls, they fliall be referr’d to the Alderman of the Ward and his 
 Deputy ; and where one of them is a Party, or where they cannot 
 compofe fuch Difference, the Lord Mayor and Court of Aldermen 
 fliall. 
 
 But by an Aft made in the 7th Year of her late Majefty QueenExpence 
 Anne , intitled, An Aft for the better preventing of Mi [chiefs of Parry- 
 that happen by Fires, it is Enafted, That the firft Builder fliall be to 
 paid by the Owner of the next Houle after the Rate of 5/. /wbepaid, 
 Rod, as foon as he fliall have built the faid Party- Wall. b V l Ann,e 
 
 And in Confederation that divers new Houfes have been, and 
 may be erefted fingly on new Foundations, within the Limits of 
 the Cities of London and M^eftminfter, or other Pariflies or Places 
 comprifed within the Bills of Mortality, there was an Aft made in 
 the 11th Year of his late Majefty King George , intitled. An Aft 
 for the better regulating of Buildings , which ftriftly forbidsSecond . 
 all fecond Builder or builders whomfoever, to make ufe of,^ 1 ^®^ 
 or take the Benefit of fuch Parry. Wall and Fence- Wall, fo firft u feParty- 
 built at the Expence of the firft Builder ; nor fliall any fuch fecond 
 Builder or Builders, his, her, or their Executor?, Adminiftrators, or^ e l ret0 
 Afligns, on any Account whatfoever, lay any Wood or Timber, or 
 cut any Hole for Cupboards, Prefles,£^r. in fuch Party- Wall, under Penalty, 
 the Penalty of forfeiting the Sum of Fifty Pounds. 
 
 The Thicknefles of Party-Walls by 19 Car. II. were appointedThkk- 
 to conftft of one Brick and half in the Cellars, and Stories abovcJ^ t esof 
 Ground, the Garrets excepted, which were to be of one Erick orWaik’by 
 nine Inches in Thicknefs only. 190^.11. 
 
 But by the aforefaid Afts made in the 6th and 7th of her late 
 Majefty, it is Enafted, That from and after the 1ft of May 1708, 
 all and every Houfe and Houfes that fliall be built or erefted upon 
 any Foundations; either new or old, with the above Limits, fliall 
 have Party-Walls between Houfe and Houfe wholly of Stone orThkk- 
 Brick, and of the Thicknefs of two Brinks length at the leaft in£ efiesof 
 the Cellar and Ground Stories, and one Brick and a half or thir Waiis" by 
 teen Inches thick upwards, from thence quite thro’ all the remaining 6 Sc 7 
 Sto. ies, unto eighteen Inches above the Roof. Anh,g ’ 
 
 And to prevent the ill Confequences that may arife from Wood 
 or Timber laid in Party- Walls, which may commui i:are Fire from 
 one Houfe into the next, it is Enafted by the aforefaid Aft: of the 
 nth of his late Majefty, Fol. 479. That it fliall not be lawful to 
 
 Y 2 make, 
 
i<?4 An AT T E N-D IX. 
 
 make, or have in any Party. Wall of any Houfe, which, after the 
 24th of June 1725, (hall be ereded or built within the preceding 
 No Door, Boundaries or Limits, any Doorcafe, Window, Lentil, Breaft- 
 or Wood Summer, or Story Polls or Plates whatfoever, unlefs where two or 
 of any more Houfes are join’d or laid together, and fo ufed as one fingle 
 kind tobef4 ou f c . anc j that to be no longer than during the Time of fuch 
 Walis^'ULgCj upon Pain or Penalty that the Owner of every fuch Houle, 
 Penalty. f° r evc vy fuch Offence, ill all forfeit the Sum of Fifty Pounds. 
 
 And in Confideration that Party-Walls built upon old Founda- 
 tions may decay, and become dangerous and needful to be rebuilt 3 
 and whereas Differences have, and may again arife, between the 
 two Landlords, concerning the Expences of taking down the fame, 
 ihoring up the Floors, and rebuilding them again, it is therefore 
 by the aforefaid Ad, Enaded, That from and after the 24th 
 Day of June 1725, all and every Perfon and Perfons inhabit- 
 ing in any Place or Places in and about the Cities of London and 
 Wejlmmjler , or any other Place or Places comprifed within the 
 weekly Bills of Mortality, or within the Parifh of St. Mary le Bone 
 and Taddington, or within ihc Parities of Chelfea and St. ‘ 'Pmcras , 
 who fhall build, or caufe to be built, any Houfe or Houfes upon 
 Party- any Foundation, old or new, and who (ball find it abfolutely ne- 
 Waiis, ceffary to take down any decay’d Party- Wall between fuch Houfe 
 built and and the next adjoining Houfe, fhall give Notice thereof in Writing 
 paid for to the Owner or Occupier of fuch adjoining Houfe, full three 
 bothVar- Months before fuch Party-Wall fhall be begun to be pull’d down, 
 ties agree, to the Intent that the fame may be view’d by four able Workmen, 
 within the Space of one Month next after the Service of fuch 
 Notice ; which four Workmen are to be equally appointed by 
 both Parties; that is, each Perfon to appoint two thereof, or more 
 if requir’d, when they both do agree thereto. But in cafe that the 
 iiovre- Landlord or Occupier of the next adjoining Houfe, will not agree 
 built to the rebuilding of fuch Party -Wall or Walls, or is incapable of 
 bothPar-P a yi n S the immediate Moiety thereto, and fhall negled to nominate 
 ties can’tand appoint, within three Weeks, (next after the Service of Notice 
 agree. as aforefaid) fuch Workmen, that then the other of the faid Parties 
 fhall nominate and appoint four, or more able Workmen, who 
 fhall view the Party-Wall requir’d to be taken down and rebuilt ; 
 which Workmen, or the major Part thereof, fhall certify in Writ- 
 ing under their Hands to the Juftic-es of the Peace, in the next 
 General or Quarter Seffions of the Peace to be holden for the 
 
 City 
 
An APPENDIX. i <5$ 
 
 "City or County, where fuch Party-Wall is limited and being, 
 that fuch Party-Wall is ruinous, and needful of being rebuilt, &c. 
 
 And provided that any Perlon or Perfons whomfoever (hall 
 think him, her, or themfelvcs injur’d by fuch Certificate, the faid 
 Juftices fnall luramon before them one or more of the faid Work Jufliccs 
 men, or other Perfon or Perfons, whom they fhall think fir, and^j^p^ 
 fhall examine the Matter upon Oath; and their Determination fhallferences 
 be final and conclufive to all Parties, without any Appeal from thcp*^2® n 
 fame. 
 
 But ’tis to be obferv’d, that a Copy of the Workmens Certificate 
 muff be deliver’d to the Occupier or Owner of fuch next adjoining 
 Houfe, or left there, within three Days after fuch Certificate fhall 
 be made to the Juftices as aforefaid ; and if there fhall be no Appeal 
 from the fame within three Months after, in every fuch Cafe, if 
 fuch Landlord or Occupier fhall refufe or neglect to fhore up and 
 fupport his, her, or their Houfes, within fix Days after the Expira- 
 tion of the faid three Months Notice, that then the firft Builder or 
 Builders, with his or their Workmen, (giving Notice as aforefaid) 
 may lawfully enter into fuch Houfe or Houles (at all feaionable 
 Times} with Workmen and Materials, and therewith fhore up and 
 fupport the fame ; the Expence whereof fhall be paid by the Land-J^ 
 lord or Occupier, as alfo the half Expence of the Parry- Wall builtpaidfor 
 by the firft Builder, after the Rate of 5 /. per Rod, for every Rod of^' j^' 
 Work contain’d therein. a s " 
 
 And when the firft Builder fhall have built the faid Party-Wall, 
 he fhall leave at fuch next Houfe, with the Landlord or Occupier, 
 a true Meafurement of the Quantity of Brick-work contain’d a 
 therein, within ten Days after fuch Party* Wall fhall be fo built trueMea- 
 and complcated, of which, one half Moiety, at the Rate aforefaid, ^. re r ^ 1 e enc 
 as alfo the Expence of fhoring and fupporting, fhall be paid by the Quantity 
 Landlord or Landlords thereof, or their Tenants or Occupiers, who and . Ex - 
 are hereby impower’d to pay and deduct the fame out of the next shoring, 
 Rent that fhall become due. And provided that Negleft or Re- 
 fufal of the faid Money, fo due, be made, and remain unpaid for 
 the Space of twenty-one Days, after Demand thereof, then it fhall Expenco 
 and may be lawful to and for fuch firft Builder or Builders, his,j.^ r ^~ 
 her, or their Executors and Adminiftrators, to fue fuch Landlord 
 or Landlords for fuch Sums, fo proportionably due, by A&ion of 
 Debt, or on the Cafe, Bill, Plainr, or Information, in any Court 
 of Record at JVeftminfter, &c. 
 
 And 
 
i66 An APPENDIX. 
 
 And here note , That the Law here deliver'd, relating to the re- 
 building of decay’d Party-Walls of either Brick or Stone, the fame 
 is to be underftood and obferv’d in old Houfes, where, inftead of 
 having one Party- Wall between them, as this A£t dire&s, have two 
 Timber Walls or Partitions, one belonging to each Houfe, and 
 Ncw p ar .feparate from one another ; therefore be it underftood on all Sides, 
 ty Wails, that wholoever, for the Safety of his or their Houfes, will pull 
 on'oid UllC ^ own own Wooden Walls or Partitions, and, inftead thereof, 
 Founda- build a Party- Wall of Brick or Stone, he or they are alfo impower’d 
 Timber to P u ^ down next WoQden Wall or Partition of the next ad- 
 Parti, joining Houfe or Houfes, (if the Landlord will not agree thereto) 
 ti°ns. an d proceed in every Step, as before deliver’d for the rebuilding of 
 decay’d Party-Walls of Brick or Stone: Which new-built Wall 
 muft be placed equally on both Premifes ; that is to fay, half the 
 Thicknefs of the Foundation on one Landlord’s Land, and the 
 other Half on the others ; and that all Settings-off in the Founda- 
 tion be equally the fame on both Sides, as dire&ed in the Beginning 
 hereof. 
 
 3 dly.. With refpetl to Front and Rear Walls. 
 
 By 19 Car. II. 
 
 Front and T-jf OUSE S of the firft Rate of Building fhall have their Cellar 
 Rear i A Walls in Front and Rear of two Bricks in Thicknefs, the firft: 
 theV’ ap d fecond Stories of one Brick and a half, and the Garrets of one 
 Thick- Brick only. 
 
 ^dres. Houfes of the fecond Rate of Building, fhall have their Cellar 
 Walls in Front and Rear two Bricks and a half in Thicknefs, the 
 . fi ft and fecond Stories two Bricks, the third Story one Brick and a 
 half, and the Garrets one Brick only. 
 
 Houfes of the third Rate of Building, fhall have their Cellar 
 Walls in Front and Rear three Brjcks thick, in the firft Story two 
 Bricks and a half, in the fecond, third, and fourth Stories one Brick 
 and a half, and in the Garrets one Brick only. 
 
 Houfes of the fourth Rate of Building, being chiefly for Noble- 
 men, &c. have their Thicknefs left to the Dil’cretion of the 
 Architect 
 
 By 
 
An APPENDIX. 
 
 1 6j 
 
 By the 7 Anna before- mention'd, no Modilion or Cornice of 
 Wood or Timber fhould thereafter be made, or fuffer’d to be fix’d 
 under the Eaves of any Houfe, or againft any Front or Rear Wall or nice in 
 Walls thereof ; but that all Front and Rear Walls of every Floufc Front or 
 and Houfes fiiall be built entirely of Brick or Stone, (the Windows walls, 
 and Doors excepted) to be carry ’d two Foot and a half high above 
 the Garret Floor, and coped or cover’d with Stone or Brick. 
 
 4 thly, With refpeff to Windows. 
 
 • 7 Anni, Pol. 26 3. 
 
 YIFHEREAS it has been the Pra&ice of Workmen to place 
 ” Window Frames and Door-cafes very near, and quite rang- 
 ing with the outfide Face of the Wall, whereby they are not only 
 fully expos'd to Weather, and thereby decay fooner than thofe 
 which are fhelter’d by being placed at a moderate Diftance within 
 the Walls, but in time of Fire are more liable to be fired, whereby 
 many Houfes may be deftroy'd : For Prevention of fuch Pra&ice it 
 is Ena&ed, That after the lft Day of June 1709, no Door Frame Window 
 or Window Frame of Wood, to be fix’d in any Houfe or Building 
 within the Cities of London and Wejtminjier , or their Liberties, cafes.how 
 fhall be fet nearer to the outfide Face of the Wall than four Inches >^ t C [ e - d n 
 nor fiiall any Brick-work be placed or bear upon Timber, or any Xe Wall. 
 Sort of Brick-work, excepting upon Plank and Piles where Foun- 
 dations are bad, on Pain of three Months Imprifonment without 
 Bail or Mainprize. 
 
 But by the nth of his late Majefty, it is made lawful to 
 place Brick- work upon or over Door-cafes and Windows, (pro- Arches to 
 vided that the Weight thereof is difeharg'd by Arches turn’d overset- 1 *™ 
 them) or on Lentils, Breaft Summers, Story Pofts or Plates, where Doorsand 
 requir’d for the Convenience of a Shop or Shops only. Windows 
 
 5 thly ^ With refpetl to the Conveyance of Water from 
 the Wops of Houfes and Balconies. 
 
 TT is Enafted by the aforefaid of his late Majefty, That the 
 * Water falling from the Tops of Houfes to be built after the 
 24th of June 1725, within the aforefaid Limits, or from the Bal- 
 conies, 
 
1 68 An APPENDIX. 
 
 conies, Penthoufcs, &c. ffiall be convey’d into the Channels by 
 Party Party Pipes, fix’d on the Sides or Fronts of the (aid Houfes, gn For* 
 fo convey fe it u r e of Ten Pounds for every Offence. 
 
 Water. 
 
 6thIy J With refpetf to Chimnies* 
 
 By the 7th Ann£, 
 
 jaumbs, IT is Enabled, That all Jaumbs and Backs of Chimnies which 
 Th'ck or nia T built, fhall confiff of one Brick in Thicknefs at 
 
 neiles. ^ ie I ca ff> from the Cellars to the Roof 5 that all the Infides of fuch 
 Chimnies fhall be four Inches and a half in Breadth. 
 
 That all Funnels fhall be plaifter’d or pargetted within from the 
 Bottom to the Top j that all Chimnies be turn’d or arch’d with a 
 Tn ruing Trimmer under the Hearths with Brick, the Ground Floor excepted, 
 and that no Timber fhall lie nearer than five Inches to any Chim- 
 ney, Funnel, or Fire-place 5 that all Mantles between the ]aumbs 
 be arched with Brick or Stone, and no Wood or Wainfcot ihall be 
 placed or affix’d to the From of any Jaumb or Mantle Tree of any 
 Chimney, nearer than five Inches from the lnfide thereof. 
 
 That all Stoves, Boilers, Coppers, and Ovens, fhall not be nearer 
 than nine Inches at the kail to the adjoining Houfe; and no Tim- 
 ber or Wood to lie nearer than five Inches to any Fire-place or 
 Flew. 
 
 Mo Tim- But by Stat. 22 Car. II. cap. 11. it is Enabled, That no Timber 
 ber to be be laid within twelve Inches of the Forefide of Chimney Jaumbs, 
 Ch 1 m-° anc * t ^ at ^11 Joifls on the Back of every Chimney, be laid with a 
 neys. Trimmer of fix Inches Diflance therefrom ; and that no Timber be 
 laid within the Funnel of any Chimney, on Penalty to the Work- 
 Penalty. man for every Default 10 s. and ios. more every Week it remains 
 unreform’d. 
 
 ythly 7 With refpeffi to Lights and Water- courts. 
 
 Fy 19 Car. II. 
 
 AID Differences arifing concerning Lights and Water-courfes, 
 art to be derermin’d by the Lord Mayor and Cou;t of Aider- 
 men in the City qf London } and by the Commiflioners of Sewers 
 eife where* 
 
An APPENDIX. 
 
 169 
 
 %thly, With refpetf to the fever al Rates of Buildings 
 after which the City of London has been rebuilt Jince 
 the Fire. 
 
 r t ' H E feveral Rates or Kinds of Buildings appointed to be built 
 after the dreadful Fire in 1660, were Four j as firft, thofe of 
 Alleys, By-lanes, &c. were term’d Buildings of the firft Rate, andFhftRate 
 were ordain’d to confift but of two Stories, exclufive of the Win-j ng Buili " 
 dows and Garrets, whofe refpe&ive Heights were fettled as follows, 
 viz. the Height of the Cellar fix Feet and a half, the Height of th^Hei^htof 
 firft and fecond Stories each nine- Feet, and the Height of the Gar- 1 
 rets at Pleafure. 
 
 The Scantlings appointed for the Timber of thefe Buildings are 
 as follow : 
 
 Summers or Girders, whofe Lengths are not to exceed 1 5 Feet, 
 muft confift of 1 2 Inches in Breadth, and s Inches in Depth or 
 Thicknefs, and Wall Plates 7 Inches by 5 Inches. 
 
 Principal Rafters under 15 Feet, to be 8 Inches by 6 Inches atscant- 
 their Feet, and 5 Inches by 6 Inches at their Top ; fingle Rafters H ?g s of 
 to be 4 Inches by 3 Inches ; and Joifts, whofe Lengths are more Tunber 
 than 10 Feet, muft be 7 Inches deep, and 3 Inches in Depth, ex- 
 cepting thofe for the Garret Floors, which muft be 3 Inches by 
 6 Inches. 
 
 And here obferve , Stat. 22. Car. II. That no Joift or Rafters beDiftance 
 laid at greater Diftances from one another than 12 Inches, and no andRaf 
 Quarters at greater Diftances than 14 Inches. ters. 
 
 Secondly , Buildings of the fecond Rate, are fuch as Front Streets, Se cond 
 Lanes of Note, confifting of three Stories in Height, exclufive of£ a lf\? f 
 the Cellars and Garrets. BmUuls - 
 
 The Height of the Cellars muft be 6 Feet and a half, (if Springs Heightof 
 will allow it) the Height of the firft and fecond Stories Jo Feet Stories ’ 
 each, the Height of the third Story 9 Feet, and the Height of the 
 Garrets at Pleafure. 
 
 The Scantlings appointed for the' Timber of thefe Buildings, are 
 as follow: 
 
 Firft y 
 
 Z 
 
1 7° 
 
 An APPENDIX . 
 
 fVry?, For the FLOORS. 
 
 Summers or y Sf Nmuft have 
 
 Girders in yi8S*to yi^ Feet yin their 
 Length, from^zi^ ^24^ /Depths 
 
 F Inches, and 
 
 » ! 4> n-jA 
 
 Breadth 
 
 Scant- 
 lings for 
 theFloors 
 
 Joifts which bear io Feet, muft have\7^ Nwhere the 
 
 in Thicknels 3 Inches, and in <7^ Inches y Depth of the ^toV Inches. 
 Depth ^Girder is ^12* 
 
 Binding joifts, with their Triming Joifts, 5 Inches in Breadth, and 
 fheir Depth equal to their own Floors. 
 
 Wall Plates, or Raifing Pieces and Beams 
 
 10 
 
 8 > Inches, and 
 73 
 
 Lintels of Oak in the 
 
 ' Flrft, Seeund, and ? c 
 
 Third S' btory 
 
 ' 8 ' 
 
 and ^ Inches. 
 
 Secondly , For the ROOF. 
 
 Scant- Principal Rafters, whofe 
 lings for Lengths are from 
 the Roof, 
 
 Purlins, whofe $ ij/ 
 Lengths are from <G.8 3 
 
 T°op 7 Inched. 
 
 S Foot 12 ) Inches, l t.a,. 
 beat ^To P 9 Sand S 8IncheS x 
 
 SFootr^InchesO Inches 
 
 C Fop 93 and 3 y 
 
 ,o $ ' 8 ? •“£? h ’ Ve L 9 ? Inches by $ 8 ? Inches. 
 
 £ 21 3 m their Squares £123 1 C 9 j 
 
 Single Rafters, whofe Cq? Feet pud have Inches b „U , 2 Inc hes. 
 
 Lengths do not exceed £63 in their Squares £43 C 3 2 3 
 
 Third Thirdly., Buildings of the third Rate, are fuch as Front the mod 
 iui!dingsP r * nc ^P a l Streets of Trade, as Cheapjide , Fleet-Jlreet , Strand, dye. 
 confiding of four Stories in Height, exciufive of the Cellars and 
 Garrets, The Height of the Cellars are as in the iaft preceding, 
 Height the Height of the firft Story 10 Feet, the fecond 10 Feet and a half, 
 of Stones the third 9 Feet, the fourth 8 Feet and a half, and the Garrets at 
 Pleafurc. 
 
 The 
 
An APPENDIX. 
 
 171 
 
 The Scantlings of Timber appointed for this third Rate of Build- Scant- 
 ing, are the fame as thofe of the fecond Rate. lings> 
 
 The fourth Rate of Buildings, being fuch as are appointed for r ° urt h 
 Perfons of extraordinary Quality, fituate in magnificent Squares, Gildings 
 &c. may have the Heights of their Srories and Scantlings of their 
 Timbers at Pleafure; but they muff not exceed four Stories in 
 Height, cxclufive of the Cellars and Garrets. 
 
 And here Note , That the Height of the firft Floor, over the Height 
 Cellars, in Houfes of the fecond and third Rates, fhall not be more 0 *’ the 
 than 18 Inches above the Pavement of the Streets, nor lefs than 6 above the 
 Inches, with a circular Step without the Building. Ground. 
 
 Scantlings of Stone appointed for the firft, fecond, and third Scant- 
 
 Rates of Building. 
 
 lings of 
 Stone. 
 
 Firft RATE. 
 
 Inch . 
 
 Corner Peers - - - 18'" 
 
 Middle or fingle Peers - - 14 
 
 Double Peers between Houfe and Houfc 14 
 Door Jaumbs and Heads - 12 
 
 by 
 
 Second and Third RATES. 
 
 Feet. Inch. 
 
 Corner Peers : - - 2^ r 6 
 
 Middle or fingle Peers - - 1 > by ^ 6 
 
 Double Peers between Houfe and Houfe 2 3 C 18 
 
 Door Jaumbs and Heads - 14 Inch, by 10 
 
 ythly, With refpeli to Materials, and 
 
 Firft , Of QUARTERING. 
 
 Single Quarters, whofe S' 8 ~l Feet, rauft S 3 i? in Breadth, 
 Doubles Lengths are £8 5 have c 4 5 an< d 
 
 1 Inches in 
 . 3 2 5 Thicknefs. 
 
 Secondly , Of L A T H S. 
 
 _ r mufl: have one Inches in 
 
 Laths, whofe Lengths are £45 Inch in Breadth, and Thicknefs. 
 
 Z z 
 
 Thirdly, 
 
iy 2 
 
 An APPENDIX. 
 
 Thirdly , Of BRICKS. 
 
 Whereas her late Majefty Queen Elizabeth , by her Letters 
 Patent or Charter, under the Great Seal of England , dated the 3d 
 Day of Augufti in the 10th Year of her Reign, did, for herfelf 
 and Succeflors, grant unto divers Perfons therein named, and all 
 other Freemen of the Myftery or Art of Tilers and Bricklayers of 
 London , and the Suburbs thereof, to be one Body Corporate, by 
 the Name of the Mafter, and Keepers or Wardens of the Society of 
 Freemen of the Myftery and Art of Tilers and Bricklayers, and by 
 that Name to have perpetual Succeflion ; giving them the faid 
 Company the Search, Correction, and Government of Perfons 
 uftng the faid Myftery or Art, and of all Materials thereunto be- 
 longing, as well within the faid Cities of London and Wejl min fter, 
 as within all and every Place or Places contain’d within 1 5 Miles 
 thereof 
 
 And whereas the faid Company of Tilers and Bricklayers did 
 exhibit to the Parliament held in 1725, that the Earth and Clay 
 digg’d for the making of Tile and Brick, were digg'd at unreafonable 
 Times in the Year, and that therewith Bricks being made were un- 
 found ; that their Dimenfions were unfizeable • that in making 
 thereof, they mix’d great Quantities of Sea-Coal Afhes, call’d Spa- 
 nijh •, that the Makers thereof did not well burn the fame j that 
 in burning thereof they ufed Breeze (that is, Cinders) inftead of 
 Coals; that they commonly burnt the Grey Stock Bricks in the 
 fame Clamp with the Place Bricks, placing the Grey Stocks in the 
 Middle of the Clamp, and the Place Bricks without Side j where- 
 by they reprefented, that great Part of the Bricks then ufually 
 made were fo hollow and unfound, as fcarcely able to fuftain their 
 own Weight: And whereas at that Time there was no provifion 
 made by any Law for the Dimenfions of Bricks or Pantiles, they 
 did therefore, in the 12th Year of his late Majefty King George the 
 Firft, obtain an Ad to prevent Abufes in the making of Bricks and 
 Tiles, and to afeertain the Dimenfions thereof, &c. and thereby it 
 isEnaded, That after the 29th Day of September 1726, all Brick- 
 makers that dig Brick Earth for the making of Bricks for Sale, (hall 
 dig the faid Earth at any Time between the 1 ft Day of November and 
 the 1 ft Day ot February in every Year ; that the faid Earth fhall be 
 turn’d at leaft once within the aforefaid T ime 3 that no Part of the 
 
 faid 
 
An APPENDIX. 
 
 faid Earth fo dug and turn’d, fhalJ be made into Bricks before the 
 i ft Day of March next enfuing, nor after the 29th Day of Septem- 
 ber following ; that no Spanijh , at any Time or Times, (hall be 
 by any Perfon mix'd with any Brick Earth or Clay, for making 
 Bricks for Sale ; that no Breeze fhall be ufed in the burning of any 
 Bricks for Sale ; that Place Bricks fhall be burnt in diftincft Clamps 
 by themfelves, and the like of Stock Bricks, and not both together 
 in one Clamp, as aforefaid } that the Dimenfions of Place Bricks 
 for Sale when burnt, be not lefs than 9 Inches in Length, and not 
 lefs than 2 Inches and a half thick, and not lefs than 4 Inches and 
 a half in Breadth ; that the Dimenfions of all Stock Bricks made for 
 Sale, fhall, when burnt, be one eighth Part of an Inch thicker than 
 the Place Bricks, but Length and Breadth the fame ; and whofoever 
 offends againft this Ad, fhall forfeit and pay the Sum of Twenty 
 Shillings for every Thouland of Bricks, as fhall be made for Sale 
 contrary to the true Intent and Meaning hereof. 
 
 And forafmuch as the faid Company did reprefent unto the faid 
 Parliament, that ’twas highly neceflary that they fhould infped into 
 the due Execution thereof, it was therefore Enabled, That they the 
 faid Mafter and Wardens of the faid Company, or any two of 
 them, or any four or more honeft. Men of the faid Art and Society, 
 by the faid Mafter and Wardens of the faid Company for the Time 
 being to be appointed, twice in every Year, or ofrner, if they think 
 fit, to enter and go into and upon any Lands, Grounds, Out-houfes, 
 Sheds, &c. to infped into the Goodnefs of the Earth, Manner of 
 making, burning, &c. within fifteen Miles of the faid City, and 
 to fine Offenders, and recover Fines, &c. But the faid Company 
 having permitted and encourag’d divers Perfonsto make Bricks con- 
 trary to the Diredions of this Ad, they, by an Ad made in the 2d 
 Year of our Sovereign Lord King George the Second, are therefore 
 divefkd of the aforefaid Powers fo given them by 12 George I. and 
 in their Stead three or more Searchers are from time to time ap- 
 pointed by the Quarter Sellions to infped therein, as before by the 
 faid Company. 
 
 And whereas the faid Company (for Reafons unknown to them- 
 felves) did ignorantly reprefent the Uie of Spanijh as mod pernici- 
 ous and deftrudivc to the making of found Bricks ; to fully prevent 
 the Ufe of any Quantity thereof in any wife whatfoever, it is there- 
 fore Enaded, That from and after the 29th Day of September 1 729, 
 when any Land fhall be dug for making of Bricks for Sale, within 
 
 the 
 
 173 
 
 t 
 
1 74. 
 
 An APPENDIX . 
 
 the Compafs of 1 5 Miles about London, the Proprietor or Pro- 
 prietors thereof are oblig’d to uncallow, and remove away all the 
 Surface thereof, until they come down unto the real and pure 
 Brick Earth 5 and in cafe that by Neglcdi or Wilfulnefs they mix, 
 or fuffer to be mix’d any of the faid Surface, which is not pure and 
 real Brick Earth, or mix or fuffer to be mix’d any Comport, Mould, 
 Soil, Mud, or Dirt of any Kind or Nature, under any Pretence 
 whatfoevcr, therewith, and Bricks made therewith, the Proprietor 
 or Proprietors therof fhall forfeit and pay the Sum of Twenty Shil- 
 lings per Thoufand for every Thoufand of Bricks fo made, to be 
 recover'd by Affion of Debt, Bill, &c. in any Court of Record at 
 Wejlminfter , by any Perfon or Perfons who will fue for the fame, 
 one half thereof fhall go to the Ufe of the Perfon or Perfons who 
 fhall fue for the fame, and the other half to the Ufe of the Poor 
 where the Offence fhall be committed ; but the Profecution fhall 
 be brought within the Space of one Year next after the Offence 
 committed, or otherwife to be void and of no Effedt. 
 
 O B S E R V A r 1 O N S. 
 
 1. It is allow’d, that between the ift of November and ift of 
 February is a good Seafon for the digging and working of Brick 
 Earth, not only with refped to Mens Labour, which is beft per- 
 form’d in cold Weather, but to the Earth alfo, which then by Frofts 
 and drying Winds hath its Crudities exhaled away in great Plenty, 
 and thereby render’d more pure, compatt, and confequently fitter 
 for making of found Bricks : And iince that the oftner Earths are 
 remov’d by turning, the greater Quantities of their Crudities are 
 evaporated, I much admire why that corporatcd Body did not re- 
 commend the ift Day of October, inftead of the ift of November , 
 to begin the digging thereof, and to have turn’d the fame at leaft 
 twice before the ift of February enfuing, that thereby its rancid 
 Vapours might in great Part, or in the whole, be exhaufted, and its 
 Parts more firmly adhered together, which unqueftionably would 
 make much founder Bricks, than when fuch Crudities are contain’d 
 therein. 
 
 I muft here beg Leave to inform the Company of Tilers and 
 Bricklayers, that for want of a due Regard being had to this very 
 Point, (which they feem wholly ignorant of) there has been greater 
 Quantities of bad Bricks produc’d, than ever yet has been by the 
 
 Mixture 
 
An APPENDIX. 
 
 Mixture of Spanijh in the Earth, which if moderately mix’d there- 
 with, and the Earth well work’d, is an excellent Ingredient therein, 
 and is a great Help to Nature, as will appear hereafter. 
 
 The Injury that Bricks receive from the confin’d humid Crudities 
 are imperceptible before they are burnt, being then in very Email 
 fpherical Bodies, too diminutive for the naked Eye, and perhaps 
 unequally diftributed ? but in Bricks burnt they are vifible enough, 
 when one is broken into two Pieces, for then appears many very 
 large Cavities or hollow Spaces, made by the Expanfion of thofe 
 crude humid Particles, as they are rarefy ’d by the Heat apply’d for 
 their burning ; and the greater Quantity of thofe Particles any 
 Earths abound with, the greater is the Imperfe&ions of the Bricks 
 made therewith ; for the ftrongeft Bricks are thofe which are made 
 of the mod compaft Earth, being well burnt. 
 
 2. I obferve that the fecond Complaint is, of the mixing Sea- 
 Coal Allies, (call’d Spantjh ) which thofe Gentlemen look’d upon, 
 as pernicious to the making of a found Brick, and therefore the 
 Ufe thereof is ftri&ly forbidden in Bricks made for Sale, where- 
 by 'tis the humble Opinion of good Judges of the Affair, that the 
 Publick is rather injur’d than fety’d thereby, as I fliall endeavour 
 to demonftrate. 
 
 But before I can proceed thereto, I am oblig’d to take fome 
 Notice of the different Qualities of Brick Earths, and their Com- 
 pounds, whereby we may be the better able to determine the 
 good or bad Effe&s of Spanijh when mix’d therein ; and I do 
 heartily vvifli, that the corporated Body of Tilers and Bricklayers 
 had been better acquainted therewith than they feem to fet forth, 
 and that they had fully inform’d themfelves therein, inftead of 
 imagining the Certainty of Fa£ts, in which they have in great mea- 
 fure been very much miflakem 
 
 Firff then, it appears by many Experiments which I have made, 
 (and "which any other Per foil may make) that all Soils whatfoever 
 were originally pure Sand, which being mix’d with various Juices, 
 appointed by Nature for that Purpofe, do thereby differ in their 
 Colour, Texture, Smell, &c . • , 
 
 T his 
 
 * 7 $ 
 
An APPENDIX. 
 
 This is moji ea/ily illuft rated 
 
 Take of any Kind of dry Sand divers Quantifies, feparate from 
 one another, and mixing them fcvcrally with different Liquids, as 
 Water, Milk, Oil, Wine, &c. you will indantly behold the Sand, 
 which, when dry, was of one Colour, will be then chang’d to fevcral 
 Colours, according to the Differences of the Liquids ; and if you 
 fo mix and work the laid feveral Parcels of Sand into folid Lumps, 
 and place them in the Sun to dry, thofe mix’d with the Water, 
 Milk, and Wine, will fall down into Heaps of dry and loofe 
 Sand again, as at fird, whild that mix’d with Oil will become a 
 compact folid hard Body, and of a Clay Texture. 
 
 From this Experiment wc may very reafonably believe, that all 
 Clays are no other than Sands incorporated with oily Juices, 
 which fo much refill the Penetration of watery Particles therein ; 
 and it is from this very Principle that Clay Bricks, which will not 
 permit the Penetration of Water into the interior Parts of the Clay, 
 are the mod com pad and founded Bricks that are made; for fince 
 that their oily Particles will not permit humid Particles within, 
 there can be no fuch hollow Cavities caus’d within by Rarefadion, 
 as I have obferv’d and explain’d before : And fince that there’s 
 much Sulphur contain’d in Oil, it is therefore that Clay Bricks 
 are fo thoroughly burnt, without the Help of Spanijb mix’d 
 therein. 
 
 To enumerate the many Kinds of Brick Earths, would be an 
 cndlefs and ufclefs Task, fince they differ according to the more or 
 lefs Quantity of Sandy Particles mix’d with the oily, or rather the 
 Clay Particles; which, to make the Cafe more intelligible, I will 
 fubditute as a pure Earth by itfelf, as Sand is. 
 
 Hence ’tis evident, that the greater Quantity of Sand is mix’d 
 with Clay, the lefs Quantity of oily Particles will be contain’d in the 
 whole, and therefore the Body will be lefs compad, and eafier pene- 
 trated by Water : And fince that the oily Particles are thus leffen’d, 
 the Quantity of Sulphur is alfo lefien’d proportionably, and confe- 
 quently Bricks made therewith, cannot be fo perfedly burnt within, 
 as when the oily Particles were in greater abundance, and therefore 
 ’tis impodible that fuch Bricks can be thoroughly burnt as they 
 ought to be : For fince that the Power of the fulphurous Particles 
 within are made lefs than is necefiary, it therefore follows, that if 
 
 the 
 
1 77 
 
 tAn ^APPEND LX. 
 
 the Outfides of Bricks are burnt but enough, their interior Parts 
 will be as much wanting thereof, as the Quantity of Sulphur 
 abated by the extraordinary Mixture of Sand with Clay ; and on 
 the contrary, when the Heat apply’d is fo great, asto bum the interior 
 Parts of the Brick, as much as a found Brick requires, at the fame 
 time the exterior Parts will be over-burnt, and become what 
 Workmen call Clinkers that is, by the too great Heat they are in 
 fome Degree melted, whereby they run into various irregular 
 Forms, caus’d by their own Gravity, and are thereby render’d unlit 
 for outfide Ufe. 
 
 Now from thefe Proofs I am apt to think, that the Ufe of Spa - 
 ni/h, which burns within the Brick, is abfolutely necelfary, pro- 
 vided that ’tis ufed with Difcretion, according to the Nature of the 
 Brick Earth ; for a ftrong Earth has lefs Occafion for fuch Help 
 than a light Earth, as having a greater Quantity of oily and 
 fulphurous Particles therein ; and until Spanijh is allow’d to be 
 ufed in fuch Manner, I much queftion that we fhall fee fuch good 
 Bricks made again, as I am a Witnefs have been made therewith : 
 But a too great Quantity thereof will, when ufed to excefs, deftroy 
 the Spirit and Strength of the Earth ; as Wine or Brandy will, 
 when immoderately drank, the Conftitution of Mankind. 
 
 3 . Whether or no the Complaint of burning Bricks with Breeze 
 (which is Cinders of Sea- Coals) is injurious, I will not take upon 
 me to determine, fince I am not a Stoker, as many of them were, 
 if my Information is right; but this I can juftly fay, that I have 
 known many Clamps of Bricks very thoroughly burnt therewith 
 in my own Parifh of Twickenham ; and I have always obferv’d, 
 that fuch Fires were ever more free and penetrating, than thofe 
 made with frefh Sea-Coal only, which at the firft is rather too 
 violent. 
 
 4. I cannot but join with the Company, in the Complaint of 
 'Place Bricks being burnt in the exterior Parts of the fame Clamp 
 with the Stock Bricks, which undoubtedly renders the Place Bricks 
 leaft burnt, and particularly in windy Weather, which very much 
 affeds their burning. 
 
 And in confideration that B lace Bricks are chiefly ufed in Foun» 
 dations, which fupport the entire Weight of Buildings, 'tis 
 highly necelfary that they fhould be perfectly burnt and found, 
 7 ' A a lefc* 
 
An APPENDIX. 
 
 left, 'by fubmitting to the Preflure laid on them, the Building .is 
 injur’d thereby. 
 
 5. As to the Alteration of the Dimcnfions of Bricks, I think 
 it to be a very great Injury to the Publick : As firft, by their extra- 
 ordinary Size, they are render’d the more incapable of being tho- 
 roughly burnt without the Help of Spanijh, and confequently can- 
 not be perfectly found. Secondly, To burn thefe augmented Bricks 
 in as good a Manner as is poflible, there’s much greater Quantities 
 of Coals requir’d, and the Labour much greater in making, where- 
 by their Prices are now rais’d from 11 and 12 s. per Thoufand unto 
 18 and 20 s. per Thoufand, and the Increafe of their folid Quantity 
 nothing comparable with the Increafe of their Price. Thirdly, By 
 their Increale of Magnitude, they arc thereby render’d fo very 
 unhandy to Workmen, that they cannot perform fo much Work 
 in a Day as before } wherefore 1 humbly conceive, that when the 
 whole is judicioufly confider’d, it will appear to be a diredl Injury 
 done to the Publick, and which our wife Legiflators will undoubtedly 
 redrefs upon due Application made. 
 
 Fourthly , Of TILES. 
 
 By an Aa made in the 17th of Edw. IV. it is Enadted, That the 
 Dimenfions of Tiles be as follow. 
 
 A plain Tile to be in Length 10 Inches and a half, in Breadth 6 
 Inches and a quarter, and inThicknefs 5 8ths of an Inch at the leaft. 
 
 A Roof or crofsTile in Length 13 Inches, Depth as convenient, 
 and Thicknefs as the preceding. 
 
 A Gutter and a Corner Tile, in Length 10 Inches, with conve- 
 nient Breadth, Depth or Thicknefs. And 
 
 By the preceding Adt of the nth of Geo. I. Pantiles, when 
 burnt, (ball not be lefs than 1 3 Inches and a half in Length, and 
 not lefs than 9 Inches and a half wide, and not lefs than half an 
 Inch in Thicknefs, 
 
 Fiftly , With refpefi to the Lengths o/Joifs, Rafters , &c. 22 Car. II. 
 
 It is Enadted, That no Joifts bear at a longer Length than 10 Feet, 
 and no lingle Rafters at more than 9 Feet. 
 
 That Roofs, Window Frames, and Cellar Floors be made of Oak. 
 
 That 
 
x 
 
 An APPENDIX. 
 
 That Tile Pins be of Oak. 
 
 That no Summers or Girders do lie over the Heads of Windows 
 or Doors. 
 
 That no Summers or Girders have lefs than io Inches bearing 
 within the Walls, and no Joifts lefs than 8 Inches, and to be laid 
 in Loam. 
 
 Laftly, If any Perfons be convicted by the Oaths of two Wit- 
 neffes before the Lord Mayor, or twojuflices of the Peace, for the 
 City, of building contrary to the preceding Rules and Directions, 
 fuch Buildings fhall be deem’d common Nuifances, and the Builder 
 fhall enter into a Recognizance for demolifhing or altering the fame, 
 or otherwife fuch Buildings fhall be demolifhed by Order of the 
 Court of Aldermen. 
 
 And for the Performance hereof, the Lord Mayor, Aldermen, 
 and Common Council, fhall appoint proper Surveyors to fee that 
 the feveral Rules are ftridtly obferv’d, and may give an Oath for the 
 due Execution thereof. 
 
 FINIS. 
 
 i 79 
 
BOOKS printed for W. Mcars, at the Lamb without Temple-bar. 
 
 j.IlOMONA: Or, The Fruit-Garden illuftrated. Containing fure Methods 
 of improving all the bell Kinds of Fruit now extant in England , calculated 
 from great Variety of Experiments made in all Kinds of Soils and Ai'petts. Illuf- 
 trated with above 500 Drawings of the feveral Fruits, curioufly engraven on 79 
 large Folio Plates. By Batty Langley of Twickenham. 
 
 t. A Philol'ophical Account of the Works of Nature. Endeavouring to fet forth 
 the feveral Gradations remarkable in the Mineral, Vegetable, and Animal Parts of 
 the Creation, tending to the Compofition of a Scale of Life, iytc. Adorn’d with 
 many curious Cuts. By Richard Bradley, Profelfor of Botany in the Univerfity of 
 Cambridge , and F. R. S- 
 
 3. The Experimental Husbandman and Gardener. Containing a new Method of 
 improving Eftates and Gardens, by cultivating and increafing Foreft Trees, Cop- 
 pice Wood, Fruit Trees, Shrubs, Flowers, and Green Houfes, and Exotick Plants, 
 after feveral Manners. By G. A. Agricola , M. D. Tranllated from the- Original, 
 with Remarks. Adorn’d wich Cuts. By R. Bradley , F. R. S. &c. 
 
 BOOKS juft publijtid , and Sold by John Wilcox in Little-Britain. 
 
 1 . r T > HE Builder’s Cheft-Rook : Or, a compleat Key to the Five Orders of 
 6. Columns in Architecture. Where, by way of Dialogue, in Nine LeCtures, 
 the Etymology, Characters, Proportions, Profiles, Ornaments, Meafutes, and 
 Dilpofitions of the Members of their feveral Columns and Entablatures, are di- 
 ftinCtly confider’d and explain’d with refpeCt to the Practice of Palladio. Together 
 with the Manner of drawing the Geometrical Elevation of the Five Orders of 
 Columns in Architecture, and to meafurethe feveral Parts of Buildings in general. 
 The whole exemplify’d, by way of Dialogue, in a very concife and familiar Man- 
 ner, illuftrated on Seven Copper Plates j being a necellary Companion for Gentle- 
 men, as well asMalons, Carpenters, Joiners, Bricklayers, Plaifterers, Painters, &c. 
 and all others concern’d in the feveral Parts of Buildings in general. By B. Langley 
 of Twickenham . 
 
 2. Magnum in Parvo : Or, The Marrow of Architecture : Shewing how to draw 
 a Column, with its Bafe, Capital, Entablature, and Pedeftal, as alfo an Arch of 
 any of the Five Orders. With Cuts, in 4to. Price 4/. 
 
 3. The true Syftem of the Planets demonftrated. By Charles Ledbetter. In 4to 
 with Cuts. Price 5 s. 
 
 4. A compleat Syftem of Aftronomy. In 2 Vols. By Charles Ledbetter. Pr. 12/. 
 y. A new Treatileof the ConftruCtion and Ule of the SeCtor. By Samuel Cunn , 
 
 8 vo. Price 4/. 
 
 ADVERTISEMENT 
 
 G ARDENS in General, as Laybrinchs, Wildernefs’s, Groves, Fruit-Gar- 
 dens, c ’ire. Made and Planted after a Grand, and more Rural Manner, than 
 has been done before. As allb Grotto’s, Cal'cades, Fountains, Canals, Fifhponds, 
 Springs Collected and Conveyed to any poftible Place afltgned. Engines of 
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 all Kinds for any Latitude. Buildings in general Survey’d, and all Sorts of Arti- 
 ficers Work and Timber Mealured. Youth taught the Principles of Geometry, 
 Trigonometry, Architecture, PerfpeCtive, Surveying Land, Menfuration, Aftro- 
 nomy, and the Ule of the Globes. By BATTT LANG LET, at Andrea Paljadie s 
 Head, near Exeter-Court, in the Strand, London. 
 
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