through six and if you describe the Scenographick Semi-circle m p q as you were taught just now you may set this Door also open to what width you please Thus Erecta Perpendicular on the point of the Semi-circle you intend to open the Door to and prolong it quite through the Door as r n s and with your Compasses measure on the Perpendicular the distance between that point in the Semi-circle and the Diameter of the Semi-circle which is the line m n where the Squares end for that distance set off on the same Perpendicular from the Base as from r shall give a point through which a straight line drawn from the Center of the Door o to the Horizon shall be the point in the Horizon from whence a straight line drawn to the upper end of the Doors Axis shall give the shortning of the upper edge of the Door and the points where the two straight lines cut the Perpendicular shall be the points that shall shew the shortning of the fore edge of the Door Above this Door is made a round Hole of the same width the Door is and of the thickness of the wall which because the lines by which it is made are so plain and the manner of working so easie I shall forbear farther Instructions on it Under this Arched Roof are drawn Parallel prickt lines to shew the devisions of the Roof and by these devisions either with Compasses or else a steddy hand you may describe the Arches as you may see them in the Figure By the making the foresaid Doors may be understood how to make Casements standing open at any width and several other Operations pleasant and necessary for all that Study Perspective OPERATION XXII To Describe in Perspective the inside of two Chambers one above the other THis is also performed by help of a Ground-plain as in the former Figure but the difference between this and the former is I. This hath another Chamber over it 2. A Portal and Hole on one side of the Wall and another right before you on the middle of the Ground-plain 3. Steps placed just within this Portal 4. A square Hole in the middle of the Ground-plain 5. Shelves on the other side of the Chamber 1. For what concerns barely the Chamber over the lowermost Room you may see by the Figure that its Operation is the same with the former where you see all the three sides of the Chamber wholey but because the Ceeling a b c d of the lower Room lies so much above the Ey you only see so much of the upper Chamber as is un-obscured by the Ceeling That is all above the Catuzes a d resting on the two Catuzes e f the rest are only noted with prickt lines as they would appear if the Ceeling were not interposed between the Ey and them and the Joysts over head are wrought as in the last Operat 2. For the Portal on the side of the Wall you may see that it stands on three Squares on the Ground-plain as doth the Portal right before you Now to make the Arch over this Portal correspond with the Arch of the Portal right before you viz. of the same height as that Portal is do thus Draw a line just where the Arching begins parallel to the Horizon as g h and prolong it to the corner of the fore-right Wall as at g Then laying a Ruler to the Visual point and the point g describe the line m g then draw another Parallel line on the top of the Arch of the Portal and prolong it also to the corner of the fore-right Wall as to i and laying a Ruler to that point i and the Visual point draw the Diametral line n o i then erect two Perpendiculars n l and o m from the sides of the Portal to intersect these Diametrals so shall you by crossing the Angles of intersection have the Center p and upper and lower bounds of the Arch which a steddy hand may easily reduce into form This way of working is exact enough for Painters or other Artisicers But if you will be yet more precise See Oper. XXV XXVI The Hole in the side of the Wall in the upper Chamber is made after the same way viz by crecting Perpendiculars to the designed width as here it is three Squares on the Ground-plain the same with the Portal and by drawing Diametrals from the Visual point for the depth of the Hole for where the Perpendiculars and Diametrals intersect each other shall be the Angles of the Square that includes the Hole and straight lines drawn from Angle to Angle shall intersect each other in the Center of the Hole By the same way of working you have the back side of this round Hole described to the thickness of the Wall and also the back side of the Portal as you may see in the Figure In the other side of the Wall on the Ground-plain is made another half-round Hole which being performed after the same manner needs no further Explanation 3. Just within the Portal are placed four Steps going straight upwards which are thus made Draw the two slope lines q q and r r to what slope you please parallel to each other for the width of the Steps then assigne a depth for the first Step as to s and Parallel to the Base draw a line for the bredth of the Step as t s then draw Diametrals from the points s and t to the slope line q q so shall the first Step be made The rest of the Steps are made after the same manner observing that all the several Steps on their several Perpendiculars are equal in depth to the first 4. In the middle of the Ground-plain is made a square Hole as v x z z which may serve for an Entrance down a pair of Stairs leading to some Vault or Cellar These Stairs are in length three Squares and in depth the transferred distance of one Square as you may see the depth of the first Step downwards is v x which is the transferred distance of v y the bredth of the Step is x a so that a Diametral drawn from the Visual point to x and so prolonged directs you to the second Step at b and by placing one foot of your Compasses at the point c which is in the same Diametral the point v is and extending the other to the point d which also is in the same Diametral the point y is you transfer the distance of d c to c b which is the distance y v transferred to v x and another Perpendicular erected from the point b to c shews the depth of the second Step. ' The rest of the Steps are made after the same manner 5. On the other side of the Chamber against the Wall is set three Shelves two above the Horizontal line and one below as e f g The further ends of them rests in the Wall right before you and the higher end is fastned to a Post erected
thickness of the wall on either side takes up one quarter of a Square as is seen at a b. In the Wall is made a Door containing in bredth three Squares on the Ground-plain as s x t v and if you draw two lines from the opposite angles of the Door where they intersect each other shall be the middle of the Door as you may try on the other side of the Wall where lines drawn from f h and g i intersect each other at k which by the Perpendicular k l you may find falls in the middle between six Scenographick Squares that is three is contained between l and i and three between l and f. In the furthermost side of the Wall is a Thorow-fare made of the same height the Door is by drawing the Diametral t v from the Visual point a and continuing it to e at the angle of the two Walls and from thence by drawing the line e d y parallel to the Horizon which Thorow-fare being of the width of three Squares as between e and g j is described by erecting Perpendiculars from the points e z to cut the Parallel d y in the points d y as you may see in the Figure And so the Thorow-fare d y e z Orthographically becomes equal to the Scenographical Door t v s x. To bear up the Roof of the Chamber here is described five Joysts laid upon the side of the Wall q h the depth of which Joysts are described by the Perpendiculars q r and p o and the bredth by m q and o h each Joyst is of equal bredth and lies of equal distance one from another so that by laying a Ruler to the Visual point and the points m q r you may draw the lines f m g q h r to represent the three corners of the first Joyst The fourth corner lies out of sight Do the like for the rest of the Joysts all but the middlemost which because the Ey lies just under it shews but two of its corners as you may see in the Figure at n. Then if you will cover these Joysts with Boards or Plancks athwart you may for your better guidance divide the Ceeling into four Scenographick parts by drawing lines from the Angles h i to the Angles r p for where they intersect one another as in the point k draw a line Parallel to r p and that line divides the Ceeling into two Scenographick halfs And other lines drawn from the points h i r p to the two ends of this Parallel 〈◊〉 do by their intersections give points on the middle Joysts through which two lines drawn Parallel to the line r p divide the whole Ceeling into four Scenographick parts as you may see in the Figure I have been the more Copious upon this Operation because it is the first in this Book that shews the drawing of inward Edisices And I would have you well understand it because I intend instead of Repetition to refer you to this Operation when I shall have occasion to speak of things of the like nature OPERATION XXI To describe the inside of a Chamber with three Doors one on either side and one right before THis is performed upon a Ground-plain of nine Squares in length and nine in bredth drawn as by Operat XV. I shall not need say any thing of the sides of the Wall it having been taught in the last Operation But the Doors standing partly open and partly shut require a little instruction to shew the designing of them in Perspective You must understand that a Door being hung upon hinges describes in its opening and shutting a Semi-circle As for Example If it stand wide open with the back side of it against the Wall it fetches the sweep of a Semi-circle before it can shut upon the Door-frame that runs range with the Wall Therefore having the width you intend your Door shall be of and pitcht upon what place in the side of a Wall it shall move as on its Axis you need but describe on a loose paper a Geometrick Semi-circle in the same number of Squares that you intend your Door shall describe its Semi-circle in and observe the points of the Parallels and Perpendiculars that this Semi-circle cuts for the Scenographick Semi-circle must pass through the same points of the Diametral and Diagonal lines described on the Scenographick Ground-plain As you may see the Door a a d d containing six Squares as from the center a to e three and from a to f three describes on the Ground-plain the Semi-circle e l h i d g f which if you draw a Geometrick Semi-circle in six Squares you will find that this Scenographick Semi-circle passes through the same points of Diametrals and Diagonals as your Geometrick Semi circle does through Parallels and Perpendiculars Then consider how neer open or shut the Door is you intend to describe that is what angle it makes with the Wall for the same quantity you must set off on your Scenographick Semi-circle as here it stands open by the distance f d g Therefore draw a straight line between a the center the Door moves on and d the edge of the Door and prolong it into the Horizon and that line d a shall be the under side of the Door Then describe the same Semi-circle over the Door that there is on the Ground-plain by erecting Perpendiculars from as many points as you please of the Semi-circle on the Ground-plain and by drawing straight lines from each of those points into the center a and prolonging them into the Horizon for where the Perpendiculars cut straight lines drawn from those several points in the Horizon through the upper center a of the Door and so prolonged shall be the points that the upper Scenographick Semi-circle e l i h d g f must run through If you would have the Door stand wider open that you may see more of the entrance as at i i Draw as before a straight line from i to the center a and prolong it into the Horizon as i a k so shall i be the under edge of the Door and if from the point i you erect the Perpendicular i i for the edge of the Door a straight line drawn from the point k in the Horizon to the point a in the upper center of the Door and prolonged shall give the line i a for the upper edge of the Door Thus may you describe a Door standing open to what width you please as at a are the Door stands wide open with its back side against the Wall at a a l l it shews less open at h h it shews a Door whose edge lies almost in the same line its Axis does and so the Door shuts neerer and neerer as at g g a a the Door appears quite shut the Door on the other side is made just after the same manner and therefore needs no more Descriptions The Door in the middle stands also on three Squares and also opens
designed Station must exceed the Object placed just above the Horizontal line in such proportion as the Tangent of that Arch does the Tangent of the Arch just above the Horizontal line This Rule is very brief and perhaps may not be understood by all Speculators in Perspective Therefore I shall a little inlarge hereon Because it is of eminent concernment in the true Seeing Judging and making of Figures Having designed your Distance from the Wall Set it off from the point your Ey is placed in then set one foot of your Compasses in that point and with the other describe the arch of a Circle and devide it into so many equal parts as you please So shall the raies that proceed from your Ey continued to the Wall shew on the Wall in what proportion the Object ought to increase to appear so large as an Object that is to be placed just before you on the Horizontal line For Example Your Distance from the Wall is a b Therefore at the point a describe the arch 1 2 3 4 c. which you may devide into so many equal parts as you please and by laying a straight Ruler on the point a and on every one of those devisions that straight Ruler will point out on the Wall or on the line b c which represents a Perpendicular line on the Wall the several sizes that an Object is to be of placed on those several Heights to make it appear equal to the Object placed just above the Horizontal line But that great Master Albert Durer hath very handsomly handled this Operation in an erected Pillar wherein he hath made an Inscription in Letters thereby demonstrating how much those Letters that stand high above the Ey must be made bigger than those that ly neer the Horizontal line as you may see by this annexed Inscription Having thus performed the Operation you will see how much bigger the Letters far above the Ey are than those that ly neerer to the Ey And this Rule is to be observed not only in the magnifying of Letters thus placed one above another but also in magnifying of Figures to be placed one above another on a Wall be they either Painted or Carved OPERATION XXXIII To Describe in Perspective a pair of Winding Stairs HItherto we have imagined the Glass to be placed Perpendicular to the Base and therefore as hath been said in CHAP. III. Those lines of a Figure that in a Geometrick Figure are Perpendiculars are in the Scenographie also Perpendiculars as here is seen in these winding Stairs where because these Stairs should diminish upwards the Glass is placed Oblique to the Base But to the matter This Geometrick Ichnographie is divided into sixteen equal parts as 1 2 3 4 5 c. which represents sixteen Steps that wind once about the Newel Therefore reduce this Geometrick Ground-plain into Scenographie as you were taught in Operat X. by erecting Perpendiculars into the Base c. and mark the Scenographick Ichnographie with the same Figures the Orthographick is then on the middle of the Scenographick Ichnographie at the point 13 erect the Perpendicular 13 a and divide it into so many equal parts as you please or intend to have Steps and erect another line on the same point 13 into the point of deminution as 13 b Then from every one of these devisions on the Perpendicular 13 a draw a Visual raie from the Visual point c to the line of deminution 13 b and from the points where those Visual raies cut this line of deminution 13 b draw Paralles to the Base into the middle of the Newel and those Parallels shall show the Distance or Height of every Step one above the other on the Newel And for the Distance or Height of the further end of every Step you must erect a Perpendicular on the extream point of the Ichnographie as d e of the same length your Newel is and devide it into so many equal parts as you have Steps or as your Newel is devided into unequal parts as f g h i k c. to t and from the Visual point draw Visual raies through every one of them to intersect every respective line of deminution raised out of the Ichnographie so shall Parallels drawn from every intersection shew the height of the further end of every respective Step as the first intersection is made on the first line of deminution d 17 at 1 therefore a Parallel drawn from the point 1 where the first Visual raie intersects the Parallel line 1 shall shew the height of the further end of the first Step. The second Visual raie is drawn into the second line of deminution to the line 2 therefore the Parallel drawn from that point shall shew the height of the further end of the second Step. The like is to be understood of all the other Steps Then for the length of every Step instead of erecting a Perpendicular on the several points of the Ichnographie to find them as you have been often taught before Draw several lines from the point of deminution which is in the top of the Newel into every one of those devisions on the Ichnographie and those lines of deminution shall bound every respective Step As that raised out of the point 1 of the Ichnographie shall shew the length of the first Step. That raised out of the point 2 of the Ichnographie shews the length of the second Step and so for all the rest OPERATION XXXIIII Shewing the further process of the last Operation BEcause the multiplicity of lines in the last Figure may somewhat confound a Practitioner here is inserted another Figure of a pair of winding Stairs quite finisht made by the Precepts of the last Operation So that the lines that were in the last Figure incumbred with other lines appear naked here and the places of the Shadows which there are troublesome to find out are here visible to the Ey Herein as before you have two turnings about the Newel and the whole Designe projecting forwards If you would have more turnings about the Newel you must devide the two lines of deminution on each side into so many the more parts As you were taught in the last Operation OPERATION XXXV The Description of a pair of Double Stairs whereon two persons the one ascending the other descending shall not come at one another THese double Stairs are insersed as a peece of Rarity and described only in Orthographie and not by the strickt Rules of Perspective lest with many lines the work should be obscured Yet such as list to be curious therein may in the last and several other Operations find Rules whereby they may effect their purpose Describe a Circle or which is equivalent a Semi-circle for the Ichnographie as 1 2 3 c. to 13 and in it describe a smaller Circle as a b c for the bigness of the Newel Then devide the great Semi-circle into twelve equal parts as 1 2 3 to 13 and
may be the better understood I shall explain the whole designe which briefly is this In this Figure is somewhat more than the Plat-form of the last Figure described viz. the Banquetting House and the long Gallery and also the Wall of the Dwelling House of his Highness the Prince of Orange Fronting the Garden This Wall is marked a a on the right hand of which as at b you have the said Banquetting House and close adjoyning to it the said long Gallery with Columns after the Derick Order containing sixteen Arches and Turrets with several Lanthorns on the top of it On the left hand as at c is placed a Bridge leading over a Mote which incompasses the whole Building into a curious fair Walk which Bridge is inclosed on both sides and covered over on the top Beyond this Walk is an high Wall beginning at the hither side of the Banquotting House and going round the Garden to the farther side of the Banquetting House within this Wall is another Walk round the Garden and at the four corners of this Walk four curious square Arbors and at the middle of the Walk is placed a Portal for the entrance into a long Gallery which goes quite cross the whole Garden which Gallery is all covered with green boughts so close that the light of the Sun cannot pierce between them On either side and at the ends of this long Gallery stands a round Arbor also close covered with green boughs within the Garden is erected on two Scenographick Circles two curious Fences of Quick-sett with four entrances into each at opposite points in the Garden which having four paths a peece leads to a curious Fountain set round about with Flower pots in the middle of the Garden Over three of the Arches of the long Gallery aforesaid is erected part of the said Banquetting House of four more of the said Arches is made an Aviary well furnished with Canary Birds And of the other nine Arches is made a Grott-work with several curious delightfull Inventions of Water Works The rest of the curiosities of this Peece may as well be understood by the Figure it self as by many words thereon OPERATION XXXIX To Describe in Perspective a Folding-chair a Frame chair and a Bedsted HAving designed the space in the Ground-plain that the Folding-chair shall stand upon as here upon the Angles of four of the Squares viz. a b c d. That is The distance of each foot is two Squares from the next foot set off such an height from the Base as is proportionable to the length and bredth of the Chair As here its heighth not being two Squares on the Base viz. not so much as its length and bredth the height wants somewhat of the Diagonal length of two Squares on the Base which you must set off from the points a to c b to f c to g and d to h but you must note that for every foot you change your measure for to the foot a that stands on the Base you take almost two of the Squares on the Base to the feet b d that stands one Square above the Base take almost two of those Squares and for the last foot that stands neerest the Visual point take almost two of the Squares in that place so that the measure of each foot 's height be taken from that Square in the Ground-plain that each foot stands on as is taught in Operat XVI And because the Square of the seat of the Chair is broader than the Square space that the feet stands upon in the Ground-plain the sides of the Seat hangs over the sides of that Square Therefore in this case you may erect a Perpendicular from the points a b c d up to the Seat towards the point e f g h but you must draw the Seat somewhat beyond it according as in your discretion you find the Seat of the Chair hangs over the said Square so have you the corners of the Seat e f g h and by a Diagonal line the height of the Back i k. The Rails in the Back and the Rails between the feet are all drawn by Diagonal lines as you may see in the Figure If you would have the Corners of this Folding-chair turned more or less towards you you must draw an Ichnographie of it as you are taught in Operat L. and then you may turn the Corners of that Ichnography into what position you will against the Base and by perpendiculars erected on the Angles of the Ichnographie as you were taught in the foresaid Operat the Corners of the Chair shall stand in their elected place The other Chair stands with its Foreside directly before the Ey and is between the two Forefeet two and an half Diagonal Squares and between the side feet two Diagonal Squares so that from these points in the Ground-plain the feet or posts of the Chair are made by erecting Perpendiculars to your designed height and then all the fore Rails of the Chair are Parallel to the Base and Horizon and the Return or side Rails are Visual lines as you may see in the Figure The Bedsted stands with its feet a b ranging directly forward and is in length six Squares and in bredth five Squares so that the Posts are perpendicularly erected at this Distance to what Height you please All the fore-Rails are parallels to the Base and Horizon and the side-Rails are Visual lines as in the fore-right Chair Therefore this Operation is very easie unless it be the Tester or Covering of the Bedsted which because it is ridged at the top and the fore and hind ends incline towards each other may seem somewhat difficult For designing of which Find the middle between the two Posts a b in the Base as at c and draw the Visual line d c and therein designe how much the Tester of the Bedsted shall fall away inwards from the upper Rail at the Feet as from c to e Therefore from the point e erect a Perpendicular to what convenient height you will above the upper Rail as into the point f and from the upper ends of the Post a b at the points g h draw straight lines into the point f for that part of the Frame of the Tester that belongs to the Foot end of the Bed-sted And to draw the hindmost slope of the Tester you may do thus Make a parallel Scale as you were taught in Operat XXXI and on that Scale you may measure how much the angle e is erected above its Base as here you will find a little more than one Square therefore in the Ground-plain at the distance of a little more than one Square of that Parallel under the line i k which is the bottom of the hind Feet Draw an occult Parallel inwards within the Bedsted because the Tester slopes inwards as m l and where that parallel cuts the Visual line d e c shall be the angular point as at l and a Perpendicular erected on that point shall
cut the Visual line drawn to tho point f in the point g which is the point that the hind part of the Frame of the Tester must be drawn unto from the two hind Posts See the Figure These Posts are made square because the hind sides and corners of them may be represented by prickt lines For in Frame-work it requires that one half of the Rails c. be drawn from the hind sides and corners as well as from the fore sides and corners which by the help of these prickt lines you are directed to OPERATION XL. To describe two square Loggs unevenly laid one upon another THe nethermost angles of the under Log is imagined to ly towards the Base and is marked with a b c d from which angles if you erect Perpendiculars into your designed Height as to e f g h and from these points and angles draw Parallels from a to b from c to d from e to f and from g to h and from the angles a b e f Visual lines you have the under Log inclosed and its hidden Sides and Angles markt out as you may see by the pricktlines g c and h d and the angle c. The other Log whose bottom is markt with i k l m lies athwart the first Log with one of its angles against the Base viz. the angle i Therefore to set this Log upon the first Log you must erect Perpendiculars from these four angles viz. from i to n o from k to p q from l to r s and from m to t v Then draw Diagonals from the point x on the left hand to p n q o rt and s v and also Diagonals from the point y on the right hand to the points q s o v p r and n t and by erecting Perpendiculars from p to q n to o r to s and t to v the Log is inclosed OPERATION XLI To describe in Perspective a Form a Table and an Andiron c. THe Form stands with its ends before the Ey upon the width of two Diagonal Squares on the Ground-plain as a b and in length ten Diagonal Squares as 1 2 3 4 5 6 7 8 9 10. You may make the Form of what height you please as you may see by the Perpendiculars marked a c b d on the Seat of the Form The Seat projects or hangs over the Form half a Diagonal Square on each side and end therefore you must draw an occult Parallel at the distance of half a Diagonal Square within the Base on the Ground-plain as e e and f f and two occult Diametrals at the distance of half a Diagonal Square on the Base from the Perpendiculars a c and b d inwards as g b which must be prolonged to the hind end of the Form and where these Visual lines cut the Parallels shall be the outward bounds of the four Feet in the Ground-plain which must be erected perpendicularly into the Seat The fore and hind Rails of this Frame are Parallels and the side Rails are Visual lines The Table on the left hand is placed with its corners against the Ey and stands in length upon ten Diagonal Squares and in bredth upon six of which the Leaf of the Table projects over its Frame one Square on each side and end The side lines for the Rails and the Leaf are drawn from the point of Distance a on the right hand and the end lines for the Rails and Leaf from the point of Distance a on the left hand and the Posts of the Frame stand each upon one Square and are all perpendiculars erected into the Leaf So that here remains nothing of difficulty in this Figure unless it be the projecting of the Leaf over the Frame which thought it be performed after the same manner of that on the Form yet because the Table stands not in the same Sight the Form does I shall explain this also The Leaf of this Table hangs perpendicularly over ten Squares one way and six another in the Ground-plain and this Square projects over the Frame one Square on each side as hath been said Therefore find the lines in the Ground-plain that include the ten Squares viz. b 6 and 10 c and by taking away one row of Squares on every side the Ground-plain you will have eight left one way and four another which is the bounds and gives the sides and angles the Frame stands on So that you see thought this projecture seem difficult it is easily performed on the Ground-plain If you would place any thing on the Table at a Designed Distance from either side and end on the Table as below which is the same with this only that is shadowed that the lineaments may appear the plainer For instance upon the edge of the hithermost side of the Table within six inches of the hither end you would place the Candlestick Then imagine the Table to be four foot long and three foot broad so shall each Square on the Ground-plain of the Table represent six inches Therefore count to the end of the first Square as to the point 1 and there erect a Perpendicular and where that Perpendicular cuts the edge of the Table shall be the place of the Candlestick Again If you would place the hither edge of the Bottom of the Beker within two foot three inches of the hither end of the Table and within one foot of the hither edge of the side of the Table then count in the row of figures that runs up on the right hand 1 2 3 4 and half one more in the Gound-plain which is two foot three inches and from that point erect a Perpendicular into the Leaf of the Table then count in the line of figures that runs down on the left hand from the point 6 to 4 which is one foot and erect a Perpendicular from that point up to the edge of the Table and draw a Diagonal from that point and the point a on the right hand and where that intersects the Perpendicular erected on the point of 4½ shall be the point where the middle of the hither edge of the Beker shall stand If you would incompass that point in the ends of the Legs of the Table which appear through the Leaf you may work as follows in this next example Count from the point b to the point 1 which is one Square of the Ground-plain and the point where one Angle of the Leg is placed and from that point 1 erect a Perpendicular into the side of the Leaf of the Table as at 1 and from the line a on the left hand draw a line to that point for the bounds of the force side of the two fore Legs Then because the Legs are one Square viz six inches every way erect another Perpendicular on the point 2 to the point 2 on the edge of the Leaf and to that point draw another line from the point a on the left hand and that line shall bound the hind side of the fore Legs
of the Figure A that is intended to be seen Reflected on a Cilinder First devide every side of the Figure into so many equal parts as you please here we will take 12 and draw lines through these devisions to cut each other at right Angles Then if you make a Projection whose Reflection on a Cilinder shall shew the same shape and number of Squares It follows by consequence that if you transfer all the Lineaments in the Figure A to this Projection and place every Lineament in its proper scituation so as to correspond with the same space from the top and sides of this Plain every one of these Lineaments in the Projection shall also appear in the Cilinder in the same shape and scituation they do in the Square Plain Therefore to make this Projection descibe on the Center a the Circle b 4 cd of the same Diameter you intend the Cilinder shall be suppose about an Inch and an half devide the Semidiameter of this Circle into 4 equal parts as 1 2 3 4 then on the devision at 3 place one foot of your Compasses and extend the other to what width you intend your outmost Circle should be as hereto e and describe the Circle f e g Then devide one of those parts of the square Plain into 20 equal parts or sub-devisions and make the first devision frome e 6 of those equal parts or sub-devisions bigger than one Square which you must set off on the Diametral line from e towards a the second from e 5 of those sub-devisions bigger than a Square which also set off from e towards a the third 4 the fourth 3 the fifth 2 the sixth 1 and the seventh equal the eighth 1 sub-devision less than a Square the ninth 2 less the tenth 3 the eleventh 4 the twelfth 5 sub-devisions less than a Square which successively set off from e towards a then on the Center at 3 aforesaid place one foot of your Compasses and extend the other successively to each of the devisions set off on the Diametral line and through every one of those divisions describe so much of a Circle as the Plain will bear so shall all these arches of Circles represent those straight lines in the Plain square A that run athwart the Plain from the left hand to the right and reflected on the Cilinder they shall become straight lines parallel to each other To represent in this Projection the Perpendiculars on the Plain square you may on the Center a describe an occult Circles as large as you can within the Projection as the Circle h i k l devide half of this Circle as k g h into 8 equal parts and through every one of these equal parts draw lines from the Center a into the Circumference of the Projection and these lines shall represent 8 Perpendiculars on the Plain square To draw the other 4 transfer the distance of one of the devisions in the Circle h i k l twice from l towards k and twice from i towards k and draw straight lines as before through these distances into the Circumference of the Projection so shall the whole Projection be finisht Note that in this Projection the whole Circle is not devided into 12 equal parts but only three quarters thereof because the Cilinder will not well gather in more raies for the other quarter lies hid behind the Cilinder Of Dioptricks or Broken Beams THe Broken beam is to be seen in a Tube through a Christal or Glass that hath its surface cut into many Faces as is the Fig. A for every one of these Faces making Angles with the Base or Flat side of the Christal shew an Object each as through its own Face and not through the Flat of the Christal And so is said to break the Raies of an Object because to the Flat of the Christal the Raies run straight but afterwards they break into the same Angle the Face on the other side of the Flat makes with the Flat Thus it comes to pass that when these Faces on the Christal are turned towards a Plain placed directly before it these Faces of the Christal dis-sever themselves at a considerable distance on the Plain because they are all directed to several remote parts of that Plain Now though there hath not as yet been any Geometrick Rule found for the assigning a place on the Plain of each of these Faces yet is there found how they may be placed on a Plain as you shall learn by the next Operation OPERATION LX. How among a great many Pictures on the Plain to see one elected and peculiar Picture quite different from any on the Plain HAving fixed your Plain fast and also fixed your Tube fast directly before the Plain look through the little Hole at the hither end of the Tube and with a point or black-lead pencil mark where the several Angles of each and every Face of the Christal falls upon the Plain so may you with your black-lead pencil draw a line by the side of a Ruler from point to point of each Face thus found on your Plain But you must remember to mark each Face on your Plain with numerical figures or some other mark so as you may know to what Face of your Christal each belongs for you will find them all reverted that is those seen through the top-faces of your Christal will be in the bottom of your Plain and those seen through the right hand Faces of your Christal will be on the left hand on your Plain Having thus prepared your Plain you must draw the figure of your Christal on a plain paper exactly of the size of your Christal and devide it into so many parts your Christal is devided and cut into Faces and mark each devision thereon in a reverted order from that on your Plain As if the bottom Face on your Plain be marked 1 then mark the top Face in your paper 1 And if 2 3 4 c. be marked towards the right hand on your Plain mark them towards your left hand on your paper as you see in the Figure On this paper therefore you must draw the Picture you intend shall be seen on the Plain Suppose the Picture of King Charles the first and having drawn it transfer all the lineaments and stroaks you find in each respective Face on the paper to the responding Face on the Plain As for example What lineaments you find in the Face marked 1 on the paper transfer to the Face marked 1 on the Plain what lineaments you find in the Face marked 2 on the paper transfer to the Face marked 2 on the Plain And so for all the rest Then looking again through your Tube you will see all the severed Faces on the Plain unite each Face contributing the lineaments drawn in it to form your intended Picture of If you have a mind further to amuse Spectators you may to every one of the Faces on the Plain draw another Picture as in the Face marked 10 on the Plain you find an Ey to this Ey make up an whole Figure To the Face marked 12 you find the Mouth to this make up another whole Figure c. But you may alter the likeness as much as you list both in countenance and dress So will the conceit appear yet so much the stranger I have inserted one Example where about the Face 1 on the Plain I have set the Picture of a Woman I II III IIII V VI VII VIII IX X XI XII XIII XIIII XV XVI XVII XVIII XIX XX XXI XXII XXIII XXIIII XXV XXVI XXVII XXVIII XXIX XXX XXXI XXXII XXXIII XXXIIII XXXV XXXVI XXXVII XXXVIII XXXIX XL XLI XLII XLIII XLIIII XLV XLVI XLVII XLVIII XLIX L LI LI LII LIII LIIII LV LVI LVII LVII LVIII LXI LX
makes Perspective be thought so difficult is the mixture of many Lines directing to many designed points Therefore when you draw some busie peece in Perspective you may for the directing your Ey Draw the Diagonals in Red the Visual Raies in Black Perpendiculars in Green or any other different Coullers from that you intend your Perspective Figure shall be of There may be some more Rules worth your Notice but as yet not comeing to my memory Take these for the present and as the rest offer themselves to me I shall present them to you In the mean time If you meet with any words of Art you understand not Look over the Leaf where I have digested them in an Alphabetical order and to them annexed their explanation An Explanation of such Un-usual words as you may find in this Book Arch. A peece of a Circle As in Oper. 2 c d is an Arch of a Circle Axis is that straight line whereon any Body moves circularly as in the line a a in Operat 21. is the Axis of the Door Base See Chap. 2 Defin. 1 Broken beams See Chap. 1 Defin. 4. Capital The top of a Column Catuzes e f in fig. 22 are Catuzes Catoptrick See Chap. 1 Defin. 3. Center The middle point of a Circle or any other figure Cilinder A straight round Body flat at either end Fig. 53. Column The upright Pillars markt x a b y c t in fig. 30. Composite Order an Order in Architect See Vignola Cone Fig. 54. Corinthian Order An Order in Architect See Vignola Cube A Square Body of six equal sides as I K L in fig. 19 are Cubes Diagonals See Chap. 2 Defin. 8. Diagonal Squares The squares in fig. 16. are all Diagonal Squares because all their sides are Diagonal lines Diametrial See Chap. 2 Defin. 7. Dioptrick See Chap. 1. Defin. 4. Direct beam See Chap. 1. Defin. 2. Distance See Chap. 2 Defin. 5. Dorick Order An Order in Architect See Vignola Equilateral Triangle A Triangle of equal sides as are the Triangles d e f in fig. 5. Geometrick Figure or Body is a Figure or Body that hath its true demensions Ground line See Operat 51. Ground-plain A plain full of Squares as fig. 15. 16. Height See Chap. 2 Defin. 2. Hexagon A figure of six equal sides is a Hexagon as the two figures in fig. 6. are Hexagons Horizon See Chap. 2. Defin. 4. Ichnography See Chap. 1 Defin. 6. Intersection Two lines crossing one another are said to intersect each other Ionick Order An Order in Architect See Vignola Luminious Body Light body as in fig. 51. 52. to 56. at a is the Luminous body Newel is the upright post a pair of winding stairs winde about Object See Chap. Defin. 9. Occult. Occult lines or Arches are dark lines or Arches which are only drawn for direction to make the Figure up by these are throughout this book represented by prickt lines and arches Octagon a Figure of eight equal sides is an Octagon As are the two Figures in Fig. 8. Opacous body A Dark body As in Fig. 51. 51. 53. 54. 55. 56. the bodies obstructing beams of Light are Opacous bodies Optick See Perspective Chap. 1 Defin. 1. Orthography See Chap. 1 Defin. 9. Parallel Parallel lines are straight lines that are all the way equally distant from one another as the Base and Horizon throughout this book are all parallel to to one another Parallellepippedon is a square body that hath its four sides longer than its two ends As in fig. 56. the square body f g. Pedestal A square body whereon a Column is set as d in fig. 28. Pentagon A Figure of five equal sides as are the two figures in fig. 7. Perpendicular A line that falls plumb upon another line without leaning to one side or another is a Perpendicular line Perspective See Chap. 2 Defin. 1. Pilasters Square Pillars that usually stand behind Columns to bear Arches c. Quadrat A square figure of four equal sides Quadrant A figure containing the fourth part of a Circle Radius Half the Diameter of a Circle Reflected beams See Chap. 1 Defin. 3. Right Angle is made by two lines exactly Perpendicular to one another Scenography See Chap. 1 Defin. 10. Section See Chap. 2 Defin 6. Semi-circle Half a Circle Station The place you stand on Tetrahedron is a Body whose four Plains are four Triangles as in fig. 55. Tube a long hollow instrument wherein is usually a Glass fitted to observe objects through Tuscan Order An Order in Architect See Vignola Visual point See Chap. 2 Defin. 3. Visual raies See Chap. 2 Defin. 7. OPERATION I. Height and Distance given To find the scituation first of a Point secondly of a Line and thirdly of a Square in the Glasse or Section THe given Height from the ground to the Ey or which is all one from the Base to the Horizon is a b the Distance from the Foot to the Glasse is a c. The given point or Object to be represented in the Glass or Section is d. The Glass erected perpendicularly on the Base is e f g h. Draw a Visual ray from the Ey at the point b to the Object at the point d as b d and another line from the point of Station a to the same point d as a d then erect a Perpeneicular on the point where this line a d cuts the line of Section as at c and where this Perpendicular cuts the Visual ray b d as here it does in i is the point that the Object d appears in the Glass To find the Scituation of a Line in the Section or Glass You must have the Height given as a b and the Distance as a c And as you were taught before to find the place of one point in the Glass so now by the same Rule the Operation must be doubled to find the place of two points in the Glass and then a straight line drawn between those two points is the line required Example The given Line is d e Therefore from the Visual point b I draw two straight lines or Visual rays to the two points at the two ends of the line d e and two other straight lines from the point of Station a to the same points d e And from the points where these two lines intersect the Glass as here they do in the points c f I erect Perpendiculars into the two Visual raies and where these Perpendiculars intersect the two Visual raies as here they do at g h is the points d e represented in the Glass and a straight line drawn between the points g and h represents in the Glass the straight line d e. To find the scituation of a Square figure in the Glass You have the given Height a b the Distance c. Draw Visual rays from the Visual point b to every angle of the Square d e f g and draw also lines from the point of Station a to every angle of the Square and where these lines of Station
other and for describing the arch which is alwaies a Quadrant of a Circle measure with your Compasses the distance between o and s and on a loose paper or other thing make a Geometrick Square whose Sides shall be equal to that measure and with a straight Ruler cross that Geometrick Square in its Diagonal Angles and the distance between the intersection of these two straight lines and one of the Angles of the Square shall be the Radius to a Circle of the same sweep the Arch o s shall be of and the Center of that Arch is found by placing one foot of your Compasses first in the point o and with the other describe an occult Arch as at v afterwards remove one foot of your Compasses to the other end of the Quadrant and with the other foot describe another occult Arch to cut the former and in that point of inter section shall be the Center of the Arch o s. Use the same way to describe the Arch g s. The Columns x a b y are all set Perpendicularly over the Columns x a b y and the two Pinacles over the Columns c d as you may see by the prickt Perpendicular lines so that what remains to be said of this Figure may be understood by the Figure it self as well as by many words upon it OPERATION XXXI To describe a Square with Ascents of Steps about it A Square that hath Steps to ascend on all four sides hath all the sides of those Steps parallel to the undermost Step Therefore in making the Ichnographie of this Figure you must include so many Squares as you think good within your outmost Square all equidistant from and parallel to the outmost Square And from one half of the Ichnographie produce the Scenographick Ground-plain for what Height and Distance you please Having therefore designed the Height a b of the first Step b c Describe a parallel Scale Thus Draw a straight line from the Base to any convenient part of the Horizon as here to d e then prolong the line b c into this line as into f then from the Visual point draw a line through f into the Base as at g and from the point g draw a line to the point e in the Horizon Then transfer the distances a h a i and a k on the Diagonal line in the Scenographick Ichnographie to the Diagonal line a l in the Structure as to a h a i a k and from those points on that Diagonal line raise the Perpendiculars h m n i o p k q r Then from the point b draw the Diagonal b m and where that Diagonal b m cuts the Perpendicular h m shall be the bottom of the under Step m s which Parallel line must be continued into t for by drawing the Visual ray from t to the Visual point you will cut the line d e in v from whence the line v n drawn parallel to the Horizon gives the top of the second Step Then by drawing the Diagonal n o you have the bottom of the third Step at o from which point a Parallel drawn into g e and a Visual ray drawn from that point in g e shall cut d e from which intersection in d e a Parallel drawn into p shall give the top of the third Step. The like you must do for the fourth Step. Then lastly draw a Visual ray from the point a and a Diagonal from the point x to y and where the foresaid Visual ray cuts this Diagonal erect a Perpendicular into the Visual ray b z and from the point z draw a line parallel to the Horizon as far as the second Step which shall shew how much of the hind part of the first Step will be seen The same way you may find how much of the other Steps appear as you may see in the Figure for where the Diagonal x y cuts the several Visual raies in those points the Perpendiculars erected into the Visual raies before it shews how much of the hind part of each respective Step appears On these Steps you may place a Fountain a Pyramid or a Column as is lately erected in Covent Garden in the middle of the Pietzo This Parallel Scale is of great use for by help of it you may set any Object in its true place as well as with a Ground-plain of Squares But you must remember to place your Perpendicular at the point of Distance and so let it fall into the Base for then by drawing a slope line from the point of Distance to any devision of the Base and by drawing a Diametral to the Prependicular in the Base where the Diametral cuts the slope line shall be the Height of the first parallel line of the Scale and by drawing another Diametral to the point where the first Parallel cuts the Perpendicular the Diametral shall cut the slope line in a point through which a Parallel drawn shall be the second Parallel line c. OPERATION XXXII How an Object that is to be placed high above the Horizontal line shall be made that it appear equal to an Object placed but a little above the Horizontal line BEcause those Visual Raies that proceed from the Center of the Ey straight and directly forwards are more strong than those that decline towards the right or left hand or are either elevated or depressed above or below the Horizontal line Therefore any Object that stands at a convenient distance in the Horizontal line directly before the middle of the Ball of the Ey appears more perfect and true in shape and demension than if it were placed any where else as may be proved by placing two Objects of the same shape and demension one in the Horizontal line just before you on a Wall and the other right above it at some considerable height on the same Wall for you will find that the Object thus elevated will appear less than that which is placed on the Horizontal line and that if the same Object be placed yet higher it will appear yet less and less Therefore to know how big you shall make an Object for any given Height and Distance above the Horizontal line that it appear equal to an Object placed right before you in the Horizontal line You must first consider That as the Object that lies right before the middle of the Ball of the Ey in the Horizontal line appears most perfect and by consequence shews its truest demension So the Object that is placed higher or lower or on the right or left hand appears less perfect and by consequence requires a greater demension to make it appear perfect for the Sight moving circularly in the Ey makes on a Wall the devisions of a Tangent line and by so much as a Tangent increases upwards in such proportion does the strength of the Optick faculty of the Ey deminish upwards Therefore the Object that shall be placed any considerable height above the Horizontal line and to be seen from a
of Opacous Bodies before Luminous Bodies which Opacous Bodies stop and hinder those Lines of Light which else would pass from the Body of Light to the Plain whereon the Oparous Body stands By Lines of Light I mean those straight lines that pass from the Body of Light to the Plain Thus the line a b is a Line of Light These Lines of Light the Plam or Line of Saddows and a Perpendicular let fall from the Body of Light makes alwaies a Triangle as is the Triangle a b c where a b represents the Line of Light c b the Plain or Ground-line of Shadows and a c the Perpendicular If in this Triangle any Opacous Body be placed so as to break the lines of Light that opacous causes a Shadow Thus the Staf d e erected perpendicularly at d breaks all the lines of Light inclosed between d e b and makes the Shadow d b by which instance alone you may see the manner and properties of Lines of Light and how a straight line drawn from the line of Shadows through the point the Opacous body stands on and a line of Light drawn from the body of Light through the top-point of that opacous body shall cut each other in the point of termination of Shadow By this proposed Staf I would have you understand a Line though in this place it would be unproper to call it so because that having no Geometrick bredth makes no shadow But as was said in the third Operation where a Line was laid down in Perspective knowing how to draw a Line in Perspective you know how to draw all Figures because they are bounded by Lines so I may say in Shadows for though the Object be a Body yet the Shadow is but a Figure and by knowing how to draw the Shadow of every Line properly you know how to draw the whole figure of Shadow As you may see in this next Operation OPERATION LII To find the Shadow of a Cube the elevation of Light above the Ground-point being assigned THe given Light is a the Ground-point b the Cube c d e f g h i k Therefore from the upper angles of the Cube c d e f I draw lines of Light through the Plain and from the point b I draw lines of Shadow through the under angles of the Cube as through g h i k and where these lines of Shadow cut the lines of Light as here a e cuts b i in l a d cuts b h in m a f cuts b k in n shall be the points that the shadowing angles of this Cube casts its shadow on the Plain as here to l m n and straight lines drawn from m to l from l to n from n to k and from m to the side of the Cube g c shall include the shadow OPERATION LIII To find the shadow of a Cilinder the elevation of the Light above the Plain of shadow being given THe Body of Light is a the Ground-point b the Cilinder c d e f g h i k The Cilindrick section above the plain of Shadows you must bring into the Plain of Shadows by letting fall Perpendiculars from the four devisions above viz. c d e f into the the plain of Shadow as at l m n o Then by drawing lines from the body of Light through the devisions in the upper end of the Cilinder as through c d e f and from the points g through l k through o i through n and h through m where the lines of Light cut the lines of Shadow as here in the points p q r shall be the bounds of a Scenographick arch which joyned to the straight lines h p and k r shall include the shadow You must note I hat the Scenographick Figures c d e f made at the top of this Cilinder and l m n o made by the Perpendiculars let fall into the Ground are true Scenographick Circles and that the circle c d e f appears smaller than the Circle l m n o because it is posited neerer the Horizontal line which alters the Scenographick appearance as you may see in the several Circles that are made about the Newel of the Winding Stairs in Operat XXXIII This I mind you of because from the devisions in that Circle and not from the Ground point the lines of Shadow are drawn to cut the lines of Light OPERATION LIIII To find the shadow of a Cone set on its point the elevation of Light being given THe Body of Light is a The Ground point b the Cone c d e f g Project the top of this Cone which is a Circle Scenographically as in Operat IX X. and by Perpendiculars let fall on the Ground draw also the other Circle h i k l from the same Visual point and point of Distance Then from the Body of Light draw lines into the Ground through the points d e f g of the upper Circle and from the Ground point draw lines through the points h i k l in the Circle on the Ground and where these lines intersect each other as here in the points m n o shall be the points through which the Scenographick arch m n o drawn to meet the straight lines i m l n and k o shall be the track that shall include the shadow OPERATION LV. To find the shadow of a Tetrahedron with one of its points set on the Ground the elevation of Light being assigned THe given Light is a the Ground point b the angles of the Tetrahedron c d e f Project the Triangle c d e Scenographically on the Ground by Perpendiculars let fall from the angles as into g h i and let the length of the Perpendicular e f be the length of the Side c d so shall the sides g h and h i be drawn from the same point in the Horizontal line that the lines c e and e d were drawn from Then from the body of Light draw lines into the Ground through the points c d e and from the Ground-point draw lines through the points g h i and where these lines intersect each other as here in the points k l m draw straight lines from f to k from k to l and from l to the side d f of the Tetrahedron where it is cut by the prickt line m n. OPERATION LVI To find the Shadow of a Staff broken by the interposition of a Parallellepippedon and by the interposition of a Cilinder The Elevation of Light being assigned THe Body of Light is a the Ground-point b the Staff c by working as by Operat LI you find a straight shadow continued from d e where the shadow breaks against the Parallellepippedon and and rises Perpendicularly on the side e f and thence on the upper side of the Parallellepippedon continues it self Parallel to the Plain of Shadows as at g and solooses it self behind the further side of the Parallellepippedon But the Saff h i makes another fashioned Shadow on the surface of a Cilinder for by working as before you find
Perpendicularly on the Ground-plain the bredth of these Shelves are one Square on the Ground-plain as you may see by the line h i from which Diametrals prolonged to the Post the several Shelves are described Here you may note that by the several places of these three Shelves you have several appearances of them for the Shelf g lying under the Horizon shews its upper Plain The Shelf f lying a little above the Horizon shews its under Plain though much fore-shortned The Shelf e lying pretty high above the Horizon discovers the under Plain more intirely But on the other side the Wall you have the Shelf k which because it stands just in the Horizontal line discovers neither the upper or under Plain but only the very edge of the Shelf OPERATION XXIII The manner of placing Columns behind one another in Perspective THough this may be performed by a Ground-plain of Scenographick Squares as before yet because in this Operation no work comes between the two rows of Collumns we shall need describe no more of the Ground-plain than will serve our turn Therefore having drawn your Horizontal line to your designed Height above the Base and set off your points of Distance at equal distance on either side the Visual point Draw the Diametrals a a b b c c d d Then from the points of Distance draw the Diagonals e d and f a and at the points of interfection of these Diagonals with the Diametrals draw straight lines parallel to the Base and these straight lines continued to the outmost Diametrals shall make four Scenographick Squares whereon four Columns must be placed as here the Squares a b and c d and g and h c. If you would have more Columns stand behind these four Draw Diagonal lines from the innermost Angle of the hindmost Squares already made as from g and h and those Diagonals shall intersect the Diametrals in c d and b a from which angles of intersection straight lines drawn parallel to the Base and Horizon shall make the Scenographick Squares whereon two other Columns shall stand By this manner of working you may set more Columns behind these till you almost fill the whole Ground-plain Having thus projected these Scenographick Squares whereon the Columns must stand you must erect Perpendiculars from every angle of these Squares through the Horizontal line and so upwards to the height your outmost Column ought to be as here to the line i k parallel to the Horizon for the points where Diametrals intersect this line and the Perpendiculars a i and d k shall be angles impending perpendicularly over the respective angles of each respective Square in the Ground-plain As here the angle i hangs directly over the angle a and the angle k hangs directly over the angle d Then from the points of Distance draw Diagonal lines to the points i k and where those Diagonals intersect the Perpendiculars erected on the Diagonal angles of the Square in the Ground-plain must another line be drawn parallel to the Horizon and also other Diagonal lines which shall include the Squares that hang over the two first Squares in the Ground-plain The other Squares are found after the same way viz. by the mutual intersections of the Diagonals with the Perpendiculars As may be seen in the Figure The Arches over these Columns are very easily made for by drawing the Perpendicular through the Visual point in the Horizon into l you have all the lines drawn parallel to the Horizon devided into two equal parts And by placing one foot of your Compasses in the middle of the respective Parallel lines and opening the other to the angles of the Square that lies in the same Parallel line you may describe those respective Arches As for example If you place one foot of your Compasses in the middle point on the line i k and extend the other to the point i or k you may describe the outmost Semi-circle and by closing the Compasses to the other angle of the Square which lies in the same line you describe the second Semi-circle for the third Semi-circle you may place one foot of your Compasses in the middle of the next parallel line and extend the other to the point o in the same line and describe the Semi-circle o p. This work is so plain and easie to be understood by the Figure that I need discourse no further upon it In this Figure you may note what correspondence the Squares above the Horizon have with those below the Horizon Yet as the Squares above the Horizon have a greater distance from the Horizon than those below the Horizon have it falls out that the upper Squares are larger than the under Squares The reason whereof you may easily see by consulting the Figure And as the Squares have a correspondence so also have the Diagonals for the crossings of the Diagonals above the Horizon respond with the crossings of the Diagonals below the Horizon OPERATION XXIIII To describe in Perspective the appearance of four Pilasters with four Beams upon them And to make an Arch over them THis is also performed by a Ground-plain of Squares which consists of seven in bredth and seven in depth Described as by Operat X V. The Pilasters a b and c d standing each on one Square erected perpendicularly on the angles of the Ground-plain and divided upwards into three equal parts as 1 2 3 with straight lines parallel to the Horizon drawn through the fore side of them But the lines that devide the inside the Pilasters are Diametrals drawn from the Visual point to the inmost corner of the foreside of the Pilaster As you may see by the Figure Upon these Pilasters is laid a Frame off our Beams serving for bond to the Pilasters as e f g h two of which viz. f h are drawn from the Visual point And over these four Pilasters is erected the Arches i k l and m n o to be seen quite through which Arches being to be made as those in Operat XXI XXIII need here no further discourse on them Only you must note that what lines of devisions you make on the Orthographick or fore-side of the Arch you must draw from the center of each respective Arch and the devisions on the under side of the Arch must be drawn by the side of a Ruler laid to the Visual point and to the devision on the corner of the foreside the Arch as the devisions of the Pilasters are OPERATION XXV The manner of making Side Arches in Perspective HAving drawn an Horizontal line describe a Ground-plain of Squares as by Operat XV. and thereon draw a Scenographick Circle as you were taught by Operat IX X. and mark it from the middle line with 1 2 3 4 5 on the Base and on the side with a b c d e f g h Then erect a Perpendicular on the corner of the Ground-plain of the height you intend your side Wall shall be as h i and erect another Perpendicular