find in the 75. fol. As for Fortifications he that would set them into Perspective shall find the Method to reduce and abreviate the plane thereof in the 39 fol. and how they ought to be elevated in fol. 114. The Treatise of Shad ws which beginneth at the 129. fol. unto the 150. teacheth how to give them to all sorts of Objects whether they be caused by the Sun by a Torch or by the Candle As for all other things in particular they are to be found according to the Order of the Table which is at the end of the Book Licensed May 2 1672. Roger L'Estrange SOME DEFINITIONS AND PRINCIPLES OF PERSPECTIVE The Definitions Names and Terms of the Points Lines and Figures which we shall use THe point hath not any parts as we see A in figure 1. In Perspective there are three sorts thereof which are called points of sight points of distance and points contingent or accidental The line is a length without breadth as A B in figure 2. The Perspective hath five principle ones the which it always useth The 1. The line of the base or plane as C D may be in figure 3. The 2. The line Perpendicular or Plomb-line which falling upon another maketh the Angles on the one part and another equal and these Angles are called Right Angles and the line is Perpendicular to that upon the which it falleth as in the figure 3. A B and E F falling upon C D do make the Angle right in G. The 3. are lines parallel These are lines the whâ—ch being continued upon the same plane and prolonged on the one part and other infinitely will never meet together as N O in the figure 6. The Horizontal line is no other thing then a parallel to the base We shall speak of it more largely in its place The 4. is the line Diagonal this is a line drawn from one Angle to another as K L in the figure 10. And the 5. The line occult or pointed is a line which ought to be made in white or with points as O N in figure 2. and these lines never ought to appear when the work is finished The right Angle is that which we speak of treating of Perpendiculars I have set it apart by it self that it may be better known what it is by E F G in Figure 4. There are two other Angles under which are comprized all the Angles which are not right the one is called the Obtuse which is more then right as H L M in figure 5. And the other sharp which is less then right as is H I K in the same figure A term is the end of any thing as in the 2. A and B are terms or the ends of the line A figure is comprized by one or by more terms as in 7. 8. 9. 13. 14 c. are figures The square hath the four sides equal and the four Angles right A B C D in fig. 7. The Parallelogram or long square hath the four Angles right but not the sides equal as C D E F in fig. 8. The Triangle Equilateral hath the three sides equal as G H I in fig. 9. Section and Intersection of lines are two lines which do cross and divide themselves in one point as in the figure 11 the lines A B and C D divide themselves in E. The bowed or crooked line is that which is drawn by a Circuit from one point to another as L M in fig. 12 A Circle or Round is a plane figure comprized in one line only called a circumference towards which all the lines coming from the Center are equal between themselves as B C D of the figure 13 the point of the midst of the Circle A is called the Center The Diameter is the right line B C of the Circle the which passing by the Center of the Circle A divideth it into two equally The Oval is a long figure comprized within one line only not Circular but bowed and Regular as E in fig. 14. The Spiral or Volute is a line that is framed by two Centers or by one only by Revolution or Diminution F in fig. 15. The Rest of the Definitiâ—ns Names and Termes TAngents are one or more lines which being drawn forth do but only touch or graze upon some Object figures or lines without dividing them in any manner as A B touch the Circle C at the points D D. I have placed here two sorts of lines which bear the same name with the Precedent and which nevertheless produce another effect by reason of the point of sight and of the Perspective for the Angle E A B ought to be held for a right Angle and all the lines C ought to be held for Perpendiculars upon the Plane in Perspective as is D F and the lines A B G I and H K are accounted Perpendiculars upon the base and all the lines which go to the point of sight either from above or from below or on the side are called Rays and lines visual or Radial The Plane or Ichnography is a description or first design the which representeth by single lineaments the Prints or foot-steps which the foundation of the thing which one would describe would make upon the Ground to the end that by one view only one may behold the correspondence scituation and interval of the parts between themselves as one may see in L and M. A Polygone is a figure which hath many Angles as is L A Degree is one little part whereby the Circle is divided into 360 and every degree is further divided by the Astronomers into 60 Minutes and these Minutes into 60 others which they call Seconds c. the which is not useful for us here It sufficeth that we know that the degrees are those little divisions which are in the Circle N O P Q for to have the knowledge of the Angles This knowledge will enable easily to make all sorts of Polygones by dividing 360 by the number of Angles which one would have in the figure for example if I would make a square I divide 360 by 4 and the Quotient will give 90 which is the right Angle N M O and so of others for those which have not the use of Arithmetick they shall finde at the fourth side of the Geometrical Orders to make such whatsoever may please them Some Orders of Geometry for to make the Lines and Figures which we are about to define 1. FOr to make the Perpendiculars or as the Workmen say the square Draught which is necessary in all our operations If that you would have it in the midst of a line as A E you must open the Compass more then the half of the line and place one leg of it at the point A and with the other frame two little Arches or Bows above and below as F and to do the same from the point E and the sections of these little Arches will give the Perpendicular upon A E 1 figure 2. If the
line be at the bottom of the table or paper and that one cannot make the Arches above and below You must divide this line into two for to have the point G then from the ends of this line to make the Arches which shall divide themselves in H then to draw a line from H to G as in the second figure 3. To elevate a Perpendicular from the end of a line as from the point I of the line I K. This may be done divers ways first as we have said but when place is wanting you must place one leg of the Compass at the point I and with the other leg to make a great portion of the Circle L M then to set the Compass so opened upon the point M and with the other to make it to divide the Circle at the point N then to take the half towards the point O for to have the right Angle O I K or without busying ones self to seek this half of the Arch M N you must with the same opening of the Compass make yet upon the N and from the same point N an Arch P Q then having laid the Ruler at the points M and N you must draw a line which shall divide this Arch P Q at the point P and elevate a line from I to P for to have the Perpendicular and the right Angle P I K figure 3. 4 Otherwise If from the point P you would raise a Perpendicular take a point at pleasure upon the line P R as Q and from the point Q make a Circle which toucheth the point P and shall divide the line P S in some part as S then to draw from S by the point Q unto the circumference of the Circle T and T P shall be the Perpendicular fig 4. For to abreviate all the orders you must have an equaller very just 5. From a point given upon a line to make a Perpendicular to fall From the point given A you must make the Arch B C which divideth the line given E F at the points G H from these points G H make two little Arches above and below which shall divide themselves as at the point I then from the point A cause a line to fall passing by I upon the line E F and that shall be the Perpendicular of the point given 6. From a point given at the end of a line to make a Perpendicular fall Let the point given be K and the line L M from the point K you must draw a line traversing at pleasure which divideth in some place the line L M as N after divide this line K N into two equal parts and from the midst O make the Arch that passeth by the point K and at the section which it will make upon the line L M as P and the point P shall be to make the Perpendicular to fall K P. 7. The parallels For to be well made ought to be over half-Rounds which they ought to touch as F G which is parallel to H I it is made over the half Round which it toucheth at the points K L. 8. To divide a line into many equal parts Let the line to be divided be A B. You must draw another above or below which may be parallel to it as C D and upon this latter which must be greater or lesser then that which is to be divided You must make as many parts as you would divide that of A B into as in our example seven then from the first and last point of these divisions to draw lines which pass by the ends of that which is to be divided which shall divide themselves in a certain point as here having drawn from C by A and from D by B the section E is made at which point F you must draw all the divisions of the line C D and the line A B shall be divided as one desireth For to frame the Figures 1. IF the line A B be given to make of it a square You must set one Leg of the compass at the point A and with the other leg take the length A B and holding firm at the point A with the other leg of the Compass make the Arch B C and make also from the point B the Arch A D which shall divide themselves at the point E without the side of the section he must transport the half of the Arch A E or B E which shall be in the points D C by the which drawing right lines one shall have a perfect square After another manner Upon the line A B draw from the point A a Perpendicular C A equal to A B then having taken with a Compass the length A B or A C you must set the leg of the Compass at the point B and with the other make an Arch and do altogether the same from the point C the section of these two Arches shall be the point D for to frame the square A B C D. 2. For to make a parallelogram or long square Draw a Perpendicular greater or smaller then E F as E G then haâ—ing taken the height E G set a leg of the Compass at F and with the other make an Arch take also the l ngth E F nd set a leg of the Compass in G and make a second Arch then divide the first at H and you shall have that which you desire you must always observe the same thing for all the four right Angles Of Polygones Circular which are Figures with divers Angles within one Circle 3. For the Triangle equilateral You must set the half Diameter at the point A and describe the Arch D E and draw a line D E this line shall be the side of the Triangle D E F. 4. For the square draw 2 Diameters at right Angles joyn their ends this shall be the square A B C D. 5. For the Pentagone or five Angles Make 2 Diameters and take D G the half of the Demy-Diameter D I and from the point G of the Interval G A make the Arch A H the subtendent H A shall be the side of the Pentagone 6 For the Hexagone or six Angles The half Diameter is the side of the Hexagone 7. For the Heptagone or seven Angles Take the half of the side of the Triangle Equilateral A. 8. For the Octogone or eight Angles Take the half of the quarter of the Circle 9 For the Ennagone or 9 Angles Take the 2 thirds of the half Diameter as E B for its side 10. For the Decagone or ten Angles Take an half Diameter and divide it in two at the point G then from the point G and the interval G A make the Arch A B the part of the half Diameter B C shall make the side of the Decagone 11 For the Hendâ—cagone or eleven Angles Make two Diameters at right Angles and from the point A make the Arch B C of the interval of the half Diameter then from the intersection C
of the Eye by reason that it is opposite to him which looketh upon it Of the Points of Distance THE Point of distance or Points of distances Is a point or points for they make two although it be not necessary which are to be set equally distant from the point of sight They call them points of distance because that the Person must be as much distant from the Figure or Picture and from the base as these points are distant from the Point Ocular and they must always be within the horizontal line as H I is the Horizon K the point of sight L and M are the points of distance which serve to afford all the Abridgements As for example if from the ends of the line E G one draw two lines to the point K and from the same points F G one draw two lines to the points of distances M and L where these two lines G L and F K shall be divided at the point X and G K and F M at the point Y this shall be the line of sinking or hollowing and the abridgment of the square whereof F G is a side and the base the lines that go to the point of sight are all visual Rays and those which go to the points of distance are Diagonals Of Points Accidental POints Contingent or Accidental Are certain Points where the Objects do end which may be cast negligently and without order under the Plane it is because they are not drawn to the Point ocular nor to the points of Distances but by chance and at adventure where they meet each other in the Horizon as for example these two pieces of wood X and Y do make the points V V V V above the Horizon P and Q and go not to the point of sight which is R nor to the points of distance S and T And sometimes the Bodies or Objects are so ill ordered that one must make these points without the Horizon as we shall cause to be seen in its place They serve also for the Openings of doors of windows of stairs and such like things The which shall be seen hereafter 1. Fig. 2. Fig. 3. Fig Of the Point of the Front THE point of sight direct or of the front it is when we have the Object whole before us without being more on the one side then the other and then one hath the Object wholly right that is to say that it sheweth nothing but the fore-part when it is elevated and a little above if it be under the Horizon but it never sheweth its sides if the Objects be not a Polygone For example the Plane A B C D is wholly the front so that one can see nothing of the sides A B nor C D if it were elevated but only the fore-part A D. The reason is for that the point of sight E being directly opposite to it it causeth the diminution of the one side and the other this ought to be understood if the Object were an Elevation for when there is nothing but the Plane it sheweth all as A B C D. Of the Point of the side THE oblique point of sight or on the side Is when we see the Object on the side of us and that we see it not but athwart or with the corner of the Eye our Eye being nevertheless always over against the point of sight for then we see the Object on the side and it sheweth us two faces for example if the Eye be in F the point of sight the Object G H I K will appear to it athwart and will shew to it two faces G K and G H and then it will be a point of the side We ought to do altogether the same in the points of the sides as in the points of the front setting a point of sight and those of distances c. briefly the same is to be done as at the view of the front 1. Fig 2. Fig. Of the visual Rayes THIS is a general Maxime That all the lines which are Perpendicular to the base within a Geometral Plane ought always to be drawn at the point of sight when one would set the same Planes in Perspective for example in the little Plane of the first figure the base is A B upon which all the lines Z are Perpendicular to it This being supposed that if one give a less or a greater line then that of the Plane as the great line A B which hath the same number of divisions with the little one and from all these divisions Z one draw to the point of sight all these lines of Z to E they will all be perpendicular to the base according to the Reasons of Perspective we may also name them Radial and properly visual Rayes the last of which are called Extremes by reason that they are at the end of the base as are these A B. Of the Diagonals or Diametrals and of their sections IT is also a Maxime that all the Diagonals of squares in Perspective are drawn at the Point of distance For example at the little Plane of the second Figure the Diagonals D O F O are drawn at the points of distances in the Plane in Perspective the which maketh that the points of distances do give us the Abridgements of the Objects that the point of sight doth remove from us in such manner as we have already said that if one draw from the ends of the line of the base F G to the points of distances L M they shall be Diagonals and where the lines shall divide the outmost Rayes F K and G K at the points O this shall be the Abridgment of the square whereof F G is one side and where the same lines shall divide the lines Z at the point Q one must draw Parallels which shall give the Abridgement of all the squares and a like number of all the sides as in the little Plane And the more these points of distances are removed from the point of sight the more the Objects do abridge themselves and close together And this is it why all the Beauty of the Perspective dependeth on the points of distances which ought neither to be too near nor too far off from the point of sight the which made me set this third figure with diversity of removals for to cause a belief of the verity of that which I am speaking Let us suppose then that R is the point of sight and S S the outmost Rays if one sets the point of distance at T he shall divide the Radius S R at the point V which shall be the abridgement of the square whereof S S is one side the which is ridiculous to see a square which should appear three times more hollow then it ought to be by reason that the point of the distance T is too near to the point of the sight R for it must be at the nearest that the point of distance be as far removed from the point of sight as the half
equal parts and drawing lines to the point of sight for to frame the bands or chains G H I yet nevertheless there is more to do for we must take heed to give to the Chains that go across the same largeness as to the others which go to the point of sight O which is a square throughout all and that there be the same number of Squares between the void ones The rest is seen sufficiently A Pavement of little Squares Octogones mingled with the Squares WE should never have done if one would set here all the fashions of Pavements which might be made by the means of the little Squares for an ingenious person would invent an infinite Company according to his fancie The seventh fashion is plain enough neither have I done it but only to open the Ingenuity and to give means to compose others thereby There is nothing to do but to divide the base into a quantity of Parts of the which we shall frame the little squares as we have said heretofore And of these squares to take a number as here nine whereof there are five all full and four at the half The full do give the inside of the figure 1 2 3 4 5. And the Diagonals of others 6 7 8 9 give the Panes or Sides The rest is sufficiently seen A Pavement of single Squares view'd in Front I Have set this manner of Pavement the last not because it is the hardest seeing that it is the beginning of all Perspective and the most easie of all the Planes but to cause to be known that it is the most useful and necessary for all the other may be made and are made ordinarily when all is done serving only for ornament And this serveth for a foundation upon the which we raise that which we desire to make appear As we shall see hereafter 1. fig. 2 fig. The Plane of a Garden abridged THAT which we are speaking of is confirmed by this Plane for drawing all these divisions which are upon the base to the point of sight the Diagonals will give the depth of the whole Plane and the Abridgement of the little Squares Then taking the same quantity as well for the Alleys as for the figures which the Geometrical Plane taketh up you shall have in Perspective the same Garden which is upon the Plane As the figure sheweth it What plane soever you have to abridge And to set into Perspective The easiest way is to Enclose it into a Square and to divide this square into many little squares For setting the square and the quantity of little squares into Perspective by the ordinary wayes You have but to take heed that you take the same Number of little squares in the Plane abridged as in the Geometricall Plane And you shall make in the one the figure of the other The Plane of a Building Abridged SErlio in his Treatise of Pespective doth highly esteem this Invention of setting the Planes into Perspective as a thing very useful to chief Builders or Architects by the which they may cause to be seen all at once a part of the buildings elevated and the rest in Plat-form and as upon the base But seeing that it is the same Order with that of the Garden which we are making now we will say nothing further of it The Figure will cause to understand the rest and by this little to gather how the greater and more hard should be In the second part you shall have the method to make to be seen in Perspective a perfect House where you shall see the Building finished and accomplished and by the same means all the divisions of each Story from the Carpenters Work unto the Cellar and the only space which the Geometrical Plane would take up The Plane of a Church Abridged THis plane of a Church is made according to that we have said at the seventh Advice That is to say that all the sides which are Perpendicular to the Base ought to be drawn upon the Base as are here the places of the Walls and of the Pilasters and from the Base to draw them to the point of sight And all the other sides which are Parallel to the Base ought to be drawn on the side And to mark upon a line as O P all the bredths as we see A b c d e f g h i k l. And then to transport all these Measures upon the Base from the which drawing to the point of distance the sections of the outmost Raye will give the Termes for to draw the Parallels which will give the Abridgement of every thing the which is shewed by the Letters a a b b c c c. This manner of Abridging upon the outmost Radius is practised by many But he that would believe me will leave it for to take the Orders of the Eighth Advice where we set a Perpendicular line at the end of the Base for to receive the sections and to take away the default of this present Practice which doth not abridge it sufficiently if it be not that the points of distances are very far removed for then the effect is wholly alike to the other Methods The Plane of an House with a Garden THE Order of setting this Plane of a House in Perspective is altogether the same with that of the Garden whereof we were speaking the which ought to suffice for the one and for the other that we may not repeat so often It is set here for to shew that one may abridge all sorts of Planes whether they be composed of equal parts or unequal The Plane of a Fortification Abridged FOR to set all Fortifications and whatsoever other Piece it be into Perspective we must use the Sixth and the Eighth Advice It is the Order that we spake of for the Church and for the House Which is to draw from all the Angles lines Perpendicular upon the base and from the base Rays to the point of sight and from the same Angles to draw also Parallels to the base which shall mark the divisions upon the line on the side as A B The which line A B ought to be set upon the base And from these Measures to draw to the point of distance for to give us the line of the section C D But because that the Place suffereth us not to set it upon the base I have transported it under the Figure as is A B. Then having set the point of Distance in E of the height E F there you must draw from all the divisions of A B to the end to divide the line of the section C D into so many parts The which line C D with its divisions ought to be transported to the foot of the outmost Ray or on the one side and other D D And from all these Points which are upon the line D C to draw Parallels or else only to mark a point upon the Ray which goeth from the Angle of the Plane which is proper to it And all
only a third of the bredth for the descent as is A 9 B Before we pass any farther we must know that which I call the middle Top are Pieces elevated Perpendicularly upon the Beams which bear the Ridg where all the rafters do meet as is G H The rafters are pieces of wood that give the descent of the Roof as is H I. The other Pieces which are set in the corner and which go unto the middle Top are called Stays and are ordinarily longer then the Rafters as is H K. Three sorts of Roofs are in use Pavilions Pynions and Appentis or Pent-house like The Pavillions have four sides the Pinions have but two and the Appentis but one for to make a Pavillion in Perspective we must know the place of the Balls or middle tops for to draw the stays thither the which hath made me make this Geometrical Plane L M N O for to shew that of the bredth of the house L N we must make a square L M N P from which we shall draw two Diagonals which shall divide themselves at the point Q some set the Ball at this point Q but that is too much advanced and maketh this bending of the end lie too flat it hath more comeliness when it is straighter wherefore we must advance it towards the wall L N by the third part of the distance Q R which shall be the point S and by this point S we must draw a Perpendicule upon the line N P which shall be T. Then to transport these Measures L T and T M upon the base and draw them to the point of distance which is here farther off then ordinary and to observe where they shall divide the Ray V and from the sections to elevate Perpendicules unto the height of the wall which shall give the points X from which me must draw Parallels to the base unto the other Ray I. Then from the midst of the wall Y to draw to the point of sight for to divide those Parallels at the point Z and from these points to elevate the Balls for to give the height to these Balls we must know wherewith we would cover them and according to that to give them the Measure that we have spoken of supposing that it be of Slates we must of the bredth of the wall make a Triangle equilateral 1 2 3. And from the point 3 to draw to the point of sight and to divide the Ball at the point 4. At which point 4 we must draw lines from the corners of the House which will give the shape to the Pavillion For the Roofs with Pinions there is not so much to order we must only of the bredth of the wall 5 6 make a Triangle equilateral 5 6 7. and as much on the other end of the wall which shall give the point 8. Then to joyn this 7 and 8 the Roof will have its shape and its measure The Figures on the other side do shew the same thing without being confused with lines This projecting which goeth beyond the Roof is made according as one will This House on the Floor is covered with a Pavillion which is made by the same Orders as that on the side In this Figure where are the Letters I have set the Horizon on very high for to make the upper part of the houses to be seen and to give the more easiness to understand the Order but as this is seldom met with I have set the other Figure above where the Horizon is low as it is ordinarily which nevertheless is not therefore any other Rule for to make the Roof then that below as one may see by the Figure The rest of the Roofs in Perspective IN the figure aforegoing we have set the Roofs with small Pinacles view'd in front to which we must give the Triangle equilateral for their height when we do make them of slate If they make them of other things as of Tile or Thatch we must take their measures at the little figure below For to set this fashion of Roofs in return we must set upon the base from the foundation of the house the breadth that it hath as is A B and of this breadth to frame a Triangle according to the height that we would give to the Roof as to this which hath a Triangle equilateral whereof C D is the height which must be set Perpendicularly at the first corner of the house at the whole height of the Wall as is E F. Then to take the breadth of the house C which is the midst of A B and to draw it to the distance and where it shall divide the Ray A at the point G to raise a Perpendicule then you must from the point F draw to the point of sight X and the section that shall be made of the Perpendicule H shall be the point of the Pinacle to which you must draw from the corners of the house E I if one would have there any advancings he may set them there at his pleasure as we may see on the other side K. For the sloping we must only prolong the line where one would set the top of the Roof as is here the line L M and to give it such a bending as we would To this there is as much of the height M N as the house hath of breadth N O if from the points M O we draw to the point of sight X we shall divide the Perpendicule of the Hollow at the point P Q. which we must joyn with a right line which shall finish the framing of the Roof The figures of the other side make the house covered to be seen after these fashions The figures above are only to make it seen that we must always keep the same order although the Horizons change I have set a Church within the floor which is covered with Pinacles and the wings of the two bendings which have only the simple draught There is also a Pavillion seen by one end of which we have spoken in the figure preceeding For to set a street into Perspective IT might suffice to see the figure for to know the order thereby which is very easie we must only make a plane of single little squares by the ordinary way and to take one square or 2 or 3 for the bredth or length of every house And upon this breadth which we shall take to set the measures of the Doors and Windows for to have thereby the abridgement by drawing to the point of distance A as are the Measures B C D E and F. The first Angle of every house may serve for the line of elevation as we at the first house the Angle G for the Roofs we have said already how they ought to be set When we would have streets going a cross we need only to leave 1. 2. or 3 little squares without elevating any thing even as are H and I. The figure below is to shew that when one would advance or
A C and draw from C to E and where this line should divide A G at the point H we shall draw H I which will appear of 24 feet of sinking in the picture According to the Perspective this line H I is equal to that A G and containeth as many feet or parts so that if one draw from the point I to the point E the section of this line I E at the Ray A G shall be for to draw a line K L sunk of 48 feet If from this we draw further to the distance E we shall have the section of the Ray A G yet a line removed 24 feet more then the others And if one would have a line sunk 30 feet we must from the point A reckon 6 small parts and from the sixth draw to the point of sight G and take notice where we shall divide the line H I as here at the point M. Then from the point M to draw to the distance E and this line M E shall divide the Ray A G where we must draw this line N if it were of 40. We should from A reckon 16 and do all the same if it were 60 we should from A reckon 12 and from 12 draw to the point of sight G unto the line K L which should be the point O Then from O to draw to the distance E and from the section of the Ray A G shall be for to draw this line For the second figure BY that which I have spoken it is easie to find a point for such a sinking as one would have There remaineth to shew how we may find it within or without the Ray A G or B C for this the line B C shall serve as a scale of six feet the one of which I shall divide into twelve inches that I may there find the half the third and the 4th of a foot All being thus ordered If one require of me a point which appeareth of 17 feet long and of a foot and half within the Ray A G. I will draw from the 17th part of the base to the point of distance E and where the Ray A G shall be divided in P I will draw a line P Q now when one requireth a foot and half within the Ray A G I will take with a Compass upon the same line P Q but on the side B C a foot 6 inches which I will carry from P unto R. And this point R shall be the point which hath been demanded And if one would have one yet at 29 feet distance within the Picture and seven and an half beyond the Ray A G. We must draw from C to the point E. and where it shall divide A G to draw a line which shall be of 24 feet then from A. taking five little parts to draw them to the point of sight G until that we divide this line at the point S and from this point S to draw to the d stance E Where the Ray A G shall be divided we must draw a line T V seeing they require 7 feet and an half beyond the Ray A we must upon the same line T V but on the side B C take 7 parts and 6 inches with a Compaâ—s and carry them from the point T. to the point X And this point X shall be the point that one desireth And so of all others at such a distance and removal as one would have Of a general manner for to exercise Perspective without setting the Point of distance out of the Picture or Field of the Work by the Sieur G D L. THIS Order obligeth us to make a Geometrical Plane or at least a device of Measures as well for thâ— Plane as for the Elevation that by the one or by the other it may be brought to set into Perspective I will take for the object or subject the same Example of the Author which is a Cage squared covered with a Point or a Building covered like a Pavillion or Tent to the which we shall give the Measures by the means of a Scale Having then made the plane of this Cage m i l k which I have set on the top of the figure it must be thâ— at such a distance as one wâ—uâ—d have that the Objâ—ct seeme recoyld within the Picture as it is here of 17 feet we makâ— a line a b which shall be the base or the bottom of the Picture which we shall place according to the aspect thâ—â— the object ought to be seen Then from the two ends of this line a b we must draw two lines Parallels the oâ— to the other and undeterminate thrt is to say it is no matter if they divide the plane nor in what place â— are a g b g upon the one of these lines as here this a g we must make little Parallels to the line a b which maâ— go unto the Angles of the plane and by the means of the scale to see how far each Angle of the plane shall be râ—moved from this line a g. the which shall be marked near to each line Now from the place which one shâ— choose for to view the Picture which is here the point c at five feet near to b. We must make a Perpendicular 〈◊〉 a b which shall be the line c t to this line c t we must give as many little parts of the scale as we would have 〈◊〉 be removed for to view the Picture which is for this 24 feet and at the end of these 24 feet which is the poinâ— t to raise a small Perpendicule of the height of the eye which shall be the line c t of four feet and an half The Cloth the Wall or the Paper being ordered for to set the plane in perspective and upon the planeâ— make the Elevation We must divide the bottom of the picture or the base A B into as many parts as that a bâ—â— the plane this having 12 thereof We must divide the great A B into 12 which will be of value each a fooâ— Above the points A B we must set the height of the line s t which is of four feet and an half Take then with thâ— Compasses four parts and an half of those which are upon the line A B and carry them perpendicularly upoâ— the points A B which shall give the points E F and draw the line E F parallel to A B and this line shall bâ— the Horizon Seeing that in the plane the point C which is the place for to view the Picture is removed â—iâ— parts from b we must reckon as many parts from B and from the fifth C Elevate a Perpendicule to A B which shâ— divide the Horizon at the point G which shall be the point of sight to which we must draw the Rays A G B G which shall represent the Parallels of the pâ—ane a g b g for the point of distance it shall be the point F and by reason that the line c t hath 24 feet
might be in trouble if there should be Bowles Cups Viols Flagons or other round pieces which have Ordinarily more breadth above then below of the which we would have the shadow by a Torch by reason that such pieces seem more difficult then the squares although that in effect it be all the same Order there being nothing but to reduce the square into round so as I have taught in the fol. 19. 20. 28. 29 and 86 Where we shall see all the Orders for to set the Planes of round pieces into Perspective the which being known all the rest is very easy to understand I have said already at fol. 138 how we must finde the Plane of a Bowle and by this Plane to have justly the greatness of the shadow by the Sun But as this of the Torch is different from that I believed it to be necessary to set that also down here by reason that it doth facilitate the Order of all the other Rounds For the shadow of this Bowle I say then that having made its Roundness with a Compass which is the the Circle A and draw his Diameter B C that we must under this Circle make a line Parallel to B C which toucheth the Circle at the point H then from the ends of the Diameter B C to Cause Perpendiculars to fall upon this line underneath as B D and C E of the which points D E we shall frame the ordinary way the Plane D E F G whereof the diameter F G shall divide this D E at the point H This Plane D E F G shall serve for to finde shadow of this Bowle A. For after having drawn from the Foot of the Light I lines which touch this plane on the one side and other as are the lines I K and I L And also another line passing by the midst of the plane H which shall be the line I H M. We must afterwards draw other lines from the Light of the Candle N which touching the Bowle shall go to divide these lines of the Plane as from the point N to draw a line which toucheth the Bowle between A and B and divideth the line I H at the point M which shall be the end of the shadow for to have the beginning of this shadow we must from the same point N draw another line which toucheth the fore-part of the Bowle and divideth also the line I H at the point Q this distance Q M shall be the length of the shadow for its bredth we must also from the point N draw two lines by the ends of the Diameter of the Bowle Z Z and they shall divide the lines I K at the point R and this I L at the point S. Wherfore if R S be the bredth of the shadow and Q M the length we have only to joyn these fower letters of Crooked lines which shall give an Ovall for the shadrw of the Bowle A I have a little Extended my self for to facilitate the shadow of this Bowle by reason that I believe this only Order sufficient for to finde the shadow of other Rounds as of the Figure V the which having two breadths unequall ought to have a Plane of two Circles And that below X which hath three differences obligeth to make a Plane of three Circles The one for the Neck of the Viol or Flagon the other for its Belly and the other for the foot all these Planes are made as of the Bowle I believe that it not necessary to use Repeâ—itions The figure being able to teach of it self Of the shadow upon many Planes Parallels THE first Plane that is the Ground where the Chair A is placed the second Plane is the upper part of the Table which is Parallel to the first Plane and either above or below the Table it might also have one or two or more of these Planes upon which we shall finde the foot of the light for to finde the shadows of the Object which should be there For example the foot of the light it is C and the fire B from these points C B we must draw lines by the under-part and the upper of the Object D for to have its shadow E upon the Table E. But to have the shadow of the Chair A which is upon the Ground we must find upon the same ground the foot of the light which is upon the Table the point C the Order following teacheth this We must from the point of distance which is here out of the Paper draw a line by the foot of the Table F then from the corner upon the Table G to make a Perpendicular G to fall which shall divide the line F at the point H and from this point H to draw a Parallel H I which is equal to the upper part of the Table and which ought to facilitate to finde that which we seek for having from the point of sight K drawn a Ray passing by the foot of the light C unto the end of the Table L we must from this point L let fall a Perpendicular upon H I which shall give the point M from which point M we must draw a Ray to the point of sight K and upon this Ray M K must be the point of the foot of the light which shall be found easily making a Perpendicular to fall from the point C the which dividing the Ray M K shall give the point N for the foot of the light This point N being found there is no more difficulty to finde the shadow of this Chair A because that it is all the same Order as of other Objects which we have seen in the leaves aforegoing that is to say that we must from the foot of the light N draw lines by all the Angles of the Plane of this Chair and from the light B to draw other lines by the upper part of the same Chair which divide those of the Plane and shall mark where the shadow ought to go the figure will make it known that all is to be ordered as I have said elsewhere The second Figure I Do not set down this second Figure for that I have any particular thing nor different from that above But only to refresh the Memory of that which I have said in the beginning that all the Objects cast their shadows diversly and according as they are set about the light as we see that which is upon the Table giveth its shadow according as it is enlightned that is to say directly either on the right or on the left that which is found by the ordinary Orders of the foot of the light P and of its fire or light O the most part of these Objects are broader above then below wherefore we must make their Planes as I have said in those folio's where I have spoken of the like figures The shadow of boarded Floores by a Torch I Have not set this figure in the shadows taken from the Sun by reason that this light is above
unto the E draw a line C D. This is the side of the Hendecagone 12. For the Dodecagone or twelve Angles divide into 2 the Arch of the Hexagone A B the subtendent shall be the side 13. The Oval is made of many fashions and all composed of portions of the Circle or of one only line by two Centers the most commonly used are these Having made a Circle with 2 Diameters as A B C D from the points A B we must make more two circles equal to the first then from the point D they draw a â—ine by the Center of the lâ—st Circle A unto the circumference E then setting a leg of the Compass at the point D with the other you must take the interval E and make the Arch E F. You must do as much on the other side and the Wall will be made 14 For an Oval more round You must draw one only line and make a Circle of the Center A and from the section of this circle upon the right line at the point B this shall be the Center of another Circle To frame the Oval you must take with a Compass all the Diameter of one of the Circles as from the point A to the point E and set at the sections of the two Circles D E a leg of the Compass and with the other leg make the Arch D G H and to do the same from the point E. 15. There is another manner of making of Ovals very easie and more useful then the former seeing that by one and the same Order they be made long narrow large short c See here how they are made You must upon a right line set two nails or two pins which serve for the Center as A B for to fasten a thread or small cord of the height and largeness that you would have the Oval as is the pack-thread A B C you must hold this thread bended with a feather or pencil which you shall turn until that you be arrived where you have begun If you would make it longer lengthen out the Center and do the contrary if you would have it short for if you set the two nails close one to the other you shall have a Round 16. For the Volute or line like unto the Spiral take two points upon one line as A B let these two points serve for a Center the one after the other for example having made the half-round A B set again the leg of the Compass on B and with the other leg take the length A and make an half-Circle A C. Then holding one leg of the Compass at A you must take the distance A C and make the half-Round C D and sâ— often as you please changing only the Centers Vignola giveth it another fashion Of the Rayes VISUAL THe Object being a Point then there is but one Ray Visual made from the Object to the Center of the Eye And this Ray is called Axe or Centrical which is the most lively and the strongest of all the other Rayes as you see in the Figure A B. It is this which divideth always the Horizontal line and which giveth the Point of the fight If the Object be a right line the Rayes Visual make a Triangle whereof the line C D is the Base and the two sides are the Rayes on the outside which come from the Eye A and make the Triangle C A D. And A B is the Centrical Radius If this line were viewed by one end it would seem as one point If the Object be a Superficies plane or spherical the Visual-Rayes will make a Pyramid the Base of which is the Object C D E F and the top is the Eye A the rest of this Pyramide are the Rayes Visual if the Superficies were view'd by the side it would make but a line Of all the Rayes Visuals the strongest is the Centrical A B and so much as the others are further off by so much they are the weaker and keep nevertheless a reasonable strength unto the opening of a right Triangle at G A P. Those which pass the right Angle are so weak that they are not seen but confusedly and therefore there is need that the out-side Rayes which may comprehend the Object make at least a right Angle within the Eye Wherefore one may see better a Perspective with one Eye only then with two According as some say the whole object is better seen with one eye only then with two because say they that the sight is then more piercing in respect that all the Visual spirits of the Eye closed are directed and brought to the other and this union of Visual spirits giveth a great force and maketh the sight very strong for every Virtue united is much more vigorous then when it is dispersed which is the cause as they say that by closing one of the Eyes all the Visual Vertue which was dispersed in the two cometh to joyn it self and to be gathered into one and by this means it is the better See here wherefore they hold it for a certain thing that any one seeth more exactly having one Eye closed then being both open Howsoever it be it is certain that one may see a Perspective better with one Eye alone then with two because that the Centrical Radius seeketh out the point of the sight where all the radials of the Picture do mâ—et which causeth the whole to be seen in its Perfection which is the reason that we do not say the point of the eyes but the point of the eye for to give to understand that the Perspective is more pleasing when it is viewed with one eye only 1 fig 2 fig The First Definition PErspective is the Art which representeth every Object seen by some Diaphane or transparent Medium through which the Visual Rayes penetrating are terminated or bounded at the Object and generally all that is seen through somthing as through the Air through the Water through the Clouds through Glass and the like things may be said to be seen in Perspective And because we can see nothing but through these things we must say that all that we see is seen in Perspective The end of Perspective is to represent upon a Plane as is E F G H the objects which are beyond such as you see here A B C D represented in I K L M for to understand this better let us suppose that there is upon the Ground an object A B C D and that the Eye of the Beholder is in O if one put between the one and the other a transparent Body marked with E F G H the Sections which the Rayes of the Eye would make of the Perpendicular Q R S T would make the Figure I K L M such as the object would appear in the transparent Body which maketh us to understand that all Perspective is no other thing then sections of a line This is the reason that Monsieur Marolois calleth always that which he putteth
in Perspective The Appearance of the Section because that the Plane E F G H divideth the visual Pyramid A B C D and O and giveth for the Section I K L M. The reason of these Sections is that one only line can determine nothing that it is necessary that there be two of them which divide themselvs for to have a Point seeing that it is certain that from our eye to the object there is always made a Radius or right line this cannot fail us but for to have another which must divide it we must imagine that from our foot there is made a Center from whence divers Lines or Rayes do proceed which go to the Angles of the objects which we behold as from the Center P to the Angles A B C D the which Rayes being divided by some transparent Plane as is E F G H all these Rays P B P A P C P D which were Horizontal raise themselves and become Perpendiculars as P B becometh Q M P D becometh R L c. For if they remained Horizontal the visual Rayes would not divide them but at the object it self where both of them do meet This is the Reason that we always suppose a Plane the which making the Rayes to reflect giveth the means to divide them and so to finde all the Points to frame the appearance of the objects whatsoever they be The Second Definition IChnography is the Pourtraiture of the Platform or the Plane upon the which we would raise any thing as A B C D is the Ichnography or the plane of a square body The Third Definition Orthography is the Pourtraict of the face or the fore-part of the object as of a Building or else it is the Representation of the Body or of the Edifice directly opposite to our eye so as E F G H is the orthography or the fore-part of a Cube or of a Building for as the Ichnography representeth the Plane so the Orthography giveth the representation of the side opposite to the Eye The fourth Definition Scenography is that which representeth the Object wholly elevated and perfect with all its diminutions and umbrages as well on the fore-part as on the sides which may be seen and are above as I K L M N O P is a perfect Cube in brief it is the work wholly accomplished which conteineth in it self the other Parts That we may make these words more Intelligible we shall name hereafter the Ichnography the Plane the Orthography the face or fore-part and the Scenography the Elevation 1. fig. 2. fig 3. fig Wherefore the Objects that are far distant seem to approach and joyn themselves together although they be in equal distance THis Figure will help to satisfie this question which is difficult enough let us suppose then that some body hath his eye †at the midst of a line it is evident that if he would see the two Ends thereof A B he must make an half-round V X the center of which is the Eye and the centrical Ray ††and making this half-Circle he discovereth the objects which are on the one side and other in such manner that it seemeth to him that the farthest distant of the side A seem to come near to the center †And those on the side B go thither also and seem as if they would joyn themselvs as much as the one and the other side can If one ask why the things so distant approach the one to the other whether they be of the side either above or below us for it seemeth that that which is on our sides would joyn themselves and that the planchers both above and below do raise up and abase themselves the farther they are distant from us Behold the Answer and the Reason in two words It is that all the objects appear under the visual Angle under the which they are seen now it is that the columns trees or whatsoever objects they be which are on the side A the farthest distant will appear to draw towards the center T because they are viewed by an Angle or by a Radius that draweth thitherward and as for example the Ray †K is much nearer the centrical T then is †C and †E and by consequent it ought to appear so and if the the objects were produced infinitely they would still approach nearer to the centrical T until that they would seem to make but one point which would be infinite as all the points of sight ought to be Now in Perspective the sides A K B S remain not Parallels but are changed into visual Rayes which divide themselves at the point of sight and by this means cause the Diminutions of the body and sides of the objects For example in the second Figure the eye being in a distance capable of seeing the line A B from the two Angles A B two Rayes begin to be made which go to finde out the point of sight T. And these Rayes A T and B T receive the sections that the point of distance giveth to objects which do close together proportionally as we shall declare in its place so that the whole Parallellogramne A K B S and all the objects that are on the one part and the other come to be reduced to the little space A V B X and if the eye were farther distant this space would be yet lesser by reason that the objects view'd afar off seem very small as I shall make it appear in the next leaf 1. Fig. 2. Fig Wherefore the Objects draw near to each other being view'd afar off WE have already said that things do appear according to the Angle in the which they are view'd this Angle is taken at the Eye where the lines do meet that do compute the Object for example the first Object being B C if the Eye A look upon it it will cause the Rayes A B and A C which give the Angle B A C so that an Object seen in a great Angle will appear great and another seen in a little Angle will appear little Now it is that the Objects being equal those that are farthest off are view'd in a less Angle we must conclude then that the Objects farthest off ought to be the least in Perspectives for example if the Eye be in A the Object B C which is the first will appear to it the greatest because that it is viewed by a greater Angle the 2 3 4 and 5 Objects will appear to it always the less although that they be equal the reason is because that the Angles diminish according as the Objects are farther distant if the Eye were remitted into N L K L it would appear the greatest and B C would be no bigger then N O. This second figure is in pursuit of that which we are speaking of for supposing that the Objects appear such as is the Angle within which they are viewed it followeth thence that if one draw many lines under one and the same
of the Picture or of the Perspective which one would have seen as is X removed from R by reason that these Removals do always give a right Angle to the Eye of the Beholder In V it would be more pleasing dividing the square at 2 and at 3 it would be better dividing it at 4. At 5 it would be far enough removed and would make the square more short in 6 as we shall give the reason in the figure following Some one may say to me why have I then set in all the Figures of this Book the points of distances so near seeing that being removed farther the whole would have been more pleasing And he might by reason if I had made the book only to have bin seen for curiosity but it being made for to teach there was need that all should be seen the better to understand our Orders this is the cause that I have put into the works as much as I could If one answer me that it were better to make the book longer I must then have made it much bigger and have set but one figure in every page the which I would avoid and make a book convenient for carriage and it will suffice to advertise that amongst the works that one shall make he ought to enlarge them the which is easie keeping the Rules which we have given 1 Fig. 2 Fig 3 Fig Of the Distance or Removal and Setting WE have said speakingf of far off visual Rayes that the Eye could not conveniently discover more then that which may be comprised within one right visual Angle That is to say that the sight receiveth not clearly nor entirely the Objects when the Rayes go beyond the right Angle And behold the reason The apple of the eye being near to the center of the eye cannot receive clearly more then a quarter of a circle so that the Rayes which are beyond that have but a confused and troubled sight when the Angle is more then 90 degrees this is the cause that it is better to make it rather lesser then greater as it may be of two thirds which are 60 degrees but not less because that the Rayes being so streightned or restrained would not give Contentment to the Eye because that the Angles being so little make as it were but one point between the Apple of the Eye let us see this difference by figures Supposing that these Planes and these Squares were the same that are in the last figure The distance of the point T to R will give us the distance of T to the Base where being it would be necessary that the Angle open it self much more for to see the Extremes Y Y for if it open but as a right Angle the Eye shall not be able to see all as T the right Angle cannot see but the points V V the which would make the Perspective wholly faulty by reason that that which should give us a square would frame us a Parallelogramme The nearest that one can set it is at the point X which is as I said even now the true Measure of the right Angle which containeth all the Piece Y Y If one withdraw it yet further from the point of sight it will be yet more pleasing as in I which hath but an Angle of 72 degrees But if one withdraw it unto Z it will be the perfection because that the Rayes being not so much dilated have the more force and conteine better the Objects but I would never goe any farther then 5. for the reason whereof we are speaking that the Angles are but as one point within the Eye and a confusion within the Object The which ought to oblige us to take good heed where we set the Points seeing that they are so important and necessary And to hold for a general Maxime that it must be at least that the distance be equall to the space which is from the right Radius unto the Corner of Perspective For xample ✚ R is the right Radius and X ✚ the lesser distance which is equall to ✚ Y whereof having taken the Measure we must Carry it on the one and other side of the Point sight as here R S S. Or of one side onely as shall be seen in the Leaf following Behold what may be said herein by the reasons of the Eye but the Practice giveth this Excellent Rule which may be Generall so that one use it with diseretion That having chosen the place where you would make the Perspective you may determine on what side it will be the better in sight and whence it ought to be looked on and then you must take the measure of this last place unto the former and set this Interval by a little scale from the point of sight unto the point of distance provided that it be not too far removed and it is in this that the discretion is requisite that one do not set it too near and to avoid that which we are speaking of nor too far off for fear that we finde no returns where one would have it set for Objects so far removed from the sight do yield no return This is why we ought to give but the draught to Buildings far distant as we shall say hereafter 1 Fig 2 Fig. 3 Fig The first Advice about the Point of the side THey never change the Rules of the Point of the Front for the points of the sides for they have all for a principle one the same cause which produceth always the like effects Wherefore I shall not speak thereof in particular seeing that the Order of the point of the side is the same with the Point of the Front as one may see in the first figure where the Base A B hath as many and the same divisions as the foregoing Let the Point of sight be in C and the point of distance in D from which if you draw the line A D you shall have the sections Q which give the abridgement of the squares in the same Number with the other The rest shal be known in the Orders following The Second Advice of the Hollowing or deepe sinkings ONe may sink or hollow the Perspectives asmuch as one would by the Means of the Base E F if one draw lines to the points of distances H I for which they shall divide the Visuals E G and F G at the point K it shall be the Abridgement of the first square as we have already said twice or thrice Now if we take his line K K for the base and from the ends K K we draw lines to the points of the distances where they shall divide the same line E G and F G at the point L L that shall be the Abridgment of the second square which shall have as many divisions and squares as the former if we shall take further this line L L and shall make the same Operations we shall have the Abridgment of the third square at the point M. And if
we shall begin again further by that we shall have a fourth and so we shall go unto a Point the which would be a length which would appear infinite And by this means it is easie to sink and to abridge the Perspectives for if you would have the double of its bredth do as we tell you if you would have but the half draw a line where the lines of the points of the distances cross themselves as in N and you shall have that which you desire Seeing that this is so infallible that as many visual Rayes as divide the Diagonal line drawn from the points at the distances to the base so many squares one hath of sinkings we may as I said give as many hollowings as we would to the Perspective for if in stead of taking from the point of distance O at the Ray F you draw it from the Ray Q. There will want two squares but that you have abridged the whole square R as we see in S which is that which you have fail'd to take of the whole square And if besides the square you would have yet two little squares make a line from the same point O which divideth two Rays as V you shall have that which you desire If you would have four take X if six N. If the square whole Z the which is a great easiness when one understands it well The third Advice of the Measures upon the Ease THE Base only may serve for to give such a sinking as one would have and in what place they would without using any little squares this is a means very ready but it is somewhat hard to understand Nevertheless I will endeavour to make it be understood the best that I shall be able for we do often use it For example let the Base be B S the point of sight A the points of distances D E If you would make the Plane of a Cube B C you must draw to the points of sight two Occult lines or pointed from the ends B C then for to give it its bredth take the same measure B C which you shall transport upon the Base C F equal to B C from which point you shall draw a line to the point of distance D and where this line shall divide the first Ray C at the point G this shall be the Abridgement of the plane of the Cube B H G C. If you would have an Object more forward towards the midst you must take the bredth of it and the distance above the Base as I K. Now for to have the sinking set such as you would have upon the same Base as it might be L M because that it is broad at that point L and asmuch for the largenes at the point M. Then from these Points L M draw an occult line to the point of distance D and where these lines shall divide the Raye K at the points N O you must draw Parallels to the Base and you shall have the square Q P O N. By this manner you may transport on the other side the square which would be above the Base as B H G C is transported to V and the Points M and T which are removed but 2 feet from the point S do give a figure very narrow because that they are very near and the same distance which they are removed as we see X. The fourth Advice of the Base and of one only point of distance SEeing that one may have the bredths and the depths by the means of this Base one shall neede no more to take the Paines to make the little squares the which I would make appear to the sight in this example Let us suppose that you would make a Ranke of Pillars or Trees on each side You must set upon the Base the place and distance that you would have with their bredth or Diameter as A B C D E F G. Then placing the Rule upon the point of the distance O unto each of these Points A B C D E F G where it shall marke the sections upon the visuall Raye A H it shall be the Termes of the Objects which you desire For to transport them on the other side upon the Raye G H Set one leg of the Compass at the Ocular Point H and with the other take the same without stirring the leg from the Point H make an Arch with the other where it shall divide the Raye G H this shall be the same Terme as M is the same with N. And so of others by the which you shall draw Parallells which will give you the bredths And for the length give it such as you would have it and set it from A as it might be P then draw from the point P to the point H and where it shall divide the other Parallells it shall be the Planes that you desire which you may make rounds or squares The fifth Advice not to deceive ones self in the Measures YOU must never set on the side of the point of distance where one would draw for to give the sinking the Objects which one desireth to produce within the Plane Example The visuall Ray upon the which one must mark let it be A B If you would produce there the point C and D it cannot be drawn from the point of distance E but well from that which is opposite to it F. If C and D were within as G H it ought to be drawn from the point E because that the line of the section meeteth between both and not from the point E and so both the one and the other shall divide themselves in the same point I K. 1. A Fig. 2. H Fig. 3. A Fig. The sixth Advice of the Point of distance only SOmetimes one is at such a streight for the smalness of the place that one hath be it against a wall or cloth or paper that it is impossible to make more then one point of distance and then those that are always accustomed to have two of them are much troubled We must draw them and cause them to understand that one Point only sufficeth for this Practice Let us suppose that we would make a Pavement of small squares and that we have already drawn all the visual Rays ar the point A for to have the Abridgement thereof we ought to draw at the points of distances and the sections will give us the points where we ought to draw as we have already said but if there be but one as B we must draw this one draught Diagonal C B which will divide all the visual Rays Now for to mark the same sections upon the Rays opposite for to draw Parallels there We must as I said but now set a leg of the Compass at the point A and with the other to run through all the sections as I P But this is not good but only for that which is viewed in front Whence there is need of one which serveth likewise for that of the
side behold it here Take a Compass and set one leg upon the base with the other take the most perpendicularly that you shall be able the section that you desire to transport as D and carry it upon this line Perpendicular as E O and mark your measure F then draw from D to F and you shall have the same as if there were two points of distances And so of all other sections The seventh Advice that we should not use the Diagonal WHEN one would use the outmost Ray for the line or section as it might be G H He ought to set the Objects upon the base as are K L M N O and from thence to draw them to the point of distance L which ought to be drawn back as far as shall be possible to the end that the Abridgement of the Perspective may be the more pleasing thereby for if the point were nearer to the point of sight G the Objects would have too much hollowness I mean for example that a square would appear a Parallelogram And from this point I to run through all the Objects K L M N O and to mark the section of the Ray G H And from these points to draw Parallels to the base or of the Horizon as is here P Q. This Method is the least in use although some do take it The Eighth Advice for to abridge in divers manners IF sometimes one be taken in a strait and that one cannot remove the point of distance we must elevate from the foot of the Ray S R a small Perpendicular as T S which shall receive the sections and give a lesser Abridgement and if one would have it yet more little he shall but only bend a line as is X the which by reason of its inclination causeth that the sections are closer together Then for to draw the Parallels he hath only to transport this line X or T upon the foot of the other Ray as is V and from all these points to draw lines Parallels to the base and you shall have that which you desire 1 Fig 2 Fig 3. Fig THE ORDERS FOR PLANES IN Perspective Of Planes viewed directly or in front ONE may have seen at the third and fourth Advice and the Elevations following will cause to know that it is not my purpose that one should use Planes Geometrical for to make Perspectives for this would be to double the labour and no Painter would take this pains seeing that I teach him to make the same thing by means of the base But as there is no Rule so general which hath not its exception so there are certain Figures which one cannot set into Perspective but by the help of these Planes further also one should be troubled if one should give one of these Planes to be set into Perspective and that one had not learned how he ought to prâ—ceed These Reasons have obliged me to set these which follow the which will suffice to learn to set into Perspective all those which may be presented and also be imagined 1. To contract or abridge a square A B C D. One must draw A B at the point of sight E and from the same Angles A B two Diagonals F B A G and where they shall divide the Rays A E and B E at the points H and I. This shall be the square A B C D abridged into A H I B for to make it without the Geometrical Plane we must draw from B to F or from A to G or else transport A B upon the base as B K and from the point K to draw to the point F it will give the same section I upon the Ray B E. 2. To abridge a square viewed by the Angle D having made the Plane A B C D. We must draw a line which toucheth the Angle B and it must be in right Angle upon the line B D. This base being produced we must set the Rule upon the sides of the square as A D and D C and where this Rule shall divide the base there to make the points H I then to draw H and B to the points of distances P and B I to the other point of distance G. And at the section of these lines to make the points which shall give you the square K L M B for to make it without the Plane you must set the Diameter on the one part and the other of the middle B as H and I. But as well in the one manner as the other you must not draw at the point of sight O. 3. To abridge a Circle It must be enclosed in a square A B C D And from the Angles A D and G B to draw Diagonals which shall divide the Circle into eight parts and where they shall divide it at the point O to draw upon the base the Perpendiculars E F then to draw two lines Diametral Q R S P which divide themselves in right Angles at the Center G. The Plane being ordered in this manner you must draw all the Perpendiculars at the point of sight H and where they are divided the Diagonals A K and B I to make points of the which the two latter M N are the draughts of the square which are to be divided into four by the section of the Diagonals at the point P. Then from the ends of this Cross they draw bended lines by these points which give the shape of a Circle in Perspective This manner may pass for little ones but we shall give one more exact for the greater 4. This Figure is composed of the two first wherefore I will say nothing of it for he that shall have made one or two of them shall be able to make it easily 5. The fifth depends also upon the two first but there is also more a Border round about which they have not for to set this Border into Perspective we must draw these four Rays A B C D at the point of sight G and where the inward Rays B and C are divided by the Diagonals A F and D E we must draw Parallels to the base and you shall have that which you demand 6. It is the same with the second except that it is compassed about with two Borders wherâ—fore I will speak no more of it Planes viewed Obliquely or on the side THESE Planes being those that we will soone dispatch ought to be made all in the same manner which maketh me believe that it would be loss of time to repeat how one ought to abridge them in Perspective for it seemeth to me that the Figures do suffice to make it appear that there is no other difference from them that went before but the scituation of the Object which is here seen on the side and the other is view'd in front All the A A A are Points of sights and the B B B points of distances Of a Triangle THE Triangles according to the Numbers ought to precede the squares but according to reason they
marketh them both and is divided at the Point C. The 3 and the 6 will give the section at the point D. And the 4 and 5 will give the last at the point E. This line A B being so divided we must transport it upon the Base of the Plane which one would abridge beginning to set the point B at the point F. as he e and then to mark the other divisions C D E from the which one shall draw to the point of distance O and from the sections of the outmost Ray to draw Parallells to the Base and where they shall divide the Rays which beare the Numbers of the Angles there we must make Points the which being conjoyn'd by right lines will give the figure which we desire For the thickness or Border it shall be made by one of the two orders afore-going 1 Fig. 2. Fig. Of the Octogone or Eight-Angles THe Octogone is made of a Circle divided into eight Parts of 45 degrees for each side from the which divisions drawing lines we have the shape of the Octogone that is to to say a figure that hath eight Angles and as many sides The fore going Orders do cause sufficiently to know how one ought to set it into Perspective either on the front or on the side I will only Advertize that the Plane abridged on the front is made according to the eighth advice And that of the side according to the seventh The point of the sight is A and that of the distance B. The rest is sufficiently seen without an Exposition Of the Octogone after another Order THe manner of making this Octogone hath bin Invented by Serlio It is made in this fashion Having framed a Square by the Ordinary way as is A B C D we must divide the base C D in ten parts and leave 3 thereof on each side and from the third division of one part and the other E F to draw lines to the points of sight G and at the sections of these lines by the Diagonalls O we must draw Parallells to the base which touch the sides of the Square at the points H I K L then joyning together by the lines of the points E H I E F K L F you shall have an Octogone as may be seen by the first figure Of the Hexagone or six-Angles The same Serlio hath made also the Hexagone after the same fashion Let a Square be drawn as this before A B C D and that the A D be divided into four Parts from one of the which on each side E F let lines be drawn to the Point of sight H Then from the section of the Diagonalls which is the midst of the Square G to draw a Parallell to the base which toucheth the sides of the square at the points I K Then draw lines by the points E I E and F K F there will be framed an Hexagone The second-figure I will say nothing of this Octogone view'd on the side seeing that as we have already said so many times it is the same Order with that of the sight of the front The third figure 1. Fig. 2. Fig. 3. Fig. Of the Octogone double SUpposing that we have already made an Octogone single for to make it double or to give it a thickness or Border you must proceed in this manner Set such a bredth or thickness as you would give to it within the square which containeth the Octogone single as here A B on one side and the other and draw from these points to the point of sight C. And where these lines shall Cross the diagonalls at the point O draw the Parallells D The which will make a welt or guard about the square Then draw from Angles unto Angles occult lines or points passing by the Center N And where these shall Cross or divide the lines of this inward square at the points E F G H I K L M it shall be the Bounds of the Octogone of the Inside Of the Hexagone double ONe may do the same with the Hexagone figured within a Square The which maketh me beleeve that there is no need to use any repetition seing that one may see by the figure that whereof he might any ways doubt The Octogone view'd on the side is all of the same frame with that of the front The point of sight is A and that of the distance B. 1. Fig. 2. Fig. 3. Fig. Of the Circle THe more that any Circular forme shall have parts the sooner and more easily shall it be converted into a Round hence it is that Serlio saith that we must frame a Demi-Circle and of this circumference one may make as many equal Parts as they would for the more that it shall have of them the more this Rotundity will be perfect for example the Demi-circle a Plomb or Down-right is divided into eight Parts which will give sixteen for the whole Round and from these divisions Z to elevate Lines Perpendicular upon the base at the point E. Then we must draw two Diagonals at the points of Distances which are here farther removed then the Plate is broad but which one ought to suppose within the horizon ordinarily which will give a square A H I B now the square being framed we must draw all the points E at the point of sight F unto the line H I and at the sections of these lines to draw Parallels throughout Then we must begin at the midst of one of the sides of the square to make a point as a another point at the Angle opposite as if one would draw a Diagonal as b continuing so to do from points of Angles to Angles following the Diagonal lines as a b c d E f g h i K l m n o p q. These points will frame a perfect Rotundity then you must bring with the hand bended lines or circular and you shall have your round in Perspective The Perspective must have this Rule and Order to abridge the Rounds very familiar and usual for it is oftentimes used as well for Columns bending Roofs Arches opening of Gates and Windows as for many other Rotundities Of the Circle double WE must suppose that the first Circle A B is that which we are now to make and that we would give it a thickness or border by making another more inward in this manner We shall give it such a bredth as shall please us as A C and from the center the great Demy-circle G we will draw the little one C D which we will divide as the other great one by drawing occult lines from the divisions of the Great unto the center G. And at the section of these lines of points of the Great upon the less demi-circle at the Points I we must draw Perpendiculars I as those that we have made in the great upon the base And to the end that they may confound nothing we must mark them with points from the points I of the base we shall draw to the
A Then to take these Measures with a Compass and carry them upon the Perpendicules elevated from the Angles of the Plane each according to their Order The first for the first step the second for the second c. For to finde these Returns P you must from the same Corners P draw to the distance Q and to take heed where that divideth the line of the Plane or the under-part of the step for example above the fourth step I have made the Plane of the fifth step Now to have its Return P we must from the same points P draw to the distance Q and take notice where it shall divide the Ray R which shall be at the point S and this point S shall be the point for to draw the line of Return S T. And so of others For to make stairs which one may shew from four sides THere are many wayes to make these Stairs see here are two which seem the most easiâ— The first Being about to make one of these Stairs we must take the lengâ—h of the first Step and set thereon the quantity of Steps that you would have as upon the line A B I have set the points C C C for four steps From these points we must make Rays to the point of sight D the Rayes shall be divided by the Diagonals A F and B E at the points I from the which we must raise Perpendicules and draw little parallels unto the bottom of the line of Elevation G which shall give the points H which they shall raise as H K. We must upon this line of Elevation G set as many equal parts as we would have Steps as here 4 from these four points 1. 2. 3. 4. We must draw to the point D for to divide the Perpendiculars H K and to give to each the height that it ought to have as that which is made of points sheweth it We must take these measures with a Compass and transport them the one after the other beginning at the first G 1. and carry it upon the first Perpendicular to the corner A as A L then to draw a parallel unto the other side B. but here I have not set it but at the half for to make the plane to be seen in the other for the second Step you must take the second measure H. 2. and carry it upon the second Perpendicular I then to draw Parallels as at the first And so of all the others Another manner The side M N being given we must make a parallel above for the thickness of the first Step as O P from which points O P we draw 2 Rayes to the point of sight Q and also to the distances R S And these Diagonalls shall frame the square in the ordinary manner and this shall be the first step For the second we must set the measure of the breadth which we would give it upon the line O P as is O T and from the point T to draw to the point of sight Q. and this line or Ray T Q. shall divide the Diagonals O where we must raise the second Step at the point V. The height of this Step shall be taken from the half of V X as M O is the half of O T. This measure being given at the point Y we must draw parallels unto the Diagonal of the other side which is drawn from the corner P then from the points Y Z to draw to the points of sight and of distance for to frame the square as at the first Step. For the third Step we are only to carry upon the line Y Z the measure V X which shall be Y A and from the point A to draw to the point of sight Q for to divide the Diagonal of the point Y which shall be the point B and the place of the third Step. Its height shall be the half of B C which is alwayes that of O T in Perspective All the rest is the same as in the first and second if there should be an hundred you must work always in the same manner The third figure causeth these Steps to be seen clearly without the confusion of Draughts which we should make for to find their places these Draughts should be made in white or in such manner that nothing may be seen of them when the figure is finished Stairs viewed on the side in Perspective YOu must set upon the base the number of steps that you would have that is to say as many points at an equal distance as here the three A B C from these points you must draw to the points of sight D. Then from the point A to the point of distance E And this Diagonal A E shall give the plane and the place of the steps at the section of the Rays B C at the points I and upon the Ray F which is the foot of the Wall the point G which is the midst of the plane of the steps from this point G you must draw to the other distance H for to find the corner of the last step at the point K and the place of others at the points I. Then from all these points I to raise Perpendiculars For to give them their height you must from the points A B C which are upon the base raise little lines for to serve for the line of elevation upon the which shall be set the heights according to their number For example A which is first shall have but one B which is the second shall have two and C which is the third shall have three Draw from all these points 1 2 and 3 to the points of sight D and you shall divide the Perpendiculars elevated from the plane to the points O which shall be the height of each step That of the other side is for to make it seem without points and without lines This manner of steps may serve for many things as for an Altar for a Throne for the forepart of a Church for a Gate c. Stairs within a Wall in Perspective SEt as many divisions at the end of the Wall as you would have steps as here for three between A and B and draw A B to the point of sight C. Then having determined the space that you would give to the steps as D E you shall draw the parallel to the base E F which shall receive at the points I I the sections of the lines drawn from the points G H to the point of sight C and from these points I I you shall raise Perpendiculars I K I K which shall receive the heights of the steps drawing from the points 1. 2. 3 to the point of sight C as is to be seen in the second figure 2 Figure For winding Stairs with Rests in Perspective WE must remember the fore-going orders about Steps and it will be easie to frame these winding Stairs but to avoid the pains of searching we will unfold the whole matter here By reason that the
its Ornaments as is A B of which having taken the bredth and made a square Plane in the ordinary way and from this square to elevate from all the Angles Perpendiculars we shall frame the body or solid part of the Pilaster Then we must only take that which projects it self from the body for example the base of the Pilaster C and transport its measures as in D E. for to set it in Perspective round about the Pilaster we must from the point of distance F draw a line Diagonal which passeth forth of the square to the point E unto G it is no matter for the length Then from the point A to make a Ray passing to the lower part of the Projector H and at the point where this Ray shall divide the Diagonal at I it shall be the advancement of the whole base the same Ray A H shall give the Projector of the bottom by dividing the other Diagonal at the point K Then for the Projector before we must from the point I draw a Parallel to the base until that it divide the Diagonal which shall give the other Corner of the Projector before at the point L then drawing lines of the height of the Base unto these points as are M to L from D to I from N to K you shall have the bredth and the hight of all the Base The Capitall is made of the same fashion Here is for the first figures above Those below shall Cause the rest to be known and shall avoid Confusion For the Pilasters O we must observe that above P where the line D H bereth all the sections of the base Wherefore from the point of sight A we must draw Rays the which passing by the divisions of D H must marke them upon the lines D I and N K And drawing Parallels from the points of D I to M L there will be no more then to give the Turnings about or wheelings as the shape of the Colum. When you shall meet with squares or Flat-bands either above or below they are made by Perpendicular As for to make the Plinth you must raise Perpendiculars from the Points L I K the from the point of sight A to pass by the Corner of the Plinth Q it will give the height upon the Perpendicules I and K. Then L must be equall to L. I beleeve that this Instruction for the Base will suffice for to make the Capitall being the same Order This last Pilaster R is only for to cause one to be seen without being mingled with lines We have broken them for to make the Bases and Capitall to be seen not having had space Enough for to make them appeare whole A great Cornish above the Horizon in Perspective IT is the same Order with that which we have explained but as it is somewhat difficult by the multitude of lines I thought it convenient to set it down again here for to avoid confusion I say then that having taken the pourfill of the Projector and the Cornish that one would make we must set it at the place where one would make it as C which is the pourfill is at the corner of the Wall A B for to find the height which it ought to have and to make those below seen we must from the point of sight D draw a Ray passing by the end of the pourfill E as is D F then to make a line Diagonal from the point of distance H passing by the corner of the Wall B and to continue it until that it divide the Ray D E at the point F from which you shall draw the line F G which must be the Angle in Perspective for to receive all the measures F G the corner of the other end of the Wall K L is drawn from the other distance I as being the other Diagonal In the figure marked 2. we shall see that all the figures which are upon the line M N must be transported by visual Rays from the point of sight D upon the line N O for to draw Parallels to the Horizon from all these points which shall give the whole Cornish perfect But before we pass any further we must mark as I have already said that all the flat-bands and squares are made by Perpendiculars For example for to make this great square of the Cornish having made the Wave or Ogee and the filet under the filet which must be the height of the square we must abase the Perpendicule P Q. Then for to know where it must be divided for to make the under part be seen we must draw from the point of distance I by the point above the quarter of the round R unto the Perpendicule P Q. and you shall have that which you seek That which I have said of the great square must be understood of little ones as are small mouldings the filets c because that they must all make that below to be seen The third figure sheweth that having found all the points and drawn Rays upon this line from the Angle S T we must there trace out or shape the mouldings out proportionally I mean that when these shall project themselves as this here doth because that its point of distance is near we must help the mouldings that is to say a little bend down the quarter of the Round set up the Ogee enlarge the filets and mark at one end the same that at the other as at V X the same that at S T after that there is no more but to draw parallels to the base and all shall be done The fourth figure sheweth the Cornish wholly made I have drawn parallels from all the points of the line of the Angle Y Z I have made an end of the Wall to pass upon the Cornish for to give to understand that one hath liberty for to make it throughout and that our rule is general for to make it where they would For to find the under parts of the Great Projectors FOR to find the Projector of the Crown of the Body or of the Wall A We must from the Corner of the quarter of the round B make as small line of the length that one would have that it come forth as is B C then from the point of sight D to draw a Ray E passing by the end of the Measure C. After that you make a Diagonall from the distance F and make it to pass by the quarter of the Round B and the section that it shall make at the Ray D E at the point G that shall be the under part aswell of the bottome as of the side as is B H the which one may see more cleerly in the opposit in the body marked K The Projector of the Body or Wall marked L is made as the first marked A There is only this difference that the Body L hath the Projector M N greater by one half then that above B C for to Shew that by the same Order one
must take six parts of the lâ—ne A B which shall be A D and divide them eaâ—â— into 4 and these 24 parts shall serve for a scale for the depths or removalls being sufficient for to let them out infinitely And the six parts that remaine between B D shall be the Scale which shall furnish the Measures of these according as the lines drawn from the points found by the plane shall divide the Rays drawn to the point of sâ—â— G For as this Scale is a pyramide whereof B D is the Base the Measures diminish in proportion as they are sunk have divided the one of these parts into Inches for to finde there all the Measures as they are upon the plane With the Scale or Removalls we finde the points of the plane and with that of the Measures the length that 〈◊〉 lines ought to have aswell for the plane as for the Elevation How for to finde the plane in Perspective we must observe all the Measures of the Geometrical plane the 〈◊〉 Angle of the planer m is removed 7 feet from the point a upon the line a g Wherefore I will reckon 17 paâ— begining at A and from the seventeenth I will to the point F dividing the Ray A G at the point R. from this pâ— R we must draw a parallel to the Base and by reason that the Plane m is within the Ray a g a foot and an hâ—â— we must upon the same line R but on the side B D take part and an half for to carry within the Ray A G whi h shall be the point M representing the Angle of the plane M for 〈◊〉 Angle l which is removed 26 feet from the point a. we must from the point D which is 24 feet from the peâ— A draw to F and where the Ray A G shall be divided at the pointy draw a Parallel Now as it is about 〈◊〉 feet that this line y is enough removed we must draw from the second part of the Scale to the point G aâ— where this Ray shall divide the Parallel y. at the point Q we must draw Q F which shall give upon A G 〈◊〉 point H from which point H we must draw a parallel to A B and upon the same line H but on the side B take the Measures for to gâ—ve 13 feet and an half from the point H unto the point L. For the point k which is removed 29 feet from A we must from the fifth part of the Scale A D draw toâ— point G and where this Ray shall divide the Parallel y at the point O to draw O F for to have upon A G 〈◊〉 point N. Then from the point N. to draw a Parallel for to take on the side B D 7 feet and an half 〈◊〉 we must Carry out of the Ray A G that is to say from N to K. For the point i. removed 38 feet from the point a. we must upon the Scale A D take 14 parts 〈◊〉 from the 14 draw a Ray to the point G which shall divide the parallel the point S. And from the point S to dâ— to F which shall divide the Ray A G at the point T removed 38 feet from the point A by reason tâ— the Parallel y is of 24 to the which having joyned 14. they make 38. at the point T. And by reason that Angle i is 4 feet and an half within the Ray A G we must upon this Parallel T but on the side D B takâ— feet and an half and Carry them from the point T to the point I. For to frame the plane we must joyn by right lines these 4 points M I K I and from their Angles raise pâ—â—pendicules as M st L ff K fr and I sp The which shall have Each 17 feet as is marked in the plane by 〈◊〉 â— ne X and from the ends of these perpendiculars to draw two Diagonals st sp ff fr which shall divide themselâ—â— in Z and upon this point Z to elevate a perpendicular Z Ae of 13 feet and an half Then to draw lines 〈◊〉 all the four corners sl ff sp and fr to the point Ae and the Cage shall be framed in perspective If one would 〈◊〉 it descend within the ground one foot we must adjoyn one foot under every point of the plane and joyn thâ— together with lines For to give justly the distance removed the Point remaining in the Picture THose that would use this common manner must know that the number of feet that we shall take upon the base ought to have respect to the distance that they shall have determined of For to cause my Proposition to be understood I will set in the first figure two distances the one of six feet the other of twelve which have respect the one to the other by reason that dividing into two each of the six parts we shall have twelve Let us suppose then that the line A B is divided into twelve parts and that from all these parts one hath drawn Rays to the point of sight C let us take now the half of these divisions A D and draw to the point E which is the distance of 6 feet it is certain that the section of the Ray A C shall be the abridgement of the squares view'd six feet distant If from the point D we draw to the point F which is the distance of twelve feet this line D F dividing the Ray A C shall give the abridgement of six little squares view'd twelve feet distance He that would have the abridgement of twelve squares view'd twelve feet distant he must from the point B which is the whole base draw to the point F and at the section of the Ray A C to the point H shall be that which is required or else from the point I to draw I F which shall give the same point H and the line H K shall be sunk twelve little squares viewed at 12 feet distance We see in this that 12 little squares viewed at 12 feet distance do meet in the same line H K that six squares viewed at six feet distance and all the lines of six squares that the section of the Diagonal D G hath given do reflect themselves by two and two to those which the Diagonal D F hath given the reason why the Diagonal D F hath given two lines for one of those D G is that the distance is doubled If it were trebled it would give three and four if it were four-fold Now for to finde on the side B D the same sections and the same number of little squares as on the side D A without the point of distance be out of the picture we must only divide into two each of the six equal parts which are between B D which will make 12 parts and from their divisions to draw occult lines to the point of sight C and if one draw Parallels to the base by all the sections that the Diagonal maketh of all these Rays
he shall have 12 squares of sinking in the same line and if the distance were of twelve feet although that G be but six feet of distance the reason of this is that by multiplying the Rays we multiply the squares and multiplying the squares we remove the distance see then how having made twelve parts of six which were between B D there ariseth twelve little squares which make the same sinking that the distance at twelve feet distant And he that would have the distance at 24 feet he must divide still into two each of the parts between B D which would make 24 parts and from the 24th to the point D to draw the line D G the section that it would make of the Ray B C at the point K would be the sinking of the 24 feet In the second figure I have set upon the line L M the same Measures as upon A B of the first figure and on the side M N the same sinking and the same distance as on the side A D which giveth the line H K to the end that we may see that he which would draw the fifth part as Q G or from the seventh as R G that he should not have the true sinking which is at K for R G would not sink enough and Q G would sink too much although from these 5 or 7 parts there would be made twelve or twenty four Wherefore we must observe to take always a Number which may be multiplied by the distance as here the distance of six may serve for 12 18 24 30 36 42 48. and so an infinite number by six The distance of 5 may serve for 10 15 20 25 30 c. The distance of eight may serve for 16 24 32 40. 48 c. We cannot fail doing thus for supposing that the point of distance could not be nearer to the point of sight then G is near to C it follOweth that if G is at 6 at 7 8 or at 10 feet from the point C that the half of the base hath the same number the which number we must divide proportionably to the removal which we will give it For example if there be eight feet from N to L and that I would have the distance of 32 feet without that G go out from his place I will divide each of the eight parts which is the half of the base as L N into 4 and 4 times 8 will be 32 Rays so the abridgements of the square should be at 32 feet of distance All these little divisions remain not after the Picture is made there are none but the principal divisions of feet which they draw to the point of sight and the abridgements that is to say the Parallel to the base which remain always A very sine Invention for to make naturally Perspectives without keeping the Rules HAving set down all the Rules that we must keep for to make exactly Perspectives I would set also this Invention and the following for to make thereby perfectly fair ones and very exact without being obliged for to use any one rule therefore This shall serve for those that love Panting and take the pleasure to use it without being willing to take the pains to open the Compass nor to take the Rule for to draw a line for in this order we shall not need neither the one nor the other And nevertheless we may make very fair Perspectives either of Buildings of Gardens or Landskips Before we proceed to the order we must know that the principal piece and necessary for this invention is a great lease of Glass very clear enclosed in a frame of Wood well smooth'd and thin which I have marked with A at the bottom of the figure this frame must slide between two pieces of Wood an Inch and an half thick the which must be fastned to the end of a board which is of the breadth of the Frame as B C sheweth fit for to receive the Frame A. The breadth of this board B D shall be of a foot C. At the midst of the fore-part of this board we must make one or more square holes E for to fasten there a little Iron Rod or Wire as a Rule pierced all along whereby to raise it or let it down at the top of this Rule F there shall be Round of 3 or 4 Inches of Diameter without thickness as it might be of white Lattin the which must have a little hole in the midst as it were for a piece to go through all these things put into one make the piece G Although the figure sheweth the order and how we must use this piece G yet I will not cease to tell how we must proceed therein Having then placed this piece G before that which one would draw he shall look through the little hole of the spectacle F if one can discover upon the Glass all that he would that should be there if any thing come not there you must put the spectacle nearer to the Glass until that he do see there that which he desireth The piece being so setled we must mark upon the Glass all that shall be seen there looking through the hole F which doth here that which the point of sight doth in other Orders it being most certain that all that shall be marked upon the leaf of Glass having the eye at the little hole of the spectacle shall be found perfectly in the Rules of the Perspective Every one knoweth how we must withdraw that which shall be designed wherefore I shall leave that for to say that one may mark upon the Glass with the Pen and Ink. and after that all is done to moisten a little the other side of the Glass for to refresh the Ink and to set on the side which we shall have traced a Paper somewhat moist and then to pass the hand upon it and the Paper will take all that which was marked upon the Glass If one will they may also use a Pensil and colours according as every one shall think good it is enough that one know the invention to use it for to retract that which they will For it is as easie to retract a Pallace as a Countrey-House or a Chamber seeing that it is nothing but to set ones self in a place where there may see that which they would design and to bring the spectacle near the Glass when there shall be neâ—d by the means of holes which are in the Board A Painter may also use this for to retract figures at such a posture as he shall have given them for to retract after the embossing In a word for all that he shall judge be assured that the use will render many things easie that were hard before Another pretty Invention for to exercise the Perspective without knowing it THis Invention is found to be as pretty as the former and some do esteem it more by reason that the other obligeth to design twice the first upon the Glass
measure which one shall take thus Having made the first figure A B we must from the top of its head and from under its feet draw in what place one would of the Horizon which is here the point C all the heights of the other Figures must be taken between this Triangle A C B. For example desirous to have the height of the Figure from the point D from this point D we must make a Parallel to the base D E unto the line A C which shall be the point E from which we must raise a Perpendicular unto the line B C which shall give the point F this Perpendicular E F shall be the height which must be to the figure from the point D. If at the point G we would have yet a figure you must make the same practise from the Point D and you shall have the Perpendicule H I which shall be for the height of the figure from the point G And by the same Method all the other figures shall take the heights from whatsoever place it be For the figure that have feet at the Horizon IT is rarely that one maketh figures upon the Horizon but if there were necessity we must make those that one would make appeare the first greater then the other that is to say to give them the Natural height and all the others will be equal to them and they shall be râ—moved according as we shall make them the lesser For example the figure K L is the greatest and the nearest and that M N is the most removed As the secret in this for the Painters is to finish well those before more then those of the bottome and the further they are removed the more they are to be far it and less perfect The Rule of these Figures and of those that have the Eyes within the Horizon is no other then their owne height for as well in the one fashion as in the other there is but only to make the Figures lesser and lâ—sse furnished which we would have backward and seeme farther off Of Figures Elevated above the Plane THere are that say that the Objects elevated from the Earth have more diminution then when they were upon the Plane and that for this reason it must be that a Figure raised up 4 or 5 feet should be lesser then if it were on the Ground this should be good if it were elevated very high as we shall say hereafter but this little maketh that the diminution is unperceiveable for supposing that such an Object or Figure could be discovered at one only view that is to say without lifting up the eye they ought to have the same height being elevated as if they were on the Ground For example the figure A must have the same height that the figure B and the figure C as that of D and that of F equal to G and so of others For the Figures below we shall mark for the same reason the Figures that are below are of the same height as those above as is the figure E equal in height to that of H and I as great as the figure K These two Examples shall serve for all those that we could make there Of the Postures that we should give to Figures in the Perspectives WE must make choice of the Postures which we should give to figures for to deceive the eye seeing that they are not all there good as we have already said Wherefore it seemed good to me to set down some which might shew a way to invent others The first is a Man which readeth being set the second readeth a proclamation fastned to a Wall the third playeth upon a Lute the fourth sleepeth the fifth sits on a rail and turneth the back on the side of them that are two and two the first marked with six look upon a design upon Paper the other farther off seven are about serious affairs One might set those that play that talk together or entertain at a Table or standing up which write which pray on their knees in one word one may set an infinite company of postures so that they be such that one may stay there long time But we must never set those that are in action for that deceiveth not to see always one Leg or an Arm in the Air nor those that run without stirring from one place to another Of Beasts and Birds in Perspective WE must keep the same Rules as in the Figures giving the height or breadth to the first and from the two ends of this first measure to draw to the Horizon to have all the measures of the others For example having made the first horse A D for to have the height of that of B we must from the line A D draw to the Horizon C and then from the point B to draw a parallel to the base B K until that it do divide the line A C which shall give the point K from which we shall raise the Perpendicule K L for the height of the horse from the point B. For the Fowls we must from the ends of the Wings E F draw Rays to the Horizon and between these two lines take the measure of the others which I suppose of the same bigness For example for to have the bigness of a Fowl at the point G we must draw a parallel to the base G H until that it divide the Rays E F which we shall give the line H I for the greatness of the Fowl G. When we would set Beasts or Birds in the Perspectives we must choose those that are most at rest as may be a Dog sleeping or gnawing a Bone a Cat watching of a Mouse or a Parret c. For to finde the height of Figures far removed the first being upon a Mountain near to the Eye IT is a thing that giveth great Contentment and Satisfaction to the Minde when we have the knowledge of that which we have done that which maketh me beleeve that any one will be glad to have the present Rule unknown to many When we are to make these Figures we must determine the height of the first that is to say the distance from the Ground whither we would ascend and at this distance to set another figure below of the same height from the feet and from the head of which we must draw to the Horizon for to have the height of other Figures which are within the Field I express my self For example the figure A which is above the Mountain hath for its height five feet Royal which is the natural I suppose that the Mountain hath twenty five feet of height if one be raised up twenty feet as this Piece in the midst whither the Beholder is raised which ought also to have five feet for his height the Horizon will meet it at twenty five feet as the Top of the Mountain and the Horizon will grate upon it as we see at the Figure of the Mountain which hath the feet
neither larger nor streighter then the Bodies that give them their shape for this reason we give all the shadows caused by the Sun by Parallels as we have seen at the second Figure of this Treatise It followeth from all this discourse that for to have the shadow of what body soever it be being opposed to the Sun we must draw a line from above this great light which may fall plumb at the place where one would take the foot of the light and from this place to draw an occult line by one of the Angles of the Plane of the Object and another of the Sun by the same Angle elevated and the section of these two lines shall shew how far the shadow must go all the other lines shall be drawn Parallel unto these For example for to take the shadow of the Cube A the Sun being at B we must from under the Sun C which is as the foot of the light draw a line which toucheth an Angle of the Plane as C D. Then from the oâ—her Angles E to draw Parallels to this for to finde the end of the shadow we must draw a line from the Sun B passing by the Angle elevated F which shall divide the line C D in G. Then drawing a Parallel to this by the Angle H it will divide the line E at the point I and we shall have the shadow of the Cube D G L. He that would cause the shadows to cast before or in any other way he must determine the place of the Sun and the point underneath to draw the lines of an Angle and make all other lines parallel to that as you may see by the figure below without repeating the Practick which is the same as that above The Shadows of the Sun are equal to the Objects of the same height although that they be removed the one from the other EXperience teacheth us that many stiles or elevations of the same height removed the one from the other cease not to give their shadows equal in the same time I say in the same time for they do lengthen or shorten themselves according as the Sun cometh near or retireth himself the which he doth every moment seeing that he never standeth still Wherefore when one desireth to cause the shadow of some object to cast we must determine of the place of the Sun and the point under it to draw from thence the two occult lines which give the term of the shadow as here the Hedge-row A giveth the point of its shadow in B and if from the point B you draw to the point of sight C this line B C shall be as well the shadow of the Hedge-row D as of that A and of all those that should be in the same line unto the point of sight and you must hold for a maxime that the shadows do always keep the same point of sight with the objects Following this experience that the objects of the same height do give the shadows equal if one would give the shadow to the Hedge-rows E F which are of the same height with A D we must only take with a Compass the distance A B and carry it to the foot of the Hedge-Row E for to have E G and from this point G to draw to the point of sight C and to make always the same Practice even when these Alleys were prolonged infinitely But if the light come from the bottom or from before as in the figure below must we change the Order No we most only set forward or draw back the foot or that under the Sun and draw lines from the one and from the other by an Angle as are H and I which shall give the bound of the shadow of the Hedge-Row K to the point L and from this point L we must draw to the point of sight M Then from all the Angles of the Plane of the Palissades we must draw Parallels to the line H unto the Ray L M and we shall have the natural shadows of the same Palissades or Hedge-Rows Of the Shadows when the Sun is directly opposite to the Eye AS often as the Sun is before our eyes that is to say above the point of sight the sides of the shadow that it shall cause shall be parallels as are all the visual Rays wherefore the point of sight shall serve always for the foot of the light And the other Ray which shall determine the shadow shall be taken from the center of the Sun For example when we would find the shadow of the Cube A we must by the Angles of its plane B C draw Rays to the point of sight D as are B E C F. Then from the center of the Sun G draw also two Rays which shall divide those at the point K L passing by the ends of the lines elevated from the angles B and C which are H and I In such manner as the shadow of this Cube shall be B K L C. The shadows of the two other pieces M and N shall be taken by the same order and so of all the others which may there be met withall It cometh into my mind that one might be troubled if instead of a Cube there were a Pyramide by reason that the Ray of the midst of the plane of the Pyramide and the Ray of the Sun that passeth by the point made but one line and by consequence can terminate nothing for to take the shadow from the point of this Pyramide When this shall happen we must from an Angle of the plane as is here O draw a Ray to the point of sight P which shall make O Q And from the same Angle O elevate a Perpendicular O S then from the point of the Pyramide T make a parallel to the base until that it divide the Perpendicular O S at the point V We must make the Ray of the Sun to pass by this point V and continue it until that it divide the Ray O Q at the point X from this point X we must make a parallel to the base unto the Ray of the midst of the Pyramide which shall be divided at the point Y the bound of the shadow We must draw to this point Y from the Angles Z and O and the Triangle Z Y O shall be the shadow of the Pyramide These Walls which are at the bottom of the one and the other figures take their shadows as we have said of the Cube A. For to give the shadow of the Objects pierced by the light WHEN the Object is square or of a right line we must from the point A from under the Sun draw lines Parallels from all the Angles of the Plane Then from the midst of the Sun B draw a line to the Angle the farâ—hest removed C which shall divide the line A at the point D and to draw from the point D to the point of sight E until that it finde the last line of the Plane F for to have
make of the shadows taken from the Sun without that there be any need of other explications for the figures seeing that they are sufficiently intelligible and all made by the Rules which one may have learned by others heretofore But as every figure hath always some particular observation it will not be besides the purpose to give notice thereof to the end there may be nothing which may not be easily understood I say then that in the first figure I have only made use of the plane A B C D for to find the shadows of the objects E and F by reason that they are both upon the same line and of the same height In the second we must observe that the piece of wood G casting its shadow upon the Wall H this shadow maketh the same figure that the Corniche I which is below the which is seen also at the Staff K set against the same Wall H. For to find the shadow of the board L we must remember the order afore-going of the Objects broader above then below for having drawn the Perpendicule M where it shall divide the Ray N O we must draw the line from under the Sun M P then from the board elevated L to draw a line which divideth M P and this section shall be the bound of the shadow The shadow of the Boul Q shall be found also making two Perpendiculars to fall of which we must frame the plane Then by the Center of this plane to draw the line from under the Sun R and from the Sun a Tangent as Q S until that we divide the line R at the point T and also another V which divideth the same R and this distance T V shall be the greatness of the shadow of the boul For to find the shadow at the Sun in all sorts of Figures THE shadow of these Figures is found by the same Orders of other bodies that is to say by parallels as well of them from under the Figure as of those that come from the Sun with this only difference that the shadow of the bodies or objects is found by the help of their plane and that the figures have none thereof but instead of these planes we must from the aspect whereby we see the Figure draw a line by the under part and upon this line make to fall perpendicularly that which is most remarkable in the figure for to help to find the shadow and then this line from below shall serve as for a plane For example the figure being naked or cloathed and without a Cloak as the first that turneth the back to us We must from under its feet A draw a line to the point of sight B and upon this line A B make to fall occult lines from all the points which can help to find the true shadow as from the hand C to make to fall a Plumb-line which shall divide the line A B at the point D and from the Elbow E to make one fall to the point F and yet another from the head G which shall give the point H from all these points D F H from the feet of the figure and from the end of his Staff I. We must draw parallels to the base Then the height of the Sun being determined of we must draw a line as K passing by the fore-part touching the brim of the Hat G and to continue the same until that it divide the line H at the point L which shall be the end of the shadow And also from the brim behind his Hat M to draw a parallel to K G L until that it divide also the line H at the point N these points N L shall be the shadow of the Hat We must draw a parallel by the point C until that it divide the line D at the point O. This point O shall be the shadow of the hand which holdeth the Staff Wherefore drawing from this point O to the point I this line O I shall be the shadow of the Staff We must also draw a parallel to the point E which shall divide F at the point P and shall be the shadow of the Elbow and so of all the places that one would as of the Knees upon the parallels which pass under the feet and from all these points to mark the shadow of the whole figure the little figure Q hath taken its shadow by the same order I have not marked all the points nor the parallels for to avoid confusion When they are cloathed at length for to find the shadows of the figures we must as I have said draw from under their feet a line to the point of sighâ— R as this S R and from the bottom of the garment on the one side and the other draw two parallels to the base as T V and between T V another X which is the midst of the figure Then from the top of the Head to draw a line Y which shall be for the Ray of the Sun which we must continue until that it divide the line X at the point Z and this point Z shall hâ—â— the bound where the shadow must end the rest of the shadow shall be drawn between the two parallels T V and if any thing flow over as the two folde ✚ and * we must draw them by parallel to Y X untill that they divide the Ray V as we see that the ✚ giveth the shadow of the Elbow and the * giveth that of the folds of the Cloak For to finde with facility the shadows by the Sun IF I would here set down the shadows of all the Objects which may be given it were to take in hand a design without end for the Objects may be given infinitely for besides the great number that there is of them each would suffice to make a Book seeing that it may be turned bended and lie down in divers manners each having its shadow different But this labour would be very unprofitable seeing that every one may make those which shall please him so that he remember well two or three Rules which he must keep as I have shewed in the Orders of the shadows taken from the Sun where two sorts of lines give the means to finde all the shadows which may be the one coming from under the Sun passing by the Plane the other which parteth from the Sun by the upper part of the Object and goeth to divide this other line where the shadow must go but as these lines must be each Parallels that is to say those from under the Sun Parallels between themselves and those of the Sun also Parallels between themselves I believed that I should oblige I gave an Invention to draw them readily the one and the other I have said elsewhere how we should draw Parallels to the base by the means of a Board well squared as this here A and of a Rule as B the which shall serve to draw lines from under the Sun when it meeteth directly opposite to
the face of the Object as may be the line C D but if it enlighten by the Angle we must use another instrument as that marked E which is a Rule fastned to the End of another piece of Wood well squared and hollowed of one side and the other in such manner that the Rule F G may move with force to the end that having taken a line bended as H D one may therby make one which may be Parallel to it which is I K with this false square or Grashoper it is so as the Workmen call it E F G this Instrument doth abbreviate exceedingly when one would make shadows of the Sun for there is not a line and of what inclination soever it be whereof one may not draw Parallels The use will make us to know its profitableness But for the shadow by the Torch and the Candle it is of no use at all by reason that all the lines are drawn from one Center The Shadows taken from a Torch from the Candle and from a Lamp are found by one and the same Order I Have already said that for to finde the shadows we must necessarily have two points the one from the foot of the Torch or of the Candle or of the Lamp which ought always to be found upon the Plane where the Object is set the other from the flame of one of these lights From the first point which is the foot of the Torch the bottom of the Lamp or of the Candle we must draw Rays by all the Angles of the plane of the Object of which one would have the shadow And the second point which is the flame will give other Rays which passing by the Angles from the top of the Objects will go to divide these lines drawn from the plane and to mark where the shadow must end it self I shall shew this by example using the same Letters for these three lights in which it shall be easie to see that it is all the same order in the one as in the other with this only difference that the foot of the Torch or of the Taper is set below and that it must suppose in others that they set it there I say then that if one would have the shadows B of the Cubes A that we must from the point O foot of the light draw lines by all the Angles of the planes of these Cubes as O D O E O F O G Then from the point C which is the light or the fire of these Luminaries draw other lines which must pass by the Angles of the objects elevated and continue these lines until that they divide the other lines drawn from the point O. For example having drawn a line from the point O passing by the Angle of the plane D if one draw from the point C another line passing by the same Angle elevated P this of the point C being continued shall divide the first of the corner D at the point H and this point H shall be the shadow of this Angle D P. If from the point C we do the same by all the Angles elevated we shall divide the lines of the Angles of the plane at the points H I K L the which points H I K L we must joyn with right lines and we shall have the shadow of the Cubes as is to be seen in the three figures By this example it is easie to see that it is all the same order in the one as is in the others In the leaf following it shall be taught to find the under parts or the feet of the Candles and Lamps Of the foot of the light SEeing that the Order for to finde the shadows for the Torch for the Candle at for the Lamp is altogether the same in the one as in the other as we have sai but now There will be no more need to set down distinctions in the Order following for when I shall set a Torch one may set a Candle or Lamp in the place by reason that the flame of the one hath the same effect with that of the other wherefore from henceforth I will use the word of light for all three For the foot of these lights which must be upon all the Planes where they set the Objects they shall be found by this Method Having a Torch lighted within a Chamber whether we shall set it in a corner on the side or in the midst as this it must be that all the Parts of the Chamber or of the Hall as the Boards above and below the sides and the bottom have a point that serveâ—h for the foot of the light that from this point we may draw by all the Angles of the Plane of the Object of which we would have the shadow as I shall shew in the leaf following contenting my self to shew in this how we must finde this point which I call the foot of the light The Torch being placed in A this point A is the foot of the light and B the fire or the light of the Torch this fire or light B remaineth firm and never changeth but the foot must be found on all sides For to have the foot of the light at the wall on the side C we must from the point A draw a Parallel to the base until that it divide the Ray D E at the point F and from the point F to raise a Perpendicular F G Then from the point B which is the fire to draw another Parallel to the base until that it divide F G at the point H and this point H shall be the foot of the light as if the Torch were lying by reason that its fire remaineth always at the point B. For to finde this foot of light at the Board above we must from the point G draw a Parallel to the base as G I and from the point B to make a Perpendicule to G I which shall give the point K which shall be the point of the foot of the light as if the Torch were turned upside down For to finde it on the other side of the Hall we must make the same Order as on the side C and we shall have the point L. For to finde the foot of the light at the bottom of the Hall we must from the point H draw to the point of sight O until that we divide the Perpendicule E at the point M then from this point M to make a Parallel to the base which shall divide the Torch at the point N this point shall be the foot of the light for the bottom of the Hall The foot of the Candle is found by the same Order as that of the Torch taking the midst of the foot of the Candlestick for the foot of the light but when it is a Pâ—ated Candlestick or an Arm set against a wall it must be that the Arm or the Branch of the Candlestick determine the line or shall be the foot of the light For example in the Plate