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 proceed . 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 F.
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 : wherefore 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 ought to go after in this work , because they are harder to set into Perspective , not because of the Plane , which is easie enough , seeing that it is composed and framed of 3 equal lines joyn’d together ; but because of the obliquity of its sides .

Let us now see the Practice of the Advice that we have given of Measures upon the base A B , for to make this Triangle in Perspective , we must from all these Angles 1,2 , and 3 , draw Perpendiculars upon A B , and set one leg of the Compass in their section , and with the other take the Removal of the Object from the base , and set also this Removal upon the same base , by making a quarter of a Round , as 1 , 1 , and 1 , the same at 2 , 2 , and 2 , and the same at 3 , 3 , and 3. Then having made another base in another place , as is this here under E F , we must transport there the Measures , which are upon that A B , and draw at the point of sight C , the points 1 , 2 , and 3 , Perpendiculars . Then having taken a point of distance D , there to draw the other points of sinking 1 , 2 , and 3 : and at the section of the visual Rays : by this we must produce the lines , which shall give you the Triangle .

If you would give to it this Border , you need but do the same again , repeating that which we are doing , setting down other cyphers , that nothing be confounded , as over against 1 , 4 , and 2 a 5. and to 3 a 6. Then draw the Perpendiculars at the point C , and where the others shall divide them , there to draw the lines as you see .

The Triangle equilateral , as this is circular ; that is to say , which they enclose within a circle , whereof each side hath 120 degrees .

There is no need to know the degrees of the Angles , for to frame all these Polygones , so as we may see at the 4 . side : but I have not omitted to set them for the contentment of those which here take notice of them .

Of the Pentagone or five-Angles .

THE Order of framing a Pentagone is , that we must make a Circle , and divide it into 5 equal Parts , of 72 degrees on each side . Now for to set it in Perspective , it is altogether the same thing with the Triangles , as one may see by this figure , except that it is with a Border ; and I have marked it upon the base : but single , by reason that one may have learned by the Triangle , how it ought to be made . The point of sight , as well on the front as the side , is A , the point of distance B ; the visual Rayes which are the Perpendiculars of the Angles of the Plane upon the base , are drawn at the point of sight A. And the others which give the Abridgement , and the place of the Angles at the point of distance B. As a divideth the Ray marked 2 , which giveth the second Angle , 4 giveth the fourth Angle , and so of others . All the rest is clear enough , we must take heed of one thing , which is , that all the Angle sought to draw to the center 6. It is therefore , that it must be set in the Planes in Perspective , as in the Geometrical Plane , for to draw there all the Angles .