0.5

1 cm

PER

£m the infide, as G and H are, you fhould not draw from the

point F, but from E ; by reafon that the line of interferon is

found between the two ; confequently the two will cut each other

in the fame points I K. See ho;. 3.

Of planes viewed directly, or in front. From the third and

fourth articles preceding, and the elevations that follow, it will

appear that my intention is not to ufe geometrical plans, in order

to the drawing of PerfpecYives; that being a double labour, and

there being very few painters who would give themfelves the

trouble, fince I teach them to do the fame thing by the ufe of

the terreftrial line.

But, as there is no rule fo general but has its exceptions, fo

there are certain figures that cannot be put in Perfpeclive with-

out the ufe of fuch plans ; befides(the confufion a man would be

under, fhould a plane be given him to put in Perfpeclive, if he

had not been infrrucled how to proceed.

On thefe confiderations I have been induced to give the fol-

lowing rules, which may fufHce to fhew how any plane that can

be required, or even imagined, may be put in Perspective.

1. To Jhorten or diminijh a fquare, as A B C D, plate XV, Jig. r*

From A and B, to the point of fight E, draw the lines, A E, B E j

and from the fame angles, A and B, 'draw two diagonals, F B,

A G ; and the points H and I, where they interfecl the rays A E

and B E, will give the fquare A B C D, diminished, in A H I B.

To do it without the geometrical plan, draw a line from B to

F, or from A to G ; or fet off" the line A B on the terreftrial line,

as in B K; and from K draw another line to F, which will

give the interfection I, on the ray B E.

2. To diminijh a Jquare viewed by the angle D. Having defcri-

bed the plane ABCD, fig. 2, draw a line to touch or rafe the

angle B, and falling perpendicularly on B D.

This being continued as a bafe line, lay your ruler on the fide

of the fquare A D and D C, and, where the ruler cuts the ter-

reftrial line, make the points H, I.

Then, from H and B, draw lines to the point of diftance P j

and from I draw a line to the other point of diftance G; and,

in the interferon of thofe lines, make pointy which will give

you the fquare K L M B.

To do without the plan ; fet oft* the diameter each way from

the middle point B, as to H and I. But in either cafe no line is

to be drawn to the point of fight O.

3. To diminijh q circle. Draw a fquare, ABCD, fig. 3,

about it, and, from the angles A D and C B, draw diagonals,

dividing the circle into eight parts ; and, through the points

where they cut it, O O, draw lines from the bafe line perpendi-

cular to D E F,

Vol. IL M Thm

£m the infide, as G and H are, you fhould not draw from the

point F, but from E ; by reafon that the line of interferon is

found between the two ; confequently the two will cut each other

in the fame points I K. See ho;. 3.

Of planes viewed directly, or in front. From the third and

fourth articles preceding, and the elevations that follow, it will

appear that my intention is not to ufe geometrical plans, in order

to the drawing of PerfpecYives; that being a double labour, and

there being very few painters who would give themfelves the

trouble, fince I teach them to do the fame thing by the ufe of

the terreftrial line.

But, as there is no rule fo general but has its exceptions, fo

there are certain figures that cannot be put in Perfpeclive with-

out the ufe of fuch plans ; befides(the confufion a man would be

under, fhould a plane be given him to put in Perfpeclive, if he

had not been infrrucled how to proceed.

On thefe confiderations I have been induced to give the fol-

lowing rules, which may fufHce to fhew how any plane that can

be required, or even imagined, may be put in Perspective.

1. To Jhorten or diminijh a fquare, as A B C D, plate XV, Jig. r*

From A and B, to the point of fight E, draw the lines, A E, B E j

and from the fame angles, A and B, 'draw two diagonals, F B,

A G ; and the points H and I, where they interfecl the rays A E

and B E, will give the fquare A B C D, diminished, in A H I B.

To do it without the geometrical plan, draw a line from B to

F, or from A to G ; or fet off" the line A B on the terreftrial line,

as in B K; and from K draw another line to F, which will

give the interfection I, on the ray B E.

2. To diminijh a Jquare viewed by the angle D. Having defcri-

bed the plane ABCD, fig. 2, draw a line to touch or rafe the

angle B, and falling perpendicularly on B D.

This being continued as a bafe line, lay your ruler on the fide

of the fquare A D and D C, and, where the ruler cuts the ter-

reftrial line, make the points H, I.

Then, from H and B, draw lines to the point of diftance P j

and from I draw a line to the other point of diftance G; and,

in the interferon of thofe lines, make pointy which will give

you the fquare K L M B.

To do without the plan ; fet oft* the diameter each way from

the middle point B, as to H and I. But in either cafe no line is

to be drawn to the point of fight O.

3. To diminijh q circle. Draw a fquare, ABCD, fig. 3,

about it, and, from the angles A D and C B, draw diagonals,

dividing the circle into eight parts ; and, through the points

where they cut it, O O, draw lines from the bafe line perpendi-

cular to D E F,

Vol. IL M Thm