DOI Page / Citation link:
https://doi.org/10.11588/diglit.18826#0100
72
Ctf PERSPECTIVE. [lECT. tl,
PLATE XXIII.
Though circles parallel to the picture be extremely eafy,
yet the moft troublefome fubjects in perfpective are reprefenta-
lions of circular members, and objects, in compofitions of ar-
chitecture, when teen obliquely. Their fquares and cubes
follow the principles recently illuftrated, but by way of ex-
plaining the difficulty of their circular parts, we (hall offer the
iollowing method of delineating them.
THE TUSCAN BASE IN PERSPECTIVE.
The difficulty in this inftanee is, to reprefent the fwell of
the torus : to accomplifh which, make a lketch of the parts
intended to be. represented, as near as convenient to the place
they are to occupy, as at X, divide this into as many parts as
are requiiite, as horizontally at 2, and vertically at x.
Take ax for the height of the plinth: divide the torus itfelf
in half, as at 2, for its height, and x for its width : rule x per-
pendicular, and 2 horizontal: then where the line x touches the
outline of the torus, rule lines parallel to 2, as 1,3; rule alfo
4, 5, parallel to 2.
Put the plinth into perfpeclive as ufual. Having procured
the perfpective center of the bale, o, by ruling the dia-
gonals of the plinth, raife a perpendicular, as o K ; through
o, draw a line for one diameter, parallel to D B, and from the
half of D B as A, draw through o, to the vanifhing point S,
for the other diameter. Procure the plan of the circles as
already explained At A erect a line, which is to receive
the divisions made on the original lketch, 1, 2, 3, 4, 5 ; this
now reprefents their heights: to reprefent their projections,
let off their meafures from the point A, as to J, from the points
A J, 2, 3, 4, 5, draw lines to the vanilhing point, cutting the
line oK, in ], 2, 3, 4, 5. Thus we have the line A 5 for the
heights of the figure next to the eve, and the line o K for their
heights at the (enii-diameter of the column. Now rule the
meafures of the projections, which arc marked between A and
J to their vanifhing point, and where they ftrike the plans of
the circles already formed, erc£t perpendiculars, as at a, b, c,
the points where thefe perpendiculars are cut by the lines
A 1, 2, 3, 4, .5, in their progrefs to oK T. 2, 3, 4, 5, are fo
many paints on the outline of the torus, and other parts of
the original lketch, which if carefully united, will defenbe its
whole form.
Having found the perfpeclive reprefentaiion of the figure
in its part neareft to the eye, rule from the line oK, hori-
zontal lines which denote heights, 1, 2, 3, 4, .5 • and as before,
on the points where the plans of the circles are cut by the
w idths of the members, erect perpendiculars, forming fo many
fections of the figure, in fuch parts of the circumference as
as may be thought neceflary.
PLATE
Ctf PERSPECTIVE. [lECT. tl,
PLATE XXIII.
Though circles parallel to the picture be extremely eafy,
yet the moft troublefome fubjects in perfpective are reprefenta-
lions of circular members, and objects, in compofitions of ar-
chitecture, when teen obliquely. Their fquares and cubes
follow the principles recently illuftrated, but by way of ex-
plaining the difficulty of their circular parts, we (hall offer the
iollowing method of delineating them.
THE TUSCAN BASE IN PERSPECTIVE.
The difficulty in this inftanee is, to reprefent the fwell of
the torus : to accomplifh which, make a lketch of the parts
intended to be. represented, as near as convenient to the place
they are to occupy, as at X, divide this into as many parts as
are requiiite, as horizontally at 2, and vertically at x.
Take ax for the height of the plinth: divide the torus itfelf
in half, as at 2, for its height, and x for its width : rule x per-
pendicular, and 2 horizontal: then where the line x touches the
outline of the torus, rule lines parallel to 2, as 1,3; rule alfo
4, 5, parallel to 2.
Put the plinth into perfpeclive as ufual. Having procured
the perfpective center of the bale, o, by ruling the dia-
gonals of the plinth, raife a perpendicular, as o K ; through
o, draw a line for one diameter, parallel to D B, and from the
half of D B as A, draw through o, to the vanifhing point S,
for the other diameter. Procure the plan of the circles as
already explained At A erect a line, which is to receive
the divisions made on the original lketch, 1, 2, 3, 4, 5 ; this
now reprefents their heights: to reprefent their projections,
let off their meafures from the point A, as to J, from the points
A J, 2, 3, 4, 5, draw lines to the vanilhing point, cutting the
line oK, in ], 2, 3, 4, 5. Thus we have the line A 5 for the
heights of the figure next to the eve, and the line o K for their
heights at the (enii-diameter of the column. Now rule the
meafures of the projections, which arc marked between A and
J to their vanifhing point, and where they ftrike the plans of
the circles already formed, erc£t perpendiculars, as at a, b, c,
the points where thefe perpendiculars are cut by the lines
A 1, 2, 3, 4, .5, in their progrefs to oK T. 2, 3, 4, 5, are fo
many paints on the outline of the torus, and other parts of
the original lketch, which if carefully united, will defenbe its
whole form.
Having found the perfpeclive reprefentaiion of the figure
in its part neareft to the eye, rule from the line oK, hori-
zontal lines which denote heights, 1, 2, 3, 4, .5 • and as before,
on the points where the plans of the circles are cut by the
w idths of the members, erect perpendiculars, forming fo many
fections of the figure, in fuch parts of the circumference as
as may be thought neceflary.
PLATE