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Langley, Batty, 1696-1751 / The city and country builder's and workman's treasury of designs, or, The art of drawing and working the ornamental parts of architecture
(1756)

Chap. 1. Of the manner of proportioning the five orders of columns in architecture,   pp. [3]-16

Page 4

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PRO B. IV. ro deiermiw the Pr~je~ioiz~ of :ke
Fig. it. Plate L
(i.) DivideQN eqothgh~ofthe
Bafe in ~ Parts, and the upjer i * ~Nm~
Make z 0 the Proje&amp;ion of the Dds, u~aial to
4Partsand+.      (2.) The Prc~je&amp;ion~(die
Plinth (qp) is equal to (r f) the Height of the
Mouldings on the Plinth, as a1h is the Projeaioa
of the Cornice, from the Upright of the Dado,
in every Order. Draw xy at Pleafure, at any
and againft the Dado, which divide in 6 Parts,
terminate the Members in the Bafe and Cot-
nice, as is expreffed by the dotted Lines proceed-
ing upward and downward from them.
Fig. G exhibits the Manner of dekribing a
Cima reverfa at large, whofe Proje&amp;ion is ~ of
its Height.
PR OR. V. !Jio proportion the Heights of the prin-
cipal Parts of the Tufcan Column, Fig. 1. P1. II.
(z.) Divide the given Height in 7 equal Parts,
and take i for the Diameter of the Column at
~sBafe; therefore note, that the He  tof the
2olumn is 7 Diameters.  (2.) The Height of
the Bafe, and of the Capital, are each half a
Diameter.
PROB. VL       ~o proportion the Iiev~hts ~f the
Members of the Ba/c of the Tufcan Columps.
Divide st the Height of the Bafe in 2 Parts, as
the Bafe on the Pedeftaj, Fig. II. Plate I. the
lower a is the Height of the P1iz~th D, and the
upper i of its Torus C, with the Ciw!ture B,
which js a fourth Part thereof.
PRO B. VII.    2'o proportion the He~hts of the
Members of the Tufcan Capital.
Divide the Wi he of the Capital MR into 3
as in Fig. II. Pla.te U. give the upper i to
its Abacus M 1~ the middle x totheOvolo0
with its Fillet P. which is a fi,ccb Parr, and the
lower   to Q the Neck of the Capital.  The
Heiglitof the Aftragal R S is equal to Half
the ~-i~jgIit of the Neck, which divide in ~:
Give a to the Aliragal R, and ito the ~i1Iet S.
N;:e, The Aftr  ii in every Orde; is a Part of
the Shaft, not oE' the Capital.
ORDER.
PROB. VIIL Thiim;k4~sfiof:h,TuCc~n,
v#~7#!C.4~w. FigJ. Plate U.
(L) Divide the giv'ca ~ight of the Shaft be..
tw~n ibp Cin&amp;~re B~ ~t 4~e A(b~a~ 4, ia~to
Z~z~4~
Bq, 85, and ,cu, xy, ea~h eq~u4 to tialf a
Dswter, ind 4ASW the [a~es ~. n. ~y ~ make
~ ix.ac-
cording to what Quantity you have a Mind to
diminilh the Shaft Come making the Diminution
~ or ~., as in this Example.  (i.) On x defcribe
the Semicircle n r, x y, and draw the Lines is r,
and c r, from the Points is c, parallel to the cen-
tral Line A B.    Divide the Arches n r and iy,
each into any Number of like equal Parts, ftp..
pofe fou~r, as at o p q, and 2, 3, z, and draw
the Ordinates q~, p3, and oz.   (s.) Divide Ax
into the fame Number of equal Parts, as in n r,
or xy, as at 1 h d, and draw the Lines, ef equal
to qz, gi equal to p3, and km equal to oz.
(hp) From ii, through the Points kge. draw the
curved Line n kg e is, and from y, through the
Points m if, the curved Line y mif, which com-
pletes the Diminution of the Shaft as required.
P R 0 B. IX.   7fo determine the Projeflions of the
Members in the Bafe of the Tufcan Column,
Fig. I. Plate I.
(.) Divide the Semidiameter in 3 Parts, and
turn i Part out for the Projeaion of the Plintli,
which, in every Order, ifands exa&amp;ly over the
Dado of the Pedeft~L   (2.) The Proje&amp;ioi~ of
the Torus is always the fame as of the Plinth.
(s.) Divide the Projeaion of the Plinth before
the Up right of the Shaft into fo~ir Parts, and the
third L'art into 4, then the firif i Part terminates
the Pro.je&amp;ion of the Cin6tur~ B.
PROD. X.       2~o det~rn4ne the Prt~#e2* ~f 4*
Members in tke Tufcan Ceejtal, Fig. ii. Vl~ U.
Thvkle the Semidiameter of the Sl~4 e~ip~im~4
to the Abacus into 2 Parts, as at f, and make
the Proje&amp;ion of die Abacus, equal to x ~of thofe
Parts, when the Abacus is finifbed with a Fillet,
and to .~ of x Part, when without a Filler.  Th~
ProjeEtion of die Fillet tinder th~ A~sga1 is
equal to twice its ewn Height, and the Pllaet
under the Ovolo, to it~ JHcig~ht.
PRO!.

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