Pi —
<*XIIL Figure 1, No. 1. —Let a b c d be half the'he e j g abacus , e f g half the plan of the cylinder, hijk* o pr 0 ; Vat ' on the same, and l m n o that of the abacus ;’Ua Cl J the shadow of any point, p', in the elevation of the
the
Plat/* <^ e ' n ° ^ ts corresponding place on the plan ; draw
#t j the ra y,p q, meeting the]semi-circumference ets
fay.’ 180 from p' draw p q the indefinite elevation of theSent tl, ** draw 9 9 parallel to i J, or h k, and qf will repre-ts t» av \ sl ‘ adow °f the point p. Find as many other pointstlle Poim 6 r ! eoessar y> in the same manner ; then, through alltfcq uil . ed ts thus found, draw a curve, which will be the shadow
Plan ? le , ra -y. R t, be drawn to touch the circle in v on thev< v "> the elevation of v, be drawn, then v'v"If t ] t a ® line of separation of light and shade.i° *he ni Fa ^ s t' ie sun * n tw0 planes, one perpendicularl °fi 2ot) ‘ ) atle of representation, but inclined 45 degrees to the*he pi ’ ar)( l the other equally inclined to the horizon and to^gre eg ne . 0 ^ representation; that is to say, making 45ea ch ; then all the points, qf, will be in the'liam ‘ erei >ce of a circle, whose diameter is equal to the?2° fthe cylinder. ’
f“i> 0 R ’ 8 Ws the elevation completely shadowed.
cylinder being capped with another1%^ C UUnder, to find the representation of the shadow.last^* ^°- 1-—Proceed to find all the points, q, as inHive ttl Pfoblem, and a curve being traced through them, willc °tfe S p® shadow required. The point p', on the elevation,P^allgi ac * ln g to p, on the plan, may be thus found : draw b rNel t! * C ’ and A r perpendicular to A c ; draw p sk 1 * 8 c A ,R> cutting b r at s. In l m make l p equal’ J ' Va 'tli ^ vv 'll be the corresponding point of p. No. 2e e levation completely shadowed.
** 0j ^ ION ’ Stereographical. See Stereography.
op Shadows, see Shadows.
^'Pen Ce ” ^ URE, in architecture, the out-jettings, or pro-'s p] ’ ' v h>ch the mouldings and members have, beyondjelled (j 6| or naked, of the wall, column, &c. They aref r ^ fbe Greeks, eephora ; by the Italians , sporti; bytt * and ' sa ^^ s > by our workmen frequently, sailingsby the Latins, projecta, from projicio, I cast for-
tl- ’ Who
vit r|1 . en ce the English , projecture.
>r ah er „ '. Us gives it as a general rule, that all the projecting
l<a glit a , S I* 1 buildings have their projectures equal to theirut ^‘i 8 is not to be understood of the particular° til ° r fccniding 3 ) as dentils, coronas, the fasciae of archi-
A of a bacus of the Tuscan and Doric capital, &c., butj.°'at 0 f , e . Projectures of entire cornices, &c. The greatfj 8 * 8 in ^ Ul , n g> according to some modern architects, con-^ c, i a» re ewing how to vary the proportions of projectures,pft'bug ea bly to the circumstances of the building.
nearness and remoteness, making a1( leot tl ln l b e view, require different projectures ; but it isk 'bile pi-^ anc ients had no such intention.i a 1 oh 8e ^ ecture of the base and cornice of pedestals, M. Per-fr^ 8 ’ by o e8 ’ ' S § reater in the antique than in modern build-of > tli e a^bivd ; which seems to follow, in good measure,file
*h ' le Ped * ' ents proportioning this projecture to the height8 Very ^ ® 3 fids ; whereas the moderns make the projecture
in all the orders, though the height of theC^eZj^Jiff^ent The reason of this change, whicha Vi evv 8 have made of the antique, the same author refers9 bw^^ATw e a PP earance solidity.
fi|' e< l to 1 ^ (from the Latin prolatus, flat) an epithet‘Cl 8 ' 8 abon 8 pheroid produced by the revolution of a semi-bs longer diameter. If the solid be formed byVo t. u lon °f a semi-ellipsis about its shorter diameter, it^ ‘ 4 R
is called an oblate spheroid; of which figure is the earth weinhabit, and, perhaps, all the planets too ; having their equa-torial diameter longer than the polar.
PRONAOS, (from r-poraos) in ancient architecture, aporch in front of a temple, church, palace, or other spaciousbuilding.
PROPORTION, (French ) the just magnitude of the mem-bers of each part of a building, and the relation of the severalparts to the whole ; e. gr. of the dimensions of a column, &c.,with regard to the ordonnance of the whole building.
One of the greatest differences among architects, M. Per-rault observes, is in the proportions of the heights of entabla-tures with respect to the thickness of the columns, to whichthey are always to be accommodated. See Entablature .There is scarcely any work, either of the ancients or moderns,in which this proportion is not different; some entablaturesare even nearly twice as high as others ; yet it is certain,that this proportion ought, of all others, to be most regulated:none being of greater importance, as there is none inwhich a defect is sooner observed, nor any in which it ismore shocking.
Proportion is likewise understood of the magnitudes ofthe members of architecture, statues, or the like, with regardto the distance whence they are to be viewed.
The most celebrated architects are much divided in theiropinions on this subject; some will have it, that the partsought to be enlarged in proportion to their elevation ; andothers, that they ought to remain in their natural dimen-sions.
PROPORTIONAL COMPASSES, an instrument con-sisting of two equal and narrow slips of metal, terminating ateach extremity in a point, the slips being connected togetherby a cylindric pin, which, when they are made to coincide, ismoveable along a slit through both pieces : so that the axis,or centre of the pin, and the two extreme points of each piece,may be in the same straight line, and fixed at any point whichwill keep its situation in each of the pieces, whether theinstrument be opened at any angle, or shut.
The two surfaces of the instrument which appear when itis shut are called the sides.
The four parts of the instrument, from the centre of motion,are called legs.
It is evident from the definition given, that two legs will beequal to each other, and of the same invariable length, what-ever angle these legs make with each other; and that thetwo which include the opposite angle will also be equal toeach other, and their length also invariable at any angleformed by them.
The application of the proportional compass with regardto the division of lines, and the circumferences of circles intoany number of equal parts, has already been shown underthe articles Compasses and Instruments. In this place itis proposed to treat of its application to perspective, and someother branches of geometry and architecture.
Problem I.— To set the proportional compasses in theratio of a line divided into any two parts.
Figure 1.—Take a line equal to the length of the instru-ment, and divide it in the ratio required ; then apply theshorter or longer part of the line thus divided on the lengthof the instrument when shut, from the extremity of the longeror shorter legs to an intermediate point, to which bring theaxis of the pin, and the compasses will be set in the ratiorequired. Thus, let A d, be a straight line, divided in e ;make a b equal to the length of the instrument ; join d b, anddraw e c parallel to D b, cutting a b at C ; shut the instru-ment ; take either distance, c a or C b, say the shorter, c b,and apply it from the shorter end of the instrument; push