CUR

219

CUR

to j( 3 e 1’ ,a l to half the vertical angle, or the angle E a c, equalb B . .implement. Make e d to e c as 5 to 3 ; join d a andtQak’j ln Al> , take any point, f; draw fg parallel to A e,and AF to g as 2 to 3 ; draw age, cutting CD at h,Cq u ,j 1 Parallel to f g or E a, cutting A d at I; make b kroof 0 A h and join k h, then A i n k b is the contour of theit (lo(. s ^ IJlret k This is so evident from its construction, thatPro n °- t , rec l u 're demonstration.e 9Ual V. Figure 5. —To describe a roof with four

taftgj.g a *ers, that shall be in equilibrio by the weight of theJoin °* a Siren width A e, and height F c.

1>eeti n C E ’ and bisect it in h by a perpendicular, DII G,<5c, d e ^ ^ E * n G ; on &, as a centre, with the distance G e or®neet t[° ri ^ e t ' le e i*'cle c e o. Draw k h i parallel to f e, to1 n c e yertical line O C in K, and the circle in i. Draw

and

' and

a b.

join de, then make the side cba similar to c d e,

^ c D, d e, will be the rafters of the roof required.

30it >*D.

in

Figure 6, complete the parallelogram cdqb, andQ : on 1F ’ and draw C L perpendicular to C F, and equal towith the distance

ft’ Wlt b the distance G e describe the circle N I f,a bo iii . le ver tical line at n and f ; produce ed to meet itt :<\ andB °*op.

lflan Sles 6cause K F is equal to k c, and r c equal R Q, theDq .. C , 1 F and c d q, are similar ; therefore i f is parallelbecaus P

C ® 0, ° 0r * e another, the angle N i F is equal to the angle? a 8le to twice the angle C e f, or twice the alternate

h alr,i Cl ->

use the two segments kif and c e o are

tl:

ie

equal to ecd + dol; but E c D is equal to

c P • I ® x ^ er lal angle m d c,tot),’ e< l«al to °a

CDQ.

and dcl is half the angleTherefore the angle n i f is equal

H'on plane, now in use, is a most completetviir cross 'grained and curling stuff; this plane, if*• work nearly as smooth against the grain as

f ^tl y -- M d c -f. CDQ, equal to the angle mdq, conse-c Q and' ° N : : c Q : c at, but c f and c n are equal, there-B 18 the C ** are e< l ua l > but c Q is to C m as the weight oneq Ua l' vei obt on b or d, therefore the weights on c andCc) ,St and 4 be rafters ab, bc, cd,de, are in equilibrio.n ,notl to h NES ’ ( som etimes written Kerb or Kirb,) thoseA 16 ^ 00t and carriage pavements in a street.

X'i 'bhj'vv, court justice. See Basilica.

,, a din g 0r ‘ L . STUFF, that which is occasioned by the’r' e fliev ?° iHng t be fibres round the boughs of the tree,douiq 6 ®.' 11 t0 s b° ot out °f the trunk.

Nl, SeE

p u -

K^ENT g

Or e,1 b f 0 e necessary slope of a piece of ground ory | 1 8Oli' ^* SC 1! ar ging the water from the surface.

*e rri0 ’ a Point screwed on a beam-compass, and which' lt 'C3 0 f . or slid along the beam, for striking greater or

^hich°i 3s a3so t3lat P art a proportional

s ar B Set • bolds the two legs together, and by which ther 0Q ^ ln an f given ratio. The sliding parts of theOtr^Es ’ ° r e lbpsograph, are also called cursors. See

big |!'E( 1 , f U| . , .STEP, the first step by which a stair is^lloPEn of lng at t b e en d in the form of a scroll, follow-! ;*" lt . '1 i'Alfq JJ, le band-rail. See the article Stair .

^boh 11 °f tlx* rorn 4 be French courtine,) in fortification,

' 8 ’ bo t( j e e Rampart which is between the flanks of two

‘E Sol(1 . red with a rampart five feet high, behind6rS stan d to fire on the covered way, and into

See Frustum and Truncated Cone .

&c S °i rt ra > s ed, embellished chair or seat of^er e b ace d in a chariot, wherein the chief officersbe carried into council. It was alsofor dictators, consuls, praetors, censors,

and ediles, who were from this circumstance called curules.Curule chairs were of various shapes, but the one generallyused was a stool without a back, so made as to be folded up,and opened again in the manner of a camp stool.

CURVATURE, that degree m a curve , in which thecurve recedes in a perpendicular from a tangent, at a givendistance from the point of contact; and consequently if twocurves, or two parts of the same curve, have each a tangent,and if any equal distance from each point of contact be taken,and a perpendicular be drawn from each point of distance tothe curve ; then, in each of these curves, or portions of thesame curve, the intercepted perpendicular being greater orless, the curvature will also be greater or less.

CURVE, a line , such that only one straight line can bemade to touch, without cutting it, when the straight line isextended on both sides of the point of contact ; or a curve isa line in which, if a point be taken, only one straight linecan pass that point without cutting the line in which thepoint is taken. The straight line so drawn is called a tangentto the curve.

The circle is the most simple of all curves, depending onlyupon the arbitrary extension of its radius, which, if given,the circle is determined in magnitude. Its circumference isone uniform curve, or has its curvature everywhere equal,and equally distant from the centre.

In every curve line whatever, it is evident that a verysmall portion may be taken as a circular arc at any point ; oithat there is a certain circular arc at that point which hasthe same curvature as an indefinitely small portion of thecurve, but a greater curvature than an indefinitely smallportion of the curve upon the one side of the point, andalso a less curvature than the nearest indefinitely smallportion on the other side of the point. The radius of acircle of equal curvature to the curve at any proposedpoint, is called the radius of curvature at that point, andis the measure of the curvature of all curves. The circle ofequal curvature with the curve, is called the equicurve circle,or the osculating circle. Hence, if the osculating circle andthe curve have a common tangent, no other circle whatevercan be drawn between the two curves ; and when the curveis continually upon the increase or decrease in its curvature,the arc of the osculating circle will be on the concave sideof tbe curve on one side of the point of contact, and on theconvex side on the other side of the said point ; or the curvewill be between the tangent and the circumference of theosculating circle on the one side of the point of contact, butthe circumference of the osculating circle will be betweenthe tangent and the curve on the other side of the point ofcontact.

The principal curves that are useful in architecture, arethe conic sections, namely, the circle, the ellipsis, the parabola,and the hyperbola ; also, the cycloid, the conchoid, the spiralof Archimedes , and the logarithmic spiral. The definitionsand the most useful properties, will be found under eachword.

Curve of Double Curvature, a curve, of which all itsparts are not in tbe same plane.

Thus, if the surfaces of two cylinders of the same diameterintersect each other, and their axes also intersect each other,the common intersection will be a curve, of which its partsare all in the same plane ; or if the surface of a cylinder andcylindroid intersect each other, and their axes also intersecteach other ; and if the semidiameter of the cylindroid beperpendicular to a plane passing through the two axes, andequal to the radius of the cylinder, then the parts of thecurve formed by the two surfaces, are likewise in one plane :or if the surface of one cylindroid meet that of another