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CIBORIUM, in ecclesiastical antiquity, the covering ofan altar; being an insulated edifice, consisting of four columnssupporting a dome. The ciborium was used during the lowerand middle ages ; but was afterwards superseded by thebaldachin. See Baldachin .

The most magnificent ciborium ever known, wa3 thaterected by Justinian, in the church of St. Sophia, at Con-stantinople . It consisted of four large red marble columns,supporting a silver dome, surmounted with a globe of massygold, weighing 118 pounds, and surrounded with lilies ofgold, falling in festoons, weighing 116 pounds ; and in themiddle was a cross of the same metal, weighing 75 pounds,covered with the most rare and precious jewels.

CILERY, the drapery or foliage on the heads of columns.

CILL. See Sill.

CIMA. See Sima, Mouldings.

CIMA-INVERSA. See Sima-Inversa, Mouldings.

CIMA-RECTA. See Sima-Recta, Mouldings.

CIMBIA, a fillet, string, list, or cincture.

CIMELIARCH, in English churches, the room wherethe plate, vestments, See. are kept.

CINCTURE, or Ceincture, an annular fillet, of a cylin-dric surface, at the ends of a column, connected to the shaftby the apophyge, or scape. The cincture at the top of thecolumn, is named also collarino.

CINQUEFOIL, an ornament in the pointed style ofarchitecture, consisting of five cuspidated divisions, or curvedpendants, inscribed in a pointed arch, or in a circular ring,applied to windows and panels. The cinquefoil inscribed ina circle, is a rosette of five equal leaves, with an open spacein the middle ; the leaves being formed by the open spaces,and not by the solids or cusps.

CIPPUS, a small low column, sometimes without a baseor capital, and most frequently bearing an inscription. Thecippus was used for various purposes among the ancients :when placed on a road, it indicated the distances of places ;in other respects, the cippi were employed as memorials ofremarkable events, as landmarks, and for bearing sepulchralepitaphs. Also the prison of a castle.

CIRCLE (from the Latin , circulus) a plane figure con-tained under one line, called the circumference, which is suchthat all lines drawn to it, from a certain point within thefigure, are equal; and the point from which the lines maybe thus drawn, is called the centre of the circle.

A circumference may be thus described : if the end of aright line be placed upon a fixed point, and kept upon thatpoint while the other end is carried progressively forward,or round, until it come to the place whence the motion began,the moveable extremity will thus trace out the circumferenceof a circle.

In order to obtain the measurements of angles, the circum-ferences of all circles are supposed to be divided into 360 equalparts, called degrees; each degree is supposed to be dividedinto 60 equal parts, called minutes ; each minute is dividedinto 60 equal parts, called seconds ; each second is supposedto be divided into 60 equal parts, called thirds; which areagain divided and subdivided ad infinitum. Any denomi-nation, whether of degrees, minutes, seconds, &c. is knownby a peculiar character, written over the right-hand figureof that denomination ; thus, °, written over the right-handfigure of a number, shows that number to represent degrees ;the character thus, ', written over the right-hand figure ofa number, shows the number thus distinguished to representminutes ; e. g. 136° 24' 48* 57'*, &c. represents 136 degrees,24 minutes, 48 seconds, 57 thirds, &c.; and, as similar arcsare such as are contained under the same, or equal angles,they contain the same number of degrees, &c., the number

of

of parts of the arc of a circle, described from the meetingtwo lines forming an angle, and comprehended between tn >is the true measure of the angle ; for the number of P a ^j, estill the same, whatever be the radius of the arc, or ot ,, gcircle, the parts being greater as the radius is greater. jarc of the circle being supposed to be divided into 360 _

parts, the radius will be found to be equal to the chord obecause the circle contains six equilateral triangles, w 1bases are chords to the circle, whose summits meet > ncentre, and whose sides are radii to the circle. And s* ,the sixth part of 360°, or of a whole circle, is 60°, the c 1 aJBof 60 is therefore equal to the radius. The parts of , y 9may be measured by parts of the radii, which are a " t ^, 0supposed to contain the same number : for if there b e 0arcs described from the angular point of an angle, h et \ jythe legs, these arcs may be measured in parts ofrespective radii. . t |, a t

The circle is the most capacious of alf plane figures; ^is, it contains the greatest area under equal perimeters, orthe least perimeter enclosing the same area.

The area of a circle is equal to the area of a trianglebase of which is equal to the circumference, and the P® 1 ^ adicular equal to the radius, and consequently equal ^rectangle, whose breadth is equal to the radius, analength equal to the semi-circumference. jj,ef

Circles, like other similar plane figures, are to one anoas the squares of their diameters. flC e,

The ratio of the diameter of a circle to its circumf er t j l6has never been exactly ascertained. Archimedes was .o first, in his book De Dimensione Circuli, who gave thein small numbers, being that of 7 to 22, which is 9tl r0 ji-most useful for practical purposes. Yieta carried the apPUgdmation to ten places of figures, by means of circuffl sC ^gand inscribed polygons of 393,216 sides, showing th® t j 1 eto be as 10,000,000,000 to 31,415,926,536 nearly,circumference being greater

than 31,415,926,535

but less than 31,415,926,537 e9 of

Van Colen carried the approximate ratio to 36 Pg r jn^figures ; which number was recalculated and ®a n , th®by Willebrod Snell. Mr. Abraham Sharp extend® ^gdratio to 72 places of figures, which was afterwards exto 100 places by the ingenious Mr. Machin; and, - e dM. De Lagny, in the Memoires de VAcad., 1719, has ®this ratio to the amazing extent of 128 places of fig ur c ;rcl eIn approximating the circumference or area of. afrom the diameter, the first authors had recourse to th 0and circumscribed polygons; since it was found t ‘. gte tetcircumference of the circle was greater than the P eT . [C gtt>‘of the inscribed polygon, but less than that of the ^Xscribing one ; and, that when the polygon containednumber of sides, the circumference of the circle did no j t omaterially from either, it would be still more nearly^® V*!

the arithmetical mean of the two. And, to gi v f tr ‘ ^y th 1 !an idea how very near the circumference obtaine.means is to the truth, the circumscribed and ,npolygons may be taken of such a number of sides,their perimeters will be each expressed by any 8* ve \ pa ifl^ 1 ’of figures of the same value, from unity, either ta* c>r<vidually, or as a whole number, and consequently the jo/ference of the circle may be expressed, or carried

fJllS

degree of accuracy required. w i>-

But the method of obtaining the circumference^^s,means, being found exceedingly laborious, other 0 gVjby a series of fractions, have been invented, so as ^grfto be much more easy in the calculation, but also ^gthow the terms may be continued at pleasure, by * *