^*Ose a word applied in mathematics to

*>inan ems which have one answer only, or at leastLjy pPn^ bn ' f e number of answers.

1(lr > of ZONING LINE, in conic sections, the iutersec-^ ie b ^ ane Parallel to the cutting plane with the planecone. In the sections of a cone which

0 r ,, le hyperbola , tbe determining line falls within theto . 1 , tbe

H,

tit

e has.

cone ; in parabolic sections, it forms a tangent

etl the" 36 ' . bn l ' le elliptic section, it falls without ; andif 88 ’ Hep Secbon Is a circle, the determining line will, in one1(5 C|, ttiu^ lllee t the plane of the base, as in this instance01 ^^COv lane ' s P ai ' il hel to the plane of the base,v 88 adl ./CON, (from Siacovew, I serve, I minister) a, e8t ttieni 0,nin g to the ancient churches, where the sacredPfer u ». -

b,

8t r .

: eca » Se

’ Ves sels, relics, and ornaments of the altar, were• Tl ' • - - -

;! als °den

■ttlffB

^his apartment was otherwise called sacristy.Nominated arm vikov, and in Latin, salutatorium ;^ e -a gers ' Vas here that the bishop received and salutedon a ° met * 1Tle s it was called yijTarwpiov, or yiTarupiov,

ni >Rb

iu was ctincu. fUfi ut wfj

^■^G-Ov 0OUn t tbe tables kept there.

W, d,.. (from the Greek, Stayoirtoc) in geometry,

Sle to ti" Vn through any figure, from the vertex of one^v erv i at of anotlier.

'Si/

rectili

■near figure may be divided into as many.as the figure has sides.a gonal divides a parallelogram into two equal

» K*e« . us

JV 7 ; antin S tlv °.

Wrts i oiaaor,.,! ,i:„:

a;

A'*- tOogj

C f ce ^ en t theorem in elementary geometry, firstdes’t ^tr. Lagny, in the Me moires de VAcademieSO t\v 0 j’. c ^ cncc s, an. 1706, is, that the sum of the squareshi th e la &onals of every parallelogram is equal to the8 47th Sc l Uar es of the four sides ; and it is evident thatfriary “/^Position of Euclid may be derived as a mere6 b 0 ’"" 8: Let 1U tb * s theorem. The demonstration is as18 the ^CDbe an oblique parallelogra

v «tt,

n — .... _,_ 8 .am, of which

A jj -8 L a., re . ater diagonal, and A C the lesser. From the

tft le obtuse angle dab, drop the perpendiculars'hij] s ' ttl ilar .°p G D > then the triangles ade, b c f, are equal)i„ /C p a ’ t°r A d is equal to b C, and the angles ade

f v, ft., l r> ~- 1

Lb

equal to each‘other; also, the angles a e d, and

oK -e. ■Nr eqUat to each other; consequently, d e is equal

b 7 proposition xii. lib. ii. of Euclid , in the

tl^l t 0 ^ triangle b d c, the square of the side b d is

SUrn of the squares bc, c d, together with double

>'• h 0o t gl . e c » by c D ; and by the 13th proposition of the

Ia the triangle dac, the square of ac is equal

^ tari gle the squares of ad and CD, abating double them, „7. °t C D 1 -

' s Ul,

l ce

X

and

r «f.

•or e

1 by d e equal to C f ; for C f is equal to d E ;bd 2 = bc’+Cd*+2(cf X CD)

ac* = ad*+ab*—2(cf X cd)

^ r c Eb * +Ac2 = BC® + CD 2 + AD* + AB*

SKln?® P ar allelogram be right-angled, the diagonals areIt c Nvnai ns equently each equal to the squares of the twoPtbSe TX other right angles opposite that diagonal./X on e 0 f the diagonals and a side be known, thea w iU likewise be known.

V'Xd K r °£ osit ion, of a similar nature to the above, wasVj'Ns Ptolemy, viz., that the rectangles of any twoSty!. to tb„ a huadrilatoral figure inscribed in a circle, isjX sid® SUm of the two rectangles contained by the51 iik, 1 Xi<,

Hi' 1 ‘^ dimensions of a building, in order to make8 X j.y Lir the most accurate and expeditious method,a gonal 3 . In carpentry and joinery, no polygonal

\

frame whatever can be rendered stationary or immovableabout the angles, without diagonal pieces, as the strengthconsists in dividing the work into triangles. In geometry,a polygon cannot be constructed by the linear dimensions ofits sides only, without the diagonals, as the area of the figuremay be variable under the same number of sides, ad infinitum,from a certain position of the sides, in which they will con-tain the greatest possible area to any less area whatever.

The impulse given to a body, at the same instant, by twoforces, in different directions, causes that body to move inthe diagonal of a parallelogram, of which, each of the forcesacting separately, would cause the body to describe a side,in the same time as the body moved conjointly by thetwo forces.

Diagonal Buttress, a buttress placed at the angle ofa building, chiefly used in churches of mediaeval date, andemployed to resist the thrust of the ribs of the last severy ofthe vaulting. It answers the same purpose as two distinctbuttresses set square with the two walls at their intersection,but with loss material. Diagonal buttresses do not seem tohave been employed to any extent previous to the fourteenthcentury, but are common in buildings of the Decorated style.Previously, two buttresses at right angles were employed.

Diagonal Moulding, the same as Zig-zag or Dancette.

Diagonal Paving. See Pavement.

Diagonal Rib, a rib or groin passing diagonally acrossa bay of vaulting from one angle to the opposite.

Diagonal Scale, a compound scale, by which a subdivisionmay be made of any part of the smallest unit upon a straightline, by means of equidistant parallels crossing others of thesame kind.

DIAGRAM, (from ciayparjiio, I describe) in geometry, ascheme for the explanation or demonstration of a figure.

DIAL, (from the Latin , dies, day) an instrument servingto measure time by the shadow of the sun. Or more par-ticularly, the surface of a body so graduated that a certainline parallel to the earth’s axis will show the hour of thedav, when the sun shines upon the surface of such body'.

DIAMETER, (from tea, through, and yerpur, to measure)a straight line passing through the centre of a circle, andterminated at each end by the circumference ; the diameteris therefore a chord passing through the centre of the circle,and is consequently greater than any other chord in thesame circle.

The diameter of a circle divides the circumference intotwo equal parts.

For other particulars, see the article Circle .

Diameter of a Column, the thickness of the lowest partof the shaft at the bottom. In a colonnade, or range ofcolumns, the intercolurnns should always be proportionedto the diameter of the column.

Diameter of a Conic Section. See Conic Section.

Diameter, Conjugate. See Conic Section.

Diameter of Diminution, the diameter at the top of theshaft.

Diameter of a Sphere. See Sphere.

Diameter, Transverse, the longest axis of an ellipsis.

Diameters, Conjugate, of a circle, two diameters at rightangles

DIAMOND, an instrument for cutting glass.

Diamond, the small instrument used by glaziers for cuttingglass, and formed by the setting of a fractured piece ofdiamond in a wooden handle. There are now in use twodescriptions of pencil diamonds, the old one, and the new orpatent pencil. The delect of the former is the difficultyexperienced in placing it on the glass in, at once, the properangle, so as to make it cut and not scratch. The patent