S TE

444

S TE

is called a cylinder; but if the ends are ellipses, and alikesituated, it is called a cylindroid.

Definition 16.—The straight line extended between thecentres of the two bases is called the axis.

Definition 17.—A solid having any plane figure for itsbase, and its sides plane triangles terminating in the samepoint, is called a pyramid.

Definition 18.—A solid having a circle for its base, andterminating in a point, such that a straight line extended fromany part of the circumference of the base to the terminatingpoint may be in the surface of the solid, is called a cone; andthe surface which lies between the circumference of the baseand the terminating point, is called the conic surface.

Definition 19.—If the plane of a circle be supposed per-pendicular to a given plane, with its circumference or edgeupon that plane ; and if there be a straight line standing oni any other point perpendicular to the said plane ; and ifanother straight line be made to move parallel to the planeon which the circle stands, so as always to touch the circum-ference and the straight line, beginning at any given point,and proceeding entirely round until it arrives at the samepoint ; then the solid bounded by the circle, and the surfacepassed over by the straight line contained between thecircumference of the circle and the straight line is calleda conoid; and the surface generated by the straight line iscalled a conoidal surface.

Definition 20.— A sphere is a solid formed by the revolu-tion of a semicircle upon its diameter.

Definition 21.— The centre of a sphere is the same withI that of the semicircle.

j Definition 22 .— The diameter of a sphere is any straighti line which passes through the centre, and is terminated bothj ways by the superficies of the sphere.

I Definition 23. — A cube is a solid figure contained by six

! equal squares.

j Definition 24.— A tetrahedron is a solid figure contained

I by four equal and equilateral triangles.

| Definition 25.— An octahedron is a solid contained byeight equal and equilateral triangles.

Definition 26.— A dodecahedron is a solid contained bytwelve equal pentagons, which are equilateral and equi-angular.

Definition 27. —An icosahedron is a solid contained bytwenty equal and equilateral triangles.

The solids defined in the last five definitions are called thefive regular solids.

STEREOMETRY (from <rfpE opcrpia, formed of Tcpeog,solid, and ptrpov, measure,') that part of geometry which| teaches to measure solid bodies, i.e., to find the solidity, or! solid content of bodies ; as globes, cylinders, cubes, vessels,j ships, &c. The methods see under the respective bodies ;

; Cylinder, Globe, Sphere , &c.

j STEREOTOMY, (from vtp toe, solid, and roprj, section,)

| the science and art of cutting solids under certain specifiedconditions.

■ Stereotomy may be regarded as a branch of stereography,

1 which is the science of solids in general. Mr. Hamilton has

intitled his complete body of perspective, Stereography, whichperhaps would have been more properly called Stereotomy.j j as the perspective representation of every object in nature isj i the section of a pyramid or cone of rays. But as it has notj I been the object of writers on perspective to show the rules1 ] for finding the sections of solids in general, under certain; specified conditions of the cutting plane, nor of finding any

■ other sections besides those of cones and pyramids, it is the! express intention of this article to explain the general prin-

ciples of the science for any given law, by which the surface

itl' er

e» c *‘

surface S ~!^ ma ^ * )e const >tuted of straight lines, or l,, “ eSdisposed ; ‘‘ y . agree w . lt . fl tile common section of two |,»svet P snne f P° SItl0ns - And as nothing of the k»» d 'Ilt r lr i P , erhaps this attem P t be the more afg.able, part.culariy as m its principles the whole art of*

Denfrv InC T^ ed ’ and tlle mechanical arts of masonry aIld ■ „^ art of stone-cutting, the sauarin 0 ' cU , i*r11 nd the / onnati °n Of hand-rails, depend en

upon the sections of solids. i

, Planes and SoKds demonstrated in the eleven

°n °f Elements, useful in Stereotomy. - n a

Deposition I—One part of a straight line cannot beplane, and another part above it.

Proposition II—Two straight lines which cut each oare one plane, and three straight lines which meetother are m one plane.

Proposition III—If two planes cut each other, their com-mon section is a straight line.

Proposition IV. If a straight line stand at right an Sto each of two straight lines in the point of their >»“f eC L e sia 1 also be at right angles to the plane which P

through them. ° r

Proposition V.—If three straight lines meet all ,n /’"fpom , and a straight line stands at right angles to e» gthem m that point, these three first straight lines are m

and the same plane. Ie9

Proposition VI—If two straight lines be at right angto Hie same plane, they shall be parallel to each other. ]|flProposition VII.—If two straight lines be pawl eh ^s raight line drawn from any point in one to any P 0,nother, is in the same plane with the parallels. , an d

Proposition VIII.—If two straight lines he par® 11 * ’ b eone of them at right angles to a plane, the other shah aat right angles to the same plane. „ r h d

roposition IX.—Two straight lines which « re e ' 9 .uii ethem parallel to the same straight line, and not in thp ane with it, are parallel to each other. I o^ ,et

Proposition X.—If two straight lines meeting eac\be parallel to two others that also meet, but are n° t4 jasame plane with the first two, both couplesequal angles. , lint

Proposition XI.— Problem. —- To draio a , stral £, e ab# 1 '*perpendicular to a plane, from a uiven point in S Pthe plane. J J ^eO

Draw any straight line in the plane, and fro® r jgiitpoint above the plane draw a second straight Jiaangles to the first ; from the point where the p eT P nh‘f’meets the first line, draw a third straight line m n pyin~ ' ri S ht an S* es to the first; and, lastly, from the S d . i.n ai space draw a fourth line at right angles to t 1

, m e

at

t¥lit*®p oi, ::;„h

oi'd.*l» c

^Ur t i?^ V a) t^ U j rtn JU,e « r, gll „

he plane. ° lae > tij us drawn, will be perp■ \ r °position XU — p ,,

f A( angles to „ 1r °^km.~7'o erect a straight

’lane. a fftven plane from a given point t»

^et'pendicuiaj.^, 6 !] P°’"t above the plane draw a straitbe plane draw pJa ne, and through the give' 1 Iecorul line will he ?f COnd b'ne parallel to the first,

.Proposition XlTT e r P er P end >nular required. _ „ n/n"®

here cannot be two si t,le Sllme P oiut in a g ’.'Z via"*’tW0 'jK’ght lines at right angles to thej

. ot R ; and there can be but one p

rom a Point above. , v ;, ( }ir> e

> which the same stra a

ll Oi L VUllliui i >i v o -^__

pon the same side of it ; and there can

icular to a plane from a point i' ..

Proposition XIV.—Planes to »•—i perpendicular, are parallel to each ot g m eet, ,' g iD®Proposition XV. —If two straight V. Jjjc liihtlier, be parallel to two other straight 1* D