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VI.

THE inclination of a plane (A B) (Fig. 1) to a plane (PL); is the acute

angle (DEF) contained by two straight lines (E D & E F) drawn in each of the planes, (that is DE in the plane A B & E F in the plane PL) from a fame point (E), perpendicular to their common fection (A N).

VII.

Two planes are faid to have the fame or a like inclination to one another, which two other planes bave, when their angles of inclination are equal.

VIII.

Parallel planes are fuch which do not meet one another tho' produced.

IX.

Similar folid figures are thofe which are contained by the fame number of furfaces, fimilar and homologous.

X.

Equal & fimilar Solids are thofe which are contained by the fame number of equal, fimilar and homologous furfaces.

XI.

A folid Angle (A) is that which is made by the meeting of more than two plane angles (BA C, CAD & BAD), which are not in the fame plane, in one point (A).

XII.

A Pyramid (E BADF) (Fig. 3) is a folid contained by more than two triangular planes (BAD, BAE &c.) having the fame vertex (A), and whose bases (viz. the lines E B, B D &c.) are in the fame plane (E B D F).

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DEFINITIONS,

XIII.

Prifm is a folid figure (AHE) (Fig. 1.) contained by plane figures, of which two that are opposite (viz. GHIKF & BCDA) are equal fimilar, and parallel to one another; and the other fides (as GA, AK, KD, &c.) are parallelograms.

If the oppofite parallel planes be triangles, the prifm is called a triangular one, (and it is only of those prifms that Euclid treats in the XIth and XIIth Book), if the oppofite planes are polygons, they are called polygon prisms.

XIV.

A Sphere is a folid figure (A EBD) (Fig. 2.) whofe furface is defcribed by the revolution of a femicircle (AEB) about its diameter, which remains unmoved.

XV.

The Axis of a Sphere is the fixed diameter (A B) about which the femicircle revolves whilft it defcribes the fuperficies of the sphere.

XVI.

The Center of a Sphere is the fame with that of the femicircle which defcribed its fuperficies.

XVII.

The Diameter of a Sphere is any ftraight line which paffes thro' the center, and is terminated both ways by the fuperficies of the sphere.

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A Cone is a folid figure (ABCD) (Fig. 1, 2, & 3.) defcribed by the

revolution of a right angled triangle (ABE), about one of the fides (BE) containing the right angle, which fide remains fixed.

If the fixed fide (B E) of the triangle (A B E) (Fig. 2.) be equal to the other fide (A E) containing the right angle, the cone is called a right angled cone; if (BE) be less than (A E) (Fig.3.) an obtufe angled, and if (BE) be greater than (AE) (Fig. 1.) an acute angled cone.

XIX.

The Axis of a Cone is the fixed ftraight line (B E) about which the triangle (A BE) revolved whilst it described the fuperficies of the cone.

XX.

The Bafe of a Cone is the circle (AGCD) (Fig. 1.) described by that fide (BE) containing the right angle, which revolves.

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DEFINITION S.

XXI.

Cylinder is a folid figure (E BDF) (Fig. 1.) described by the revolution of a right angled parallelogram (AN M Č) about one of its fides (A C) which remains fixed.

XXII.

The Axis of a Cylinder is the fixed ftraight line (A C) about which the parallelogram revolved, whilft it defcribed the fuperficies of the cylinder.

XXIII.

The Bafes of a Cylinder (viz. EN B, & FMD) are the circles described by the two oppofite fides (N A, M C) of the parallelogram, revolving about the points A & C.

XXIV.

Similar Cones and Cylinders are those which have their axes and the diameters of their Bafes proportionals.

XXV.

A Cube or Exabedron (Fig. 2.) is a solid figure contained by fix equal squares.

XXVI.

A Tetrahedron is a pyramid (BDCA) (Fig. 3) contained by four equal and equilateral triangles (viz. A B DC, BAD, ADC & BAC).

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AN

DEFINITIONS.
XXVII.

N Octabedron (Fig. 1.) is a folid figure contained by eight eqaul and equilateral triangles.

XXVIII.

A Dodecbabedron (Fig.2.) is a folid figure contained by twelve equal pentagons which are equilateral and equiangular.

XXIX.

An Icofabedron (Fig. 3.) is a folid figure contained by twenty equal and equilateral triangles.

XXX.

A Parallelepiped is a solid figure contained by fix quadrilateral figures whereof every oppofite two are parallel.

XXXI.

A Solid is faid to be infcribed in a Solid, when all the angles of the infcribed folid touch the angles, the fides, or the planes of the folid in which it is inscribed.

XXXII.

A Solid is faid to be circumfcribed about a Solid, when the angles, the fides, or the planes of the circumfcribed folid touch all the angles of the inscribed folid,

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