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ERRATA for the first fix Books.

A

I.

Solid, is that which hath length, breadth, and thick-Book XI,

ness.

II.

The term of a solid, is a superficies.

III.

A right line is perpendicular to a plain, when it makes right angles with all the lines that touch it, and are drawn in the same plain.

IV.

A plain is perpendicular to a plain, when all the right lines in one plain, drawn at right angles to the common section of the two plains, are at right angles to the other plain.

V.

The inclination of a right line to a plain, is the acute angle contained under that line, and another right one drawn in the plain, from that end of the inclining line, which is in the plain, to the point where a right line falls from the other

end of the inclining line, perpendicular to the plain.

VI

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The inclination of a plain to a plain, is the acute angle contained by the right lines drawn in both plains, to the fame point of their common fection, and making right angles with

it.

VII.

Plains are inclined similarly, when their angles of inclination are equal.

VIII.

Parallel plains are such, which being produced, never meet.

IX.

Similar folid figures are such as are contained under an e

qual number of similar plains.

Χ.

Equal and similar solid figures are fuch as are contained by an equal number of similar and equal plains.

ΧΙ.

A folid angle is the inclination of more than two right lines

that meet in one point, but are not in the same superficies.

XII.

A pyramid is a solid figure, contained by more than two plains fet upon one plain, and meeting at one point in the

vertex.

XIII.

A prism is a solid figure contained by plains, whereof the two opposite are equal, similar, and parallel; and the other parallelograms.

XIV.

A sphere is a folid figure, described by a semicircle revolving about its diameter, which remains fixed in the same pofi

tion.

XV.

The axis of a sphere is that fixed right line about which the femicircle revolves.

XVI.

The centre of a sphere is the fame with that of the femicircle.

XVII.

The diameter of a sphere is a right line drawn through the centre, and terminated on either side by the superficies of the sphere.

XVIII.

A cone is a solid figure described by a right angled triangle revolving about one of the fides, containing the right angle, remaining fixed. If the fixed right line be equal to the other fide containing the right angle, then it is a rectangular

cone; if less, an obtuse angled cone; and if greater, an a- Book XI.

cute angled cone.

XIX,

The axis of a cone is that fixed right line about which the triangle is moved.

The base of a cone is the circle described by the revolving line.

ΧΧΙ.

A cylinder is, a figure described by a right angled parallelogram, revolving about one of the fides, containing the right angle, remaining fixed.

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ΧΧΙΙ.

The axis of a cylinder is that fixed right line about which the parallelogram is moved.

ΧΧΙΙΙ.

The bases of a cylinder are the circles described by the motion of the two opposite fides of the parallelogram.

XXIV.

Similar cones and cylinders are such, whose axes and diameters

of their bases are proportional.

A cube is a folid figure contained by fix equal squares.

XXVI.

A tetrahedron is a folid figure contained by four equal equilateral triangles.

XXVII.

An octahedron is a folid figure contained by eight equilateral triangles.

XXVIII.

A dodecahedron is a folid figure contained by twelve equal equi

lateral and equiangular pentagons.

ΧΧΙΧ.

An icosahedron is a folid figure contained by twenty equal e

quilateral triangles.

Xxx.

A parallelopipedon is a folid figure contained by fix quadrilateral figures, whereof those that are opposite are parallel.

PROP. Ι. THEO R.

NE part of a right line cannot be in a plain fuperficies, and
another part above it.

For,