## The Elements of Plane and Solid Geometry: With Chapters on Mensuration and Modern Geometry (Google eBook) |

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A-BCD ABCD altitude angle ABC angles BAD apothem bisect centre of similitude chord circle ABC circumference cone Corollary 1.—The cylinder decagon describe diagonals diameter divided draw equal angles equal sides equiangular feet figure four right angles frustum given circle given straight line greater Hence included angle inscribed interior angles intersection Let ABC line joining lune meet middle point multiplied number of sides opposite angles parallelogram parallelopiped pass perimeter perpendicular plane pole polyedron prism Problem.—To produced Prop proportional Proposition 11 Proposition 13 proved pyramid quadrilateral radical axis radii radius rectangle contained regular polygon right angles Scholium segment semicircle similar slant height solid solid angle sphere spherical angle spherical triangle square surface symmetrical tangent theorem Theorem.—If three sides triangle ABC vertex

### Popular passages

Page 54 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.

Page 75 - The angles in the same segment of a circle are equal to one another.

Page 79 - If a straight line touch a circle, and from the point of contact a...

Page 128 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the...

Page 15 - AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals the wholes are equal. 3. If equals be taken from equals the remainders are equal.

Page 108 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 62 - If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section.

Page 166 - A be a solid angle contained by any number of plane angles BAC, CAD, DAE, EAF, FAB: these together are less than four right angles. Let the planes...

Page 15 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line.

Page 127 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the...