## Elements of Geometry |

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### Common terms and phrases

ABCD altitude approaches axis base bisector called centre chord circle circumference circumscribed coincide common cone construct contains corresponding curve cylinder describe diagonals diameter diedral angles difference distance divided draw drawn edges equal equivalent Exercise extremities faces figure Find formed four geometry given given point GIVEN—the greater half Hence included inscribed intersection lateral length less limit line joining locus mean measured meet method middle points parallel parallelogram parallelopiped pass perimeter perpendicular plane pole polyedron polygon prism PROBLEMS projection proportional PROPOSITION PROVE pyramid quadrilateral radii radius ratio rectangle respectively right angles right triangle segment sides similar similitude sphere spherical square straight line surface symmetrical tangent tetraedron THEOREM third triangle triangle ABC triedral unit vertex vertices volume

### Popular passages

Page 36 - If two triangles have two sides and the included angle of one, equal respectively to two sides and the included angle of the other, the triangles are equal. C...

Page 472 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.

Page 321 - The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and a mean proportional between the two bases of the frustum.

Page 211 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems.

Page 42 - ... greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 385 - Two triangles are congruent if (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other...

Page 144 - ... twice the product of one of these sides and the projection of the other side upon it.

Page 63 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.

Page 141 - If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment.

Page 153 - The product of two sides of a triangle is equal to the product of the diameter of the circumscribed circle and the altitude upon the third side.