## Elements of Geometry and the First Principles of Modern Geometry |

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### Common terms and phrases

ABCD altitude axis base bisect called centre chord circle circumference circumscribed common cone congruent construct contained conversely corresponding cylinder diagonals diameter difference dihedrals direction distance divided draw edges element equal equally distant equations EXERCISE extremities face angles fall figure follows formed four given gives greater hence HYPOTH included inscribed intersection joining lateral less lines drawn locus manner measure meet number of sides opposite sides parallel parallelogram pass perpendicular plane polar pole polygon polyhedral polyhedron position prism Problem PROOF proportional PROVED pyramid radii radius regular respectively right angles SCHOLIUM segments shown sides similar solid SOLUTION sphere spherical square straight line supplements surface symmetrical tangent Theorem third triangle triangle ABC vertex vertices volume

### Popular passages

Page 19 - IF two triangles have two sides of the one equal to two sides of the...

Page 34 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.

Page 14 - A Polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a pentagon; one of six sides, a hexagon; one of seven sides, a heptagon; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon, &c.

Page 75 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.

Page 170 - Two prisms are to each other as the products of their bases by their altitudes ; prisms having equivalent bases are to each other as their altitudes; prisms having equal altitudes are to each other as their bases ; prisms having equivalent bases and equal altitudes are equivalent.

Page 69 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.