## A Treatise on Elementary Geometry: With Appendices Containing a Collection of Exercises for Students and an Introduction to Modern Geometry |

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### Common terms and phrases

ABCD altitude axis base bisects called centre chord circle circumference circumscribed coincide common cone construct contain Corollary cylinder Definition denote describe diagonals diameter diedral angle difference distance divided draw drawn edges equal equally distant equivalent expressed extremities faces figure fixed follows formed four given circles given plane given point given straight line greater hence homologous indefinitely inscribed intersection joining lateral less limit locus mean measure meet middle point one-half parallel parallelogram pass perimeter perpendicular plane plane MN polar pole polyedron polygon preceding prism problem proportional PROPOSITION proved pyramid quadrilateral quantities radii radius ratio rectangle respectively right angles Scholium secant segment sides similar sphere spherical square suppose surface symmetrical taken tangent tetraedron theorem third triangle ABC unit vertex vertices volume

### Popular passages

Page 96 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.

Page 118 - The area of a rectangle is equal to the product of its base and altitude.

Page 102 - In any triangle, the square of the side opposite to an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of these sides and the projection of the other upon that side.

Page 206 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.

Page 69 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.

Page 244 - The angle of two arcs of great circles is equal to the angle of their planes, and is measured by the arc of a great circle described from its vertex as a pole and included between its sides (produced if necessary). Let AB and AB...

Page 107 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.

Page 253 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...

Page 187 - A right prism is a prism •whose lateral edges are perpendicular to the planes of the bases.

Page 27 - The sum of the three angles of any triangle is equal to two right angles.