## Elements of Geometry and Trigonometry |

### From inside the book

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Page 12

... angles , are named

... angles , are named

**homologous sides**or angles . Definitions of terms employed in Geometry . An axiom is a self - evident proposition . A theorem is a truth , which becomes evident by means of a train of reasoning called a demonstration ... Page 68

... angles of the one equal to the angles of the other , each to each , and the sides about the equal angles proportional . 2. Any two sides , or any two angles , which have like po- sitions in two similar figures , are called

... angles of the one equal to the angles of the other , each to each , and the sides about the equal angles proportional . 2. Any two sides , or any two angles , which have like po- sitions in two similar figures , are called

**homologous sides**... Page 84

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**homologous sides**propor- tional , and are similar . Let ABC , CDE be two triangles which have their angles equal each to each , namely , BAC - CDE , ABC - DCE and ACB - DEC ; then the**homologous sides**, or the sides adjacent to the equal ... Page 85

... sides are opposite to the equal angles ; thus the angle ACB being equal to DEC , the side AB is homologous to DC ; in like manner , AC and DE are homologous , because opposite to the equal angles ABC , DCE . When the

... sides are opposite to the equal angles ; thus the angle ACB being equal to DEC , the side AB is homologous to DC ; in like manner , AC and DE are homologous , because opposite to the equal angles ABC , DCE . When the

**homologous sides**... Page 87

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**homologous sides**parallel , or perpendicular to each other , are similar . Let BAC , EDF , be two triangles . First . If the side AB is parallel to DE , and BC to EF , the angle ABC will be equal to DEF ( Book I. Prop . XXIV . ) ; if AC ...### Other editions - View all

### Common terms and phrases

adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex