## Elements of Geometry and Trigonometry |

### From inside the book

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**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 . A problem is a ... Page 68

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**homologous**sides or angles . A 3. In two different circles , similar arcs , sectors , or segments , are those which correspond to equal angles at the centre . Thus , if the angles A and O are equal , the arc BC will be similar to DE ... 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 ... Page 85

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**homologous**to DC ; in like manner , AC and DE are**homologous**, because opposite to the equal angles ABC , DCE . When the**homologous**sides are de- termined , it is easy to form the proportions : AB : DC : AC : DE :: BC : CE . PROPOSITION ... Page 87

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**homologous**sides parallel , or perpendicular to each other , are similar . Let BAC , EDF , be two triangles . First ...**homologous**sides are the perpendicular ones . Thus in the latter case DE is**homologous**with AB , DF with 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