## Elements of Geometry |

### From inside the book

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**angles**not adjacent , as AC ( fig . 42 ) . 19. An equilateral polygon is one which ...**sides**equal , each to each , and placed in the same order ; that is , when ...**homologous**( A ) . 21. An Axiom is a proposition , the truth of which is ... Page 45

... sides proportional . By

... sides proportional . By

**homologous sides**are to be understood those , which have the same position in the two figures , or which are adjacent to equal angles . The angles , which are equal in the two figures , are called**homologous angles**... Page 58

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**homologous sides**proportional , and are similar . Demonstration . Let ABC , CDE ( fig . 119 ) , be two triangles , which have their angles equal , each to each , namely , BAC - CDE , ABCDCE , and ACB - DEC ; the**homologous sides**, or ... Page 59

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**homologous sides**are opposite to equal angles ; thus , the angle ACB being equal to DEC , the side AB is homologous to DC ; likewise AC , DE , are homologous , being opposite to the equal angles ABC , DCE . Knowing the**homologous sides**... Page 61

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**homologous sides**are the parallel sides , and in the second the**homologous sides**are those which are perpendicular to each other . Thus in the second case , DE is homologous to AB , DF to AC , and EF to BC . The case of the ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence