## Elements of Geometry |

### From inside the book

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**opposite**to the right angle is called the hypothenuse . Fig . 10. Thus ABC ( fig . 10 ) is a triangle right - angled at A , and the side BC is the hypothenuse . Fig . 11 . Fig . 12 . Fig . 13 . Fig . 14 . Fig . 15 . 17. Among ... Page 6

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**opposite**angle BCE . It may be demonstrated , in like manner , that the angle ACE is equal to its**opposite**angle BCD . 35. Scholium . The four angles , formed about a point by two straight lines which cut each other , are together equal ... Page 9

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**opposite**to equal sides ; thus , the equal angles A and D are op- posite to the equal sides BC and EF . THEOREM . 45. In an isosceles triangle , the angles**opposite**to the equal sides are equal . Demonstration . Let the side AB = AC ... Page 10

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**opposite**to the greater angle ; and conversely , of the two angles of a triangle , that is the greater , which is**opposite**to the greater side . Demonstration . 1. Let the angle C > B ( fig . 30 ) , then will the side AB ,**opposite**to ... Page 11

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**opposite**sides of the perpendicular , and at equal distances BC , BE , from it , are equal to one another ; 3. Of any two oblique lines AC , AD , or AE , AD , that which is more remote from the perpendicular is the greater ...### 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