## Elements of Geometry |

### From inside the book

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**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 quadrilateral figures we distinguish ; The square ... Page 13

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**hypothenuse**and a side of the one are equal to the**hypothenuse**and a side of the other , each to each . Demonstration . Let the**hypothenuse**AC DF ( fig . 33 ) , and Fig . 33 . the side AB = DE ; the right - angled triangle ABC will be ... Page 39

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**hypothenuse**CA common , and the side CB = CD ; therefore AD = AB , and at the same time the angle CAD CAB . = PROBLEM . 153. To inscribe a circle in a given triangle ABC ( fig . 87 ) . Fig . 87 . Bisect the angles A and B of the ... Page 50

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**hypothenuse**of a right - angled triangle is equal to the sum of the squares described upon the two other sides . Demonstration . Let ABC ( fig . 109 ) be a triangle right - angled at A. Having constructed squares upon the three sides ... Page 51

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**hypothenuse**minus -2 the square of the other side ; or AB = BC — AC . - 188. Corollary 1. Let ABCD ( fig . 118 ) be ...**hypothenuse**is to the square of one of the sides of the right angle , as the**hypothenuse**is to the segment adjacent ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAD 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 and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence