## 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 other , each to each . Demonstration . Let the**hypothenuse**ACDF ( fig . 33 ) , and Fig . 33 . the side AB = DE ; the right - angled triangle ABC will be equal to the right - angled triangle DEF . The ... Page 41

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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 ) . Bisect the angles A and B of the triangle by the ... Page 52

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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 53

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**hypothenuse**minus the square of the other side ; or AB = AB = BC — AČ . 188. Corollary II . Let ABCD ( fig . 118 ) ...**hypothenuse**is to the square of one of the sides of the right angle , as the**hypothenuse**is to the segment adjacent to ...### 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