Elements of Geometry |
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Page 2
... 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 ...
... 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
... 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 ...
... 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
... 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 ...
... 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
... 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 ...
... 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
... 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 ...
... 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 ...
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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