Elements of Geometry |
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Page 2
... sides are equal . 16. A right - angled triangle is that which has one right angle . The side 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 ...
... sides are equal . 16. A right - angled triangle is that which has one right angle . The side 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 ...
Page 7
... side AB equal to the side DE , and the side AC equal to the side DF ; the two triangles ABC , DEF , will be equal ... BC ; therefore the triangle DEF is equal to the triangle ABC ( 26 ) . 37. Corollary . When , in two triangles ...
... side AB equal to the side DE , and the side AC equal to the side DF ; the two triangles ABC , DEF , will be equal ... BC ; therefore the triangle DEF is equal to the triangle ABC ( 26 ) . 37. Corollary . When , in two triangles ...
Page 8
... BC = EF , B = E , and C = F , we may thence infer , that the other three are also equal , namely , AB = DE , AC = DF , and A = D. THEOREM . 40. One side of a triangle is less than the sum of the other two . Demonstration . The straight line ...
... BC = EF , B = E , and C = F , we may thence infer , that the other three are also equal , namely , AB = DE , AC = DF , and A = D. THEOREM . 40. One side of a triangle is less than the sum of the other two . Demonstration . The straight line ...
Page 9
... BC ; therefore EF < BC . Case 1. If the point G ( fig . 26 ) fall upon the side BC , then Fig . 26 it is evident that GC , or its equal EF , is less than BC . Case III . If the point G ( fig . 27 ) fall within the triangle Fig . 27 ...
... BC ; therefore EF < BC . Case 1. If the point G ( fig . 26 ) fall upon the side BC , then Fig . 26 it is evident that GC , or its equal EF , is less than BC . Case III . If the point G ( fig . 27 ) fall within the triangle Fig . 27 ...
Page 10
... side AC will be equal to the side AB . For , if these sides are not equal , let AB be the greater . Take BD = AC , and join DC . The angle DBC is , by hypothesis , equal to ACB , and the two sides DB , BC ... side . Demonstration . 1 ...
... side AC will be equal to the side AB . For , if these sides are not equal , let AB be the greater . Take BD = AC , and join DC . The angle DBC is , by hypothesis , equal to ACB , and the two sides DB , BC ... side . Demonstration . 1 ...
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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 convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent 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 pyramid S-ABC 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