## Elements of Geometry |

### From inside the book

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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

... 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

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**BC**; therefore the triangle DEF is equal to the triangle ABC ( 26 ) . 37. Corollary . When , in two triangles , these ...**side**FD will take the direction CA , and therefore the point D will be somewhere in CA ; whence the point D , which ... Page 8

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**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 ... Page 9

... BC ; therefore EF < BC . Case II . If the point G ( fig . 26 ) fall upon the

... BC ; therefore EF < BC . Case II . 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

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**side**AC will be equal to the**side**AB . For , if these**sides**are not equal , let AB be the greater . Take BDAC , and join DC . The angle DBC is , by hypothesis , equal to ACB , and the two**sides**DB ,**BC**...**side**. Demonstration . 1. Let the ...### 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