## Elements of Geometry |

### From inside the book

Results 1-5 of 58

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

...

...

**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

...

...

**BC**= EF , B = E , and CF , 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**... Page 9

... BC ; therefore EF < BC . Case 11. If the point G ( fig . 26 ) fall upon the

... BC ; therefore EF < BC . Case 11. 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. Let the ...### 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