## Elements of Geometry |

### From inside the book

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**line**is length without breadth . The extremities of a**line**are called points ...**AC**, ( fig . 2 ) , meet , the quan- Fig . 2 . tity , whether greater or less ...**AC**, are its sides . An angle is sometimes denoted simply by the letter at ... Page 3

Adrien Marie Legendre. 18. A diagonal is a

Adrien Marie Legendre. 18. A diagonal is a

**line**which joins the vertices of two angles not adjacent , as**AC**( fig . 42 ) . 19. An equilateral polygon is one which has all its sides equal ; an equiangular polygon is one which has all its ... Page 6

... AC , CB , are in the same straight line . Demonstration . For if CB is not the

... AC , CB , are in the same straight line . Demonstration . For if CB is not the

**line AC**produced , let CE be that line produced ; then , ACE being a straight line , the angles ACD , DCE , are together equal to two right angles ( 28 ) ... Page 7

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**AC**equal to the side DF ; the two trian- gles ABC , DEF , will be equal . Indeed the triangles may be so placed ...**lines**BA and CA , can only be at their intersection A ; therefore the two triangles ABC , Fig . 23 . Fig . 24 . Fig . Of ... Page 8

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**lines**OB , OC , to the extremities of BC , one of its sides , the sum of these**lines**will be less than that of AB ,**AC**, the two other sides . Demonstration . Let BO be produced till it meet the side**AC**in D ; the straight**line**OC is ...### 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