## Elements of Geometry |

### From inside the book

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**line**is length without breadth . The extremities of a**line**are called points . A point , therefore , has no ...**AC**, ( fig . 2 , ) meet , the quan- Fig . 2 . tity , whether greater or less , by which they depart from each other as to ... 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 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 ... Page 9

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**AC**( fig . 28 ) , then will Fig . 28 . the angle C be equal to B. Draw the straight**line**AD from the vertex A to the point D , the middle of the base BC ; the two triangles ABD , ADC , will have the three sides of the one equal to 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