## Elements of Geometry |

### From inside the book

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**joining**those points lies wholly in that surface . 7. Every surface which is neither a plane , nor composed of planes , is a curved surface . 8. A solid is that which unites the three dimensions of ex- ension . 9. When two straight ... Page 2

... ) , which has its sides equal , without having its angles right angles ; Fig . 15 . The trapezoid ( fig . 15 ) , which has two only of its sides parallel . 18. A diagonal is a line which

... ) , which has its sides equal , without having its angles right angles ; Fig . 15 . The trapezoid ( fig . 15 ) , which has two only of its sides parallel . 18. A diagonal is a line which

**joins**the vertices 2 Elements of Geometry . Page 3

Adrien Marie Legendre. 18. A diagonal is a line which

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 8

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**join**CG ; then the triangle GAC is equal to the triangle EDF ( 36 ) , and therefore CG = EF . Now there may be three cases , according as the point & falls without the triangle ABC , on the side BC , or within the triangle . Case 1 ... Page 10

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**join**DC . The angle DBC is , by hypothesis , equal to ACB , and the two sides DB , BC , are equal to the two sides AC , CB , each to each ; therefore the triangle DBC is equal to the triangle ACB ( 36 ) ; but a part cannot be equal to ...### 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 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