## Elements of Geometry |

### From inside the book

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**ABCD**is a parallelogram . THEOREM . 84. If two opposite sides AB , CD ( fig . 44 ) , of a quadrilateral are equal and parallel , the two other sides will also be equal and parallel , and the figure**ABCD**will be a parallelogram ... Page 36

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**ABCD**are together equal to two right angles ; for the angle BAD has for its measure the half of the arc BCD , and the angle BCD has for its measure the half of the arc BAD ; hence the two angles BAD , BCD , taken together , have for ... Page 45

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**ABCD**, ABEF ; since they are supposed to have the same altitude , the sides DC , FE , opposite to the bases , will be situated in a line parallel to AB ( 78 ) . Now , by the nature of a parallelogram , AD = BC ( 81 ) , and AF BE ; for ... Page 46

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**ABCD**; therefore the two parallelograms**ABCD**, ABEF , which have the same base and the same altitude , are equivalent . 167. Corollary . Every parallelogram**ABCD**( fig . 97 ) is equivalent to a rectangle of the same base and altitude ... Page 47

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**ABCD**: AEFD :: AB : AE . Let us suppose , in the second place , that the bases AB , AE ( fig . 100 ) , are incommensurable ; we shall have , notwithstanding , Fig . 100 .**ABCD**: AEFD :: AB : AE . For , if this proportion be not true ...### 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