## Elements of Geometry |

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**bases**and equal alti- tudes , are equivalent . Demonstration . Let AB ( fig . 96 ) be the common**base**of the Fig . 96 . two parallelograms**ABCD**, ABEF ; since they are supposed to have the same altitude , the sides DC , FE , opposite to the ... Page 46

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**ABC**( fig . 98 ) is half of a parallelogram**ABCD**of the same**base**and altitude . Demonstration . The triangles**ABC**, ACD , are equal ( 81 ) ; therefore each is half of the parallelogram**ABCD**. 169. Corollary 1. A triangle**ABC**is half of ... Page 48

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**ABCD**, AEHD , have the same altitude AD ; they are , con- sequently , to each other as their**bases**AB , AE ...**base**by its altitude , provided that , by this product , we understand that of two numbers which are the num- ber of linear ... Page 49

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**ABCD**. 175. Corollary . Parallelograms of the same**base**are to each other as their altitudes , and parallelograms of the same altitude are to each other as their**bases**; for , A , B , C , being any three magnitudes whatever , we have ... Page 50

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**ABCD**is equivalent to the parallelogram ADKL , and has for its measure EF × AL . But AL = DK ; and , since the ...**base**AB , the point H will also be the middle of AD ; for the figure AHIL is a parallelogram , as well as DHIK , since 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