## Elements of Geometry |

### From inside the book

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**altitude**of a parallelogram is the perpendicular which measures the distance between the opposite sides AB , C.D ( fig . 93 ) , considered as bases . The**altitude**of a triangle is the perpendicular AD ( fig . 94 ) , let fall from the ... Page 46

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**altitude**, are equivalent . 167. Corollary . Every parallelogram ABCD ( fig . 97 ) is equivalent to a rectangle of the same base and**altitude**. THEOREM . 2 Fig . 98 . 168. Every triangle ABC ( fig . 98 ) is half of a parallelogram ABCD ... Page 47

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**altitude**, are to each other as their bases AB , AE . THEOREM . 172. Any two rectangles ABCD , AEGF ( fig . 101 ) , are to each Fig . 101 other as the products of their bases by their**altitudes**; that is , ABCD : AEGF :: AB × AD : AE ... Page 48

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**altitude**AD ; they are , con- sequently , to each other as their bases AB , AE . Likewise the two rectangles AEHD , AEGF , have the same**altitude**AE ; these are therefore to each other as their bases AD , AF . We have thus the two ... Page 49

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**altitude**. Demonstration . The parallelogram ABCD ( fig . 97 ) is equiva- Fig . 97 . lent to the rectangle ABEF , which has the same base AB and the same**altitude**BE ( 167 ) ; but this last has for its measure AB × BE ( 173 ) ...### 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