## 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 , CD ( fig . 93 ) , considered as bases . Fig . 93 . The**altitude**of a triangle is the perpendicular AD ( fig . 94 ) , Fig . 94 ... Page 44

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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 . 168. Every triangle ABC ( fig . 98 ) is half of a parallelogram ABCD of the same ... Page 45

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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 ... Page 46

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**altitude**AD ; they are consequently 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 proportions ... Page 47

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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 ABX BE ( 173 ) ; therefore ...### Other editions - View all

### Common terms and phrases

ABC fig ABCD adjacent altitude angle ACB applied base called centre chord circ circle circumference circumscribed common cone consequently considered construction contained convex surface Corollary cylinder Demonstration described diameter difference distance divided draw drawn entire equal equivalent example extremities faces figure follows formed four give given greater half hence homologous sides inclination inscribed join less let fall manner mean measure meet moreover multiplied namely opposite parallel parallelogram parallelopiped pass perimeter perpendicular plane plane angles polyedron polygon prism PROBLEM proportional proposition pyramid radii radius ratio reason rectangle regular polygon respect right angles Scholium sector segment sides similar solid angle Solution sphere spherical square straight line suppose surface taken THEOREM third triangle ABC triangular pyramids vertex vertices whence