## 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 conse- quently 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 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 AB × BE ( 173 ) ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAD 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 and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence