Elements of Geometry |
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Page 43
... 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 ...
... 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
... 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 ...
... 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
... 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 ...
... 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
... 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 ...
... 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
... 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 ) ...
... 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 ) ...
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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