Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 45
... equal to the third part of two right angles ; so that , if the right angle ... bases , the sides of the polygon , except the two which form the angle A. It ... equal to two right angles , taken as many times as there are triangles ; that ...
... equal to the third part of two right angles ; so that , if the right angle ... bases , the sides of the polygon , except the two which form the angle A. It ... equal to two right angles , taken as many times as there are triangles ; that ...
Page 94
... bases ; one the upper , and the other , the lower base . 6. The ALTITUDE OF A TRAPEZOID , is the perpendicular ... equal bases and equal altitudes , are equal . Let the parallelograms ABCD and EFGH have equal bases and equal altitudes ...
... bases ; one the upper , and the other , the lower base . 6. The ALTITUDE OF A TRAPEZOID , is the perpendicular ... equal bases and equal altitudes , are equal . Let the parallelograms ABCD and EFGH have equal bases and equal altitudes ...
Page 95
... equal to the parallelogram EG ( A. 3 ) ; which was to be proved . PROPOSITION II . THEOREM . A triangle is equal to one - half of a parallelogram having an equal base and an equal altitude . Let the triangle ABC , and the parallelogram ...
... equal to the parallelogram EG ( A. 3 ) ; which was to be proved . PROPOSITION II . THEOREM . A triangle is equal to one - half of a parallelogram having an equal base and an equal altitude . Let the triangle ABC , and the parallelogram ...
Page 96
... equal altitudes , are proportional to their bases . There may be two cases : the bases may be commensu- rable , or they may be incommensurable . 1o . Let ABCD and HEFK , be two rectangles whose altitudes AD and HK are equal , and whose ...
... equal altitudes , are proportional to their bases . There may be two cases : the bases may be commensu- rable , or they may be incommensurable . 1o . Let ABCD and HEFK , be two rectangles whose altitudes AD and HK are equal , and whose ...
Page 97
... bases , let us sup- pose that 1 D FK C A ABCD : AEFD :: AB A0 ; : Divide AB into in which AO is greater than AE . equal parts , each less than OE ; at least one point of division , as I , will fall between E and 0 ; at this point , draw ...
... bases , let us sup- pose that 1 D FK C A ABCD : AEFD :: AB A0 ; : Divide AB into in which AO is greater than AE . equal parts , each less than OE ; at least one point of division , as I , will fall between E and 0 ; at this point , draw ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence