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 29
... less than BC ; or , ince GC EF , we have , = D A BC > EF . B G СЕ 3o . When G is within the triangle ABC . From ... less than , EDF In the former case , BC would be equal to EF ( P. V. ) , and in the latter case , BC would be less than ...
... less than BC ; or , ince GC EF , we have , = D A BC > EF . B G СЕ 3o . When G is within the triangle ABC . From ... less than , EDF In the former case , BC would be equal to EF ( P. V. ) , and in the latter case , BC would be less than ...
Page 30
... less than D , the side BC would be less than EF . But BC is equal to EF , by hypothesis ; therefore , the angle A can neither be greater nor less than D : hence , it must be equal to it . The two triangles have , therefore , two sides ...
... less than D , the side BC would be less than EF . But BC is equal to EF , by hypothesis ; therefore , the angle A can neither be greater nor less than D : hence , it must be equal to it . The two triangles have , therefore , two sides ...
Page 32
... less than ABC , the side AB would be less than the side AC , from what has just been proved ; if ACB were equal to ABC , the side AB would be equal to AC , by Prop . XII .; but both conclusions are contrary to the hypothesis : hence ...
... less than ABC , the side AB would be less than the side AC , from what has just been proved ; if ACB were equal to ABC , the side AB would be equal to AC , by Prop . XII .; but both conclusions are contrary to the hypothesis : hence ...
Page 33
... less than , nor equal to , ABC ; it must , therefore , be greater ; which was to be proved . PROPOSITION XIV . THEOREM . From a given point only one perpendicular can be drawn to a given straight line . Let A be a given point , and AB ...
... less than , nor equal to , ABC ; it must , therefore , be greater ; which was to be proved . PROPOSITION XIV . THEOREM . From a given point only one perpendicular can be drawn to a given straight line . Let A be a given point , and AB ...
Page 34
... less than any of the oblique lines , AC will be equal to AE , and AD greater than AC . D F BE Prolong AB until BF is equal to AB , and draw FC , FD . 1o . In the triangles ABC , FBC , we have the side AB equal to BF , by construction ...
... less than any of the oblique lines , AC will be equal to AE , and AD greater than AC . D F BE Prolong AB until BF is equal to AB , and draw FC , FD . 1o . In the triangles ABC , FBC , we have the side AB equal to BF , by construction ...
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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