Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 22
... proved . Cor . 1. If one of the angles about all of the others will be right angles also . each of its adjacent angles will be a right angle ; and from the proposition just demonstrated , its opposite angle will also be a right angle ...
... proved . Cor . 1. If one of the angles about all of the others will be right angles also . each of its adjacent angles will be a right angle ; and from the proposition just demonstrated , its opposite angle will also be a right angle ...
Page 23
... proved , and then continuing the reasoning until the assumed hypothesis is shown to be false . Its contradictory is thus proved to be true . This method of demonstration is often used in Geometry . PROPOSITION IV . THEOREM . If a ...
... proved , and then continuing the reasoning until the assumed hypothesis is shown to be false . Its contradictory is thus proved to be true . This method of demonstration is often used in Geometry . PROPOSITION IV . THEOREM . If a ...
Page 26
... proved . · PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is greater than the third side . Let ABC be a triangle : then will the sum of any two sides , as AB , BC , be greater than the third side For , the distance ...
... proved . · PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is greater than the third side . Let ABC be a triangle : then will the sum of any two sides , as AB , BC , be greater than the third side For , the distance ...
Page 27
... is equal to AC , we have , BD + DC < BA + AC . But it was shown that BO + OC is less than BD + DC ; still more , then , is BO + 00 less than BA + AC ; which was to be proved . PROPOSITION IX . THEOREM . If two triangles have two BOOK I. 27.
... is equal to AC , we have , BD + DC < BA + AC . But it was shown that BO + OC is less than BD + DC ; still more , then , is BO + 00 less than BA + AC ; which was to be proved . PROPOSITION IX . THEOREM . If two triangles have two BOOK I. 27.
Page 31
... proved . B D Cor . 1. An equilateral triangle is equiangular . Cor . 2. The angle BAD is equal to DAC , and BDA to CDA hence , the last two are right angles . Conse- quently , a line drawn from the vertex of an isosceles triangle . to ...
... proved . B D Cor . 1. An equilateral triangle is equiangular . Cor . 2. The angle BAD is equal to DAC , and BDA to CDA hence , the last two are right angles . Conse- quently , a line drawn from the vertex of an isosceles triangle . to ...
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Common terms and phrases
AB² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following