Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 28
... . VII . ) , B4 C E GI + IC > GC , and BI + IA > AB ; whence , by addition , recollecting that the sum of BI and IC is equal to BC , and the sum of GI and IA , to GA , we have , AG + BC > AB + GC Or , since AG = AB , and GC = 28 GEOMETRY .
... . VII . ) , B4 C E GI + IC > GC , and BI + IA > AB ; whence , by addition , recollecting that the sum of BI and IC is equal to BC , and the sum of GI and IA , to GA , we have , AG + BC > AB + GC Or , since AG = AB , and GC = 28 GEOMETRY .
Page 52
... whence , :: clearing of fractions , we have , BC AD ; B D = A C ; which was to be proved . Cor . If B is equal to C , there will be but three pro- case , the square of the mean is portional quantities ; in this equal to the product of ...
... whence , :: clearing of fractions , we have , BC AD ; B D = A C ; which was to be proved . Cor . If B is equal to C , there will be but three pro- case , the square of the mean is portional quantities ; in this equal to the product of ...
Page 53
... whence , and , A B F : G ; whence , :: 1424 D = Ā ; В G A F From Axiom 1 , we have , D G व = F ; whence , C D :: F : G ; which was to be proved . Cor . If the antecedents , in two proportions , are the same the consequents will be ...
... whence , and , A B F : G ; whence , :: 1424 D = Ā ; В G A F From Axiom 1 , we have , D G व = F ; whence , C D :: F : G ; which was to be proved . Cor . If the antecedents , in two proportions , are the same the consequents will be ...
Page 54
... whence , Ā C If we take the reciprocals of both members ( A. 7 ) , we have , A C = ; whence , B A :: D : C ; B D which was to be proved . PROPOSITION VI . THEOREM . If four quantities are in proportion , they will be in pro- portion by ...
... whence , Ā C If we take the reciprocals of both members ( A. 7 ) , we have , A C = ; whence , B A :: D : C ; B D which was to be proved . PROPOSITION VI . THEOREM . If four quantities are in proportion , they will be in pro- portion by ...
Page 55
... whence , = A C If we multiply both terms of the first member by m , and both terms of the second member by n , we shall have , = MA mB nD nd i mB whence , mA :: nC nD .; which was to be proved . PROPOSITION IX . THEOREM . If two ...
... whence , = A C If we multiply both terms of the first member by m , and both terms of the second member by n , we shall have , = MA mB nD nd i mB whence , mA :: nC nD .; which was to be proved . PROPOSITION IX . THEOREM . If two ...
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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