Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 4
... Equations of the Point , the Straight Line , the Conic Sections , and Surfaces of the first and second order . Babies ' Bifferential and Integral Calculus . Babies ' Descriptive Geometry - With its application to Spherical Trigonome ...
... Equations of the Point , the Straight Line , the Conic Sections , and Surfaces of the first and second order . Babies ' Bifferential and Integral Calculus . Babies ' Descriptive Geometry - With its application to Spherical Trigonome ...
Page 11
... equation . part on the left of the sign of equality , is called the first member ; that on the right , the second member . The Sign of Inequality , < : Thus , AB , indicates that the square root of A is less than the cube root of B. The ...
... equation . part on the left of the sign of equality , is called the first member ; that on the right , the second member . The Sign of Inequality , < : Thus , AB , indicates that the square root of A is less than the cube root of B. The ...
Page 52
... AD = BC , by changing the members of the equation , we have , BC = AD ; dividing both members by AC , we have , B = D T ' or A : B :: C : D ; A which was to be proved . PROPOSITION III . THEOREM . If four quantities are in 52 GEOMETRY .
... AD = BC , by changing the members of the equation , we have , BC = AD ; dividing both members by AC , we have , B = D T ' or A : B :: C : D ; A which was to be proved . PROPOSITION III . THEOREM . If four quantities are in 52 GEOMETRY .
Page 58
... equations , member by member , we have ; BF DH = AE CG ; whence , AE : BF :: CG : DH ; which was to be proved . Cor . 1. If the corresponding terms of two proportions are equal , each term of the resulting proportion will be the square ...
... equations , member by member , we have ; BF DH = AE CG ; whence , AE : BF :: CG : DH ; which was to be proved . Cor . 1. If the corresponding terms of two proportions are equal , each term of the resulting proportion will be the square ...
Page 109
... equations , member to member ( A. 2 ) , recollect . ing that BE is equal to EC , we have , AB2 + A02 2BE2 + 2 EA2 ; which was to be proved . Cor . Let ABCD be a parallelogram , and BD , AC , its diagonals . Then , since the diagonals ...
... equations , member to member ( A. 2 ) , recollect . ing that BE is equal to EC , we have , AB2 + A02 2BE2 + 2 EA2 ; which was to be proved . Cor . Let ABCD be a parallelogram , and BD , AC , its diagonals . Then , since the diagonals ...
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Common terms and phrases
ABĀ² 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