Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 10
... multiplied by B. The Sign of Division , ÷ : Thus , AB , or , divided by B .. A B ' The Exponential Sign : indicates that A is to be Thus , 43 , indicates that A is to be taken three times as a factor , or raised to the third power . The ...
... multiplied by B. The Sign of Division , ÷ : Thus , AB , or , divided by B .. A B ' The Exponential Sign : indicates that A is to be Thus , 43 , indicates that A is to be taken three times as a factor , or raised to the third power . The ...
Page 18
... multiplied by equals , the products will be equal . 7. If equals be divided by equals , the quotients will be equal . 8. The whole is greater than any of its parts . 9. The whole is equal to the sum of all its parts . 10. All right ...
... multiplied by equals , the products will be equal . 7. If equals be divided by equals , the quotients will be equal . 8. The whole is greater than any of its parts . 9. The whole is equal to the sum of all its parts . 10. All right ...
Page 51
... . Equimultiples of two or more quantities , are the pro- Jucts obtained by multiplying both by the same quantity . Thus , mA and mB , are equimultiples of A and B. PROPOSITION I THEOREM . If four quantities are in proportion BOOK II . 51.
... . Equimultiples of two or more quantities , are the pro- Jucts obtained by multiplying both by the same quantity . Thus , mA and mB , are equimultiples of A and B. PROPOSITION I THEOREM . If four quantities are in proportion BOOK II . 51.
Page 53
... Multiplying both members by we have , B C D = A B ; A : C :: or , B : D ; which was to be proved . PROPOSITION IV . THEOREM . If one couplet in each of two proportions is the same , the other couplets will form a proportion . Assume the ...
... Multiplying both members by we have , B C D = A B ; A : C :: or , B : D ; which was to be proved . PROPOSITION IV . THEOREM . If one couplet in each of two proportions is the same , the other couplets will form a proportion . Assume the ...
Page 55
... multiply both terms of this fraction by m , its value will not be changed ; and we shall have , mB B = ; MA Α : whence , mA : mB A : B ; which was to be proved . PROPOSITION VIII . THEOREM . If four quantities are in proportion , any ...
... multiply both terms of this fraction by m , its value will not be changed ; and we shall have , mB B = ; MA Α : whence , mA : mB A : B ; which was to be proved . PROPOSITION VIII . THEOREM . If four quantities are in proportion , any ...
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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