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 10
... multiplied The Sign of Division , ÷ : A Thus , A ÷ B , or , B ' indicates that A is to be divided by B. The Exponential Sign : Thus , A3 , indicates that A is to be taken three times as a factor , or raised to the third power . The ...
... multiplied The Sign of Division , ÷ : A Thus , A ÷ B , or , B ' indicates that A is to be divided by B. The Exponential Sign : Thus , A3 , 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 are equal . 7. If equals are divided by equals , the quotients are 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 angles are ...
... multiplied by equals , the products are equal . 7. If equals are divided by equals , the quotients are 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 angles are ...
Page 53
... . 10. Equimultiples of two or more quantities , are the products obtained by multiplying each by the same quan tity . Thus , mA and mB , are equimultiples of A and B. / PROPOSITION I. THEOREM . If four quantities are in BOOK II . 53.
... . 10. Equimultiples of two or more quantities , are the products obtained by multiplying each by the same quan tity . Thus , mA and mB , are equimultiples of A and B. / PROPOSITION I. THEOREM . If four quantities are in BOOK II . 53.
Page 55
... Multiplying each member by C A = D B which was to be proved . or B whence , = A C B " we have , A : C C : B : D ; :: 210 PROPOSITION IV . THEOREM . If one couplet in each of two proportions is the same , the other couplets form a ...
... Multiplying each member by C A = D B which was to be proved . or B whence , = A C B " we have , A : C C : B : D ; :: 210 PROPOSITION IV . THEOREM . If one couplet in each of two proportions is the same , the other couplets form a ...
Page 57
... multiply each term of this fraction by m , its value will not be changed ; and we shall have , mB B = ; whence , MA : mB :: A : B ; та A which was to be proved . PROPOSITION VIII . THEOREM . If four quantities are in proportion , any ...
... multiply each term of this fraction by m , its value will not be changed ; and we shall have , mB B = ; whence , MA : mB :: A : B ; та A 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 AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence