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 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 Radical Sign , √ : Thus , A , B , indicate that the square root of A , and the cube root of ...
... multiplied 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 Radical Sign , √ : Thus , A , B , indicate that the square root of A , and the cube root of ...
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 C D = A B C B ' we have , D ; or , AC : 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 ...
... Multiplying both members by C D = A B C B ' we have , D ; or , AC : 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 ...
Page 55
... multiply both terms of this fraction by m , its value will not be changed ; and we shall have , mB B MA A = 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 A = 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 AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence