Elements of Geometry and Trigonometry |
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Page 10
... multiplied Thus , AB , or , A divided by B. B ' indicates that A is to be The Exponential Sign : 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 ...
... multiplied Thus , AB , or , A divided by B. B ' indicates that A is to be The Exponential Sign : 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 ...
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
... 10 Equimultiples of two or more quantities , are the pro- ducts 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.
... 10 Equimultiples of two or more quantities , are the pro- ducts 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 с A = D B D C B ' we have , B : D ; ; or , A : C :: 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 ...
... Multiplying both members by с A = D B D C B ' we have , B : D ; ; or , A : C :: 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 ...
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
ABCD ACē adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence