Elements of Geometry and Trigonometry |
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Page 28
... , A D C F E GI + IC > GC , and BI + IA > AB ; whence , by addition , recollecting that the sum of BI and IC is equal to BC , and the sum of GI and IA , to GA , we have , AG + BC > AB + GC = Or , since AG AB , and GC EF 28 GEOMETRY .
... , A D C F E GI + IC > GC , and BI + IA > AB ; whence , by addition , recollecting that the sum of BI and IC is equal to BC , and the sum of GI and IA , to GA , we have , AG + BC > AB + GC = Or , since AG AB , and GC EF 28 GEOMETRY .
Page 52
... whence , ; A clearing of fractions , we have , BC = AD ; which was to be proved . Cor . If B is equal to C , there will be but three pro- portional quantities ; in this case , the square of the mean is equal to the product of the ...
... whence , ; A clearing of fractions , we have , BC = AD ; which was to be proved . Cor . If B is equal to C , there will be but three pro- portional quantities ; in this case , the square of the mean is equal to the product of the ...
Page 53
... whence , : A B G and , A : B :: F : G ; F G ; whence , Ā F From Axiom 1 , we have , D G C ; F whence , C : D :: F : G ; which was to be proved . Cor . If the antecedents , in two proportions , are the same , the consequents will be ...
... whence , : A B G and , A : B :: F : G ; F G ; whence , Ā F From Axiom 1 , we have , D G C ; F whence , C : D :: F : G ; which was to be proved . Cor . If the antecedents , in two proportions , are the same , the consequents will be ...
Page 54
... whence , A If we take the reciprocals of both members ( A. 7 ) , we have , A C D B ; whence , B A :: D : C ; which was to be proved . : PROPOSITION VI . THEOREM . If four quantities are in proportion , they will be in pro portion by ...
... whence , A If we take the reciprocals of both members ( A. 7 ) , we have , A C D B ; whence , B A :: D : C ; which was to be proved . : PROPOSITION VI . THEOREM . If four quantities are in proportion , they will be in pro portion by ...
Page 55
... whence , Ā If we multiply both terms of the first member by m , and both terms of the second member by n , we shall have , mB nD n C MA ; whence , m4 : mB :: nC : D ; which was to be proved . PROPOSITION IX . THEOREM . If two quantities ...
... whence , Ā If we multiply both terms of the first member by m , and both terms of the second member by n , we shall have , mB nD n C MA ; whence , m4 : mB :: nC : D ; which was to be proved . PROPOSITION IX . THEOREM . If two quantities ...
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
ABē ABCD ACē adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right-angled triangle Scholium secant segment semi-circumference side BC similar Sine slant height sphere spherical angle spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prisms upper base vertex vertices whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 100 - The area of a triangle is equal to half the product of its base by its altitude.
Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 59 - A chord is a straight line joining the extremities of an arc.
Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 123 - Similar triangles are to each other as the squares of their homologous sides.
Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...