Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
From inside the book
Results 1-5 of 37
Page 28
... GA 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 = 28 GEOMETRY .
... GA 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 = 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 , and , A : B :: F : G ; whence , [ [ = Ā C ; B G = A F From Axiom 1 , we have , D G = ट ; 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 , and , A : B :: F : G ; whence , [ [ = Ā C ; B G = A F From Axiom 1 , we have , D G = ट ; 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 , = If we take the reciprocals of both members ( A. 7 ) , we have , A C B Ꭰ ; = whence , B : A :: D : 0 ; which was to be proved . PROPOSITION VI . THEOREM . If four quantities are in proportion , they will be in pro- portion by ...
... whence , = If we take the reciprocals of both members ( A. 7 ) , we have , A C B Ꭰ ; = whence , B : A :: D : 0 ; which was to be proved . PROPOSITION VI . THEOREM . If four quantities are in proportion , they will be in pro- portion by ...
Page 55
... whence , : = · • B D Ā C 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 = MA nC ; whence , mA : mB :: nC : nD ; which was to be proved . PROPOSITION IX . THEOREM ...
... whence , : = · • B D Ā C 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 = MA nC ; whence , mA : mB :: nC : nD ; which was to be proved . PROPOSITION IX . THEOREM ...
Other editions - View all
Common terms and phrases
AB² AC² 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 straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin 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 polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence