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 47
... ABCD be a parallelogram : then will AB be equal to DC , and AD to BC . D For , draw the diagonal BD . Then , because AB and DC are parallel , the A angle DBA is equal to its alternate angle BDC ( P. XX . , C. 2 ) : and , because AD and ...
... ABCD be a parallelogram : then will AB be equal to DC , and AD to BC . D For , draw the diagonal BD . Then , because AB and DC are parallel , the A angle DBA is equal to its alternate angle BDC ( P. XX . , C. 2 ) : and , because AD and ...
Page 48
... ABCD , let AB be equal to DC , and AD to BC : then will it be a parallelogram . Then , the A Draw the diagonal DB . triangles ADB and CBD , will have D the sides of the one equal to the sides of the other , each to each ; and therefore ...
... ABCD , let AB be equal to DC , and AD to BC : then will it be a parallelogram . Then , the A Draw the diagonal DB . triangles ADB and CBD , will have D the sides of the one equal to the sides of the other , each to each ; and therefore ...
Page 49
... ABCD be a parallelogram , and B AC , BD , its diagonals : then will AE be equal to EC , and BE to ED . For , the triangles BEC and AED , have the angles EBC and ADE equal E ( P. XX . , C. 2 ) , the angles ECB and DAE equal , and the ...
... ABCD be a parallelogram , and B AC , BD , its diagonals : then will AE be equal to EC , and BE to ED . For , the triangles BEC and AED , have the angles EBC and ADE equal E ( P. XX . , C. 2 ) , the angles ECB and DAE equal , and the ...
Page 50
... A B C D , and read , A is to B , as C is to D. 8. A CONTINUED PROPORTION is one in which several ratios are successively equal to each other ; as , A : B :: 0 : D :: E : F :: G H , & c 4. There are four terms in every proportion . The ...
... A B C D , and read , A is to B , as C is to D. 8. A CONTINUED PROPORTION is one in which several ratios are successively equal to each other ; as , A : B :: 0 : D :: E : F :: G H , & c 4. There are four terms in every proportion . The ...
Page 53
... A B C D ; whence , : Multiplying both members by C D A B = or , which was to be proved . B = A C we have , A : C :: B : D ; PROPOSITION IV . THEOREM . If one couplet in each of two proportions is the same , the other couplets will form ...
... A B C D ; whence , : Multiplying both members by C D A B = or , which was to be proved . B = A C we have , A : C :: B : D ; PROPOSITION IV . THEOREM . If one couplet in each of two proportions is the same , the other couplets will form ...
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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