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 103
... described on AB and BC . The part CBIG is equal to the rect- angle of AB and BC ; the part DGLK is also equal to the rect- K E D A C B angle of AB and BC . If from the whole figure ABILKE , the two parts CBIG and DGLK be taken , there ...
... described on AB and BC . The part CBIG is equal to the rect- angle of AB and BC ; the part DGLK is also equal to the rect- K E D A C B angle of AB and BC . If from the whole figure ABILKE , the two parts CBIG and DGLK be taken , there ...
Page 104
... described on the hypothenuse of a right - angled triangle , is equal to the sum of the squares described on the other two sides . Let ABC be a triangle , right - angled at A : then will B02 = AB2 + AC2 . Construct the square BG on the ...
... described on the hypothenuse of a right - angled triangle , is equal to the sum of the squares described on the other two sides . Let ABC be a triangle , right - angled at A : then will B02 = AB2 + AC2 . Construct the square BG on the ...
Page 106
... described on the diagonal of a square is double the given square . For , the square of the diagonal is equal to the sum of the squares of the two sides ; but the square of each side is equal to the given square : hence , = AC2 2AB2 ; or ...
... described on the diagonal of a square is double the given square . For , the square of the diagonal is equal to the sum of the squares of the two sides ; but the square of each side is equal to the given square : hence , = AC2 2AB2 ; or ...
Page 108
... described on two sides is equal to the square described on the third side . PROPOSITION XIV . THEOREM . In any triangle , the sum of the squares described on two sides is equal to twice the square of half the third side , increased by ...
... described on two sides is equal to the square described on the third side . PROPOSITION XIV . THEOREM . In any triangle , the sum of the squares described on two sides is equal to twice the square of half the third side , increased by ...
Page 137
... described from O as a centre , with OP as a radius , it will be tangent to all of the sides or the polygon , and consequently , will be inscribed in it ; which was to be proved . Scholium . If the circumference of a circle be divided ...
... described from O as a centre , with OP as a radius , it will be tangent to all of the sides or the polygon , and consequently , will be inscribed in it ; which was to be proved . Scholium . If the circumference of a circle be divided ...
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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