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 106
... hypothenuse . For , by combining the propor- tions of the preceding corollary ( B. II . , P. IV . , C. ) , we have , B AB2 AC2 :: BD : DC . D Cor . 4. The square described on the diagonal of a square is double the given square . For ...
... hypothenuse . For , by combining the propor- tions of the preceding corollary ( B. II . , P. IV . , C. ) , we have , B AB2 AC2 :: BD : DC . D Cor . 4. The square described on the diagonal of a square is double the given square . For ...
Page 119
... hypothenuse and the adjacent segment : 3 ° . The perpendicular will be a mean proportional between the two segments of the hypothenuse . 1o . Let ABC be a right - angled triangle , A the vertex of the right angle , BC the hypo- thenuse ...
... hypothenuse and the adjacent segment : 3 ° . The perpendicular will be a mean proportional between the two segments of the hypothenuse . 1o . Let ABC be a right - angled triangle , A the vertex of the right angle , BC the hypo- thenuse ...
Page 126
... hypothenuse is equal to the sum of the squares of the other sides , and conse- quently , the polygon on the hypothenuse will be equal to he sum of the polygons on the other sides . PROPOSITION XXVIII . THEOREM . If two chords intersect ...
... hypothenuse is equal to the sum of the squares of the other sides , and conse- quently , the polygon on the hypothenuse will be equal to he sum of the polygons on the other sides . PROPOSITION XXVIII . THEOREM . If two chords intersect ...
Page 212
... hypothenuse SB , is called the convex surface of the cone ; the circle generated by the side AB , is called the base of the cone ; and the point S , is called the vertex of the cone ; the distance from the vertex to any point in the ...
... hypothenuse SB , is called the convex surface of the cone ; the circle generated by the side AB , is called the base of the cone ; and the point S , is called the vertex of the cone ; the distance from the vertex to any point in the ...
Page
... angled triangles , in each of which we know the hypothenuse and the base ; hence , the angles of these triangles may be found , and consequently , those of the given triangle . EXAMPLES . 1. Given α = 40 , b = 46 PLANE TRIGONOMETRY .
... angled triangles , in each of which we know the hypothenuse and the base ; hence , the angles of these triangles may be found , and consequently , those of the given triangle . EXAMPLES . 1. Given α = 40 , b = 46 PLANE TRIGONOMETRY .
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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