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 iii
... corresponds more exactly to the idea intended . Many other departures have been made from the original text , the value and utility of which have been made manifest in the practical tests to which the work has been subjected . In the ...
... corresponds more exactly to the idea intended . Many other departures have been made from the original text , the value and utility of which have been made manifest in the practical tests to which the work has been subjected . In the ...
Page 12
... are equal in all their parts when each part of one is equal to the corresponding part of the other , when taken either in the same or in the reverse order . ELEMENTS OF GEOMETRY . BOOK I. ELEMENTARY PRINCIPLES . DEFINITIONS 12 GEOMETRY .
... are equal in all their parts when each part of one is equal to the corresponding part of the other , when taken either in the same or in the reverse order . ELEMENTS OF GEOMETRY . BOOK I. ELEMENTARY PRINCIPLES . DEFINITIONS 12 GEOMETRY .
Page 46
... corresponding exterior angle , is equal C / c to two right angles ( P. I. ) ; hence , the sum of all the inte- rior and exterior angles is equal to two right angles taker But the sum of as many times as the polygon 46 GEOMETRY .
... corresponding exterior angle , is equal C / c to two right angles ( P. I. ) ; hence , the sum of all the inte- rior and exterior angles is equal to two right angles taker But the sum of as many times as the polygon 46 GEOMETRY .
Page 59
... corresponding consequent . From the definition of a continued proportion ( D. 3 ) , A : B C D :: E : F :: GH , & c .; hence , BA B = whence , BA = AB ; Α A BA D = ; whence , BC = AD ; В BA BA LL F - E ; whence , BE = AF ; H = whence ...
... corresponding consequent . From the definition of a continued proportion ( D. 3 ) , A : B C D :: E : F :: GH , & c .; hence , BA B = whence , BA = AB ; Α A BA D = ; whence , BC = AD ; В BA BA LL F - E ; whence , BE = AF ; H = whence ...
Page 60
... corresponding terms of two proportions are equal , each term of the resulting proportion is the square of the corresponding term in either of the given proportions : hence , If four quantities are proportional , their squares are ...
... corresponding terms of two proportions are equal , each term of the resulting proportion is the square of the corresponding term in either of the given proportions : hence , If four quantities are proportional , their squares are ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence