Elements of Geometry and Trigonometry Translated from the French of A.M. Legendre, by David Brewster: Revised and Adapted to the Course of Mathematical Instruction in the United States |
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Page 19
... contained by equal sides , ( Prop . V. ) ; therefore CG is equal to EF . Now , there may be three cases in the proposition , according as the point G falls without the triangle ABC , or upon its base BC , or within it . First Case . The ...
... contained by equal sides , ( Prop . V. ) ; therefore CG is equal to EF . Now , there may be three cases in the proposition , according as the point G falls without the triangle ABC , or upon its base BC , or within it . First Case . The ...
Page 34
... contain the measuring unit an exact number of times , there may perhaps be a smaller unit which will be contained an exact number of times in each of the magnitudes . But if there is no unit of an assignable value , which shall be ...
... contain the measuring unit an exact number of times , there may perhaps be a smaller unit which will be contained an exact number of times in each of the magnitudes . But if there is no unit of an assignable value , which shall be ...
Page 51
... contained by the radii will also be equal . Let C and C be the centres of equal circles , and the angle ACB = DCE . First . Since the angles ACB , DCE , are equal , they may be placed upon each other ; and since their sides are equal ...
... contained by the radii will also be equal . Let C and C be the centres of equal circles , and the angle ACB = DCE . First . Since the angles ACB , DCE , are equal , they may be placed upon each other ; and since their sides are equal ...
Page 52
... contained times in the angle ACB , and 4 times in DCE M כך The seven partial angles ACm , mCn , nCp , & c . , into which ACB is divided , being each equal to any of the four partial angles into which DCE is divided ; each of the partial ...
... contained times in the angle ACB , and 4 times in DCE M כך The seven partial angles ACm , mCn , nCp , & c . , into which ACB is divided , being each equal to any of the four partial angles into which DCE is divided ; each of the partial ...
Page 60
... contain , being given , to describe the triangle . Let the lines B and C be equal to TB TC the given sides , and A the given an- gle . Having drawn the indefinite line DE , at the point D , make the angle EDF equal to the given angle A ...
... contain , being given , to describe the triangle . Let the lines B and C be equal to TB TC the given sides , and A the given an- gle . Having drawn the indefinite line DE , at the point D , make the angle EDF equal to the given angle A ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine Sine Cotang cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater hence homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex