Elements of Geometry and Trigonometry |
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Page 32
... four right angles . PROPOSITION XXVIII . THEOREM . In every parallelogram , the opposite sides and angles are equal . D Let ABCD be a parallelogram : then will AB = DC , AD = BC , A = C , and ADC = ABC . For , draw the diagonal BD . The ...
... four right angles . PROPOSITION XXVIII . THEOREM . In every parallelogram , the opposite sides and angles are equal . D Let ABCD be a parallelogram : then will AB = DC , AD = BC , A = C , and ADC = ABC . For , draw the diagonal BD . The ...
Page 35
... four magnitudes A , B , C , and D , having such B. D values that is equal to then A is said to have the same ratio A C ' to B , that C has to D , or the ratio of A to B is equal to the ratio of C to D. When four quantities have this ...
... four magnitudes A , B , C , and D , having such B. D values that is equal to then A is said to have the same ratio A C ' to B , that C has to D , or the ratio of A to B is equal to the ratio of C to D. When four quantities have this ...
Page 36
... four quantities are proportional ; that is , MN : P : Q. PROPOSITION III . THEOREM . If four quantities are in proportion , they will be in proportion when taken alternately . Let M , N , P , Q , be the numerical representatives of four ...
... four quantities are proportional ; that is , MN : P : Q. PROPOSITION III . THEOREM . If four quantities are in proportion , they will be in proportion when taken alternately . Let M , N , P , Q , be the numerical representatives of four ...
Page 37
Adrien Marie Legendre. PROPOSITION IV . THEOREM . If there be four proportional quantities , and four other propor- tional quantities , having the antecedents the same in both , the consequents will be proportional . Let M : N :: P : Q ...
Adrien Marie Legendre. PROPOSITION IV . THEOREM . If there be four proportional quantities , and four other propor- tional quantities , having the antecedents the same in both , the consequents will be proportional . Let M : N :: P : Q ...
Page 38
... four quantities , so that M : N :: P.Q ; then will M ± N : M :: P ± Q : P . For , from the first proportion , we ... four proportional quantities , if there be taken any equimul- tiples of the two antecedents , and any equimultiples of ...
... four quantities , so that M : N :: P.Q ; then will M ± N : M :: P ± Q : P . For , from the first proportion , we ... four proportional quantities , if there be taken any equimul- tiples of the two antecedents , and any equimultiples of ...
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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 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 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-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex