Elements of Geometry and Trigonometry |
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Page 31
... four right angles . Let the sides of the polygon ABCD- FG , be produced , in the same direction ; then will the sum of the exterior angles a + b + c + d + f + g , be equal to four right angles . A a D B / b For , each interior angle ...
... four right angles . Let the sides of the polygon ABCD- FG , be produced , in the same direction ; then will the sum of the exterior angles a + b + c + d + f + g , be equal to four right angles . A a D B / b For , each interior angle ...
Page 32
... four right angles . PROPOSITION XXVIII . THEOREM . In every parallelogram , the opposite sides and angles are equal . 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 . 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. values that is equal to A D -C ' then A is said to have the same ratio 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. values that is equal to A D -C ' then A is said to have the same ratio 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 M : N :: P : Q . = MxN P MxN P ; conse- PROPOSITION III . THEOREM . If four quantities are in proportion , they will be in proportion when taken alternately . Let M , N , P , Q , be the ...
... four quantities are proportional ; that is M : N :: P : Q . = MxN P MxN P ; conse- PROPOSITION III . THEOREM . If four quantities are in proportion , they will be in proportion when taken alternately . Let M , N , P , Q , be the ...
Page 37
Adrien Marie Legendre Charles Davies. 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 ...
Adrien Marie Legendre Charles Davies. 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 ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex