Elements of Geometry and Trigonometry: Translated from the French of A.M. Legendre by Daniel Brewster : Revised and Adapted to the Course of Mathematical Instruction in the United States |
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Page 13
... line AB , which expresses the distance between the points A and B. The expression Ax ( B + C - D ) represents the ... given line . 13. Magnitudes , which being applied to each other , coincide throughout their whole extent , are equal ...
... line AB , which expresses the distance between the points A and B. The expression Ax ( B + C - D ) represents the ... given line . 13. Magnitudes , which being applied to each other , coincide throughout their whole extent , are equal ...
Page 22
... given point , without a straight line , only one perpendicu lar can be drawn to that line . Let A be the point , and DE the given line . A BE Let us suppose that we can draw two perpendiculars , AB , AC . Produce either of them , as AB ...
... given point , without a straight line , only one perpendicu lar can be drawn to that line . Let A be the point , and DE the given line . A BE Let us suppose that we can draw two perpendiculars , AB , AC . Produce either of them , as AB ...
Page 23
... given point , DE the given line , AB the perpendicular , and AD , AC , AE , the oblique lines . Produce the perpendicular AB till BF is equal to AB , and draw FC , FD . First . The triangle BCF , is equal to the triangle BCA , for they ...
... given point , DE the given line , AB the perpendicular , and AD , AC , AE , the oblique lines . Produce the perpendicular AB till BF is equal to AB , and draw FC , FD . First . The triangle BCF , is equal to the triangle BCA , for they ...
Page 24
... given straight line , C the middle point , and ECF the perpendicular . First , Since AC = CB , the two oblique lines AD , DB , are equally distant from the perpen- dicular , and therefore equal ( Prop . XV . ) . So , likewise , are the ...
... given straight line , C the middle point , and ECF the perpendicular . First , Since AC = CB , the two oblique lines AD , DB , are equally distant from the perpen- dicular , and therefore equal ( Prop . XV . ) . So , likewise , are the ...
Page 28
... line ; hence they are parallel ( Prop . XVIII . ) . A R Q P D B PROPOSITION XXIII . THEOREM . Two parallels are every where equally distant . Two parallels AB , CD , being C H G D given , if through two points E and F , assumed at ...
... line ; hence they are parallel ( Prop . XVIII . ) . A R Q P D B PROPOSITION XXIII . THEOREM . Two parallels are every where equally distant . Two parallels AB , CD , being C H G D given , if through two points E and F , assumed at ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equal angles 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 plane MN polyedron PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex