Elements of Geometry and Trigonometry |
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Page 66
... described on AB as a diameter . PROBLEM XVII . To find the numerical ratio of two given straight lines , these lines being supposed to have a common measure . Let AB and CD be the given lines . From the greater AB cut off a part equal ...
... described on AB as a diameter . PROBLEM XVII . To find the numerical ratio of two given straight lines , these lines being supposed to have a common measure . Let AB and CD be the given lines . From the greater AB cut off a part equal ...
Page 76
... described on the whole line is equivalent to the sum of the squares described on the parts , together with twice the rectangle contained by the parts . • Let AC be the line , and B the point of division ; then , is AC2 or ( AB + BC ) 2 ...
... described on the whole line is equivalent to the sum of the squares described on the parts , together with twice the rectangle contained by the parts . • Let AC be the line , and B the point of division ; then , is AC2 or ( AB + BC ) 2 ...
Page 77
... described on BC : hence we have square ( AB + BC ) × ( AB - BC ) = AB2 — BC2 . Scholium . This proposition is equivalent to the algebraical formula , ( a + b ) × ( a — b ) = a2 — b2 . G * PROPOSITION XI . THEOREM . The square described ...
... described on BC : hence we have square ( AB + BC ) × ( AB - BC ) = AB2 — BC2 . Scholium . This proposition is equivalent to the algebraical formula , ( a + b ) × ( a — b ) = a2 — b2 . G * PROPOSITION XI . THEOREM . The square described ...
Page 78
... described on the other two sides . Let the triangle ABC be right angled at A. Having described squares on the three sides , let fall from A , on the hypothenuse , the perpendicular AD , which produce to E ; and draw the H diagonals AF ...
... described on the other two sides . Let the triangle ABC be right angled at A. Having described squares on the three sides , let fall from A , on the hypothenuse , the perpendicular AD , which produce to E ; and draw the H diagonals AF ...
Page 79
... described on the diagonal AC , is double of the square described on the side AB . E B F G This property may be exhibited more plainly , by drawing parallels to BD , through the points A and C , and parallels to AC , through the points B ...
... described on the diagonal AC , is double of the square described on the side AB . E B F G This property may be exhibited more plainly , by drawing parallels to BD , through the points A and C , and parallels to AC , through the points B ...
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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 convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines 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 sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex