Elements of Geometry and Trigonometry |
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Page 76
... square ACDE ; take AF E AB ; draw FG parallel to AC , and BH par- allel to AE . = F HD G BC The square ACDE is made up of four parts ; the first ABIF is the square described on AB , since we made AF - AB : the second IDGH is A the square ...
... square ACDE ; take AF E AB ; draw FG parallel to AC , and BH par- allel to AE . = F HD G BC The square ACDE is made up of four parts ; the first ABIF is the square described on AB , since we made AF - AB : the second IDGH is A the square ...
Page 77
... square ABIF ; take AE L F = AC ; draw CG parallel to to BI , HK parallel to AB , and complete the square K EFLK . The two rectangles CBIG , GLKD , are each measured by AB × BC ; take them away from ... square described on the BOOK IV . vyry.
... square ABIF ; take AE L F = AC ; draw CG parallel to to BI , HK parallel to AB , and complete the square K EFLK . The two rectangles CBIG , GLKD , are each measured by AB × BC ; take them away from ... square described on the BOOK IV . vyry.
Page 78
Adrien Marie Legendre Charles Davies. PROPOSITION XI . THEOREM . The square described on the hypothenuse of a right angled tri- angle is equivalent to the sum of the squares described on the other two sides . Let the triangle ABC be ...
Adrien Marie Legendre Charles Davies. PROPOSITION XI . THEOREM . The square described on the hypothenuse of a right angled tri- angle is equivalent to the sum of the squares described on the other two sides . Let the triangle ABC be ...
Page 79
... square of the hypothenuse diminished by the square of the other side ; which is thus ex- pressed : AB2BC ? —AC2 ... described on the diagonal AC , is double of the square described on the side AB . E B F G This property may be exhibited ...
... square of the hypothenuse diminished by the square of the other side ; which is thus ex- pressed : AB2BC ? —AC2 ... described on the diagonal AC , is double of the square described on the side AB . E B F G This property may be exhibited ...
Page 81
... described on the two sides are together equivalent to the square described on the third ; for if the angle contained by the two sides is acute , the sum of their squares will be greater than the square of the opposite side ; if obtuse ...
... described on the two sides are together equivalent to the square described on the third ; for if the angle contained by the two sides is acute , the sum of their squares will be greater than the square of the opposite side ; if obtuse ...
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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