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 G B C 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 G B C 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
... Describe the square ABIF ; take AE L F = AC ; draw CG parallel to to BI , HK parallel to AB , and complete the ... described on BC : hence we have · ( AB + BC ) × ( AB - BC ) = AB2 - BC2 . Scholium . This proposition is equivalent to the ...
... Describe the square ABIF ; take AE L F = AC ; draw CG parallel to to BI , HK parallel to AB , and complete the ... described on BC : hence we have · ( AB + BC ) × ( AB - BC ) = AB2 - BC2 . Scholium . This proposition is equivalent to the ...
Page 78
Adrien Marie Legendre Charles Davies. PROPOSITION XI . THEOREM The square described on the hypothenuse of a right angled tr . angle is equivalent to the sum of the squares described on the other two sides . Let the triangle ABC be right ...
Adrien Marie Legendre Charles Davies. PROPOSITION XI . THEOREM The square described on the hypothenuse of a right angled tr . angle is equivalent to the sum of the squares described on the other two sides . Let the triangle ABC be right ...
Page 79
... square of the hypothenuse diminished by the square of the other side ; which is taas ex- pressed : AB2BC2_AC2 . Cor ... described on the diagonal AC , is double of the square described on the side AB . A D G E B F This property may be ...
... square of the hypothenuse diminished by the square of the other side ; which is taas ex- pressed : AB2BC2_AC2 . Cor ... described on the diagonal AC , is double of the square described on the side AB . A D G E B F This property may be ...
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 altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine cotangent 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 homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular 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 slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex