 | Charles Butler - 1814 - 582 ページ
...AED are equiangular (29. 1.), v AF : FB : : AE : ED (4. 6.) and AF : AE:: FB : ED (16. 5.) ; that is, the sum of the sides : is to their difference : : as the tangent of half the sum of the angles at the base : to the tangent of half their difference. QED When two sides... | |
 | Euclides - 1814 - 560 ページ
...and CF their difference; and since BC, FG are parallel (2. 6.), EC is to CF, as EB to BG ; that is, the sum of the sides is to their difference, as the tangent of half the sum of the angles at the base, tothe tangent of half their difference. •'• - °" •'... | |
 | Jeremiah Day - 1815 - 172 ページ
...construction, equal to the sum, and FH to the difference of AC and AB. And by theorem II, [Art. 144.] the sum of the sides is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. Therefore, R:Tan (ACH-45°;::Tan... | |
 | Jeremiah Day - 1815 - 388 ページ
...construction, equal to the sum, and FH to the difference of AC and AB. And by theorem II, [Art. 144.] the sum of the sides is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. Therefore, R:Tan (ACH-45°;::Tan... | |
 | Euclides - 1816 - 588 ページ
...and CF their difference; and since BC, FG are parallel (2. 6.), EC is to CF, as EB to BG; that is, the sum of the sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. PROP. IV. FIG. 18.... | |
 | Thomas Leybourn - 1817 - 456 ページ
...ix. QUESTION 1037, by Mr. Edward Warren. When the vertical angle of any plane triangle is bisected ; the sum of the sides is to their difference, as the tangent of the angle made by the bisecting line and base, is to the tangent of half the vertical angle. Required a... | |
 | Thomas Leybourn - 1819 - 430 ページ
...major ACM ; then / о X oi : Qo X oq:: ß C* : AC*. Required a proof. 8. Prove, geometrically, that in any plane triangle, the sum of the sides is to their difference as the tangent of half the sum of the angles at the base to the tangent of half their difference. 9. Shew that tan.*... | |
 | Rev. John Allen - 1822 - 516 ページ
...ratios for the former, the cotangent of the half sum of the angles A and ABC is to the tangent of half their difference, as the tangent of the half sum of the angles ACD and BCD is to the tangent of half their difference; and, forming rectangles from the two first... | |
 | Jeremiah Day - 1824 - 440 ページ
...construction, equal to the sum, and FH to the difference of AC and AB. And by theorem II, [Art. 144.] the sum of the sides is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. Therefore, R : Tan (ACH-450):... | |
 | Nathaniel Bowditch - 1826 - 732 ページ
...angle C. LIX. In any triangle (supposing any side to be the basr, and calling the other two the sides) the sum of the sides is to their difference, as the tangent of half the sum of the angles at the base is to the tangent of half the difference of the tame angles.... | |
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II, (Art. 144.) the sum of the sides is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. 
