| 1798 - عدد الصفحات: 410
...Eti. IVarrc* . When' the verfiele ar.jle of any plan: triangle is bifeñcd ; the Гц m of the fides is to their difference, as the tangent of the angle made by the bilecVmg line and fcafe , is to the tangent of half th: vertí tal angle. Required a demonftration.... | |
| Charles Butler - 1814 - عدد الصفحات: 582
...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 - عدد الصفحات: 560
...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 - عدد الصفحات: 172
...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 - عدد الصفحات: 388
...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 - عدد الصفحات: 588
...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 - 1819 - عدد الصفحات: 430
...oi : Q o X oq : : BC* : 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.3... | |
| Jeremiah Day - 1824 - عدد الصفحات: 440
...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 - عدد الصفحات: 732
...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.... | |
| Robert Simson - 1827 - عدد الصفحات: 546
...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.... | |
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