 | William Hawney - 1725 - عدد الصفحات: 504
...The Demon ftr At ion of this fecond Axiom is briefly thus. I fay, the fum of the Legs of any Angle a, is to their Difference, as the Tangent of half the fum of their oppofite Angles, is to the Tangent of half their Difference. Let Let A* B and C represent the... | |
 | Archibald Patoun - 1734 - عدد الصفحات: 568
...In any plain Triangle, as ABC, thefum of the fides, AB and BC, is to the difference of thefe fides, as the Tangent of half the fum of the Angles at the bafe, viz. A and C, is to the Tangent of half the difference of thefe Angles. Demon. Produce AB and make... | |
 | Francis Holliday - 1749 - عدد الصفحات: 360
...method offohing this qucjiion is thus : AS the fum of the ratios ( ij) is to their difference (3), fo is the tangent of half the fum of the angles at the bafe to the tangent of half their difference ; whence all the angles are known, and consequently the triangle.... | |
 | Antoine-René Mauduit - 1768 - عدد الصفحات: 252
...the tangent of half the difference cf the fegments of the bafe-, and the fécond this ; The coßne of half the fum of the angles at the bafe is to the coftne cf half their difference, as the tangent of half the difference of their oppofttefides is io... | |
 | William Flower - 1768 - عدد الصفحات: 276
...point from the middle of the bafe. TbeoretQ VII. In any fpberic triangle it will be, as the cotangent of half the fum of the angles, at ' the bafe is to the tangent of half their difference* fo is the tangent of half the vertical angle to the tangent of the... | |
 | Paul Hoste - 1769 - عدد الصفحات: 294
...confequently, fince (by 4. AE is to DA, as CE toDF, it is certain, tha* the fum of the fides BA, BC, is to their difference, as the tangent of half the fum of the angles A and C, is to the tangent of an angle, which added to the faid half, will make the greater angle C.... | |
 | John Muller - 1769 - عدد الصفحات: 152
...BC-CA: BD + DA. PROP. Fig. 27. 80. In any unequal Jided triangle ABC, the fum of the fides BC, AC, is to their difference, as the tangent of half the fum of the oppofae angles A, B, is to the tangent of half their difference. Let the fame conftru&ion be as the... | |
 | John Muller - 1773 - عدد الصفحات: 202
...: BC-CA:BD + DA. PROP. Fig. 27: 80. In any unequal fided triangle ABQ the fum of the fides BC, AC, is to their difference, as the tangent of half the fum of the oppofite angles A, B, is to the tangent of half their difference. Let the fame conftruction be as the... | |
 | Robert Simson - 1775 - عدد الصفحات: 534
...; and fince BC, FG are parallel (2.6.) EC is to CF, asEB to BG; that is, the fum of the H h 3 fides fides is to their difference, as the tangent of half the fum of the angles at the bafe to the tangent of half their difference. PROP. IV. FIG. 18. TN any plain triangle BAC, whole two fides... | |
 | Euclid - 1776 - عدد الصفحات: 326
...angle BIC, or BAC f. Wherefore, Sec, f fcho1PROP. Ill, TN any right lined triangle, ths fum of any two fides., is to their •*• difference, -as the tangent of half the fum of the angles at the kafe, is to the tangent of half their difference. Let ABC be the triangle, the fum of any two of its... | |
| |
BG; that is, the fum of the fides is to their difference, as the tangent of half the fum of the angles at the bafe to the tangent of half their difference. 
