| Francis Holliday - 1749 - 316 pages
...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. Mr J. lodd ingenioufly has lolved... | |
| William Flower - 1768 - 228 pages
...hypothenufe, to the tang" ent of its adjacent perpendicular. Lemma, As the fum of tbeßnes of two unequal arcs **is to their difference, fo is the tangent of half the fum of** thofe arcs, to the tangent of half their difference. And, as the fum of their cq/ines is to their difference,... | |
| Robert Simson - 1775 - 520 pages
...difference. Let ABC be a plain triangle, the fum of any two fides AB, AC will be to their difference as **the tangent of half the fum of the angles at the bafe** ABC, ACB to the tangent of half their difference. About A as a center, with AB the greater fide for... | |
| Euclid - 1776 - 264 pages
...therefore the c 5. i. angles HBE, EBC, are likewife equal d; and, it BE be made ra- a 32 i dius, then EC **is the tangent of half the fum of the angles at the bafe.** Draw BD parallel to AC, then the angle DBC is equal to the angle ACB e. Take HF equal to DC, and join... | |
| Euclid - 1781 - 520 pages
...given. PROP. III. FIG. 8. IN a plain triangle, the fum of any two 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.** Let ABC be n plain triangle, the fum of any two fides AB, AC will be to their difference as the tangent... | |
| Euclid, Robert Simson - 1781 - 466 pages
...difference. Let ABC be a plain triangle, the fum of any two fides AB, AC will be to their difference as **the tangent of half the fum of the angles at the bafe** ABC, ACB to the tangent of half their difference. About A as a center, with AB the greater fide for... | |
| Vasiliĭ Nikitich Nikitin, Prokhov Ignatévich Suvorov - 1786 - 101 pages
...fum of the fides В A, AC, to their difference, fo is the cotangent of half the contained angle A, or **the tangent of half the fum of the angles at the bafe,** AC В, C В A, to the tangent of half the difference of thofe anles. О<, ED In every plane triangle... | |
| Charles Hutton - 1788 - 703 pages
...Sides and the dngle Included by them, to find the reft. In a plane triangle, As the fum of any two **fides is to their difference, fo is the tangent of half the fum of** their oppofite angles, to the tangent of half their difference. Then the half difference added to the... | |
| John McGregor (teacher of mathematics.) - 1792 - 431 pages
...and BC are parallel, EC : CF as EB :. 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,** is to the tarn. Cent of half their difference. THEOTHEOREM III. in a plane triangle, the bafe is to... | |
| John Playfair - 1795 - 400 pages
...will the radius be to the tangent of the difference between, that angle and half a " right angle, as **the tangent of half the fum of the angles at the bafe** of the triangle to the tangent of half their difference. TLet ABC be a triangle, the fides of which... | |
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