| William Hawney - 1725
...oppofite Angles is to the Tangent of half their Difference. But Wholes are as their Halves : Therefore **the Sum of the Legs is to their Difference, as the Tangent of half the Sum of the** oppofite Angles, is to the Tangent of half their Difference. Which was, &c. From this Axiom the following... | |
| John Ward (of Chester.) - Mathematics - 1747 - 480 pages
...as the Tangent of half the Sum of the oppofite Angles is to the Tangent of half their Difference : **But Wholes are as their Halves ; wherefore the Sum...Difference, as the Tangent of half the Sum of the** Angles oppofice is to the Tangent of half their Difference. j£. ED Axiom IV. -4. The Bale, or greateu... | |
| John Ward - Gaging - 1747 - 480 pages
...as the Tangent of half the Sum of the oppofite Angles is to the Tangent of half their Difference : **But Wholes are as their Halves ; wherefore the Sum of the Legs is to their** Dtfference^as the Tangent of half the Sum of the Angles oppofite is to the Talent of half their Difference,... | |
| Mathematics - 1751 - 399 pages
...writers of Trigonometry, that the Sum of the Sides, including any given Angle Angle of a plain Triangle, **is to their Difference, as the Tangent of half the Sum of the** unknown Angles, is to the Tangent of half their Difference ; therefore, if the including Sides of two... | |
| John Ward - Mathematics - 1771 - 480 pages
...BC : : Si. С : Si. A. ' & £• D. Axiom III. The Sum of the Leg« of any Angle of a Plane Triangle **is to their Difference, as the Tangent of half the Sum of the** Angles oppofite to thofe leg* is to the Tangent of half their Difference. SDcmoaírcatíon» In the... | |
| Robert Gibson - Surveying - 1795 - 319 pages
...II. In any plane Triangle ABC, the Sum of the two given Sides AB and BC, including a given Angle ABC, **is to their Difference ; as the Tangent of half the Sum ' of the** two unknown Angles A and C is to the Tangent ef half their Difference. Fig. 1 1 . Produce Plate V.... | |
| Euclid, Robert Simson - Euclid's Elements - 1806 - 518 pages
...given, the fourth is also given. ' PROP. III. FIG. 8. In a plane triangle, the sum of any two 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. . * Let ABC be a plane triangle, live... | |
| John Bonnycastle - Trigonometry - 1806 - 419 pages
...• Hence, since AC, OF are parallel, EcistocrasEA. is to AC; that is, the sum of the sides AB, B c **is to their difference, as the tangent of half the sum of** their opposite angles B AC, BCA is to the tangent of half their difference. , QE u. THEOREM III. 95.... | |
| Robert Gibson - 1808 - 440 pages
...la any plane triangle ABC, the sum of the two. given sides AB and £C, including a given angle ABC, **is to their difference, as the tangent of half the sum of the** two unknown angles A and C is to the tangent of half their difference. Fig. 11. PLANE TRIGONOMETRY.... | |
| Sir John Leslie - Geometry, Plane - 1809 - 493 pages
...dt 3"-V zp: « <f-*s"-*+n. n -- * 3 2 -7 s -6 &c . PROP. IV. THEOR. The sum of the sines of two arcs **is to their difference, as the tangent of half the sum of the** arcs to the tangent of half the difference. If A and B denote two arcs; the S,A + S,B : S, A — S,B... | |
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