 | Philip Ronayne - 1717 - 478 pągines
...С : : 5, С • S, A " - S,C: 3 D) == S, A, QED' AXIOM AXIOM. III. The Sum of che Legs of an Angle is to their Difference as the Tangent of half the Sum of the Angles oppofite to rhofe Legs, is to the Tangent of half their Difference. Demonßrütion. „ In the... | |
 | William Hawney - 1725 - 504 pągines
...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.) - 1747 - 516 pągines
...the Tangent of half their Difference : But Wholes are as their Halves ; wherefore the Sum of the Legs is to their 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... | |
 | 1751 - 420 pągines
...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... | |
 | Robert Gibson - 1795 - 384 pągines
...ie S. C : AB ; : S. A : BC, tfc. Q^ED THEO. II. In any plane Triangle ABC, the Sum of the two given Sides AB and BC, including a given Angle ABC, is to...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. , i Produce AB, and make... | |
 | John Bonnycastle - 1806 - 464 pągines
...circle is to the radius of the tables. THEOREM II. 94. The sum of any two sides of a plane triangle ABC, is to their difference, as the tangent of half the sum of their opposite angles is to the tangent of half their difference. . &> For about one of the angular... | |
 | Robert Simson - 1806 - 546 pągines
...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... | |
 | Robert Gibson - 1806 - 486 pągines
...AH : IH : : CE : ED, that is .as the sum of the two sides AB and BC, is to their difference ; so is the tangent of half the sum of the two unknown angles A and C, to the tangent of half their difference. QED 104 PLANE TRIGONOMETRY. Plate V. THEOREM JII. In any... | |
 | Robert Gibson - 1808 - 482 pągines
...S. A : BC, &c. QED THEO. II. la any plane triangle ABC, the sum of the two. given sides AB and £C, including a given angle ABC, is to their difference,...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. Plate V. Produce AB and... | |
 | Sir John Leslie - 1809 - 522 pągines
...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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C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. 
