| Humphry Ditton - Mathematics - 1709 - 276 pages
...M (whofe Direction is AB) is to Power N (whofe Direction is AC) as AB to AC or BD, that is (becaufe **in any Triangle the Sides, are proportional to the Sines of the** oppofite Angles) as the Sine of the Angle ADB or CAD, to the Sine of the Angle DAB. Now CAD is the... | |
| Samuel Heynes - Trigonometry - 1716 - 180 pages
...feme way you may work them all by your Guntert Scale. * V . . AXIOM II. , Of Oblique Plane Triangles. **In any Triangle, the Sides are Proportional to the Sines of the** Angles oppofite. DEMONSTRATION. Produce the lefler Side AB to F, making AF=BC, let fall the Perpendiculars... | |
| Philip Ronayne - Algebra - 1717 - 478 pages
...AB /SA » .R ::. AC » AB А С AB В С А ап( С А В tr,A •• т, А :: А С .. AB 7 AXIOM **In any Triangle the Sides are Proportional to the Sines of the** oppofite Angles. Demonßration. Produce the lefler fide of the Д ABG, to wit, А В to F," making... | |
| Samuel Heynes - Trigonometry - 1725 - 462 pages
...partsAfter the fame way you may work them all by your Gunter's Scale. AXIOM II. Of Oblique Plane Triangles. **In any Triangle, the Sides are Proportional to the Sines of the** Angles oppofite. DEMONSTRATION, Produce the leiTer Side А В to F, making AF=BC, let falsche Perpendiculars... | |
| Archibald Patoun - Navigation - 1734 - 568 pages
...Oblique-angled Plain Trigonometry, in order to which we muft premife the following Theorems. Theorem i. **In any Triangle, the Sides are proportional to the Sines of the** oppofite Angles. Thus in the Triangle ABC, I fay AB : BC : : S, C: S,A and AB : AC : : S, C : S, B... | |
| John Ward (of Chester.) - Mathematics - 1747 - 516 pages
...: Cod. A ; : AC : Aß. Sec. A : R : : AC : AB. Cof. A : Cot. A : : AC : AB. AC AB BC 7 С Axiom II. **In any Triangle the Sides are proportional to the Sines of the** cppofite Angles. ¡Dcmtmffratiott, ce A i> :E Produce the leffer Side of the Triangle ABC, to wit AB... | |
| Nicolas Pike - Algebra - 1808 - 470 pages
...4-8°,4.8' 9-87G4-6 So is AC 126 2- 10031To BC 9*'S 1-97683 SECTION 1 1. Of oUiquc angular Trigonometry. **In any triangle, the sides are proportional to. the sines of the opposite angles.** When two angles of any triangle are given, their sum, being subtracted from 1 80°, leaves the third... | |
| Roswell Park - Best books - 1841 - 722 pages
...hypothenuse, as the cosine of the angle at the base, is to radius, or the sine of 90°. In an oblique angled **triangle, the sides are proportional to the sines of the opposite angles** : also, the sum of any two sides is to their difference, as the tangent of the half sum of the two... | |
| James Bates Thomson - Plane trigonometry - 1844 - 148 pages
...ACD, BCD, CD=r AC sin A=BC sinB; whence (Euc. VI. 16) AC : BC : : sin B sin A ; that is, in any plane **triangle, the sides are proportional to the sines of the opposite angles.** Hence, also, ^nr; = - — — . ,,, . , TT i 22. One of the most important problems in trigonometry,... | |
| Nathaniel Bowditch - 1846 - 854 pages
...from the introduction of the demonstrations among the precepto for calculatiou. LVIII. In any plane **triangle, the sides are proportional to the sines of the opposite angles.** Let ABC be the triangle ; produce the shorter side, AB, to v F, making AF equal to BC ; from В and... | |
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