 | Humphry Ditton - 1709 - 276 Seiten
...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 - 1716 - 180 Seiten
...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 - 1717 - 478 Seiten
...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 - 1725 - 462 Seiten
...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 - 1734 - 568 Seiten
...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.) - 1747 - 516 Seiten
...: 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 - 1808 - 470 Seiten
...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 - 1841 - 722 Seiten
...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 - 1844 - 148 Seiten
...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 Seiten
...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... | |
| |
Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B... 
