 | Humphry Ditton - 1709 - 276 sider
...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 Angle which the Line... | |
 | Samuel Heynes - 1716 - 180 sider
...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... | |
 | Samuel Heynes - 1725 - 462 sider
...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 sider
...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 ; alfo AC : BC :... | |
 | John Ward - 1747 - 492 sider
...R : Cofi. A : : AC : AB. Sec. A : R : : AC : AB. Cof, A : Cot. A : : AC : AB. AC AB BC 7 478 Axiom II. In any Triangle the Sides are proportional to the Sines of the oppofite Angles. jDcmonftrancn, ABE CC AD Produce the letter Side of the Triangle ABC, to wit AB to F, making AFrzBC... | |
 | John Ward (of Chester.) - 1747 - 516 sider
...AB R : 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 sider
...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°,... | |
 | Richard Wilson - 1831 - 372 sider
...sin а + cos — sin ß 2 ß _ tan a -ß SECTION III. ON THE SOLUTION OF PLANE TRIANGLES. 108. PROP. In any triangle the sides are proportional to the sines of the opposite angles. For let ABC be the triangle. Let the angles be denoted by A, B, C,. and the sides... | |
 | Sir John Budd Phear - 1850 - 304 sider
...triangle. The parallelogram and the triangle of forces are therefore identical propositions. 19. Since in any triangle the sides are proportional to the sines of the opposite angles, our proposition shews us, that of three forces keeping any point in equilibrium, each... | |
 | John William Colenso (bp. of Natal.) - 1851 - 382 sider
...V. ON THE TRIGONOMETRICAL PROPERTIES OF TRIANGLES, QUADEILATEBALS, AND POLYGONS. 105. To shew that in any triangle the sides are proportional to the sines of the opposite angles. In future we shall use the letters a, b, c, to denote the sides BC, AC, AB, opposite... | |
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In any triangle, the sides are proportional to the sines of the opposite angles, ie. t abc sin A sin B sin C... 
