 | Humphry Ditton - 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 - 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 - 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 - 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 - 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... | |
 | Philip Ronayne - 1738 - 458 pages
...Right-angled Triangles. [ See the next foregoing Fig.] Given. \Req¿- [ <Proportions. i Rad. \Cafe. II. In any Triangle the Sides are proportional to the Sines of the oppofite Angles. AB A and С sA-SA:: AB-BC. AC AB BC BC R.-TA:: AB-BC. т A.- R :: AB-BC. z AB A and... | |
 | Nicolas Pike - 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°,... | |
 | Richard Wilson - 1831 - 372 pages
...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 pages
...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 pages
...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... 
