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 Livres Livres 1 - 10 sur 102 pour In any triangle, the sides are proportional to the sines of the opposite angles,....
In any triangle, the sides are proportional to the sines of the opposite angles, ie. t abc sin A sin B sin C...
The Young Mathematician's Guide: Being a Plain and Easy Introduction to the ... - Page 476
de John Ward - 1747 - 480 pages
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## The General Laws of Nature and Motion: With Their Application to Mechanicks ...

1709 - 232 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 Angle which the Line...
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## A Treatise of Trigonometry, Plane and Spherical ...: As Likewise a Treatise ...

Samuel Heynes - 1716 - 132 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...
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## A Treatise of Algebra in Two Books: The First Treating of the Arithmetical ...

Philip Ronayne - 1717 - 408 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 AF = В С j let...
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## A Treatise of Trigonometry, Plane and Spherical, Theoretical and Practical ...

Samuel Heynes - 1725 - 132 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...
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## A Compleat Treatise of Practical Navigation Demonstrated from It's First ...

Archibald Patoun - 1734 - 414 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 ; alfo AC : BC :...
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## A Treatise of Algebra in Two Books: The First Treating of the Arithmetical ...

Philip Ronayne - 1738 - 421 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 С 2A» R :: AB-AC....
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## A New and Complete System of Arithmetick: Composed for the Use of the ...

Nicolas Pike - 1808 - 480 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°,...
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## A System of Plane and Spherical Trigonometry: To which is Added a Treatise ...

Richard Wilson - 1831 - 330 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...
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## Elementary mechanics

Sir John Budd Phear - 1850 - 252 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...
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## Plane trigonometry. [With] Solutions of examples

...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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