 | Humphry Ditton - 1709 - 232 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... | |
 | Samuel Heynes - 1716 - 132 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... | |
 | Philip Ronayne - 1717 - 408 sider
...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 - 132 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 - 414 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... | |
 | John Ward (of Chester.) - 1747 - 480 sider
...: 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 - 480 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°, leaves the third... | |
 | Richard Wilson - 1831 - 330 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 opposite to them... | |
 | Euclid, James Thomson - 1837 - 390 sider
...R = 1, this becomes simply b = c sin I! — c cosA. PROP. II. THEOR. THE sides of a plane triangle are proportional to the sines of the opposite angles. Let ABC be any triangle; a : b : : sinA : sin 15 ; a : c : : sin A : sinC ; and b : c : : sin I! : sinC. Draw AD perpendicular... | |
 | Roswell Park - 1841 - 587 sider
...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... | |
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In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B... 
