 | Humphry Ditton - 1709 - 276 σελίδες
...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 σελίδες
...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 σελίδες
...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... | |
 | Samuel Heynes - 1725 - 462 σελίδες
...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... | |
 | John Ward - 1747 - 492 σελίδες
...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 σελίδες
...: 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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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... 
