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" THEOREM I. The sides of a plane triangle are proportional to the sines of their opposite angles. "
Elements of Surveying, and Navigation: With a Description of the Instruments ... - Page 40
by Charles Davies - 1841 - 359 pages
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - Geometry - 1816 - 352 pages
...angles of a right-angled plane triangle is (Art. 13. and E. 32. 1.) the cosine of the other. (21.) The sides of a plane triangle are proportional to the sines of the angles opposite to them. For, if a circle be described (E. 5. 4.) about any plane triangle, the...
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Elements of Surveying: With the Necessary Tables

Charles Davies - Surveying - 1830 - 318 pages
...larger arc can enter into the calculations of the sides and angles of plane triangles. THEOREM. 43. The sides of a plane triangle are proportional to the sines of their opposite angles. Let ABC (PI. I. Fig. 2) be a triangle ; then, CB : CA : : sin. A : sin. B. For, with A as a centre,...
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Elements of Surveying: Including a Description of the Instruments and the ...

Charles Davies - Navigation - 1837 - 342 pages
...tangent 9.979110 Ans. 43° 37' 21". 4. Find the arc answering to cosine 9.944599 Ans. 28° 19' 4 5". We shall now demonstrate the principal theorems of...triangle ; then will CB : CA : : sin A : sin B. For, with *# as a centre, and AD equal to the less side BC, as a radius, describe the arc DI : and with B as...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...cosine of the adjacent' angle. When 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...
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The Elements of Plane and Spherical Trigonometry: And Its Application to ...

Richard Abbatt - Spherical astronomy - 1841 - 234 pages
...9=2° 30' 36", and thence, cos 9 =9.9995833. Then log c=log a + 10— cos 6: from this c=760.129. (48.) The sides of a plane triangle are proportional to the sines of the opposite angles. Let ABC be a plane triangle (fig. 8.), and BD the perpendicular from B upon the...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...cosine of the adjacent angle. When R=l, this becomes simply 6 = c sin B = c cos A. PROP. II. THEOR. — The sides of a plane triangle are proportional to the sines of the opposite angles. Let ABC be any triangle; then a : 6 : : sin A : sin B; a : c :: sin A : sin C...
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Navigation and Nautical Astronomy: For the Use of British Seamen

James Inman - Nautical astronomy - 1849 - 302 pages
...hour in still water, and the current run at the rate of 3 miles an hour, AB : BC : : 6 : 3. But since the sides of a plane triangle are proportional to the sines of the opposite angles, AB : BC : : sin C : sin A ; where C is the angle between the bearing of D and...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...Ans. 28° 19' 45". 20. We shall now demonstrate the principal theorems of Plane Trigonometry. THEOEEM I. The sides of a plane triangle are proportional to the sines of their opposite angles. 21. Let ABC be a triangle ; then will CB : CA : : sin A : sin B. For, with A as a centre, and AD equal...
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A Treatise on Plane and Spherical Trigonometry

William Chauvenet - 1852 - 268 pages
...are enabled to deduce all the formulae for their solution from those of the preceding chapter. 117. The sides of a plane triangle are proportional to the sines of their opposite angles. Denote the angles of the triangle ABC, Fig. 16, by A, B and С, and the sides opposite these angles...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...9.979110. Ans. 43° 37' 21". 4. Find the are answering to cosine 9.944599. Ans. 28° 19• 45". 20. We shall now demonstrate the principal theorems of...proportional to the sines of their opposite angles. . 21. Let ABC be a triangle ; then CB : CA :: sin A : sin B. For, with A as a centre, and AD equal...
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