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" In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B... "
Elementary text-book of trigonometry - Side 118
av Robert Hamilton Pinkerton - 1884 - 176 sider
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The Elements of Plane and Spherical Trigonometry: And Its Application to ...

Richard Abbatt - 1841 - 191 sider
...=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 side AC ; then by (470, BD=AB...
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Elements of Plane and Spherical Trigonometry: With the First Principles of ...

James Bates Thomson - 1844 - 126 sider
...ACD, BCD, CD=r AC sin A=BC sinB; whence (Euc. VI. 16) AC : BC : : sin B sin A ; that is, in any plane triangle, the sides are proportional to the sines of the opposite angles. Hence, also, ^nr; = - — — . ,,, . , TT i 22. One of the most important problems in trigonometry,...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 sider
...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 ; and 6 : c : : smB : sin C. Draw AD perpendicular...
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The New American Practical Navigator; Being an Epitome of Navigation ...

Nathaniel Bowditch - 1846 - 451 sider
...from the introduction of the demonstrations among the precepto for calculatiou. LVIII. In any plane triangle, the sides are proportional to the sines of the opposite angles. Let ABC be the triangle ; produce the shorter side, AB, to v F, making AF equal to BC ; from В and F let fall...
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Pantology

Roswell Park - 1847 - 580 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 ihe two...
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Elementary Mechanics

Sir John Budd Phear - 1850 - 252 sider
...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 is proportional...
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Plane trigonometry. [With] Solutions of examples. Appendix &c., to adapt the ...

John William Colenso (bp. of Natal.) - 1851
...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 to the angles...
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First book on plane trigonometry, comprising geometrical trigonometry

George Wirgman Hemming - 1851
...C, and the sides respectively opposite to them by the letters a, b, c. 52. The sides of any triangle are proportional to the sines of the opposite angles. Let ABC be the triangle ; from C draw CD perpendicular to AB or AB produced. In the first figure, A and B are...
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A Treatise on Plane and Spherical Trigonometry

William Chauvenet - 1852
...formulae from a direct consideration of the solid angle itself. 3. In a spherical triangle, the sines of the sides are proportional to the sines of the opposite angles. Let A В о, Fig. 1, be a spherical triangle, O the center of the sphere. The angles of the triangle are...
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Five Years in an English University, Volum 2

Charles Astor Bristed - 1852
...(45° + B ) = tan (45° — B) + 2 tan 2 B. cot 3 6 — cot d _ I ' ' cot 3 t + cot i ~ ~2cos20' 4. In any triangle the sides are proportional to the sines of the angles opposite to them. Also prove that sin A = ~ VS.(S — a)(S — b)(S — c). be 5. Given two...
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