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" CB : CA : : sin A : sin B. For, with A as a centre, and AD equal to the less side... "
A Manual of Civil Engineering - Page 42
by William John Macquorn Rankine - 1883 - 808 pages
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A Course of Mathematics ...: Designed for the Use of the Officers ..., Volume 1

Isaac Dalby - Mathematics - 1807 - 476 pages
...angles (3S ), and are respectively the same as the three angles of the triangle CBA; therefore the sum of the three angles of a plane triangle is equal to two right angles. Carol. 1. Hence the difference between an exterior angle of B triangle and either of the interior opposite...
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A Treatise on Surveying, Containing the Theory and Practice: To which is ...

John Gummere - Surveying - 1814 - 398 pages
...cut one another, the opposite angles will be equal : thus AEC=BED and AED=CEB. Fig. 36. 4. The sura of the three angles of a plane triangle is equal to two right angles, or 180°. 5. If the sum of two angles of a triangle be subtracted from 180°, the remainder will be...
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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 sides...
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A Treatise on Surveying: Containing the Theory and Practice : to which is ...

John Gummere - Plane trigonometry - 1817 - 392 pages
...lines cut one another, the opposite angles will be equal : thus AEC=BED and AED-CEB. Fig. 36. 4. The' sum of the three angles of a plane triangle is equal to two right angles, or 180°. 5. If the sum of two angles of a triangle be subtracted from 180°, the remainder will be...
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Elements of Analytic Trigonometry: Plane and Spherical

Ferdinand Rudolph Hassler - Trigonometry - 1826 - 212 pages
...to the sine of its supplement, not only in magnitude, but also in sign ; and because the. sum of all the three angles of a plane triangle is equal to two right angles, the sine of any one of the angles is equal to the sine of the sum of the two others. Calling d the perpendicular...
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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,...
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Elements of Surveying

Charles Davies - Surveying - 1830 - 390 pages
...supplement (39). 42. We have not considered the sines, cosines, &c. of arcs greater that 180 ; for, as the sum of the three angles of a plane triangle is equal to IN0 ", it follows, that no larger arc can enter into the calculations of the sides and angles of plane...
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A Course of Mathematics: For the Use of Academies as Well as ..., Volume 1

Charles Hutton - Mathematics - 1831 - 660 pages
...some property is asserted, and the truth of it required to be proved. Thus, when it is said that, The sum of the three angles of a plane triangle is equal to two right angles, that is a Theorem, the truth of which is demonstrated by Geometry. — A set or collection of such...
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A Course of Mathematics: For the Use of Academies as Well as ..., Volume 1

Charles Hutton - Mathematics - 1831 - 632 pages
...property is asserted, and the truth of it required to be proved. Thus, when it is said that, The sun of the three angles of a plane triangle is equal to two right angles, that is a Theorem, the truth of which is demonstrated by Geometry. — A set or collection of such...
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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 b : c : : sin I! :...
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