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" The law of sines states that in any spherical triangle the sines of the sides are proportional to the sines of their opposite angles: sin a _ sin b __ sin c _ sin A sin B sin C... "
Academic Trigonometry: Plane and Spherical - Page 25
by Thomas Marcus Blakslee - 1888 - 35 pages
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A Treatise of Trigonometry: Plane and Spherical, Theoretical and Practical ...

Samuel Heynes - Electronic books - 1701 - 334 pages
...Therefore, T,B P. T, DP : : g DP A. SBP A. AXIOM. III. In any Triangle (whether Right-angled or Ohlique) the Sines of the Sides are proportional to the Sines of the Oppof1te Angles. For hy the 1ft Axiom, S,BP.R::S,PA.S,B S,DP.R::S,PA.S,D. Therefore, S,BPxS,B=RxS,...
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Elements of Plain and Spherical Trigonometry: Together with the Principles ...

John Harris - Spherical projection - 1706 - 298 pages
...A'S), J3P:T,PA.-.-R,S/BPA-) Eret And CT,BP:T,DP::S' T,DP:T,PA::R:^,DPAJ (DPA:g,BPA! AXIOM III. In any Triangle, the Sines of the Sides are proportional to the Sines of the Oppofite Angles. DEMONSTRATION. By Axiom i. S, BP : R : : S, PA: S, B. And S,DP : R :: S, PA : S, Dergo...
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A Treatise of Trigonometry, Plane and Spherical ...: As Likewise a Treatise ...

Samuel Heynes - Trigonometry - 1716 - 180 pages
...Therefore, T,B P. T, DP : :gDPA.gBP A. AXIOM III. In any Triangle ( whether Right-angled or Oblique) the Sines of the Sides are proportional to the Sines of the Oppofite Angles. For by the ifl: Axiom, S,BP.R ::S, PA. S,B S,DP.R ::S,PA.S,D. Therefore, S, BP x S,...
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A Treatise of Algebra in Two Books: The First Treating of the Arithmetical ...

Philip Ronayne - Algebra - 1717 - 478 pages
...Therefore, T.BPx 2.BPA (= r X T.PA) =: T,DP AXIOM lit In any Triangle (whether Right-angled, or Oblique) the Sines of the Sides are proportional to the Sines of the oppo╗ fite Angles. Demon▀ration. . Therefore, S, BP x S, B (= rx S, PA) = S, DP XS, D ; Wherefore,...
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The Elements of Trigonometry: Containing, the Properties, Relations, and ...

William Emerson - Trigonometry - 1749 - 214 pages
...letting fall a Perpendicular dividing it into two right angled Triangles. PROP. XXIX. In any fpherical Triangle, the Sines of the Sides are proportional to the Sines of their oppo▀te Angles. 43' . On AB, AF let fall the Perpendiculars FH, В I i then by Prop. XXVI. S.AF:S.FH...
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Mathematics: Compiled from the Best Authors and Intended to be the ..., Volume 2

Mathematics - 1801 - 658 pages
...three sides and right angle being known, the other angks may be determined by this proposition — The sines of the sides are proportional to the sines of the opposite angles. But if an angle be first required, the process must be as above. 3. To find the /_ A. RX sin. BC =...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...than a quadrant. PROP. XXIII. FIG. 16. IN spherical triangles, whether right angled or oblique angled, the sines of the sides are proportional to the sines of the angles opposite to them. First, let ABC be a right angled triangle, having a right angle at A; therefore...
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A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ...

Francis Nichols - Plane trigonometry - 1811 - 162 pages
...triangles may be resolved. PROP. X. 58. In all spherical triangles, whether right or obliqueangled, the sines of the sides are proportional to the sines of the angles opposite to them. Fig. 4 and 6. Let ABC be either a right or an oblique-angled triangle; the...
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - Geometry - 1816 - 352 pages
...theorems, is that which foreign writers have called the Theorem of the Four Sines ; according to which, the sines of the sides, are proportional to the sines of the opposite angles, of a spherical triangle : and it is that, of all others, which is the most easily retained. Of next,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...than a quadrant. PROP. XXIII. FIG. 16. IN spherical triangles, whether right angled or oblique angled, the sines of the sides are proportional to the sines of the angles opposite to them. First, Let ABC be a right angled triangle, having a right angle at A ; therefore,...
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