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Books Books 1 - 10 of 92 on In spherical triangles, whether right angled or oblique angled, the sines of the....  
" 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. "
Revue Semestrielle Des Publications Mathématiques - Page 87
1899
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A Treatise of Trigonometry: Plane and Spherical, Theoretical and Practical ...

Samuel Heynes - 1701 - 8 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 - Mathematics - 1706 - 253 pages
...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 - 132 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 - 408 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. Demonßration. . Therefore, S, BP x S, B (= rx S, PA) = S, DP XS, D ; Wherefore,...
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Mathematics, Volume 2

Mathematics - 1801 - 610 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: viz. the first six books, together with the eleventh ...

Euclid, Robert Simson - Euclid's Elements - 1806 - 518 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 - 128 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, Spherical - 1816 - 294 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 - 528 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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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...cos ABC : sin BCA. Q, ED PROP. XXIV. 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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