| 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,... | |
| John Harris - Spherical projection - 1706 - 298 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... | |
| 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,... | |
| 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. Demonßration. . Therefore, S, BP x S, B (= rx S, PA) = S, DP XS, D ; Wherefore,... | |
| 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 =... | |
| 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... | |
| 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... | |
| 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,... | |
| 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,... | |
| John Playfair - 1819 - 354 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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