| 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,... | |
| 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... | |
| 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,... | |
| 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,... | |
| 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 =... | |
| 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... | |
| 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... | |
| 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,... | |
| 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,... | |
| 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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