 | Samuel Heynes - 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 - 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 S, BP : S, DP::S,DS,B.... | |
 | Philip Ronayne - 1717 - 478 pages
...•• 2,BPA: AndT.DP.. r::T,PA •• S.DPA. '' Therefore, T.BPx 2.BPA (= r X T.PA) =: T,DP AXIOM lit In any Triangle (whether Right-angled, or Oblique)...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,... | |
 | 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 /_... | |
 | Robert Simson - 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 - 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 - 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... | |
 | 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,... | |
 | William Nicholson - 1821 - 356 pages
...obtuse angle. And an acute-angled triangle is that which has all its angles acute. In every triangle the sines of the sides are proportional to the sines of the opposite angles; also the sine of all the three angles is equal to two right ones ; and the external... | |
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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. 
