 | Samuel Heynes - 1701 - عدد الصفحات: 334
...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 - عدد الصفحات: 298
...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... | |
 | Samuel Heynes - 1716 - عدد الصفحات: 180
...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 - 1717 - عدد الصفحات: 478
...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,... | |
 | William Emerson - 1749 - عدد الصفحات: 214
...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 oppoßte Angles. 43' . On AB, AF let fall the Perpendiculars FH, В I i then by Prop. XXVI. S.AF:S.FH... | |
 | 1801 - عدد الصفحات: 658
...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 - 1806 - عدد الصفحات: 546
...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 - عدد الصفحات: 162
...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 - عدد الصفحات: 352
...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 - عدد الصفحات: 588
...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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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... 
