 | Samuel Heynes - 1701 - 334 pàgines
...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 pàgines
...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 - 180 pàgines
...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 - 478 pàgines
...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 - 214 pàgines
...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 - 658 pàgines
...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 - 546 pàgines
...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 pàgines
...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 pàgines
...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 pàgines
...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... 
