 | William Leybourn - Geometry - 1704 - 432 pages
...the Difference of the Sides, (as the Sine of the Sum of the Angles : Sine of the Difference of the Angle*) So is the Tangent of half the Sum of the Angles, To the langent of half the Difference of the Angles. That is, As X К : XH : : AP : A O. Therefore,... | |
 | William Nicholson - 1809 - 722 pages
....75486 Axiom III. In every plane triangle it will bn as the sum of any two sides is to their difference; so is the tangent of half the sum of the angles opposite there, to the tangent of half their difference. Which lialf difference, being added to half the sum... | |
 | Jeremiah Day - Measurement - 1815 - 388 pages
...perpendicular to BG. (Euc. Def. 10. 1.) If then CE is made radius, GE is the tangent of GCE, (Art. 84.) that is, the tangent of half the sum of the angles opposite to A3 and AC. If from the greater of the two angles ACB and ABC, there be taken ACD their half sum ; the... | |
 | Jeremiah Day - Logarithms - 1815 - 172 pages
...perpendicular to BG. (Euc. Def. 10. 1.) If then CE is made radius, GE is the tangent of GCE, (Art. 84.) that is, the tangent of half the sum of the angles opposite to AB and AC. If from the greater of the two angles ACB and ABC, there be taken ACD their half sum ; the... | |
 | John Playfair - 1819 - 354 pages
...: BE : BG, (2. 6.) that is, the sum of the two sides of the triangle ABC is to their difference as the tangent of half the sum of the angles opposite...those sides to the tangent of half their difference. QED PROP. V. If a perpendicular be dravnfrom any angle of a triangle to the opposite side, or base... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...the sum of the two sides of the triangle ABC is to their difference as the tangent of half the sam of the angles opposite to those sides to the tangent of half their difference. Q, ED PROP. V. If a, perpendicular be drawnfrom any angle of a triangle to the opposite side, or base... | |
 | William Nicholson - Natural history - 1821 - 356 pages
...Axiom III. In every plane triangle, it will be as the sum of any two sides is to their difference ; so is the tangent of half the sum of the angles opposite there, to the tangent of half their difference. Which half difference, being added to half the sum... | |
 | William Nicholson - Natural history - 1821 - 356 pages
....Axiom III. In every plane triangle, it will be us the sum of any two sides is to their difference ; so is the tangent of half the sum of the angles opposite there, to the tangent of half their difference. AVhich half difference, being added to half the sum... | |
 | Edward Riddle - Nautical astronomy - 1824 - 572 pages
...tan DAC = cot C. PROPOSITION VI. The slim of any two sides of a triangle is to tlieir difference, as the tangent of half the sum of the angles opposite to those sides is to the tangent of half their difference. Let А В С be any plane triangle. Then AB : AC : : sin... | |
 | Jeremiah Day - Geometry - 1824 - 440 pages
...perpendicular to BG. (Euc. Def. 10. 1.) If then CE is made radius, GE is the tangent of GCE, (Art. 84.) that is, the tangent of half the sum of the angles opposite to AB and AC. If from the greater of the two angles ACB and ABC, there be taken ACD their half sum ; the... | |
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Def. 10. 1.) If then CE is made radius, GE is the tangent of GCE, (Art. 84.) that is, the tangent of half the sum of the angles opposite to AB and AC. If from the greater of the two angles ACB and ABC, there be taken ACD their half sum ; the remaining... 
