 In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of...  Easy Introduction to Mathematics - Σελίδα 353των Charles Butler - 1814Πλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | John Dougall - 1810 - 734 σελίδες
...to EF; AD, however, is the sum of the sides, and AE their difference; while DC was shown above to be the tangent of half the sum of the angles at the base, and EF is the tangent of rulf their difference ; the proposition is, therefore, demonstrated. PROP.... | |
 | Francis Nichols - 1811 - 162 σελίδες
...ACB, which is the supplement of the angles at A and B, may be found by Cor. 32. 1. PROP VI. 61. In any triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference. Let ABC be the proposed triangle, whose... | |
 | William Enfield - 1811 - 476 σελίδες
...side MR. In the triangle SRM, the sides RS, RM, being thus found, the sum of the two sides RS, RM, is to their difference, as the tangent of half the sum of the angles at the base RSM, RMS, is to the tangent of half their difference. To half the sum add half the difference, and... | |
 | Robert Gibson - 1811 - 580 σελίδες
...In any Jilane triangle ABC, the sum of the two given sides AB and BC, including a given angle ABC, is to their difference, as the tangent of half the sum of the two unknown angles A and C is to Che tangent of half their difference. Produce AB and make HB=BC, and... | |
 | Charles Hutton - 1811 - 424 σελίδες
...k readily converted into a very nsefnl proportion, viz, The sum of the sines of two arcs or angles, is to their difference, as the tangent of half the sum of those arcs ' or angles, is to the tangent of half their difference. 2f . Operating with the third and... | |
 | Charles Hutton - 1812 - 624 σελίδες
...readily converted into a very useful proportion, viz, The sum of the sines of tiuo arcs or angles, is to their difference, as the tangent of half the sum of those arcs or angles, is to the tangent of half their difference. 26. Operating with the third and... | |
 | Euclides - 1814 - 560 σελίδες
...difference; and since BC, FG are parallel (2. 6.), EC is to CF, as EB to BG ; that is, the sum of the sides is to their difference, as the tangent of half the sum of the angles at the base, tothe tangent of half their difference. •'• - °" •' • -.-.. • •> i PROP. IV. Fio.JS, .... | |
 | John Gummere - 1814 - 398 σελίδες
...therefore since BC, FG are parallel EB : BF : : EC : CG (2. 6.) ; that is, the * sum of the sides AC, AB, is to their difference, as the tangent of half the sum of the angles ABC, ACB, is to the tangent of half their difference. • *• •• To demonstrate the latter part... | |
 | Robert Gibson - 1814 - 558 σελίδες
...aIn any jilane triangle AUC, the sum of the two gruen sides AB and BC, including a given angle ABC, is to their difference, as the tangent of half the sum of the two unknown angles A and Cix tg the tangent of half their difference. Produce AB, and make HB— BC,... | |
 | Jeremiah Day - 1815 - 172 σελίδες
...equal to the sum, and FH to the difference of AC and AB. And by theorem II, [Art. 144.] the sum of the sides is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. Therefore, R:Tan (ACH-45°;::Tan tfACB+B)... | |
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