 | William Nicholson - 1809 - 722 páginas
................... l .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... | |
 | Thomas Simpson - 1810 - 152 páginas
...co-sine AC : : tang. C : co-tang. A. £>. E, D. LEMMA. As the sum of the sines of two unequal arches is to their difference, so is the tangent of half the sum of those arches to the tangent of half their difference : and, as the sum of* the co-sines is to their... | |
 | John Dougall - 1810 - 734 páginas
...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.... | |
 | Robert Gibson - 1811 - 580 páginas
...wholes are as their halves, that is, AH: Iff : : CE : ED, that ia as the sum of the two sides AB and BC, is to their difference ; so is the tangent of half the sum of the two unknown angles A and C, to the tangent of half their difference. 2. E. DK THEO. III. fig. 12. In... | |
 | William Enfield - 1811 - 476 páginas
...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... | |
 | Charles Hutton - 1811 - 404 páginas
...of half their difference : also, that the base is to the sum of the other two sides, as the cosine of half the sum of the angles at the base, to the cosine of half their difference. Ex. 14. How must three trees, A, B, c, be planted, so that the angle... | |
 | Charles Hutton - 1812 - 624 páginas
...Prove that, in any plane triangle, the base is to the difference of the other two sides, as the sine of half the sum of the angles at the base, to the sine of half their difference : also, that the base is to the sum of the other two sides, as the cosine... | |
 | George Adams - 1813 - 648 páginas
...the angle CDB, and the side CD: to find CDB we use this proportion; as the sum of the two given aides is to their difference, so is the tangent of half the sum of the two unknown angles to the tangent of half their difference; the angle C'DB being found; the following... | |
 | Charles Butler - 1814 - 582 páginas
...6.) and AF : AE:: FB : ED (16. 5.) ; that is, the sum of the sides : is to their difference : : as the tangent of half the sum of the angles at the base : to the tangent of half their difference. QED When two sides and the included angle are given, the remaining angles may be found by this proposition... | |
 | Charles Butler - 1814 - 528 páginas
...preceding article. 71. In a plane triangle, tte sum of any two sides : is to their difference ,: : as the tangent of half the sum of the angles at the base : to the tangent of half the difference. Let ABC be a triangle, from C as a centre with the .least side CJ3 as radius, describe... | |
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AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. 
