| William Nicholson - 1809
................... 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 - 125 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 - 580 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 - 508 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 - 428 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
...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
...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 - 534 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
...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
...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... | |
| |