 | John Bonnycastle - Trigonometry - 1806 - 464 pages
...their difference. , QE u. THEOREM III. 95. The base of any plane triangle ABC, is to the sum of the sides, as the difference of the sides is to the difference of the segments of the base. 336 and F, and the base c B in G : also draw the perpendicular AD. Then, because AE, AF are each equal... | |
 | Thomas Keith - Navigation - 1810 - 478 pages
...When the three sides of a triangle are given tojind the angles.^ Double the base, or longest side, Is to the sum of the other two sides; As the difference between those two sides, Is to the distance of a perpendicular from the middle of the base. * If the... | |
 | Charles Hutton - Mathematics - 1811 - 424 pages
...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 of half the sum of the angles at the base, to the cosine of half their difference. Ex. 14. How... | |
 | Charles Hutton - Mathematics - 1812 - 624 pages
...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 of half the sum of the angles at the base, :o the cosine of half their difference. Ex. 14. How... | |
 | John Gummere - Surveying - 1814 - 398 pages
...cor.) j therefore AB : AE : : AG : AF (1(>. 6) ; that is, the base, is to the sum of the sides, «3 the difference, of the sides, is to the difference of the segments of . tye-bu* • •', ' - Cor. If AF be considered the 'tase of the triangle AFC, then will CD be a perpendicular... | |
 | Charles Butler - 1814 - 582 pages
...within a triangle, a perpendicular be drawn from the opposite angle to the base, then will the base : be to the sum of the other two sides : : as the difference of these sides : to the difference of the segments of the base. Let ABC be a triangle, having the straight... | |
 | John Gummere - Surveying - 1817 - 384 pages
...AG-(36. 3. cor.); therefore AB : AF, : : AG : AF (16. 6) ; that ¡s, the base, is to the sum of the sides, as the difference of the sides, is to the difference of the segments of the base. Cor. If AF be considered the base of the triangle AFC, then will CD be a perpendicular on the base... | |
 | Edward Riddle - Nautical astronomy - 1824 - 572 pages
...geometrically that rad . sect 2 A = tan A . tan 2 A + rad*., 4. Shew that in any plane triangle the base is to the sum of the other two sides as the sine of half the vertical angle is to the cosine of half the difference of the angles at the base.... | |
 | Thomas Keith - Navigation - 1826 - 504 pages
...When the three sides of a triangle are given, toßnd the angles. * Double the base, or longest side, Is to the sum of the other two sides ; As the difference between those two sides, Is to the distance of a perpendicular from the middle of the base. This distance... | |
 | Charles Davies - Surveying - 1830 - 318 pages
...perpendicular to the opposite sidr, dividing it into two segments, the whole side or sum of the segments, is to the sum of the other two sides, as the difference of those sides, to the differ' ence of the segments. * The references marked thus, ( )*, refer to the... | |
| |
If a perpendicular be let fall from any angle of a triangle to its opposite side or base, this base is to the sum of the other two sides, as the difference of the sides is to the difference of the segments of the base. 
