 | John Radford Young - Geometry, Analytic - 1850 - 294 pages
...Given one side, the difference between the square of the other side, and the square of the base, and the difference of the segments of the base, made by a perpendicular from the vertical angle, of a plain triangle, to determine the triangle. Put a = the given sides Z?2 = the difference... | |
 | Horatio Nelson Robinson - Mathematics - 1851 - 96 pages
...AC in E. Join EF ; produce AC to D,, and join DB & BE. AE is the difference of the sides, and AF is the difference of the segments of the base made by a perpendicular from C, The triangle AEF gives the following proportion : This proportion is the theorem, as will appear... | |
 | Horatio Nelson Robinson - Conic sections - 1854 - 350 pages
...the sides of spherical triangles are proportional to the sines of their opposite angles. 2. The sines of the segments of the base, made by a perpendicular from the opposite angle, are proportional to the cotangents of their adjacent angles. 3. The cosines of the... | |
 | Elias Loomis - Trigonometry - 1859 - 218 pages
...B. (216.) Cor. 1. In any spherical triangle, the cosines oftht sides are proportional to the cosines of the segments of the base, made by a perpendicular from the opposite angle. For, by Theorem I., Cor. 2, cos. CD : R : : cos. AC : cos. AD. Also, cos. CD : R :... | |
 | Anthony Nesbit - Measurement - 1859 - 494 pages
...(for which the longest side is taken) : sum of the other two sides : : difference of these two sides : difference of the segments of the base made by a perpendicular from its opposite angle. Add this number to, and subtract it from, the base ; then Half sum = greater segment... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...given straight line. 130. Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle. 131. Given the vertical angle, and the lengths of two lines drawn from the... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...the sides of spherical triangles are proportional to the sines of their opposite angles. 2. The sines of the segments of the base, made by a perpendicular from the opposite angle, are proportional to the cotangents of their adjacent angles. 3. The cosines of the... | |
 | Euclides - 1862 - 140 pages
...The difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base made by a perpendicular from the opposite angle. 50. The three straight lines bisecting the three angles of a triangle, all meet in... | |
 | Euclides - 1864 - 262 pages
...given straight line. 130. Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle. 131. Given the vertical angle, and the lengths of two lines drawn from the... | |
 | Euclides - 1864 - 448 pages
...given straight line. 130. Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle. 131. Given the vertical angle, and the lengths of two lines drawn from the... | |
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Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle. 
