 | Euclides - 1845 - 546 σελίδες
...given straight line. 61. 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. 62. On a given straight line to describe a triangle having its vertical angle... | |
 | Euclid, James Thomson - 1845 - 382 σελίδες
...is, sin j (A — B) :sinJ(A + B) :: a— b : c. PROP. V. THEOR. — In any plane triangle, the sum of the segments of the base made by a perpendicular from the vertex, is to the sum of the other sides, as the difference of those sides to the difference of the segments.... | |
 | Scottish school-book assoc - 1845 - 444 σελίδες
...from (arts. 36 and 59), and (Alg. 69). 7. Prove that the difference of the sides of a triangle, is to the difference of the segments of the base made by a perpendicular upon it from the vertex, as the cosine of half the sum of the angles at the base, is to the cosine... | |
 | Euclides - 1846 - 292 σελίδες
...AB.AF + AD.AH=AC.AG. 100. Given the vertical angle, the difference of the sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex : construct the triangle. BOOK IV, DEFINITIONS. i. A RECTILINEAL figure is said to be inscribed in... | |
 | Dennis M'Curdy - 1846 - 166 σελίδες
...QED . 5 Th. The base of a triangle is to the sum of both the sides, as the difference of the sides is to the difference of the segments of the base, made by a perpendicular falling upon it from the vertex, or to the sum of the segments, when the base must be produced to meet... | |
 | John Radford Young - 1848 - 300 σελίδες
...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 62 = the difference... | |
 | Euclid, Thomas Tate - 1849 - 120 σελίδες
...the greatest angle ? 37. 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 ; to construct the triangle. THEOREMS. 1. If two circles cut each other, the straight line joining... | |
 | John Radford Young - 1850 - 294 σελίδες
...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 - 1851 - 96 σελίδες
...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 - 1854 - 350 σελίδες
...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... | |
| |
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. 
