 | Euclid - 1835 - 540 pages
...is, the given ratio of AD to BC, must be less than the ratio of GH to EF, which the straight line, in a segment of a circle containing an angle equal to the given angle, that bisects the base of the segment at right angles, has to the base. COR. 1. If two triangles, ABC,... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...PROB. GIVEN the angles and diagonals of a parallelogram ; to construct it. On one of the diagonals describe a segment of a circle containing an angle equal to the given angle at either extremity of the other ; from the middle point of this diagonal as centre, with half the... | |
 | William Desborough Cooley - Geometry - 1840 - 106 pages
...triangle, of which the base, the ratio of the sides, and the vertical angle are given. On the given base AB describe a segment of a circle, containing an angle equal to the given vertical angle (m. Prop. 33). Complete the circle, and draw the diameter EC making right angles with... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...PROB. — Given the angles and diagonals of a parallelogram ; to construct it. On one of the diagonals describe a segment of a circle containing an angle equal to the given angle at either extremity of the other ; from the middle point of this diagonal as centre, with halt' the... | |
 | Euclides - 1845 - 546 pages
...of given length. Bisect PQ in R and on PR describe a rectangle equal to the given area ; also on PQ describe a segment of a circle containing an angle equal to the angle BAC, and let the arc of this segment cut the side of the rectangle opposite to PR in S. Join... | |
 | 1847 - 364 pages
...intersecting CB in C : take CH and CL, each equal to the sum of the sides, and draw HL and HO. On HO describe a segment of a circle containing an angle equal to the angle CLH and let it intersect CL in B : draw BA touching the circle DEF in F, and ABC is the triangle... | |
 | Euclid, Robert Potts - Euclid's Elements - 1847 - 118 pages
...of given length. Bisect PQ in R and on PR describe a rectangle equal to the given area ; also on PQ describe a segment of a circle containing an angle equal to the angle BAC, and let the arc of this segment cut the side of the rectangle opposite to PR in S. Join... | |
 | 1851 - 428 pages
...external to, or wholly internal to, but not concentric with, the other. 3. On a given unite straight line, describe a segment of a circle, containing an angle equal to the three-fourths of a right-angle. 4. Show that if d be the distance in miles of the offing, and h the... | |
 | Thomas Percy Hudson - Trigonometry - 1862 - 218 pages
...at P by the two sides of the triangle AB, BC respectively. Upon AB, [figs. (1) and (2),] on the map describe a segment of a circle containing an angle equal to the observed angle APB. Similarly upon BC describe a segment containing an angle equal to the observed... | |
 | Euclides - 1864 - 448 pages
...vertical angle, and the perpendicular in a plane triangle, '- — 'struct it. Upon the given base AB describe a segment of a circle containing an angle equal to the given angle. (in. 33.) At the point B draw BC perpendicular to AB, and equal to the altitude of the triangle. (I.... | |
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AB be equal to the given bisecting line ; and upon it describe a segment of a circle containing an angle equal to the given angle. 
