 | Robert Simson - Trigonometry - 1806 - 546 pages
...is, *he 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 unto the base. Con. 1. If two triangles,... | |
 | Miles Bland - Euclid's Elements - 1819 - 444 pages
...triangle. Take any line AB, and divide it in C, in the given ratio of the segments. On AB describe a segment of a circle containing an angle equal to the given difference. From C draw the perpendicular CD. Join AD, DB ; and take DE : DA in the ratio of the given... | |
 | Miles Bland - Euclid's Elements - 1819 - 442 pages
...triangle. Take any line AB, and divide it in C, in the given ratio of the segments. On AB describe a segment of a circle containing an angle equal to the given difference. From C draw the perpendicular CD. Join AD, DB; and take DE : DA in the ratio of the given... | |
 | Sir John Leslie - Curves - 1821 - 518 pages
...D(V and COc are likewise given. COMPOSITION. Draw any diameter KO, on which describe (III. 23. El.) a segment of a circle containing an angle equal to the given inclination of the conjugate diameters, and meeting the curve in a point G, join GE, G?, and parallel... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...the given ratio of AD to BC, must be less \ than the ratio of GH to KF, 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 unto the base. COR. 1. If two triangles,... | |
 | Henry Parr Hamilton - Mathematics - 1834 - 272 pages
...admits of the following geometrical solution. Draw any diameter whatever Rr, and upon it describe Tf a segment of a circle, containing an angle equal to the given angle, and cutting the ellipse in Q ; draw Qr, QR, and, parallel to these, the diameters Pp, Dd; these will... | |
 | Henry Parr Hamilton - Conic sections - 1834 - 240 pages
...geometrical construction. Draw any diameter Rr, meeting the hyperbola in R, r, and upon it describe a segment of a circle containing an angle equal to the given angle, and cutting the hyperbola in Q, draw QR, Qr, and, parallel to these, the semi-diameters CP, CD ; these... | |
 | 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
...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
...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... | |
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AB describe a segment of a circle containing an angle equal to the given angle, (in. 
