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" Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle. "
Elements of Plane Geometry - Page 123
by Franklin Ibach - 1882 - 196 pages
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - Geometry, Plane - 1809 - 522 pages
...23.), and consequently AG, AK touch the circle DGHK at the points G, K (III. 26.) PROP. XXXI. PROB. On a given straight line, to describe a segment of a circle, that shall contain an angle equal to a given angle. Let AB be a straight line, on which it is required...
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Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - Geometry - 1817 - 456 pages
...equal to CK, CA common, are equal (I. 21.), and consequently AG is equal to AK. PROP. XXIII. PROB. On a given straight line, to describe a segment of a circle, that shall contain an angle equal to a given angle. Let AB be a straight line, on which it is required...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...angle B4C is equal to the angle ADC in the alternate segment ADC. ED. B « PROPOSITION XXXIII. PROBLEM. On a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle ; that is, to describe a segment such that all the angles...
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First lessons in Plane Geometry. Together with an application of them to the ...

Francis Joseph Grund - Geometry, Plane - 1830 - 274 pages
...touching the circles on opposite sides. The demonstration is the same as the last. PROBLEM XVI. Upon a given straight line to describe a segment of a circle, which shall contain a given angle ; that is, a segment, such that the inscribed angles, having their vertices in the arc of the segment...
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Part 1

Francis Joseph Grund - Geometry, Plane - 1834 - 202 pages
...touching the circles on opposite sides. The demonstration is the same as the last. PROBLEM XVII. Upon a given straight line to describe a segment of a circle, which shall contain a given angle ; that is, a segment, such that the inscribed angles, having their vertices in the arc of the segment...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...of the circle. Wherefore, if a straight line, &c. QBD /> PROPOSITION XXXIII. See N. PROR. — Upon a given straight line to describe a segment of a circle, which shall contain aa angle equal to a given rectilineal angle. Let AB be the given straight line, and the angle at C...
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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - Mathematics - 1836 - 524 pages
...greater, and greater in the case of less. 11. We are now prepared to solve the following problem : Upon a given straight line, to describe a segment of a circle, which shall contain an angle equal to a given angle. This problem is often of much service, to those who are handy with...
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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - Mathematics - 1836 - 542 pages
...greater, and greater in the case of less. 11. We are now prepared to solve the following problem : Upon a given straight line, to describe a segment of a circle, which shall contain an angle equal to a given angle. This problem is often of much service, to those who are handy with...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...proved equal to • 2 Ax. BAD: therefore the remaining angle DBE is equal * to PROP. XXXIII. PROB. Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle. Let AB be the given straight line, and C the given rectilineal...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...segment of the circle, (ax. 2.) Wherefore, if a straight line, &c. QED PROPOSITION XXXIII. PROBLEM. Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle. Let AB be the given straight line, and the angle at C...
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