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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. "
The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text, Based ... - Page 119
by Euclides - 1853
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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...
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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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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Part 1

Francis Joseph Grund - Geometry, Plane - 1834 - 190 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...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...ingenuity, in problems of contact. PROP. 60. Prob. 7. (Eue. iii. 33.) Upon a given straight line AB to describe a segment of a circle which shall contain an angle equal to a given angle ABC. Let AQ В be the segment required, and P its centre. Then, because the angle А В С is equal...
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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...which shall contain an angle equal to a given angle. This problem is often of much service, to those who are handy with a pair of compasses, in the construction...
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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...which shall contain an angle equal to a given angle. This problem is often of much service, to those who are handy with a pair of compasses, in the construction...
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The Element of Geometry

John Playfair - Geometry - 1836 - 114 pages
...lines, &c. QED PROP. XXV. PROB. Upon a given straight line to describe a segment of a circle, containing an angle equal to a given angle. Let AB be the given straight line, and the angle at C the given rectilineal angle ; it is required to describe upon the given straight line...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 pages
...line to apply ta parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given angle. Let AB be the given straight line, C the given triangle, and D the given angle. It is required to apply to AB a parallelogram equal to...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...angle at C the given rectilineal angle ; it is required to describe upon the given straight line AB a segment of a circle, which shall contain an angle equal to the angle C. First, let the angle at C be a right angle : „ ,• bisect* AB in F, and from the...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 pages
...line, and C the given rectilineal angle; it is required to describe upon the given straight line AB, a segment of a circle, which shall contain an angle equal to the angle C. First, let the angle C be a right angle; bisect* AB in F, and from '"*' the centre F,...
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