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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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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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A Treatise on Mechanics: Intended as an Introduction to the Study of Natural ...

Bewick Bridge - Mathematics - 1814 - 622 pages
...pairs of forces which should always act at some given angle to each other, then upon AB (Euc. 33. 3.) describe a segment of a circle which shall contain an angle equal to the given 2 If angle, and the number of pairs of forces into which the given force can be resolved...
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Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - Geometry - 1817 - 454 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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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 444 pages
....AF=GB. (13.) To draw a straight line which shall touch a given circle, and make with a given line, an angle equal to a given angle. Let AB be the given line, and O the centre of the given circle. From any point A in the given line, draw AC making with...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 442 pages
...AF= GB. (13.) To draw a straight line which shall touch a given circle, and make with a given line, an angle equal to a given angle. Let AB be the given line, and O the centre of the given circle. From any point A in the given line, draw AC making with...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...be a given right line, and ca given rectilineal angle. It is required upon the given right line AB to describe a segment of a circle which shall contain an angle equal to the angle at c. At the right line AB, and at the given point A in it, make the angle BAD* equal to...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 236 pages
...be a given right line, and ca given rectilineal angle. It is required upon the given right line AB to describe a segment of a circle which shall contain an angle equal to the angle at c. At the right line AB, and at the given point A in it, make the angle BAD" equal to...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 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 * 10- 1centre...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 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...circle, which shall contain an angle equal to a given rectilineal angle ; that is, to describe a segment such that all the angles described in it shall be...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...ingenuity, in problems of contact. PBOP. 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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