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" If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. "
A Supplement to the Elements of Euclid - Page 92
by Daniel Cresswell - 1819 - 410 pages
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853
...gnomon." J PROPOSITIONS. PROPOSITION I. THEOB. If there be two straight lines, one of which is divided into any number of parts ; the rectangle contained...lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let A and BC be two straight lines ; and...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...which make the gnomon." PROP. I. — THEOREM. If there be two straight lines, one of which is divided into any number of parts, the rectangle contained...lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let A and BC be two straight lines ; and...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 147 pages
...gnomon. Ъ о k PROPOSITION I. — THEOREM. If there be two straight lines, one of which is divided into any number of parts, the rectangle contained...straight lines is equal to the rectangles contained by tlie undivided line, and the several parts of the divided line. LET a and b С be two straight lines...
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Orr's Circle of the Sciences: The mathematical sciences

William Somerville Orr - Science - 1854
...L— Tn-EOBEM. If there be two straight lines (A and В С), one of which (BC) is divided into miy number of parts, the rectangle contained by the two...lines is equal to the rectangles contained by the undivided line and the several parts (BD, DE, &c.) of He divided line. From В draw В Г at right...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...BD, A and DE, and A and EС. -Wherefore, if there be two straight Hnes, &c. QED Corodary. — If two straight lines be divided each into any number of...contained by the two straight lines is equal to the sum of the rectangles contained by the several parts of the one and each of the several parts of the...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...contained by these two sides is a right angle. 6. If there be two straight lines, one of which is divided into any number of parts ; the rectangle contained...lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line. 7. To describe a square that shall be equal...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...also a right angle. XLVIII.— EUCLID II. 1. If there be two straight lines one of which is divided into any number of parts, the rectangle contained...lines is equal to the rectangles contained by the undivided line and the several parts of the divided line. Let A and BC (Fig. 38) be two straight lines...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...which make the gnomon." PROPOSITION I. THEOREM. If there be two straight lines, one of which is divided into any number of parts; the rectangle contained...lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line, Let A and .BCbe two straight lines ; and...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1860 - 332 pages
...&c. • PROP. I. THEOR. If there be two straight lines, one of which is divided into any number oj parts; the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let A and BC be two straight lines ; and...
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862
...I.— THEOREM. If there be two straight lines, one of which is divided into any number of parts ; then the rectangle contained by the two straight lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line. (References— Prop. i. 3, 11, 31, 34.)...
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