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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. Let... "
The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... - Page 40
by Robert Simson - 1827 - 513 pages
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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text ..., Book 1

Euclides - Geometry - 1853
...shall be equal to the rectangles contained by the undivided and the several parts of the divided l1ne. Let A and BC be two straight lines, and let BC be divided into any number of parts BD, DE, EC, in u, E. Then the rectangle contained by A, BC shall be equal to the rectangle...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 147 pages
...parts, the rectangle contained by the two 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 ; and let b С be divided into any parts in the points d, e ; the rectangle...
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Orr's Circle of the Sciences: The mathematical sciences

William Somerville Orr - Science - 1854
...and В С), one of which (BC) is divided into miy 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 (BD, DE, &c.) of He divided line. From В draw В Г at right angles to В С,* andmakeBG=A. t Through...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Geometry - 1855 - 318 pages
...rectangle contained by the two straight lines is equal to the rectangles contained by the undivided liiie, and the several parts of the divided line. Let A and...into any parts in the points D, E ; the rectangle A.BC is equal to the several rectangles A.BD, A.DE, A.EC. From the point B draw (Prop. 11.1.) BF at...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...any number of parts ; the rectangle contained by the two straight lines, is equal to the rectangle contained by the undivided line, and the several parts of the divided line. Let A and B С be two straight lines; and let B С be divided into several parts at the points D and E. The rectangle...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...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...the several parts of the divided line. Let A and BC (Fig. 38) be two straight lines whereof BC is divided into parts by the points D, E, etc. The rectangle...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...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...undivided line, and the several parts of the divided line. 7. To describe a square that shall be equal to a given rectilineal figure. 8. If two circles cut one...
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The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - Civil engineering - 1858 - 324 pages
...straight lines, one of which is divided into any number of parts, the rectangle contained by the two lines is equal to the rectangles contained by the...undivided line, and the several parts of the divided line. If a straight line be divided into any two parts, the rectangle contained by the whole and ono part...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858
...st. lines, one of which is divided into any number of parts, the rectangle contained by the two st. lines is equal to the rectangles contained by the...undivided line and the several parts of the divided line. CONS. — 11. I. At a point in a st. line to draw a right angle. 3. I. From the greater of two lines...
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Skeleton propositions &c. of Euclid, books i and ii, with ..., Volume 2

Euclides - 1858
...is divided into tunj number of parts, the rectangle continued by the two st. lines is equal to tlie rectangles contained by the undivided line and the several parts of the divided line. Соя. V. 11. 3, 31, I. OEM. :UI, AT. Я. K. 1 Hjp. Concl. h...,ii n '., я. I MI ; .;. I. : :J1....
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