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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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Guide to obtaining an army school certificate, 1st class, by an army ...

George Lund Dunnett - 1884
...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. The sum of the perpendiculars let fall from any point within any equilateral figure upon its sides...
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Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884
...rectangle contained by the two straight lines, is equal to the rectangles contained by the tmdivided line, and the several parts of the divided line. Let A and BC be two straight lines ; of which BC is divided into any parts in the points D, E. Then the rectangle contained by A and BC,...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884
...one of which is divided internally into any number of segments, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line and the several segments of the divided line. 0 EFD O "H •B Let AB and CD be the two straight lines, and let CD be...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889
...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. If A, B, C, D are points in a straight line, taken in order, prove that the rectangle AC . BD = AB...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...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...divided line. Let A and BC be two straight lines, of which BC is divided at D, E; then rect. A. BC=A. BD, A. DE, A. EC, Draw BF ir to BC, and cut off...
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - Geometry - 1890 - 400 pages
...into any number of parts, the rectangle contained by the two straight lines is equal to the sum of the rectangles contained by the undivided line and the several parts of the divided line. EFQ Let AB be the one line, divided in C and D ; and X the other. Draw AE so that it = X, and _L to...
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Rider Papers on Euclid: Books i and Ii, Graduated and Arranged in Order of ...

Rupert Deakin - Euclid's Elements - 1891 - 79 pages
...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. 2. If a straight line be divided into any two parts, the rectangles contained by the whole and each...
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A Text-book of Geometrical Deductions: Book I [-II] Corresponding to ..., Book 2

James Andrew Blaikie, William Thomson - Geometry - 1892
...is divided into any number of parts, the rectangle contained by the two lines is equal to the sum of the rectangles contained by the undivided line and the several parts of the divided line. 2. If a straight line be divided into any two parts, the square on the whole line shall be equal to...
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Elementary Geometry: Plane

James McMahon - Geometry, Plane - 1903 - 358 pages
...at given points, the rectangle of the two given lines is equivalent to the sum of the rectangles of the undivided line and the several parts of the divided line. Let AB, CF be the two lines, and let CF be divided at the points D and E into the parts CD, DE, EF. GH...
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A School Geometry, Parts 1-4

Henry Sinclair Hall - 1908
...Equivalents of some Algebraical Formulae. DEFINITIONS .......... 219 the two lines is equal to the sum of the rectangles contained by the undivided line and the several parts of the divided line. 2-20 COROLLARIES. [Euc. II. 2 and 3.] 221 THEOREM 51. [Euc. II. 4.] If a straight line is divided Internally...
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