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" PROP. I. THEOR. If there oe 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. "
The Elements of Euclid; viz. the first six books,together with the eleventh ... - Page 50
by Euclides - 1841 - 351 pages
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - Geometry - 1890 - 400 pages
...abbreviated into ' AB . CD ' in the Addenda and Exercises. Proposition 1. THEOREM — If there are two straight lines, one of which is divided into any...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...
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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
...the other two sides, the angle contained by these two sides is a right angle. BOOK II. 1. If there be two straight lines, one of which is divided into any...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
...squares on the two sides. APPENDIX I. Enunciations of the Propositions of EUCLID, BOOK II. 1. If there be two straight lines, one of which 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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 518 pages
...numerical equivalents by which they may be expressed arithmetically. PROPOSITION 1. THEOREM. If there are two straight lines, one of which is divided into any number of parts, the rectangle , contained by tlis. two straight lines is equal to the sum of the rectangles contained by the undivided straight...
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Euclid's Elements of Geometry, Books 1-6

Henry Martyn Taylor - 1893 - 504 pages
...contained by AB, CE, and by AB, ED. Wherefore, if there be two straight lines &c. COROLLARY 1. If there be two straight lines, one of which is divided into any...contained by the two straight lines is equal to the sum of the rectangles contained by the undivided line and each of the parts of the divided line. If...
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Euclid's Elements of Geometry, Books 1-6; Book 11

Henry Martyn Taylor - 1895 - 657 pages
...contained by AB, CE, and by AB, ED. Wherefore, if there be two straight lines &c. COROLLARY 1. If there be two straight lines, one of which is divided into any...contained by the two straight lines is equal to the sum of the rectangles contained by the undivided line and each of the parts of the divided line. If...
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A Text-book of Euclid's Elements for the Use of Schools, Books I.-IV., Book 1

Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 304 pages
...numerical equivalents by which they may be expressed arithmetically. PROPOSITION 1. THEOREM. If there are two straight lines, one of which is divided into ....contained by the two straight lines is equal to the sum of the rectangles contained by the undivided straight line and the several parts of the divided...
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Elementary Geometry: Practical and Theoretical

Charles Godfrey, Arthur Warry Siddons - Geometry - 1903 - 355 pages
...tlieorcms (Ex. 1090 — 1093) ai an algebraical ldentity; prove the identity. Ex. 1O9O. If there are two straight lines, one of which is divided into any number of parts (x, y, z say) while the other is of length a, then the rectangle contained by the two straight lines...
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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 Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid - Euclid's Elements - 1904 - 456 pages
...which they may be expressed arithmetically. EUCLID-S ELEMENTS. PROPOSITION 1. THEOREM. If there are two straight lines, one of which is divided into any...contained by the two straight lines is equal to the sum of the rectangles contained by the undivided straight line and the several parts of the divided...
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