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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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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...rectangle contained by the two lines is equal to the sum of the rectangles cont.tined by ,the whole line and the several parts of the divided line. Let...divided into any parts in the points D, E; the rectangle A.BC is equal to the sum of the several rectangles A.BD, A.DE, A.EC, or A.BC = Am + A.DE + A.EC. From...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 272 pages
...divided into any number of partt, the rectangle contained by the tiro lines shall be equal to tht sum of the rectangles contained by the undivided line, and the several parts of the tliridfd line. Let AB and С be two straight lines, of which AB is divided into the parts AI), DE,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1835 - 316 pages
...which is divided into any number of parts ; the rectangle contained by the two straight lines is equ2l to the rectangles contained by the undivided line,...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 (Prob. 6. 1.) BF at...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 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...Let A and BC be two straight lines ; and let BC be divid- Book II. ed into any parts in the points D, E ; the rectangle contained l-— v*"' by the straight...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...divided into any number of parts, the rectangle contained by the two lines shall be equal to the sum of the rectangles contained by the undivided line, and the several parts of the divided line. Let А В and С be two straight lines, of which AB is divided into the parts AD, DE, EB: the rectangle...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 513 pages
...rectangles contained by the undivided line, and the several parts of the divided line. b3. I. e 31. 1. Let A and BC be two straight lines ; and let BC be divid- Book II. ed into any parts in the points D, E ; the rectangle contained v- v*"' by the straight...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 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. II. If a straight line be divided into any two parts, the rectangles contained by the whole and each...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 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...the rectangle contained by the straight lines A, BC, is equal ^ T~T~ to the rectangle contained by A, BD, together with that contained by A, DE, and that...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 390 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...and BC be two straight lines ; and let BC be divided * This book treats of right-angled parallelograms, and in particular of squares. } That is, by any...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 88 pages
...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. JL LH CB Proved by' showing that A x BC * = figures BK + DL + EH ; and that these are = A x BD +...
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