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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. "
Elements of Euclid Adapted to Modern Methods in Geometry - Page 77
by Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 216 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1835 - 336 pages
...brevity, be called the gno' mon AGK or EHC." A. E H I PROP. I. THEOR. 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 equ2l to the rectangles contained by the undivided line, and the several parts of the divided line....
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...Rectangles under the par Is of divided lines. PROP. 30. (Eue. 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 shall be equal to the sum of the rectangles contained by the undivided line, and the several...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...together with the two complements, is called a Gnomon. PHOP. I. If there be two straight lines, one of which is divided into any number of parts ; the...contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. II. If a straight...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...the parallelograms which make the gnomon. PROPOSITION I. THEOREM. If there be two straight lines, one of which is divided into any number of parts, the...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...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...demonstration of the subsequent Propositions. PROPOSITION I. Theorem. If there be two straight lines, one of which is divided into any number of parts, the...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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...occasionally used for brevity, " in what follows." PROP. I. THEOR. 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 rectangles contained by the undivided line, and the several parts of the divided...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 pages
...H 'lelograms which make the gnomon.' F D K BGC PROP. I. THEOR. IF there be two straight lines, one of which is divided into any number of parts; the...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...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...-parallelograms which make the gnomon.PROP. I. THEOR. If there be two straight lines, one of which is dieided into any number of parts ; the rectangle contained by the two straight lines, is equal to the rectangles contained by the undieided line, and the seeeral parts of the dieided line. Let A and BC...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 pages
...THEOR. The rectangle contained by two straight lines, of which one is divided into any number of parts, is equal to the sum of the rectangles contained by...undivided line and the several parts of the divided line. PROP. II. THEOR. If a straight line be divided into any two parts, the square of the whole line is...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 pages
...=L'HB. Therefore, L'AB, or the rectangle contained by the two lines, is equal to L'AF+L'FH+L'HB, or the sum of the rectangles contained by the undivided line and the parts of the divided line. PROP. II. THEOR. If a straight line (AB) be divided into any two parts (AF,...
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