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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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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 390 pages
...These signs will be 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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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...-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...lines, is equal to the rectangles contained by the undieided line, and the seeeral parts of the dieided line. Let A and BC be two straight lines; and...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...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 the 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
...and AB), of which one (AB) is divided into any number of parts (AF, FH, HB), is equal to the sum of the rectangles contained by the undivided line and the several parts of the divided line. From A draw AC perpendicular to AB, make it equal to L, and complete the parallelogram AD (that is...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...at the opposite angles of the " ' parallelograms which make the gnomon.' PROP. I. THEOR. IF there be two straight lines, one of which is divided into any...undivided line, and the several parts of the divided line. by A, BD, together with that contained by A, DE, and that contained by A, EC. From the point в draw...
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The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844
...into two equal |>orts. 6. If (here be two straight lines, one of which is divided into any number ot parts, the rectangle contained by the two straight...undivided line and the several parts of the divided line. 7. If a straight line be divided into any two parts, the squares of the whole line, and of one of the...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 352 pages
...will be occasionally used for brevity, in what follows." PROPOSITIONS. 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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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845
...PROPOSITION V. THEOREM. If there be two right lines, of which one is divided into parts, the sum of the rectangles contained by the undivided line and the several parts of the other, will be equal to the rectangle contained by the two whole lines. Let the lines be AB, AC, of...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846
...expressed by the words " rectangle of AB and AD j" or by " AB . AD." PROP. XLI. THEOR. 1. 2 En. angle contained by the two straight lines, is equal to the...several parts of the divided line. Let A and BC be two str. lines, and let BC be divided into any parts in D and E; then A.BC=A.BD + A.DE+A.EC B DEC Draw...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846
...words " rectangle of AB and AD;" or by " AB . AD." PROP. XLI. THEOR. ,. 2Eu . angle contained by tlie two straight lines, is equal to the rectangles contained...several parts of the divided line, Let A and BC be two str. lines, and let BC be divided into any parts in D and E; then A.BC=A. BD + A. DE+A. EC B DEC Draw...
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