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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. "
A Supplement to the Elements of Euclid - Page 92
by Daniel Cresswell - 1819 - 410 pages
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...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 rectangle contained...lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. II. If a straight line be divided into any...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...which make the gnomon. PROPOSITION I. THEOREM. If there be two straight lines, one of which is divided into any number of parts, the rectangle contained...lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let A and BC be two straight lines, and...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...subsequent Propositions. PROPOSITION I. Theorem. 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. JL LH CB Proved...
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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...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 Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 pages
...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 rectangle contained...lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let A and BC be two straight lines ; and...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 pages
...parallelograms, which make the gnomon.' PROP. I. THEOR. If there oe two straight lines, one of which is divided into any number of parts; the rectangle contained...lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let A and BC be two straight lines; and...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...called the gnomon AGK "orEHC." B PROP. I. THEOR. If there be two straight lines, one of which is divided into any number of parts ; the rectangle contained...lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let A and BC be two straight lines ; and...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 320 pages
...parallelograms which make the gnomon.' PROP. I. THEOR. IF there be two straight lines, one of which is divided into any number of parts : the rectangle contained...lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line. by A, BD, together with that contained by...
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The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844 - 688 pages
...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 lines is equal to the rectangles contained by the undivided line and the several parts of the divided line. 7. If a straight line be divided into any...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...make the gnomon.' PROPOSITION I. THEOB. — If there be two straight lines, one of which is divided into any number of parts; the rectangle contained...lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let A and BC be two straight lines ; and...
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