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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. "
The Elements of Geometry - Page 101
by George Bruce Halsted - 1886 - 366 pages
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 552 pages
...'of the parallelograms which make the gnomon." PROP. I. THEO R. K C TF there be two ftraight lines, one of which is divided into any number of parts ; the rectangle contained by the two ftraight lines, is equal to the rectangles contained by the undivided line, and the feveral parts of...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - Trigonometry - 1799 - 374 pages
...angles of the parallelograms which make the gnomon.' PROP. I. THEOR. F there be two ftraight lines, one of which is divided into any number of parts ; the rectangle contained by the two ftraight lines, is equal . to the reftangles contained by the undivided line, and the feveral parts...
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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

John Playfair, Euclid - Circle-squaring - 1804 - 468 pages
...brevity, be called the gnomon AGK, or EHC.' a ii. i. PROP. I. THEOR. IF there be two ftraight lines, one of which is divided into any number of parts ; the rectangle contained by the two ftraight lines, is equal to the reftangles contained by the undivided line, and the feveral parts of...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804 - 530 pages
...angles of the parallelograms which make the gnomon.' PROP. I. THEOR. IF there be two ftraight lines, one of which is divided into any number of parts ; the rectangle contained by the two ftraight lines, is. equal to the rectangles contained by the undivided line, and the feveral parts...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...angles of the pa< rallelograms which make the gnomon.' G 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 equal to the rectangles contained by the undivided line and the several parts of...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...together with the two complements, is called a gnomon. 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 equal to the rectangles contained by the undivided line, and the several parts of...
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volume 2

Charles Butler - Mathematics - 1814 - 528 pages
...several parts a, b, and c, of the divided line s." QED Cor. Hence, if two given straight lines be each divided into any number of parts, the rectangle contained by the two straight lines will be equal to the sum of the rectangles contained by each of the parts of the one,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...angles of the parallelograms ' which makes the gnomon.' 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 equal to the rectangles contained by the undivided line, and the several parts of...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...brevity, be ' called the gnomon AGK or ' EHC." A E. K G PROP. I. THEOR. ff 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...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...с parallelograms which make the gnomon.' Propońlion. 7. 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...
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