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. Euclid's Elements of Geometry - Page 135edited by - 1893 - 504 pagesFull view - About this book
| Euclid - 1781 - 550 pages
...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... | |
| Alexander Ingram - Trigonometry - 1799 - 351 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... | |
| Robert Simson - Trigonometry - 1804
...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... | |
| John Playfair - Euclid's Elements - 1804 - 470 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... | |
| John Playfair - Euclid's Elements - 1806 - 311 pages
...brevity, 4 be called the gnomon ' AGK, or EHC.' 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... | |
| Robert Simson - Trigonometry - 1806 - 518 pages
...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...contained by the two straight lines, is equal to the** rectangles contained by the undivided line and the several parts of the divided line. D K H Book II.... | |
| John Mason Good - 1813 - 722 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...contained by the two straight lines, is equal to the** rectangles contained by the undivided line, and the several parts of the divided line. Prop. II. Theor.... | |
| 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, and each of the... | |
| Euclides - 1816 - 528 pages
...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...contained by the two straight lines, is equal to the** rectangles contained by the undivided line, and the several parts of the divided line. BouK II. Let... | |
| Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...THE FIRST SIX BOOKS OF i .' • : BOOK II. PROP, I. (I.) IF two given straight lines be divided, each **into any number of parts, the rectangle contained by the two straight lines, is equal to the** rectangles contained by the several parts of the one and the several parts of the other. PROP. V. (H.)... | |
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