| John Mason Good - 1813
...about a diameter, 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...undivided line, and the several parts of the divided line.** Prop. II. Theor. If a straight line be divided īnto any two parts, the rectangles contained by the... | |
| Charles Butler - Mathematics - 1814
...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
...at the opposite angles of the parallelograms ' which makes 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.** BouK II. Let A and BC be two straight lines ; and let BC be di-^ " vided into any parts in the points... | |
| Daniel Cresswell - Euclid's Elements - 1817 - 436 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...lines, is equal to the rectangles contained by the** several parts of the one and the several parts of the other. PROP. V. (H.) If a straight line be divided... | |
| John Playfair - Circle-squaring - 1819 - 333 pages
...for the sake of 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...undivided line, and the several parts of the divided line.** • */ -i Let A and BC be two straight lines ; and let BC be divided into any parts in the points D,... | |
| John Mason Good - 1819
...about a diameUr, together with the two complements, is called a gnomon. Prop. I. Thpor. If there be **two straight lines,, one of which is divided into...lines, is equal to the rectangles contained by the** undirided lin--, and the several parts of the divided line. , Prop. 1 1. Theor. If a straight line... | |
| Daniel Cresswell - Geometry - 1819 - 410 pages
...THE ELEMENTS OF EUCLID. BOOK II. PROP. I. 1 . THEOREM. If two given straight lines be divided, each **into any number of parts, the rectangle contained...lines, is equal to the rectangles contained by the** several parts of the one and the several parts of the other. Let the given straight line AB be divided... | |
| Euclid - 1826 - 180 pages
...angles of the parallelograms, which make the gnomon. PROPOSITION I. THEOREM. If tliere be two right **lines, one of which is divided into any number of parts, the rectangle** comprehended under the whole and divided line, is equal to the rectangles contained under the whole... | |
| Robert Simson - Trigonometry - 1827 - 513 pages
...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 number of parts; the rectangle contained by the** 1wo straight lines, is equal to the rectangles contained by the undivided line, and the several parts... | |
| John Radford Young - Euclid's Elements - 1827 - 208 pages
...PROPOSITION IV. THEOREM. If there be two straight 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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