 | John Mason Good - 1813 - 714 pages
...parallelograms 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...undivided line, and the several parts of the divided line. Prop. II. Theor. If a straight line be divided înto any two parts, the rectangles contained by the... | |
 | 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 - 588 pages
...' which are 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...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 - 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...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 - 350 pages
...also, ' 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...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 - 800 pages
...parallelograms 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...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 - 486 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 - 234 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 - 546 pages
...EHC, which are 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...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 - 246 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... | |
| |
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. 
