| Euclides - 1862 - 140 páginas
...of which is dicided into any number of parts, the rectangle contained by the tiro straight lin<!,< **is equal to the rectangles contained by the undivided line, and the several parts of the divided line.** , (References— Prop. I. 3, 11, 31, 34.) Hypothesis. — Let A and BC be two straight lines ; and... | |
| Euclides - 1862 - 172 páginas
...which are at the opposite angles of the parallelograms which make the Gnomon.' PROP. I.— THEOREM. **If there be two straight lines, one of which is divided into any number of parts** ; then the rectangle contained by the two straight lines, is equal to the rectangles contained by the... | |
| University of Oxford - 1863 - 316 páginas
...subtending the right angle is equal to the squares described on the sides which contain the right angle. 11. **If there be two straight lines, one of which is divided...contained by the two straight lines is equal to the** rectangle contained by the undivided line, and the several parts of the divided line. 12. Describe... | |
| Euclides - 1864 - 448 páginas
...sometimes " the rectangle ABC." To this proposition may be added the corollary : If two straight lines be **divided into any number of parts, the rectangle contained...lines, is equal to, the rectangles contained by the** several parts of one line and the several parts of the other respectively. The method of reasoning... | |
| Euclides - 1864 - 262 páginas
...sometimes " the rectangle ABC." To this proposition may be added the corollary : If two straight lines be **divided into any number of parts, the rectangle contained...lines, is equal to the rectangles contained by the** several parts of one line and the several parts ol the other respectively. The method of reasoning... | |
| Euclides - 1865 - 402 páginas
...Define a rectangle. By what is it contained? 2. Define a gnomon. PROPOSITIONS AND COROLLARIES. Prop. 1. **If there be two straight lines, one of which is divided...undivided line, and the several parts of the divided line.** Prop. 2. If a straight line be divided into any two parts, the rectangles contained by the whole and... | |
| Robert Potts - 1865 - 528 páginas
...sometimes " the rectangle ABC." To this proposition may be added the corollary;: If two straight lines "be **divided into any number of parts, the rectangle contained...lines, is equal to the rectangles contained by the** several parts of one line and the several parts of the other respectively. The method of reasoning... | |
| Horatio Nelson Robinson - 1865 - 474 páginas
...into any number of parts, the rectangle contained by the two lines is equal to the sum of the several **rectangles contained by the undivided line and the several parts of the divided line. Let** AB and AD be two lines, and suppose AB divided into any number of parts at the points E, F, G, etc.... | |
| John Playfair - 1855 - 350 páginas
...may also, for the sake of 4 brevity, be called the gnomon AGK •or EHC." JJ DEC PROP. I. THEOR. I/ **there be two straight lines, one of which is divided into any number** ej parts ; the rectangle contained by the two straight lines is equal to the rectangles contained by... | |
| Isaac Todhunter - 1867 - 426 páginas
...at the opposite angles of the parallelograms which make the gnomon. AE K DE PROPOSITION 1. THEOREM. **If there be two straight lines, one of which is divided...any number of parts, the rectangle contained by the** tiro sir-tight lines is equal to the rectangles contained by the undleided line, and the several parts... | |
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