 | Euclides - 1862 - 140 pages
...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 pages
...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 - Education, Higher - 1863 - 316 pages
...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 pages
...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 pages
...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 pages
...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 pages
...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 - Conic sections - 1865 - 474 pages
...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 - Geometry - 1855 - 350 pages
...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... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...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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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. 
