| Euclides - 1862
...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
...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 into any...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
...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
...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
...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 into any...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... | |
| Horatio Nelson Robinson - Conic sections - 1865 - 444 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 - 317 pages
...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...contained by the undivided line, and the several parts** nj the divided line. Let A and BC be two straight lines ; and let BC be divided into any parts in the... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...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 into 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... | |
| Robert Potts - 1868 - 410 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 - Geometry - 1868 - 262 pages
...to £ (AB+CD)xEF. Hence the theorem; the area of a trapezoid, etc. THEOREM XXXV. If one of two lines **is divided 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... | |
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