| Euclides - 1855
...various other places, but particularly in this book. E С К. i H PROPOSITION I. THEOBEM. 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. Let A and B С... | |
| Euclides - 1856
...but CAD is a right angle, wherefore CAB is also a right angle. XLVIII.— EUCLID II. 1. If there be **two straight lines one of which is divided into any...the several parts of the divided line. Let A and BC** (Fig. 38) be two straight lines whereof BC is divided into parts by the points D, E, etc. The rectangle... | |
| Cambridge univ, exam. papers - 1856
...the other two sides of it ; the angle contained by these two sides is a right angle. 6. If there be **two straight lines, one of which is divided into any...undivided line, and the several parts of the divided line.** 7. To describe a square that shall be equal to a given rectilineal figure. 8. If two circles cut one... | |
| W. Davis Haskoll - Civil engineering - 1858 - 324 pages
...subtending the right angle is equal to the square under the sides containing the right angle. If there be **two straight lines, one of which is divided into any...number of parts, the rectangle contained by the two** lines is equal to the rectangles contained by the undivided line, and the several parts of the divided... | |
| Euclides - 1858
...The learner is supposed to be familiar with most of them. PROP. 1. — THEOREM. If there be two st. **lines, one of which is divided into any number of parts, the rectangle contained by the two** st. lines is equal to the rectangles contained by the undivided line and the several parts of the divided... | |
| Euclides - 1858
...is divided into tunj number of parts, the rectangle continued by the two st. lines is equal to tlie **rectangles contained by the undivided line and the several parts of the divided line.** Соя. V. 11. 3, 31, I. OEM. :UI, AT. Я. K». 1 Hjp. Concl. h...,ii n '., я. I MI ; .;. I. :» :J1.... | |
| Euclides - 1860
...which are at the opposite angles of the parallelograms which make the gnomon. _D—..E_ C H there be **two straight lines, one of which is divided into any...undivided line, and the several parts of the divided line.** Given the two straight lines A and BC, and let BC be divided into any parts in the points D, E ; to... | |
| Robert Potts - Geometry, Plane - 1860 - 361 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 - 1860 - 453 pages
...( AB+ CD) x EF. 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 tJ.c several... | |
| Euclides - 1862
...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... | |
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