| Morris Kline - Mathematics - 1990 - 434 pages
...there be two straight lines (Fig. 4.8) and one of them be cut into any number of segments whatever, **the rectangle contained by the two straight lines is equal to the rectangles contained by the** uncut straight line and each of the segments. Propositions 2 and 3 are really special cases of Proposition... | |
| W.S. Anglin, J. Lambek - Science - 1998 - 347 pages
...thus: If there are two straight lines, and one of them be cut into any number of segments whatever, **the rectangle contained by the two straight lines is equal to the rectangles contained by the** uncut straight line and each of the segments (Elements II 1). The law (a + b)2 = a2 + lab + b2 is illustrated... | |
| Reinhard Laubenbacher, David Pengelley - Mathematics - 2000 - 292 pages
...(Proposition 1): If there be two straight lines, and one of them be cut into any number of segments whatever, **the rectangle contained by the two straight lines is equal to the rectangles contained by the** uncut straight line and each of the segments. Translated into algebraic notation, this corresponds... | |
| I. G. Bashmakova, G. S. Smirnova - Mathematics - 2000 - 200 pages
...that: If there be two straight lines, and one of them be cut into any number of segments whatever, **the rectangle contained by the two straight lines is equal to the rectangles contained by the** uncut straight line and each of the segments (note that by "straight line" Euclid always means a bounded... | |
| Michael N. Fried - History - 2001 - 516 pages
...reads: "If there be two straight lines, and one of them be cut into any number of segments whatever, **the rectangle contained by the two straight lines is equal to the rectangles contained by the** uncut straight line and each of the segments". Though mathematically equivalent, historically and epistemologically... | |
| Audun Holme - Mathematics - 2002 - 408 pages
...Formula 1 If there be two straight lines, and one of them be cut into any number of segments whatever, **the rectangle contained by the two straight lines is equal to the** (sum of the) rectangles contained by the uncut straight line and each of the segments. Again, the parenthesis... | |
| Jean Christianidis - Mathematics - 2004 - 502 pages
...translation of HEATH: If there be two straight lines, and one of them be cut into any number of segments, **the rectangle contained by the two straight lines is equal to the rectangles contained by the** uncut straight line and each of the segments. Fig. 2. Diagram to EUCLJDS Prop. II. 1. Geometrically,... | |
| 268 pages
...rects AB, CD ; AD, BC=rect. AC, BD. 137, 2. If there be two straight lines, each of which is divided **into any number of parts, the rectangle contained by the two straight lines is equal to the** sum of the rectangles contained by each of the parts of the first line and each of the parts of the... | |
| 130 pages
...also be used when convenient. 91. PROP. 1. 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** sum of the rectangles contained by the second line and each part of the first. A c D u Let AB and X... | |
| Euclid - 1845 - 328 pages
...parallel. CHAPTER vI AREAS (CONT.) 159. PROP. 1. 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** sum of the rectangles contained by the second line and each part of the first. A c DB Let AB and X... | |
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