| Euclid - Mathematics, Greek - 1908
...PROPOSITION i. 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. Let A, BC be two straight lines, and let BC be cut at... | |
| Henry Sinclair Hall - 1908
...line AB is the sum of the segments AX, XB. THEOREM 50. [Euclid II. 1.] If of two straight lines, one **is divided into any number of parts, the rectangle contained by the two** lines is equal to the sum of the rectangles contained by the undivided line and the several parts of... | |
| David Eugene Smith - Geometry - 1911 - 339 pages
...follows : 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. This amounts to saying that \lx=p + q + r-\ , then ax... | |
| Morris Kline - Mathematics - 1990 - 428 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 - 331 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 - 278 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 - 179 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 - 499 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 - 378 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 - 474 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,... | |
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