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. A Supplement to the Elements of Euclid - Page 92by Daniel Cresswell - 1819 - 410 pagesFull view - About this book
| 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,... | |
| ...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... | |
| ...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... | |
| Euclid - 1845 - 262 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... | |
| Euclid - 454 pages
...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. 5 Let A, BC be two straight lines, and let BC be cut... | |
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