| 1920
...illustration of the algebraical content of one of these theorems, let us examine Euclid II, 5: "If a line be **cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole,** together with the square on the straight line between the points of section, is equal to the square... | |
| Euclid - 1908
...with twice the rectangles contained by every pair of the parts. PROPOSITION 5. If a straight line be **cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole** together with the square on the straight line between the points of section is equal to the square... | |
| Muḥammad ibn Mūsá Khuwārizmī, Muhammad ibn Mūsa (al-Khuwārazmī) - 1915 - 164 páginas
...following Heath, The Thirteen Books of Euclid's Elements, reads as follows : " If a straight line be **cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole** together with the square on the straight line between the points of section is equal to the square... | |
| Edward Grant - 1974 - 864 páginas
...(DC)*; therefore, CE = 1. 84. Elements, Book II, Proposition 5 (Heath, 1, 382): "If a straight line be **cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole** together with the square on the straight line between the points of section is equal to the square... | |
| A. Szabó - 1978 - 358 páginas
...II. 6, let me begin by quoting both of these propositions: Proposition II. 5: "If a straight line be **cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole** together with the square on the straight line between the points of section is equal to the square... | |
| John N. Crossley - 1987 - 222 páginas
...propositions are as follows (in Heath's translation: Book II, Proposition 5. If a straight line be **cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole** together with the square on the straight line between the points of section is equal to the square... | |
| Reinhard Laubenbacher, David Pengelley - 2000 - 278 páginas
...a gnomon. FIGURE 5.2. Gnomon. CD B FIGURE 5.3. Proposition 5. PROPOSITION 5. If a straight line be **cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole** together with the square on the straight line between the points of section is equal to the square... | |
| Jean-Pierre Tignol - 2001 - 333 páginas
...the Elements. For instance, Proposition 5 of Book II states [30, v. I, p. 382]: If a straight line be **cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole** together with the square on the straight line between the points of section is equal to the square... | |
| K. Neal - 2002 - 175 páginas
...the standard version given in Heath leaps out. The proof is usually stated as "If a straight line be **cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole** together with the square on the straight line between the points of section is equal to the square... | |
| Jean Christianidis - 2004 - 474 páginas
...= ¿ Let us now proceed to the promised examples. Proposition 11.5 states: ‘If a straight line be **cut into equal and unequal segments, the rectangle contained by the unequal segments** ofthe whole together with the square on the straight line between the points of section is equal to... | |
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