AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. Introduction and books 1,2 - Page 402by Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - 1908Full view - About this book
| Reinhard Laubenbacher, David Pengelley - Mathematics - 1999 - 275 pages
...Hint: See Figure 5.6. Exercise 5.9: Proposition 1 1 in Book II states: To cut a given straight line **so that the rectangle contained by the whole and one...segments is equal to the square on the remaining segment.** Which type of quadratic equation can be solved with the help of this proposition and how? Exercise... | |
| Michael N. Fried - History - 2001 - 499 pages
...from the following example.48 Proposition II. 1 1 of the Elements reads: To cut a given straight line **so that the rectangle contained by the whole and one...the segments is equal to the square on the remaining** segment.49 Euclid's purely geometrical, constructive proof amounts to the following: Let AB be the... | |
| Georgia Lynette Irby-Massie, Paul Turquand Keyser - History - 2002 - 392 pages
...segments is equal to die square on the remaining segment. Let AB be die given straight line (Figure 2.2); **thus it is required to cut AB so that the rectangle...contained by the whole and one of the segments is equal to** die square on the remaining segment. For let die square ABAF be constructed on AB; let AFbe bisected... | |
| Georgia Lynette Irby-Massie, Paul Turquand Keyser - History - 2002 - 392 pages
...proportion used in the Parthenon, which we call (sqrt(5)+1)/2 = 1.618...] To cut a given straight line **so that the rectangle contained by the whole and one...segments is equal to the square on the remaining segment.** Let AB be the given straight line (Figure 2.2); thus it is required to cut AB so that the rectangle... | |
| Peter D. Schumer - History - 2004 - 199 pages
...particular. Chapter II. Proposition ll of Euclid's Elements directs us "to cut a given straight line so thai **the rectangle contained by the whole and one of the...is equal to the square on the remaining segment."** In modern parlance, we are asked to find a point -v along a unit line segment such that the ratio l... | |
| Teun Koetsier, Luc Bergmans - Mathematics - 2004 - 716 pages
...that this proportion occurs: in Book II, prop. 11, Euclid instructs us to "cut a given straight line **so that the rectangle contained by the whole and one...is equal to the square on the remaining segment".** 10 This implies that the division of AB in H must be made according to extreme and mean ratio (AE —... | |
| Israel Kleiner - Mathematics - 2007 - 168 pages
...algebraically as (a + b)2 — a2 + 2ab + b2. Proposition II. 1 1 states: "To cut a given straight line **so that the rectangle contained by the whole and one...is equal to the square on the remaining segment."** It asks, in algebraic language, to solve the equation a(a — x) — x2. See [7, p. 70]. Note that... | |
| 1926
...us independent of any recollection of results. PROPOSITION 3. If a straight line be cut at random, **the rectangle contained by the whole and one of the segments is equal to the** rectangle contained by the segments and the square on the aforesaid segment. For let the straight line... | |
| Georgia Lynette Irby-Massie, Paul Turquand Keyser - Foreign Language Study - 2002 - 392 pages
...remaining segment. Let AB be the given straight line iFigure 2.2): thus it is required to cut AB so hat **the rectangle contained by the whole and one of the segments is equal to the** quare on the remaining segment. For let the square ABAF be constructed on AB : let AF be bisected at... | |
| Peter M. Engelfriet - Mathematics - 1998 - 488 pages
...the following propositions. 3. -itmff ffi#;2:£7c»ffiffif Heath If a straight line be cut at random, **the rectangle contained by the whole and one of the segments is equal to the** rectangle contained by the segments and the square on the aforesaid segment. Again, Ricci gives an... | |
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