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
| United States. Bureau of Education - Education - 1907
...with twice the rectangle contained by (lie two parts. 8. Divide a given straight line into two parts, **so that the rectangle contained by the whole and one of the** parts may be equal to the square on the other part. The following is a list of the names of the Rhodes... | |
| Muḥammad ibn Mūsá Khuwārizmī - Algebra - 1915 - 164 pages
...geometrical solution, it is given in full, following Heath's Euclid. BOOK II OF THE Elements of Euclid, **PROPOSITION n " To cut a given straight line so that...segments is equal to the square on the remaining segment.** 1 References and citations from the Elements are to Heath's Euclid and the Data (Greek and Latin) edited... | |
| Jay Hambidge - Design - 1920 - 161 pages
...(who flourished about 300 BC), the following propositions occur: (i) "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"** (Book II, proposition II); (2) "To cut a given finite line in extreme and mean ratio" (Book VI, proposition... | |
| David Eugene Smith - Mathematics - 1958 - 736 pages
...also gives in the Elements such geometric problems as the following : To cut a given straight line **so that the rectangle contained by the whole and one of the segments** shall be equal to the square on the remaining segment.3 This may be represented algebraically by the... | |
| Morris Kline - Mathematics - 1990 - 390 pages
...EUCLID AND APOLLONIUS H D Figure 4. 10 Figure 4. 11 Proposition 1 1 . 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.** This requires that we divide AB (Fig. 4.10) at some point H so that AB . BH = AH. AH. Euclid's construction... | |
| David Bennett - Technology & Engineering - 1997 - 198 pages
...beauty. It was neatly summarised by Euclid in two of his propositions: "to cut a given straight line **so that the rectangle contained by the whole and one of the segments is equal to the square** m the remaining segment" and "to cut a given finite line in extreme and mean ratio." Simply translated... | |
| John J. Roche - Mathematics - 1998 - 330 pages
...Euclid book II, proposition 1 1 is an example of a construction problem: 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'.** Heath points out24 that this is equivalent, in modern notation, to the following quadratic equation... | |
| Johannes de Muris, Hubertus Lambertus Ludovicus Busard - History - 1998 - 392 pages
...radius of the circle (Campanus IV. 15 Porism). Prop. 3 reads as follows: 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** (Campanus 11.11). From Prop. 4: If the radius of a circle be cut in extreme and mean ratio, its greater... | |
| 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... | |
| |