 | Robert Simson - 1835 - 544 σελίδες
...given rectilineal angle BAC is bisected by the straight line AF. Which was to be done. PROP. X. PROB. To bisect a given finite straight line, that is, to...it is required to divide it into two equal parts. a 1. 1. Describe a upon it an equilateral triangle ABC, and bisect b9. 1. bthe angle ACB by the straight... | |
 | John Playfair - 1835 - 336 σελίδες
...given angle may be divided into four equal parts, into eight, into sixteen, and so on. PROP. V. PROB. To bisect a. given finite straight line, that is,...straight line ; it is required to divide it into two 6<1 Describe (Prob. 1.) upon it an equilateral triangle ABC, and bisect (Prob. 4.) the angle ACB by... | |
 | Euclid - 1835 - 540 σελίδες
...rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. Let 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... | |
 | John Playfair - 1836 - 488 σελίδες
...given rectilineal angle BAC is bisected by the straight line AF. Which was to be done. PROP. X. PROB. To bisect a given finite straight line, that is, to...it is required to divide it into two equal parts. Book 1, a 1. 1. b9. I. c 4. 1. a 3. 1. b 1. I. c8. Describe a upon it an equilateral triangle ABC,... | |
 | John Playfair - 1836 - 148 σελίδες
...rectangle con tained by the whole and one of the parts shall be equal to the square of the other part. Let 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... | |
 | Euclides - 1837 - 112 σελίδες
...and XII. depend wholly on Proposition VIII. and that of X. wholly on Proposition IV. c PROPOSITION X. Problem. To bisect a given finite straight line; that is, to divide it into two equal parts. Problem. a straight line at right angles to a given straight line from a given point in the same. PROPOSITION... | |
 | Andrew Bell - 1837 - 290 σελίδες
...and of the mean distance. PROPOSITION XI. PROBLEM. To divide a given straight line in medial section. Let AB be the given straight line ; it is required to divide it in medial section. Upon AB describe the square ABDC (I. 46) ; bisect AC in E (1. 10), and join BE ;... | |
 | Euclid, James Thomson - 1837 - 410 σελίδες
...: which was to be done. PROP. XXX. PROB. To divide a given straight line in extreme and mean ratio. Let AB be the given straight line; it is required to divide it in extreme and mean ratio. Divide AB (II. 11.) in the point C, so that the rectangle AB.BC may be equal... | |
 | Robert Simson - 1838 - 434 σελίδες
...given rectilineal angle BAC is bisected by the straight line, AF, which was to be done. PROP. X. PROB. To bisect a given finite straight line, that is, to...given straight line : it is required to divide it intotwo equal parts. Describe (1. 1.) upon it an equilateral triangle ABC, and bisect (9. 1.) the angle... | |
 | Euclides - 1838 - 264 σελίδες
...rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. Let 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... | |
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To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts. 
