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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. "
Elements of Plane Geometry According to Euclid - Page 9
by Andrew Bell - 1837 - 240 pages
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 544 pages
...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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1835 - 336 pages
...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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1836 - 488 pages
...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,...
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The Element of Geometry

John Playfair - Geometry - 1836 - 148 pages
...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...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...Propositions IX. XI. 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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...: 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...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 pages
...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...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...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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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...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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