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" AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part. "
A Text-book of Euclid's Elements for the Use of Schools, Books I.-IV. - Página 162
por Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 304 páginas
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 páginas
...« 46. 1. •6.2. t Constr. • 47. 1. t 3 Ax. t 30 Def. t lAx. t 3 Ax. t 30 Def. PROP. XL PROB. To divide a given straight line 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. Let AB be the given...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 páginas
...AD, DB are double the squares of AC, CD. Wherefore, " if a straight line," &c. QED PROP. XI. PROB. To divide a given straight line 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. Let AB be the given...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 páginas
...HB, AD are equal. Then c B (II. 9.) HB2 + BD*, or AD2 + BD2= 5-a ' — 2CD2+2AC2.* PROP. XI. PROB. To 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 of the other part. Let AB be the given straight...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 páginas
...that this = AC* + CE* + EF! + FG", and that these = 2 AC* + 2 CD!. H PROPOSITION XI. E ._ Problem. To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square of c KT~i the other part. Steps of the...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...AD, DB are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROP. XI. PROS. To divide a given straight line 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. Let AB be the given...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 páginas
...DB are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROP. XI. PROB. 1 To divide a given straight line 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. Let AB be the given...
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Elements of Geometry

Adrien Marie Legendre - 1841 - 235 páginas
...from the given points. (215.) Fig. 364. Q. LXXVIII. To divide a straight line AB into two parts such that the rectangle contained by them may be equal to the square of their difference. Upon AB describe a semicircle ADB. From B draw BC at right angles, and equal to...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 páginas
...(2a-f*)2+*2=2a2+2(a+i)2, and the proposition is evident from this algebraical equality. PROP. XI. PROB. To 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 of the other part. Let AB be the given...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...equivalent to double the squares of AC, CD. If therefore a straight line, &c. QED PROP. XI. PROB. To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equivalent to the square of the other part. Let AB be the...
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The British Annals of Education for ...: Being The Scholastic ..., Volúmenes1-2

1844
...contained by the whole and each of the parts are together equal to the square of the whole line. 7. Divide a given straight line 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. 8. If in a circle two...
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