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Books Bücher 31 - 40 von 194 in To divide a given straight line into two parts, so that the rectangle contained by...
" 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. "
Military examinations. Mathematical examination papers, set for entrance to ... - Seite 34
von Woolwich roy. military acad, Walter Ferrier Austin - 1880
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837
...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...and one of the parts shall be equal to the square of c KT~i the other part. Steps of the Demonstration. 1. Prove that CF x FA + AE* = EF*, and that this...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 390 Seiten
...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...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 line ; it is required to...
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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...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...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841
...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...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...
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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...contained by the whole, and one of the parts, shall be equivalent to the square of the other part. Let AB be the given straight line : it is required to divide...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 Seiten
...(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...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 line ; it is required to...
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Proceedings

Scotland free church, gen. assembly - 1847
...the squares described on the other two sides, these sides contain a right angle. 3. Divide a given line into two parts, so that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. 4. The angle in a semicircle...
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The British Annals of Education for ...: Being The Scholastic ..., Band 1

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...and one of the parts shall be equal to the square of the other part. 8. If in a circle two straight lines cut one another, which do not both pass through...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1844 - 317 Seiten
...straight line ; it is required to divide it into two parts, so that the rectangle contained by Ji ^j. the whole, and one of the parts, shall be equal to the square of the other part. Upon AB describe (46. 1.) the square ABDC ; bisect (10. 1.) AC in E, and join BE...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Robert Potts - 1845
...double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROPOSITION XI. PROBLEM. To divide a given straight line into two parts, so that...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 AB into two parts, so...
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