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" If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Side 39
av Euclides - 1834
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The Student's Guide to Accountancy

Lawrence Robert Dicksee - 1897 - 99 sider
...sides of a parallelogram is equal to the sum of the squares of its diagonals. Q. 6.—Prove that, if a line be divided into any two parts, the rectangle contained by the sum and difference of the two parts is equal to the difference of the squares on the two parts. Q....
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Calendar

University of Sydney - 1898
...2. Shew how to bisect a given triangle by a line drawn through a given point in one side of it. 3. If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts is equal to the rectangle contained by the two parts together with the square...
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A Text-book of Euclid's Elements for the Use of Schools, Books I.-IV., Bok 1

Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 304 sider
...b units, then AB = a + b units ; and we have (« + bf PROPOSITION 3. THEOREM. If a straight line is divided into any two parts, the rectangle contained...by the whole and one of the parts is equal to the square on that part together with the rectangle contained by the two parts. ACB Let the straight line...
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The School World, Volum 3

1901
...figure DFBH is equal in area to the parallelogram AH. either В.— BOOK II. (6) If a straight line is divided into any two parts, the rectangle contained...by the whole and one of the parts is equal to the square on that part, together with the rectangle contained by the two parts. If the point of division...
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Euclid, Bok 1

Euclid, Rupert Deakin - 1903 - 164 sider
...and b denote the two parts of a line which contains a + 6 units of length. PROP. 3.— Theorem.— It a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts, is equal to the square on that part together with the rectangle contained...
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A Text-book of Euclid's Elements for the Use of Schools, Bok 1

Euclid - 1904 - 456 sider
...length, and let CB contain 6 units, BOOK II. PROP. 3. PROPOSITION 3. THEOREM. 133 If a straight line is divided into any two parts, the rectangle contained...by the whole and one of the parts is equal to the square on that part together with the rectangle contained by the two parts. ACB Let the straight line...
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Books 3-9

Euclid - 1908
...construction of this triangle depends upon n. n, or the problem of dividing a straight line so that the rectangle contained by the whole and one of the parts is equal to the square on the other part. This problem of course appears again in Eucl. vi. 30 as the problem of cutting...
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Report of the examination held (Dec. 1859)-73

Cowley Oxon, dioc. school - 1860
...described on the other two sides of it,the angle contained by these two sides is a right angle. 8. If a straight line be divided into any two parts,...parts, together with the square of the aforesaid part. 9. If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle...
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The Thirteen Books of Euclid's Elements

Euclid
...construction of this triangle depends upon u. n, or the problem of dividing a straight line so that the rectangle contained by the whole and one of the parts is equal to the square on the other part. This problem of course appears again in Eucl. vi. 30 as the problem of cutting...
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The Dream of the West, Pt II, Del 2

Brian Lasater - 2008 - 600 sider
...is a variation on (a + b)(a - b) = a2 -- b2. Theorem 7 (II, 11) To cut a given straight line so that the rectangle contained by the whole and one of the parts is equal to the square of the other. Let the given line be AB. The problem is to find a point H on it so that AB x...
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