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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 student's guide to the University of Durham, with information respecting ... - Página 136
1880 - 144 páginas
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ELEMENTARY SYNTHETIC GEOMETRY OF THE POINT, LINE AND CIRCLE IN THE PLANE

N. F. DUPUIS, M.A., F.R.S.C. - 1894
...the construction of 183° solves the problem, " To divide a given segment so that the rectangle on the whole and one of the parts is equal to the rectangle on the other part and the segment which is the sum of the whole and the first part." 11. Construct...
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Euclid's Elements of Geometry, Libros 1-6;Libro 11

Henry Martyn Taylor - 1895 - 657 páginas
...BC, DC be equal to the squares on AB, AC respectively, the angle BAC is a right angle. PROPOSITION 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 sum of the square on that part and the rectangle contained...
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - 1897
...together equal to two right angles. 6 5. Prove Eue. I. 20, without producing a side of the triangle. 7 6. 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 square on that part together with the rectangle contained...
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The Student's Guide to Accountancy

Lawrence Robert Dicksee - 1897 - 99 páginas
...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., Libro 1

Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 304 páginas
...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, Volumen3

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, Libro 1

Euclid, Rupert Deakin - 1903 - 164 páginas
...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, Libro 1

Euclid - 1904 - 456 páginas
...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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