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" Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that... "
An Elementary Treatise on the Geometrical and Algebraical Investigation of ... - Strona 154
autor: Daniel Cresswell - 1817 - Liczba stron: 436
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - Liczba stron: 410
...on the other part, Let AB be the given straight line. It is required to divide 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. FQ Upon AB describe the square A CDB ; (I. 46.) bisect AC...
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Elementary geometry

James Maurice Wilson - 1869
...therefore remembering that AD = DC, we obtain by addition that AB* + BC* = 2AD* + 2DB*. Ex. 3. To divide a straight line into two parts such that the rectangle contained by the whole line and one of the parts is equal to the square of the other part. Let AB be the given line. Construction. Draw a square ACDB...
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Elements of geometry, containing the first two (third and fourth ..., Część 1

Euclides - 1871
...that BGD is a straight line. /i as a If. a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter Mason - 1872
...whole line BC and each of its parts. PBOPOSITION III. If a right 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 by the two parts. The propositions...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - Liczba stron: 349
...straight line. PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square on the otJter part, is equal to the square on the straight line which is made...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...square on CD. QED PROP. XI.— PKOBLEM. (Euc. II. 11). To divide a straight 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. Let AB be a straight line, it is required to find a point...
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Euclidian Geometry

Francis Cuthbertson - 1874 - Liczba stron: 349
...rectangle BP, PQ + rectangle BP, QC. Hence, if a straight line be divided into any number of parts, the rectangle contained by the whole line and one of the parts is equal to the square on that part together with the rectangles contained by that part and the other...
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Pure mathematics, Tom 1

Edward Atkins - 1874
...line, &c. QED Proposition 8. — Theorem. If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...line, &c. QED PROPOSITION 8. —Theorem. If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square on the other part, is equal to the square on the straight line, which is made...
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A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C ...

Euclides - 1874
...represented in symbols, PROPOSITION 8. THEOREM. If a straight line be divided into any two parts, four times the rectangle contained- by the whole line and one of the parts together with the square on the other part, is equal to the square on the straight line which is made...
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