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" IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Page 45
by Euclides - 1814
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 333 pages
...rectangles contained by the whole and each of the parts, are together equal to the square of the whole line. Let the straight line AB be divided into any two parts in the point C ; the rectangle AB.BC, together with the rect- P "R angle AB.AC, is equal to the square...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1820 - 332 pages
...than in ordinary language. The proposition, (Euc. 4. 2.) that when a straight line is divided into two parts, the square of the whole line is equal to...squares of the two parts, together with twice the product of the parts, is demonstrated, by involving a binomial. Let the side of a square be represented...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821
...are the given quantities : then 6 X 6 -f- 6 X 2 is = to 8 X 8 — 8 X 2. PROP. 4T THEQR. If a right line be divided into any two parts, the square of the whole line is equal to the sum of the squares of the parts and twice the rectangle under the parts On the given line describe...
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The Youth's instructer [sic] and guardian, Volume 14

1854
...product. Geometry furnishes us with a parallel to both these cases ; for, as Euclid tells us (II., 4), if a straight line be divided into any two parts,...together with twice the rectangle contained by the parts ; and, were we to represent the line as a divided into two parts m, x, the algebraical expression for...
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Elements of algebra, compiled from Garnier's French translation of L. Euler ...

Charles Tayler - 1824
...iv. Book ii., viz., that If a number be divided into any two parts, the square of the •whole number is equal to the squares of the two parts, together with twice the product (or rectangle) of the twojiarts. For (c) Prime numbers are such as cannot be represented by...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...CB, together with the square of BC. If therefore a straight line, &c. QED Proposition IV. Theorem. ', If a straight line be divided into any two parts, the square or in* ELEMENTS OP KUCUD. 191 vhole line is equal to the squares of the two parts, together with twice...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1826 - 320 pages
...BCB; therefore AB.BC = AC.CB -f BC3. Therefore, if a straight line, &e. QED C B D E C PROP. IV. THEOR. If a straight line be divided into any two parts,...equal to the squares of the two parts, together with twiee the reetangle eontained by the parts. Let the straight line AB be divided into any two parts...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 pages
...and it be ag =fg + g2. Q- ED PROPOSITION IV. THEOREM. If a right line be divided into any two part:!, the square of the whole line is equal to the squares...parts, together with twice the rectangle contained under the parts. Let the right line AB be divided into any two parts in the point c ; the square of...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1827 - 332 pages
...than in ordinary language. The proposition, (Euc. 4- 2.) that when a straight line is divided into two parts, the Square of the whole line is equal to...squares of the two parts, together with twice the product of the parts, is demonstrated, by involving a binomial. Let the side of a square be represented...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C: the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the...
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