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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 ... - Seite 41
von Euclides - 1816 - 528 Seiten
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1821 - 514 Seiten
...BC. If therefore a straight line, &c. QED PROP. IV. THEOR. IP a straight line be divided into any twq parts, the square of the whole line is equal to the squares of the two pai ts, together with twice the rectangle contained by the parts. Let the straight line AB be divided...
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The Youth's instructer [sic] and guardian, Band 14

1854 - 1110 Seiten
...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, the...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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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - 1822 - 618 Seiten
...up of the four figures, viz. the two squares AF, FD, and the two equal rectangles EF, FB. That is, the square of AB is equal to the squares of AC, CB, together with twice the rectangle of AC, CB. ft. ED Corol. Hence, if a line be divided into two equal...
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Elements of algebra, compiled from Garnier's French translation of L. Euler ...

Charles Tayler - 1824 - 350 Seiten
...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 - 1825 - 372 Seiten
...', 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...straight line AB be divided into any two parts in С ; the square of AB is equnl to the squares of AC, CB, and to twice the rectangle contained by AC,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1826 - 326 Seiten
...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, the...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 - 236 Seiten
...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 - 1827 - 332 Seiten
...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 - 1827 - 513 Seiten
...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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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 544 Seiten
...rectangle under either of them and a third of the other, #c. #c. PROPOSITION II. THEOREM. (223) If a right line (AB) be divided into any two parts (in C), the square of the whole line is equal to the sum of the rectangles under the whole (AB) and each of the parts (AC,...
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