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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. "
Elements of Geometry and Conic Sections - Page 63
by Elias Loomis - 1857 - 226 pages
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...IV. THEOR. If a straight line be divided into any tiio parts, the square, of the whole line is equal to the squares of the two parts, together with twice...straight line AB be divided into any two parts in C ; Uie square of AB is equal to the squares of AC, CB, and to twice the rectangle contained by AC, CB,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Circle-squaring - 1819 - 348 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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...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...AB be divided into any two parts in C; the square of AB is equal to the squares of AC, CB, and to twice the rectangle contained by AC, CB. G K D Upon...
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The Youth's instructer [sic] and guardian, Volume 14

1854 - 1110 pages
...us (II., 4), 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 ; and, were we to represent the line as a divided into two parts m, x, the algebraical expression for...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...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...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 - Euclid's Elements - 1826 - 326 pages
...the whole line is 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 in C ; the square of AB is equal to the squares of AC, CB, and to twiee the reetangle eontained by AC, CB, that is, AB3...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 236 pages
...IV. THEOREM. If a right line be divided into any two part:!, the square of the whole line is equal to the squares of the two 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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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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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 544 pages
...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...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...foresaid part. 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 two parts. Or, in other words, the square of the sum of two lines is greater than the sum of their...
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