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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 - 1810 - 518 Seiten
...rectangle AC, CB, together with the square of BC. If therefore a straight line, &c. QED PROP. IV. THEOR. IF a straight line be divided into any two parts, the...straight line AB be divided into any two parts in Cj the square of AB is equal to the squares of AC, CB, and t» twice the rectangle contained by AC,...
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A Course of Mathematics: For the Use of Academies as Well as Private ..., Band 1

Charles Hutton - 1812
...made 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. QED Corol. Htnct, if a line be divided into two equal...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Band 5

John Mason Good - 1813 - 722 Seiten
...rectangle contained by the two parts, together with the aquarc of the foresaid part. Prop. IV. Theor. If a straight line be divided into any two parts, the...•with twice the rectangle contained by the parts. Prop. V. Theor. If a straight line be divided into two equal parts, and also into two unequal parts)...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 558 Seiten
...AC'. CB, together with the square of BC. If therefore u straight line, &c. QED PHOP. IV. THKOR. E IF a straight line be divided into any two parts, the...be divided into any two parts in C; the square of ABU equal to the squares of AC, CB, and to twice the rectangle contained by AC, CB. •46. 1. 'St....
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1814 - 303 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 the squares of the two parts, togedier with twice die product of the parts, is demonstrated, by involving a binomial. Let the side...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 Seiten
...if a straight If D -E line, &c. Q, ED PROP. IV. THEOR. If a straight line be divided into any tiio parts, the square, of the whole line is equal to the...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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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Band 5

John Mason Good - 1819 - 740 Seiten
...rectangle contained by the two parts, together with tiie square of the furesaicl part. Prop. IV. Theor. If a straight line be divided into any two parts, the square of the whole line n equal to the squares of the two parts, together with twice the rectangle contained by the parts....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1819 - 348 Seiten
...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 - 1820 - 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 geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821 - 294 Seiten
...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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