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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 geometry [Euclid book 1-3] in general terms, with notes &c ... - Page 100
by Euclides - 1833
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...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 square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. Let the straight...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...AB.BC =AC.CB+BC2. Therefore, if a straight line, &c. QED c B •33 PROP. IV. THEOR. \ -^ 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. Let the straight...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...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 square of the whole line is equal to the squares of the two parts, together •with twice the rectangle contained by the parts. Prop. V. Theor....
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1814 - 303 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 the squares of the two parts, togedier with twice die product of the parts, is demonstrated, by involving...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...together with the square of BC. If therefore a straight line, &c. QED PROP. IV. THEOR. Is 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. Let the straight...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 333 pages
...AB.BC '= AC.CB -f BC2. Therefore, if a straight -F line, &c. Q, ED — D PROP. IV. THEOR. 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, Let the straight...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819
...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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The Youth's instructer [sic] and guardian, Volume 14

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

Charles Hutton - Mathematics - 1822
...is equal to the .-11111 of all the other rectangles AD . AE, AD . EF, AD . FB. 4. c. D. E FB Carol. If a right line be divided into any two parts ; the square on the whole line, is equal to both the rectangles of the whole line and each of the parts. THEOREM...
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A Course of Mathematics for the Use of Academies: As Well as ..., Volume 1

Charles Hutton - Mathematics - 1825
...equal to the sum of ;tll the other «• •* * M rectangles AD . AE, AD . EF, AD . FB. «. ED Corol. If a right line be divided into any two parts ; the square on the whole line, is equal to both the rectangles of the whole line and each of the parts. • THEOREM...
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