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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 Geometry of the Circle and Mathematics as Applied to Geometry by ... - Page 174
by James Smith - 1869 - 405 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Mathematics - 1806 - 320 pages
...Therefore 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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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...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 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 - 714 pages
...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 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 - 304 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 - 588 pages
...rectangle AC, CB, 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 - 350 pages
...therefore 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 - 800 pages
...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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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821 - 294 pages
...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 a D% draw a...
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The Youth's instructer [sic] and guardian, Volume 14

1854 - 1110 pages
...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 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 Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 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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