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" If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the two parts. "
Report of the Federal Security Agency: Office of Education - Page 49
by United States. Office of Education - 1907
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Elements of geometry: containing the first six books of Euclid, with a ...

John Playfair - Trigonometry - 1806 - 311 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...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Euclid, Robert Simson - Euclid's Elements - 1806 - 518 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...
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton, Olinthus Gregory - Mathematics - 1811
...is equal to the sum of all the ether rectangles AjJ . AE, AD. EF, AD . FB. c^. 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 die whole line and each of the parts. CB THEOREM XXXI. THE Square of the Sum...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory, and N ...

John Mason Good, Olinthus Gilbert Gregory - 1813
...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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Trigonometry - 1819 - 333 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...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton, Robert Adrain - Mathematics - 1822
...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 XXXI. THE Square of the Sum of...
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The Youth's instructer [sic] and guardian

1854
...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...
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A Course of Mathematics for the Use of Academies: As Well as Private Tuition

Charles Hutton, Robert Adrain - Mathematics - 1825
...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 XXXI. THE Square of the Sum...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 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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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...rectangle AC, CB, together with the square of BC. If therefore a straight line, &c. QED PROP. IV. THEOK. 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...
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