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" If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to 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... "
Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ... - Página 53
por Euclides - 1860
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 páginas
...PffP. VII. T If a straight line be-cKvided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole andfthat part, together with the square of the other part. i Let the straight line AB be divided into...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 333 páginas
...therefore AD. DB + CB3 = CD3. Therefore, • "" "" " if a straight line, &c. Q, ED PROP. VII. THEOR. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 páginas
...square of CD. Wherefore, if a straight line, &c. Q. £. D. whole line, and of one of the parts, яге equal to 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 С ; the squares...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826
...into any ^yo parts, AC, CB, the squares of the whole line, and of one of the parts, are equivalent to twice the rectangle contained by the whole, and that part, together with the square of the other part. By the Prop. AB2 = AC2+CB2 + 2AC.CB, add CB2 to each; then AB2+CB2 = AC2 + i?CB2...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 páginas
...of CB, is equal to the square of CD. Wherefore, if a straight line, &c. Q. £. JO. PROP. VII. THEOR. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 páginas
...square of CB, is equal to the square of CD. Wherefore, " if a straigtd line" &c. QED PROP. VII. THEOR. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole...
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The Element of Geometry

John Playfair - 1836 - 114 páginas
...so that the rectangle AB, BH is equal to the square of AH. Which was to be done. E PROP. XXV. THEOR. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts are equal to twice the rectangle contained by the whole...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 páginas
...is equal to the square of the straight line which is made up of the half and the part produced. VII. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 páginas
...the diiferencc between the squares of half the line and the mean distance. PROPOSITION TIL THEOREM. to 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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 páginas
...figure, as there will remain the rectangle AM and the square LG, together equal to tb« square CF. IF a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole...
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