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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... "
The first and second books of Euclid explained to beginners, by C.P. Mason - Σελίδα 149
των Euclid, Charles Peter MASON - 1872
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 σελίδες
...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...

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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Robert Simson - 1827 - 513 σελίδες
...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...

Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 186 σελίδες
...1. If a straight line AB be divided into any two parts AC, CB, the squares of the whole line and of one of the parts are together equal to twice the rectangle contained by the whole line and that part together with the square of the other part. That is, ABa + BO « 2 AB . BC + AC3,...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 σελίδες
...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...

The Element of Geometry

John Playfair - 1836 - 114 σελίδες
...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...

The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

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...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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Andrew Bell - 1837 - 240 σελίδες
...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...

The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 σελίδες
...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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...these = AL + CM + LG, which = AM + LG, and that these last = AD X DB + CB*. PROPOSITION VII. Theorem. 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 line...




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