 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...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... | |
 | George Lees - 1826 - 276 pages
...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... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...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... | |
 | John Playfair - Geometry - 1829 - 210 pages
...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,... | |
 | Euclid - 1835 - 540 pages
...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... | |
 | John Playfair - Geometry - 1836 - 148 pages
...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... | |
 | Mathematics - 1836 - 488 pages
...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... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...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... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...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... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...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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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... 
