| Meyer Hirsch - Trigonometry - 1827 - 264 pages
...construction is founded on Eue. VI. 13, 17. SECTION LXXIII. PROB. To produce a given line, so that **the rectangle contained by the whole line thus produced, and the part** produced, may be equal to the square of a given line. SOLUT. Let the line AB be given (ßg. 86) : lengthen... | |
| John Playfair - Euclid's Elements - 1833 - 333 pages
...taking away the equal rectangles 2BC. CD and 2AC.CD, there re" mains AD2+DB2=2ACH2CD2." PROP. X. THEOR. **If a straight line be bisected, and produced to any point, the** square of the whole line thus produced, and the square of the part of it produced, are together double... | |
| John Playfair - Euclid's Elements - 1835 - 316 pages
...difference of two quantities, is equivalent ta the difference of their squares, B ID PROP. VI. THEOR. **If a straight line be bisected, and produced to any...together with the square of half the line bisected, is** equ2l to the square of the straight line which is made up of the half and the part produced. Let the... | |
| Euclid, Robert Simson - Geometry - 1835 - 513 pages
...AD, DB are double the squares of AC, CD. " If, therefore, a straight " line," &c. QED PROP. X. THEOR. **If a straight line be bisected, and produced to any point, the** square of the whole line thus produced, and the square of the part of it produced, are together double... | |
| Robert Mudie - Mathematics - 1836 - 496 pages
...geometrically, or as it applies to lines ; and for this purpose it is usually enunciated in these tcnns : " **If a straight line be bisected, and produced to any point ; the** square of the whole line thus produced, and the square of the part of it produced, are together double... | |
| Robert Mudie - Mathematics - 1836 - 496 pages
...geometrically, or as it applies to lines ; and for this purpose it is usually enunciated in these terms : " **If a straight line be bisected, and produced to any point ; the** square of the whole line thus produced, and the square of the part of it produced, are together double... | |
| Mathematics - 1836 - 472 pages
...double of the square of half the line, and of the square of the line between the points of section. X. **If a straight line be bisected, and produced to any point, the** square of the whole line thus produced, and the square of the part of it produced, are together double... | |
| John Playfair - Geometry - 1836 - 114 pages
...square of CB, is equal to the square of CD. Wherefore, if a straight line, &c. QED PROP. XXIII. THEOR. **If a straight line be bisected, and produced to any point, the** square of the whole line thus produced*, and the square of the part of it produced, are together double... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...DB ; therefore the squares of AD, DB, are double of the squares of AC, CD. PROPOSITION X. THEOREM. **If a straight line be bisected, and produced to any point, the** square of the whole line thus produced, and the square of the part of it produced, are together double... | |
| Euclid - Geometry - 1837 - 390 pages
...AD*=AC8+CD2+2AC.CD. Add these equals together, and from the sums take 2AC.CD; then PROP. X. THEOR. **IF a straight line be bisected, and produced to any point, the** squares of the whole line thus produced, and of the part of it produced, are together double of the... | |
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