| Walter Henry Burton - Astronomy - 1828 - 84 pages
...understand this proposi-Prop. xix. tion, which is necessary for our further progress: that if a straight line be divided into two equal, and also into two unequal parts, the square of either of the equal parts (or the rectangle under both) is equal to the rectangle under the... | |
| Euclid - 1835 - 540 pages
...Wherefore, " if a straight line" &c. QED HL A. M X CB D / G K M 0 P / R / PROP. IX. THEOR. If a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the... | |
| Mathematics - 1836 - 488 pages
...manifest, that the square of any line is quadruple of the square of half that line. IX. If a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the... | |
| John Martin Frederick Wright - Mathematics - 1836 - 776 pages
...to a given rectilinear figure, having an angle equal to a given rectilinear angle. 2. If a straight line be divided into two equal, and also into two unequal, parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...that these = 4 AK + XH, and that these last = 4 AB x BC + AC*. PROPOSITION IX. Theorem. If a straight line be divided into two equal and also into two unequal parts, the squares of the two un- ^ equal parts are together double / GJ.^J? of the square of half the line, and /'^..^... | |
| Euclid, James Thomson - Geometry - 1837 - 410 pages
...together in one straight line. * Wherefore, if a straight line, &c. PROP. IX. THEOR. IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the unequal parts are together double of the square of half the line, and of the square of the line... | |
| Andrew Bell - Euclid's Elements - 1837 - 290 pages
...square of any line is quadruple of the square of half that line. PROPOSITION IX. THEOREM. If a straight line be divided into two equal, and also into two unequal parts, the squares of the two unequal parts are together double of the square of half the line, and of the square of the... | |
| Euclides - 1838 - 264 pages
...together in one straight line. Wherefore, if a straight line, &c. QED PROP. IX. THEOR. If a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together doable of the square of half the line, and of the square of the... | |
| Euclides - Geometry - 1841 - 378 pages
...together in one straight line. Wherefore, if a straight line, &c. QED PROP. IX. THEOR. //' a straight line be divided into two equal, and also into two unequal parts, the squares of the two unequal parts are together double of the square of half the line, and of the square of the... | |
| Euclid - Geometry - 1845 - 218 pages
...one straight line. Wherefore, if a straight line, &c. QED PROPOSITION IX. THEOR. — If a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the... | |
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