| 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... | |
| John Playfair - Euclid's Elements - 1832 - 358 pages
...Now BC' + BC.AC = AB.BC "(3. 2.) and therefore AD = AC +4 AB.BC. 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** purls are together double of the square of half the line, and of the square of the line between the... | |
| Euclides - 1834 - 518 pages
.../ K / / lt 2 HL 1 PROPOSITION IX. THEOR. — If a straight line be divided into two equal, andalso **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 line between the points of section.... | |
| 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...the squares of the two unequal parts are together** double of the square of half the line, and of the square of the line between the points of section.... | |
| 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...the squares of the two unequal parts are together** double of the square of half the line, and of the square of the line between the points of section.... | |
| 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...the squares of the two unequal parts are together** double of the square of half the line, and of the square of the line between the points of section.... | |
| 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...the squares of the two unequal parts are together** double of the square of half the line, and of the square of the line between the points of section.... | |
| 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 /'^..^ \ \ \ of... | |
| 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 between... | |
| Robert Simson - Geometry - 1838 - 434 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...the squares of the two unequal parts are together** double of the square of half the line, and of the square of the line between the points of section.... | |
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