 | 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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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 line between the points of section. 
