 | Walter Henry Burton - Astronomy - 1828 - 84 pages
...you will 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... | |
 | John Martin Frederick Wright - Astronomy - 1831 - 282 pages
...side subtending the right angle, is equal to the square on the sides containing the right angle. 7. If a straight line be divided into two equal, and also into two unequal parts, prove that the squares of the two unequal parts are, together, double of the square of half the line,... | |
 | Euclid - 1835 - 540 pages
...straight line. 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... | |
 | Mathematics - 1836 - 488 pages
...it is also 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... | |
 | John Martin Frederick Wright - Mathematics - 1836 - 776 pages
...parallelogram equal 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... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...+ XH ; and 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,... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...AB and BC added 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... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...of CB, the 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... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...each member of this equality, we shall have, 4aJ+c2=c2+4ic+4*2, or4ai+c2=(c-|-2i)2. PROP. IX. THEOR. If a straight line be divided into two equal, and also into twn unequal parts ; the squares of the two unequal parts are together double of the square of half... | |
 | Euclides - 1838 - 264 pages
...and BC added 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... | |
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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. 
