 | Robert Simson - 1827 - 546 sider
...and BC added together in one straight line. Wherefore, if a straight line, &c. GED PROP. IX. THEOR. If a straight line be divided into two equal, and...unequal parts; the squares of the two unequal parts arc together double of the square of half the line, and of the square of the line between the points... | |
 | Walter Henry Burton - 1828 - 84 sider
...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 the... | |
 | John Martin Frederick Wright - 1831 - 282 sider
...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,... | |
 | Euclides - 1834 - 518 sider
.../ 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...points of section. Let the straight line AB be divided into two equal parts at the point C, and into two unequal parts at the point D : the squares of AD,... | |
 | John Martin Frederick Wright - 1836 - 776 sider
...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...square of the line between the points of section. 3. If two straight lines within a circle cut one another, the rectangle contained Ъу the segments... | |
 | 1836 - 488 sider
...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...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,... | |
 | Euclides - 1837 - 112 sider
...+ 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, and /'^..^ \ \ \ of... | |
 | Euclid, James Thomson - 1837 - 410 sider
...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 of the line between... | |
 | John Playfair - 1837 - 332 sider
...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 sider
...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...the squares of the two unequal parts are together doable of the square of half the line, and of the square of the line between the points of section.... | |
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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 line between the points of section. 
