 | John Playfair - Euclid's Elements - 1833 - 333 pages
...+ 4BC. AC. Now BC2+ BC.AC = AB.BC " (3. 2.) and therefore AD2=AC+ 4AB.BC. QED" PROP. IX. THEOR. If a straight line be divided into two equal, and also...points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts ; The squares of AD, DB are together... | |
 | Euclid - 1835 - 540 pages
...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...points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts : The squares of AD, DB are together... | |
 | 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...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... | |
 | Mathematics - 1836 - 472 pages
...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...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,... | |
 | Andrew Bell - Euclid's Elements - 1837 - 240 pages
...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...points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts ; the squares of AD, DB, are together... | |
 | John Playfair - Geometry - 1837 - 332 pages
...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...points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts ; The squares of AD, DB are together... | |
 | 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, and /'^..^ \ \ \ of... | |
 | Euclid - Geometry - 1837 - 410 pages
...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... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...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...points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts : the squares of AD, DB are together... | |
 | Euclides - 1838 - 264 pages
...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...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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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. 
