| 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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