| John Playfair - Circle-squaring - 1826 - 326 pages
.../ P R C. Now BO+RC.AC=\B.BC (3.2.) and therefore AD3==AC + 4\B.BC. Q, E, D," -V 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 square of... | |
| Robert Simson - Trigonometry - 1827 - 546 pages
...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 also into two 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... | |
| 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 the... | |
| 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 square of the... | |
| Mathematics - 1836 - 488 pages
...demonstration 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 square 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 square of the... | |
| 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 of the line... | |
| 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 /'^..^... | |
| 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 square of the... | |
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