| John Mason Good - 1813 - 714 pages
...other part, is equal to the square of the straight line which is made up of the whole and that part. **Prop. IX. Theor. If a straight line be divided into two equal, and also into two unequal parts; the** tqniMN of the two unequal parts arc together double of the square of half the line, and of the square... | |
| Miles Bland - Euclid's Elements - 1819 - 442 pages
....: EB : GI :: EH : HG, whence (Eucl. v. 15.) EF : FG :: EH : HG and alt. EF . EH :: FG : HG. (23.) **If a straight line be divided into two equal, and also into two unequal parts,** and be produced, so that the part produced may have to the whole line so produced the same ratio that... | |
| Miles Bland - Euclid's Elements - 1819 - 444 pages
....-. EB : GI :: EH . HG, whence (Eucl. v. 15.) EF : FG :: EH : HG and alt. EF . EH . FG . HG. (23.) **If a straight line be divided into two equal, and also into two unequal parts,** and be produced, so that the part produced may have to the whole line so produced the same ratio that... | |
| Euclid - 1826 - 234 pages
...PROPOSITION IX. ТНЕОПЕМ. J/1 a rzgAf Kne ie any how cut into two equal and two unequal parts, then **the squares of the two unequal parts are, together, double of the square of** the half line, and the square of the intermediate part. Let any right line AB be cut into two equal... | |
| Euclides - 1826 - 226 pages
...PROPOSITION IX. THEOREM. If a right line be any how cut info two equal and two unequal parts, then **the squares of the two unequal parts are, together, double of the square of** the half line, and the square oftJie intermediate part. Let any right line AB be cut into two equal... | |
| Robert Simson - Trigonometry - 1827 - 546 pages
...AD, that is, of AB 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...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 - 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, James Thomson - Geometry - 1837 - 410 pages
...AD is equal to 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...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... | |
| 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... | |
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