| John Mason Good - 1813 - 722 pages
...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... | |
| John Playfair - 1819 - 317 pages
...AD3=AC3+4BC3-HBC.AC. Now BC3-f BC.AC=AB.BC(3. 2); " and therefore ADs=AC3+4AB.BC. q. ED" PROP. IX. THEOR. **'If /a straight line be divided into two equal, and also into** too untquai parts ; the squares of the two unequal parts are together double of the square of half... | |
| Robert Simson - Trigonometry - 1827 - 513 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...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
...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,... | |
| John Playfair - Euclid's Elements - 1832 - 333 pages
...AC!+4BC'+4BC. AC. Now BC' + BC.AC = AB.BC "(3. 2.) and therefore AD = AC +4 AB.BC. QED" PROP. IX. THEOR. **If a straight line be divided into two equal, and...two unequal parts; the squares of the two unequal** purls are together double of the square of half the line, and of the square of the line between the... | |
| 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
...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... | |
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