 | John Mason Good - 1813 - 714 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 - 354 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 - 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...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,... | |
 | John Playfair - Euclid's Elements - 1832 - 358 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, 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 between... | |
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If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section. 
