 | Robert Simson - 1806 - 546 Seiten
...and 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 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... | |
 | John Playfair - 1806 - 320 Seiten
...AD2=AC2+4BC2+4BC.AC. Now BC* + BC.AC = AB.BCb ; therefore AD2=AC2+ U3.2. 4AB.BC. QED" Book II. 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... | |
 | John Mason Good - 1813 - 714 Seiten
...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... | |
 | Euclides - 1816 - 588 Seiten
...straight line. Wherefore, if a straight line, &c. QED TIL F ACBT z .... 6 K / 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... | |
 | Miles Bland - 1819 - 444 Seiten
....-. 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 - 1819 - 442 Seiten
....: 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 Seiten
...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... | |
 | Euclid, Robert Simson - 1821 - 514 Seiten
...together in one straight line. Wherefore, if a straight line, &c. Q. ED. PROP. IX. THEOR. • . | IP 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... | |
 | Peter Nicholson - 1825 - 1046 Seiten
...added together in one straight line. ^herefore, if a straight line, &c. QED 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... | |
 | John Martin Frederick Wright - 1825 - 798 Seiten
...given rectilinear figure, having an angle equal to a given rectilinear angle. 2. If a straight Hue 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... | |
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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 line between the points of section. 
