| John Playfair - 1806 - 320 páginas
...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... | |
| Robert Simson - 1806 - 546 páginas
...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... | |
| John Mason Good - 1813 - 714 páginas
...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... | |
| Euclides - 1816 - 588 páginas
...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... | |
| Miles Bland - 1819 - 444 páginas
...divided; then will nil lines drawn from that point meeting the three lines be harmonically divided. 23. If a straight line be divided into two equal and also into two unequal parts, and be |>roduced, so that the part produced may have to the whole line so produced, the same ratio that the... | |
| John Playfair - 1819 - 354 páginas
...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... | |
| Miles Bland - 1821 - 898 páginas
...divided ; then will all lines drawn from that point meeting the three lines be harmonically divided. 23. If a straight line be divided into two equal and...of unequal section from one extremity of the given line, from its middle point, from the extremity of the part produced, and from the other extremity... | |
| Euclid, Robert Simson - 1821 - 514 páginas
...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... | |
| Peter Nicholson - 1825 - 1046 páginas
...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... | |
| Euclid, John Playfair - 1826 - 326 páginas
.../ 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... | |
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