| John Playfair - Euclid's Elements - 1806 - 311 pages
...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... | |
| Euclid, Robert Simson - Euclid's Elements - 1806 - 518 pages
...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
...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 - Euclid's Elements - 1816 - 528 pages
...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 - Geometry - 1819 - 377 pages
...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 - 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... | |
| Miles Bland - Geometry - 1821 - 438 pages
...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 - Geometry - 1821 - 516 pages
...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 - Mathematics - 1825 - 372 pages
...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 - Euclid's Elements - 1826 - 320 pages
.../ 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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