| John Playfair - Mathematics - 1806 - 320 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 square of the... | |
| Robert Simson - Trigonometry - 1806 - 546 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 square of the... | |
| 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... | |
| Euclides - 1816 - 588 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 square of the... | |
| 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... | |
| Euclid, Robert Simson - Geometry - 1821 - 514 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 square of the... | |
| Peter Nicholson - Mathematics - 1825 - 1046 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 square of the... | |
| John Martin Frederick Wright - Mathematics - 1825 - 798 pages
...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 of the... | |
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