| Euclid - 1810 - 518 sider
...straight line. WhereforCi if a straight line, &c. QED A CB G s / M / N 9 u X / • 'E F PROP. IX. THEOR. **IF a straight 'line be divided into two equal, and...half the line, and of the square of the line between** tlie points, of section. Let the straight line AB be divided at the point C into two equal, and at... | |
| 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 square... | |
| Euclides - 1814
...times the rectangle AB, BC, is equal to the gnomon AOH. To G P / K / EHJ / R N 0 , F PROP. IX. THEOR. **IF a straight line be divided into two equal, and...square of the line between the points of section.** From the point C draw3 CE at right angles to AB, and • 11. i. make it equal to AC or CB, and join... | |
| Miles Bland - 1819 - 377 sider
....-. 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 - 377 sider
....: 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... | |
| Euclid, Robert Simson - 1821 - 516 sider
...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...square of the line between the points of section.** • •M Let the straight line AB be divided at the point C into two equal, and at D into two unequal... | |
| John Martin Frederick Wright - 1825
...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,...square of half the line, and of the square of the** Une between the points of section. 3. If two straight lines within a circle cut one another, the rectangle... | |
| George Lees - 1826 - 207 sider
...a straight line AB be divided into two equal parts AC, CB, and also into two unequal parts AD, DB ; **the squares of the two unequal parts are together...square of half the line, and of the square of the** tine CD, between the points of section. • . ; Or, AD2 + DB2 = 2AC2 .+ 2CD2. From the point C, draw... | |
| Euclid, Phillips - 1826 - 180 sider
...PROPOSITION IX. ТНЕОПЕМ. J/1 a rzgAf Kne ie any how cut into two equal and two unequal parts, then **the squares of the two unequal parts are, together, double of the square of** the half line, and the square of the intermediate part. Let any right line AB be cut into two equal... | |
| Euclides - 1826
...PROPOSITION IX. THEOREM. If a right line be any how cut info two equal and two unequal parts, then **the squares of the two unequal parts are, together, double of the square of** the half line, and the square oftJie intermediate part. Let any right line AB be cut into two equal... | |
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