 | Robert Simson - 1806 - 546 σελίδες
...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...square of the line between the points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts... | |
 | John Playfair - 1806 - 320 σελίδες
...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...square of the line between the points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts.... | |
 | Euclid - 1810 - 554 σελίδες
...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 - 714 σελίδες
...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 σελίδες
...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...square of the line between the points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts:... | |
 | John Playfair - 1819 - 350 σελίδες
...AD2=AC-+4AB.BC. QED" PROP. IX. THEOR. If a straight line be divided into too equal, and also into tzeo unequal parts ; the squares of the two unequal parts...square of the line between the points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts... | |
 | Miles Bland - 1819 - 444 σελίδες
....-. 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 σελίδες
....: 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 σελίδες
...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 σελίδες
...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... | |
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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. 
