 | John Playfair - 1806 - 320 pagina’s
...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...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. The squares of AD, DB are... | |
 | Robert Simson - 1806 - 546 pagina’s
...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...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 : the squares of AD, DB are... | |
 | Euclid - 1810 - 554 pagina’s
...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 pagina’s
...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 - 560 pagina’s
...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... | |
 | Euclides - 1816 - 588 pagina’s
...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...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: The squares of AD, DB are... | |
 | John Playfair - 1819 - 350 pagina’s
...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...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 : The squares of AD, DB are... | |
 | Miles Bland - 1819 - 442 pagina’s
....: 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 - 444 pagina’s
....-. 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 pagina’s
...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... | |
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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. 
