 | John Playfair - 1806 - 311 Seiten
...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 - 518 Seiten
...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 - 518 Seiten
...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... | |
 | Euclides - 1816 - 528 Seiten
...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 - 333 Seiten
...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 - 377 Seiten
....: 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 Seiten
....-. 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 - 317 Seiten
...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. 
