 | 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 also...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 together... | |
 | Robert Simson - 1806 - 546 σελίδες
...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...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 together... | |
 | Euclid - 1810 - 554 σελίδες
...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 also...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
...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 σελίδες
...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 also...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 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 also...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 together... | |
 | 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...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 together... | |
 | John Playfair - 1819 - 354 σελίδες
...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 the iinCi ahd of th-e square of the line between the points of section. • » v. Let the straight line... | |
 | Miles Bland - 1819 - 442 σελίδες
...; then will all lines drawn from that point meeting the three lines be harmonically divided. 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 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... | |
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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. 
