...the line, to which that root corresponds. Fig- 2' Ex. 2. To dhidf a given straight line AB (fig. 2) into two parts, so that the rectangle contained by the parts may be equal to a given square. Let c be a side of the square, a the given line, x one of the parts, and therefore...

...which beinij ijivru. ihr .«'iíe». o;' the reetnnt/lii e,m be found. Mi 105 PRоP. XI. PRоB. To divide a line into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. SoL. 46. I, 10. I, 3. I....

...the line between the points of section is equal to .the square on half the line. Hence show how to divide a line into two parts so that the rectangle contained by them may be a maximum. 3. In every triangle the square on the side subtending an acute angle is less...

...parts together with twice the rectangle contained by the parts. Express this also algebraically. 5. Divide a line into two parts, so that the rectangle contained by the whole and one part shall be equal to the square on the other part. 6. If a =- 2, b = 3, c = o, what...

...of the line between the points of section is equal to the square on half the line. Hence show how to divide a line into two parts so that the rectangle contained by them may be a maximum. 3. In every triangle the square on the side subtending an acute angle is less...

...the sum of the squares on these two parts may be the least possible. 11. Divide a line 20 in. long into two parts so that the rectangle contained by the parts may be the greatest possible. 12. Find the fraction which has the greatest excess over its square. 235. Two...

...the line between the points of section, is equal to the square on half the line. Divide a straight line into two parts so that the rectangle contained by the parts may be equal to the square on one of the parts together with the square on a given line. What limitation is...

...made up of the half and the part produced. — (Eu. II. 6.) 9. Divide a given straight line internally into two parts so that the rectangle contained by the parts may be a mciximum (ie, the greatest possible). PROP. 9 and 10. THEOR. If a straight line be bisected and cut...

...minimum. 107. We will conclude this part of the subject with one more example. " Divide a straight line into two parts, so that the rectangle contained by the parts may be a maximum." Let « be the straight line, and x one of the parts, a - #=other part, and the rectangle = (a — x(* or...

...;—-. - j - - — = £ (by question) rate of variation of angle angle = 60°. 4. Divide a straight line into two parts, so that the rectangle contained by the parts may be the greatest possible. Let a = the line, then rectangle=(a — x] = ax — op, therefore there is a...