Prop. 10. To divide a straight line in a given ratio.
Prop. 11. To find a third proportional to two given straight lines.
Prop. 12. To find a fourth proportional to three given straight lines.
Prop. 13. To find a mean proportional between two given straight lines.
The last three may be written as equations with one unknown quantity—viz. if we call the given straight lines a, b, c, and the required line x, we have to find a line x so that
Prop. 11.
a : b = b : x;
Prop. 12.
a : b = c : x;
Prop. 13.