Ptolemy as a Mathematician
Ptolemy's main scientific interest was the mathematical description of the phenomena of nature. In pure mathematics he did but little work, and what he wrote had but little value. Thus Simplicius tells us that the gifted Ptolemy in his book On Dimension showed that there are not more than three dimensions; for dimensions must be deter-minate, and determinate dimensions are along perpendicular straight lines, and it is not possible to find more than three straight lines at right angles one to another, two of them determining a plane and the third measuring depth; therefore, if any other were added after the third dimension, it would be completely immeasurable and undetermined In libr. de caelo i, 1; trans. Thomas ii, 411).