Page:Philosophical Transactions - Volume 003.djvu/22

 By anyone of which three Series, it is not hard to calculate, as near as you please, these and the like Hyperbolic spaces, whatever be the Rational Proportion of AE to BC. As for Example, when AE is to BC, as 5 to 4. (whereof the Calculation follows after that where the Proportion is, as 2 to 1. and both by the third Series.)

First then when (in Fig.1.) AE. BC:: 2. 1.

For, it has been demonstrated that of any terme in the left Column is less than the terme next after it; and therefore that, of the last terme, at which you stop