ABSTRACT
LAYING aside all Prefaces, and having dispersed the Clouds of Ambiguities, which lay in our Way, we come now to enquire into and explain the Nature of Geometrical Reason. Geometrical Reason or simply Reason (for in this Sense we will always hereafter use this Word, as also its equivalent, Proportion) I say Reason or Proportion λόγo is defined by Euclid (or by Eudoxus, if he, as is said, be the Composer of the fifth Book of the Elements) to be a certain Habitude (or Relation) of two homogeneous Magnitudes to one another, according to Quantity. About which Definition two things may be enquired into and disputed; first what is his genuine Meaning; and then whether it be Sufficiently just and accurate, I will endeavour to satisfy each Disquisition applying certain Observations to his Terms, that we may at the same Time interpret the Sense, and defend the Authority, of our Master. Be pleased to pardon my Contentiousness, and take it not for the worse that being led with a certain Piety I study to vindicate the Father and Prince of Geometry from the undeserved Reproaches, which are every where thrown upon him.
