leave him destitute of proper information. In the distribution of the first book of this work into chapters, I have followed the order of Barocius, because it is natural and obvious; and must beg leave to solicit the reader’s indulgence for using the words _partible_ and _impartible_, differently from their common signification. These words I have generally employed to express the meaning of μεριστός[2] and αμεριστος[3] in the Greek, as I do not conceive that the words _divisible_ and _indivisible_ always convey their full signification. I have likewise used _quadrangle_ instead of square, and _quinquangle_ for the word pentagon. For if τρίγωνος be rendered _triangle_, why should not τετραγώνος be rendered _quadrangle_? And, as Barocius observes, why, for a similar reason, should not πεντάγωνος and ἑξάγωνος be rendered _quinquangle_ and _sexangle_; and so of the rest? Uniformity is always desirable when it can be obtained; and is no where so necessary as in scientifical disquisitions. It is likewise necessary to inform the reader, that though I have always endeavoured to give the faithful meaning of my Author, yet I have occasionally paraphrased his sense, when most obscure, and added such elucidations of my own, as I either thought necessary to the full comprehension of his matter; or which were naturally excited by the fire and spirit of the Original. If it shall appear that I have succeeded in the execution of this work, and rendered it intelligible to the lovers of truth, I shall rejoice in my success, and consider my labours sufficiently rewarded. The applause of the multitude I am neither likely nor desirous to gain; but I am anxious to procure the approbation of the discerning few, who know that the age of philosophy is past; and who esteem the works of her ancient heroes as the most precious treasures which have escaped the ravages of time. * * * * *