[C]onsider the steps by which the antients were able... from the mensuration of right-lined figures, to judge of such as were bounded by curve lines;… - Colin MacLaurin

This way of considering what is called the sublime part of geometry has so far prevailed, that it is generally known by no less a title than the Science, Arithmetic, or Geometry of infinites. These terms imply something lofty, but mysterious; the contemplation of which may be suspected to amaze and perplex, rather than satisfy or enlighten the understanding... and while it seems greatly to elevate geometry, may possibly lessen its true and real excellency, which chiefly consists in its perspicuity and perfect evidence; for we may be apt to rest in an obscure and imperfect knowledge of so abstruse a doctrine... instead of seeking for that clear and full view we ought to have of geometrical truth; and to this we may ascribe the inclination... of late for introducing mysteries into a science wherein there ought to be none.

Though there can be no comparison made betwixt the extent or usefulness of the antient and modern Discoveries in Geometry, yet it seems to be generally allowed that the Antients took greater care, and were more successfull in preserving the Character of its Evidence entire.

The greatest part of the first Book was printed in 1737: but it could not have been so useful to the Reader without the second; and I... recommend... to peruse the first Chapters of the second Book, before the five last of the first; there being a few passages... that will be better understood by... [having] some knowledge of the principal Rules of the Method of Computation... in the second Book.