"They only take those things into consideration, of which they have clear and distinct ideas, designating them by proper, adequate, and invariable names, and premising only a few axioms which are most noted and certain to investigate their affections and draw conclusions from them, and agreeably laying down a very few hypotheses, such as are in the highest degree consonant with reason and not to be denied by anyone in his right mind. In like manner they assign generations or causes easy to be understood and readily admitted by all, they preserve a most accurate order, every proposition immediately following from what is supposed and proved before, and reject all things howsoever specious and probable which can not be inferred and deduced after the same manner.—Barrow, Isaac."

“These Disciplines serve to inure and corroborate the Mind to a constant Diligence in Study; to undergo the Trouble of an attentive Meditation, and cheerfully contend with such Difficulties as lie in the Way. They wholly deliver us from a credulous Simplicity, most strongly fortify us against the Vanity of Scepticism, effectually restrain from a rash Presumption, most easily incline us to a due Assent, perfectly subject us to the Government of right Reason, and inspire us with Resolution to wrestle against the unjust Tyranny of false Prejudices. If the Fancy be unstable and fluctuating, it is to be poised by this Ballast, and steadied by this Anchor, if the Wit be blunt it is sharpened upon this Whetstone; if luxuriant it is pared by this Knife; if headstrong it is restrained by this Bridle; and if dull it is roused by this Spur. The Steps are guided by no Lamp more clearly through the dark Mazes of Nature, by no Thread more surely through the intricate Labyrinths of Philosophy, nor lastly is the Bottom of Truth sounded more happily by any other Line. I will not mention how plentiful a Stock of Knowledge the Mind is furnished from these, with what wholesome Food it is nourished, and what sincere Pleasure it enjoys. But if I speak farther, I shall neither be the only Person, nor the first, who affirms it; that while the Mind is abstracted and elevated from sensible Matter, distinctly views pure Forms, conceives the Beauty of Ideas, and investigates the Harmony of Proportions; the Manners themselves are sensibly corrected and improved, the Affections composed and rectified, the Fancy calmed and settled, and the Understanding raised and excited to more divine Contemplation. All which I might defend by Authority, and confirm by the Suffrages of the greatest Philosophers.”

“Among these Ways, or any other whatever, of generating Magnitudes, the Primary and Chief is, that perform'd by local Motion, which all of them must in some Sort suppose, because without Motion, nothing can be generated or produced and therefore this must first be considered. The following Axiom of Aristotle concerning Motion is famous... He that is ignorant of Motion, must necessarily know nothing of Nature... in Nature every Thing created is produc'd by Motion, or certainly not without Motion.”

“Smiling always with a never fading serenity of countenance, and flourishing in an immortal youth.”

“But perhaps you may ask, whether Time was not before the World was created? And if Time does not flow in the Extramundane Space, where nothing is: A mere Vacuum? I answer, that since there was Space before the World was created, and that there now is an Extramundane, infinite Space, ... Time existed before the World began, and does exist together with the World in the Extramundane Space, because 'tis possible that some Thing might have existed long before the World was made; and there may now be something in the Extramundane Space, capable of such a Continuance: Some Sun might have given Light long before; and at present this, or some other like it, may diffuse Light thro' Imaginary Spaces. Time therefore does not imply an actual Existence, but only the Capacity or Possibility of the Continuance of Existence; just as Space expresses the Capacity of a Magnitude contain'd in it.”

“It cannot be justly inferr'd... We do not perceive the Thing, therefore there is no such Thing, that is a false Illusion, a deceitful Dream, that wou'd cause us to join together two remote Instants of Time. But nevertheless this is very True... That is, for as much Motion as there was, so much Time seems to have been elapsed; nor, when we mention such a Quantity of Time, do we merely mean any Thing else, than the Performance of so much Motion, to the continued successive Extension of which we imagine the Permanency as Things is co-extended.”

“For to pass by those Ancients, the wonderful Pythagoras, the sagacious Democritus, the divine Plato, the most subtle and very learned Aristotle, Men whom every Age has hitherto acknowledged as deservedly honored, as the greatest Philosophers, the Ring-leaders of Arts; in whose Judgments how much these Studies were esteemed, is abundantly proclaimed in History and confirmed by their famous Monuments, which are everywhere interspersed and bespangled with Mathematical Reasonings and Examples, as with so many Stars; and consequently anyone not in some Degree conversant in these Studies will in vain expect to understand, or unlock their hidden Meanings, without the Help of a Mathematical Key: For who can play well on Aristotle’s Instrument but with a Mathematical Quill; or not be altogether deaf to the Lessons of natural Philosophy, while ignorant of Geometry? Who void of Arithmetic can comprehend Plato’s 218 Socrates lisping with Children concerning Square Numbers; or can conceive Plato himself treating not only of the Universe, but the Polity of Commonwealths regulated by the Laws of Geometry, and formed according to a Mathematical Plan?”