“Since… nature is a principle of motion and mutation… it is necessary that we should not be ignorant of what motion is… But motion appears to belong to things continuous; and the infinite first presents itself to the view in that which is continuous. …[F]requently …those who define the continuous, employ the nature or the infinite, as if that which is divisible to infinity is continuous.”

Book III, Ch. I, pp. 135-136.
Physics

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Classical Greek philosopher, student of Plato and founder o… -384–-321 BC

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“The smallest natural point is larger than all mathematical points, and this is proved because the natural point has continuity, and any thing that is continuous is infinitely divisible; but the mathematical point is indivisible because it has no size.”

Leonardo Da Vinci (1452–1519) Italian Renaissance polymath

The Notebooks of Leonardo da Vinci (1883), II Linear Perspective

“All those… who discourse concerning nature, always subject a certain other nature of… elements, to the infinite… But no one of those who make the elements to be finite introduces infinity. Such, however, as make infinite elements, as Anaxagoras and Democritus, say that the infinite is continuous by contact. …Rationally, too, do all philosophers consider the infinite as a principle; for it cannot be in vain, nor can any other power be present with it than that of a principle: for all things are either the principle, or from the principle; but of the infinite there is no principle, since otherwise it would have an end. …it is also unbegotten and uncorruptible, as being a certain principle: for… end is the corruption of everything. …It likewise appears to comprehend and govern all things, as those assert who do not introduce other causes beside the infinite… It would seem also that this is divine: for it is immortal and indestructible, as Anaximander says, and most of the physiologists.”

Aristotle book Physics

Book III, Ch. IV, pp. 152-155.
Physics

“Whatever is in motion must be put in motion by another. If that by which it is put in motion be itself put in motion, then this also must needs be put in motion by another, and that by another again. But this cannot go on to infinity, because then there would be no first mover, and, consequently, no other mover; seeing that subsequent movers move only inasmuch as they are put in motion by the first mover; as the staff moves only because it is put in motion by the hand. Therefore it is necessary to arrive at a first mover, put in motion by no other; and this everyone understands to be God.”

Thomas Aquinas book Summa Theologica

I, q. 2, art. 3
Summa Theologica (1265–1274)

“Since the science of nature is conversant with magnitudes, motion, and time, each of which must necessarily be either infinite or finite…[we] should speculate the infinite, and consider whether it is or not; and if it is what it is. …[A]ll those who appear to have touched on a philosophy of this kind… consider it as a certain principle of beings. Some, indeed, as the Pythagoreans and Plato, consider it, per se, not as being an accident to any thing else, but as having an essential subsistence… the Pythagoreans… consider the infinite as subsisting in sensibles; for they do not make number to be separate; and they assert that what is beyond the heavens is infinite; but Plato says that beyond the heavens there is not any body, nor ideas, because these are no where: he affirms, however, that the infinite is both in sensibles, and in ideas. …Plato establishes two infinities, viz. the great and the small.”

Aristotle book Physics

Book III, Ch. IV, pp. 150-152.
Physics

“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.”

Isaac Barrow (1630–1677) English Christian theologian, and mathematician

p, 125
Geometrical Lectures (1735)

“There is… something which is in energy only; and there is something which is both in energy and capacity. …of relatives, one is predicated as according to excess and defect: another according to the effective and passive, and, in short, the motive, and that which may be moved… Motion, however, has not a substance separate from things… But each of the categories subsists in a twofold manner in all things. Thus… one thing pertaining to it is form, and another privation. …So the species of motion and mutation are as many as those of being. But since in every genus of things, there is that which is in entelecheia, and that which is in capacity; motion is the entelecheia of that which is in capacity… That there is energy, therefore, and that a thing then happens to be moved, when this energy exists, and neither prior nor posterior to it, is manifest. … [N]either motion nor mutation can be placed in any other genus; nor have those who have advanced a different opinion concerning it spoken rightly. …for by some motion is said to be difference, inequality, and non-being; though it is not necessary that any of these should be moved… Neither is mutation into these, nor from these, rather than from their opposites. …The cause, however, why motion appears to be indefinite, is because it can neither be simply referred to the capacity, nor to the energy of beings. …[I]t is difficult to apprehend what motion is: for it is necessary to refer it either to privation, or to capacity, or to simple energy; but it does not appear that it can be any of these. The above-mentioned mode, therfore remains, viz. that it is a certain energy; but… difficult to be perceived, but which may have a subsistence.”

Aristotle book Physics

Book III, Ch. I, pp. 137-147.
Physics

“The Calculus required continuity, and continuity was supposed to require the infinitely little; but nobody could discover what the infinitely little might be.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

Source: 1910s, Mysticism and Logic and Other Essays http://archive.org/stream/mysticism00russuoft/mysticism00russuoft_djvu.txt (1918), Ch. 5: Mathematics and the Metaphysicians

“[O]ur [small] knowledge of the relation of finite to infinite... is... continually increasing—science and philosophy are continally presenting... broader views of the relation of man to nature and of individual thought to abstract thought.”

Karl Pearson (1857–1936) English mathematician and biometrician

The Ethic of Freethought (Mar 6, 1883)

“We are a little piece of continual change, looking at an infinite quantity of continual change.”

B.K.S. Iyengar (1918–2014) Indian yoga teacher and scholar

Source: Light on Life: The Yoga Journey to Wholeness, Inner Peace, and Ultimate Freedom, p. 7

“[B]ecause that which is finite is always bounded with reference to something… it is necessary that there should be no end… [N]umber also appears to be infinite, and mathematical magnitudes, and that which is beyond the heavens. And since that which is beyond is infinite, body also appears to be infinite, and it would seem that there are infinite worlds; for why is there rather void here than there? …If also there is a vacuum, and an infinite place, it is necessary that there should be an infinite body: for in things which have a perpetual subsistence, capacity differs nothing from being. The speculation of the infinite is, however, attended with doubt: for many impossibilities happen both to those who do not admit that it has a subsistence, and to those who do. …It is …especially the province of a natural philosopher to consider if there be a sensible infinite magnitude.”

Aristotle book Physics

Book III, Ch. V, p. 156.
Physics

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