“More evidently still astronomy attains through arithmetic the investigations that pertain to it, not alone because it is later than geometry in origin—for motion naturally comes after rest—nor because the motions of the stars have a perfectly melodious harmony, but also because risings, settings, progressions, retrogressions, increases, and all sorts of phases are governed by numerical cycles and quantities. So then we have rightly undertaken first the systematic treatment of this, as the science naturally prior, more honorable, and more venerable, and, as it were, mother and nurse of the rest; and here we will take our start for the sake of clearness.”

—  Nicomachus

Book I, Chapter V
Nicomachus of Gerasa: Introduction to Arithmetic (1926)

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Nicomachus 22
Ancient Greek mathematician 60–120

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“I tell you that if natural bodies have it from Nature to be moved by any movement, this can only be circular motion, nor is it possible that Nature has given to any of its integral bodies a propensity to be moved by straight motion. I have many confirmations of this proposition, but for the present one alone suffices, which is this. I suppose the parts of the universe to be in the best arrangement, so that none is out of its place, which is to say that Nature and God have perfectly arranged their structure. This being so, it is impossible for those parts to have it from Nature to be moved in straight, or in other than circular motion, because what moves straight changes place, and if it changes place naturally, then it was at first in a place preternatural to it, which goes against the supposition. Therefore, if the parts of the world are well ordered, straight motion is superfluous and not natural, and they can only have it when some body is forcibly removed from its natural place, to which it would then return by a straight line, for thus it appears that a part of the earth does [move] when separated from its whole. I said "it appears to us," because I am not against thinking that not even for such an effect does Nature make use of straight line motion.”

Galileo Galilei (1564–1642) Italian mathematician, physicist, philosopher and astronomer

A note on this statement is included by Stillman Drake in his Galileo at Work, His Scientific Biography (1981): Galileo adhered to this position in his Dialogue at least as to the "integral bodies of the universe." by which he meant stars and planets, here called "parts of the universe." But he did not attempt to explain the planetary motions on any mechanical basis, nor does this argument from "best arrangement" have any bearing on inertial motion, which to Galileo was indifference to motion and rest and not a tendency to move, either circularly or straight.
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“Nor is primitive matter productive of motion, because it is itself passive.”

Robert Grosseteste (1175–1253) English bishop and philosopher

De Luce seu de Inchoatione Formarum (c. 1215-1220)
Context: One cause, in so far as it is one, is productive of only one effect. I do not rule out several efficient causes of which one is nearer and another more remote in the same order. Thus when I say simply 'animal', I do not exclude another substance or particular substance. Hence motion, in so far as it is one, is productive of only one effect. But motion is present in every body from an intrinsic principle which is called natural. Therefore an efficient cause simply proportional to the motion is present in all bodies. But nothing is present in common in every body except primitive matter and primitive form and magnitude, which necessarily follows from these two, and whatever is entailed by magnitude as such, as position and shape. But simply through magnitude a body does not receive motion, as is clear enough when Aristotle shows that everything that moves is divisible, not, therefore, simply because of magnitude or something entailed by magnitude is a body productive of motion. Nor is primitive matter productive of motion, because it is itself passive. It is therefore necessary that motion follow simply from the primitive form as from an efficient cause.

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“Money alone sets all the world in motion.”

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