“The elucidation of the theory of centripetal and disturbing forces is necessarily less complete. Still… a general conception of the nature of the action of those forces… sufficient to preserve the student from the gross errors… may be obtained from explanations like those here offered. The methods of ascertaining the weight of the Earth and other bodies are… more difficult of explanation; yet… something may be done even in these.”

— George Biddell Airy

Introduction
Popular Astronomy: A Series of Lectures Delivered at Ipswich (1868)

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George Biddell Airy 13

English mathematician and astronomer 1801–1892

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“By this way of Analysis we may proceed from Compounds to Ingredients, and from Motions to the Forces producing them; and in general, from Effects to their Causes, and from particular Causes to more general ones, till the Argument end in the most general. This is the Method of Analysis: and the Synthesis consists in assuming the Causes discover'd, and establish'd as Principles, and by them explaining the Phænomena proceeding from them, and proving the Explanations.”

Isaac Newton book Opticks, or a Treatise of the Reflections, Refractions, Inflections and Colours of Light

Query 31
Opticks (1704)

“And so if any one would suppose that Æther (like our Air) may contain Particles which endeavour to recede from one another (for I do not know what this Æther is) and that its Particles are exceedingly smaller than those of Air, or even than those of Light: The exceeding smallness of its Particles may contribute to the greatness of the force by which those Particles may recede from one another, and thereby make that Medium exceedingly more rare and elastick than Air, and by consequence exceedingly less able to resist the motions of projectiles, and exceedingly more able to press upon gross Bodies, by endeavouring to expand it self.”

Isaac Newton book Opticks, or a Treatise of the Reflections, Refractions, Inflections and Colours of Light

Query 21
Opticks (1704)

“From the standpoint of exact natural science, of the explanation of nature from causes, the assumption of an earth-soul is… an hypothesis for the explanation of Being and of the historical development of the organic world.”

Bernhard Riemann (1826–1866) German mathematician

Gesammelte Mathematische Werke (1876)

“[W]e shall be concerned with the general nature of pure mathematics, and how it is distinguished from other sciences. Here there are… two distinct categories of things of which an account must be given—the ideas or concepts of mathematics, and the propositions of mathematics. …the great majority of writers on the subject have concentrated their attention on the explanation of one or the other… and erroneously supposed that a satisfactory explanation of the other would immediately follow.”

Frank P. Ramsey (1903–1930) British mathematician, philosopher

Footnote: In the future by 'mathematics' will always be meant 'pure mathematics'.
The Foundations of Mathematics (1925)

“The more closely one studies Nietzsche's work, the less inclined one is to look outside it for an elucidation of its meaning or an explanation of its origin.”

R. J. Hollingdale (1930–2001) British Author

1. The Child
Nietzsche (1965, 1999)

“Our design, not respecting arts, but philosophy, and our subject, not manual, but natural powers, we consider chiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces, whether attractive or impulsive; and therefore we offer this work as mathematical principles of philosophy; for all the difficulty of philosophy seems to consist in this — from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena…”

Isaac Newton book Philosophiae Naturalis Principia Mathematica

Preface
Philosophiae Naturalis Principia Mathematica (1687)

“May these explanations of the myths find favour in the eyes of the Gods themselves and the souls of those who wrote the myths.”

Sallustius Roman philosopher and writer

IV. That the species of myth are five, with examples of each.
On the Gods and the Cosmos

“Although I am not aware of having omitted any thing that is requisite to the full explanation of the subject, yet I cannot flatter myself that it will be thoroughly understood from this Work alone. For, in general it may be laid down as true, that no doctrine, of novelty and intricacy, can be completely taught by a single Treatise. It seems to be indispensably necessary for the student, that the subject should be put under several points of view: that if not apprehended under one, it may be under another.”

Robert Woodhouse (1773–1827) English mathematician

Preface p. viii
A Treatise on Isoperimetrical Problems, and the Calculus of Variations (1810)

“Much less are children capable of reasonings from remote principles. They cannot conceive the force of long deductions. The reasons that move them must be obvious, and level to their thoughts, and such as may be felt and touched. But yet, if their age, temper, and inclination be consider'd, they will never want such motives as may be sufficient to convince them.”

John Locke book Some Thoughts Concerning Education

Sec. 81
Some Thoughts Concerning Education (1693)
Context: The foundations on which several duties are built, and the foundations of right and wrong from which they spring, are not perhaps easily to be let into the minds of grown men, not us'd to abstract their thoughts from common received opinions. Much less are children capable of reasonings from remote principles. They cannot conceive the force of long deductions. The reasons that move them must be obvious, and level to their thoughts, and such as may be felt and touched. But yet, if their age, temper, and inclination be consider'd, they will never want such motives as may be sufficient to convince them.

“Theories rarely arise as patient inferences forced by accumulated facts. Theories are mental constructs potentiated by complex external prods (including, in idealized cases, a commanding push from empirical reality). But the prods often include dreams, quirks, and errors—just as we may obtain crucial bursts of energy from foodstuffs or pharmaceuticals of no objective or enduring value. Great truth can emerge from small error. Evolution is thrilling, liberating, and correct. And Macrauchenia is a litoptern.”

Stephen Jay Gould book Leonardo's Mountain of Clams and the Diet of Worms

"Mr. Sophia's Pony", pp. 157 - 158
Leonardo's Mountain of Clams and the Diet of Worms (1998)

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George Biddell Airy 13

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