“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

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Opticks (1704)

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Isaac Newton171

British physicist and mathematician and founder of modern c… 1643–1727

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“Theory consists in referring particular operations to the principles, or general laws, under which they are comprehended; or in referring particular effects to the causes from which they proceed.”

Adam Ferguson (1723–1816) Scottish philosopher and historian

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“Analysis and synthesis, though commonly treated as two different methods, are, if properly understood, only the two necessary parts of the same method. Each is the relative and correlative of the other. Analysis, without a subsequent synthesis, is incomplete; it is a mean cut of from its end. Synthesis, without a previous analysis, is baseless; for synthesis receives from analysis the elements which it recomposes.”

Sir William Hamilton, 9th Baronet (1788–1856) Scottish metaphysician (1788–1856)

Lectures on Metaphysics and Logic: "6th Lecture on Metaphysics", p. 69, ed. 1871, Boston; partly reported in Austin Allibone ed. Prose Quotations from Socrates to Macaulay. (1903), p. 34

“Analysis… takes that which is sought as if it were admitted and passes from it through its successive consequences to something which is admitted as the result of synthesis: for in analysis we assume that which is sought as if it were (already) done (ɣϵɣονός) and we inquire what it is from which this results, and again what is the antecedent cause of the latter, and so on, until by so retracing our steps we come upon something already known or belonging to the class of first principles, and such a method we call analysis as being solution backwards”

Pappus of Alexandria (290–350) Greek mathematician of Antiquity

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The Thirteen Books of Euclid's Elements (1908)

“[L]et us consider, with respect to causes, what they are, and how many there are in number… this also must be done by us in discoursing concerning generation and corruption, and all physical mutation… knowing the principles of these…
Cause… is after one manner said to be that, from which, being inherent, something is produced… But after another manner cause is form and paradigm (and this is the definition of the essence of a thing) and the genera of this. …But it happens… that there are also many causes of the same thing, and this is not from accident. …seed, a physician, he who consults, and, in short, he who makes, are all of them causes, as that whence the principle of mutation, or permanency, or motion is derived. …It is, however, necessary always to investigate the supreme cause of every thing …Further still, it is necessary to investigate the genera of genera; and the particulars of particulars… We should also explore the capacities of the capabilities, and the energizers of the things affected by energy.”

Aristotle book Physics

Book II, Ch. III, pp. 107-113.
Physics

“Either one or the other [ analysis or synthesis ] may be direct or indirect. The direct procedure is when the point of departure is known-direct synthesis in the elements of geometry. By combining at random simple truths with each other, more complicated ones are deduced from them. This is the method of discovery, the special method of inventions, contrary to popular opinion.”

André-Marie Ampère (1775–1836) French physicist and mathematician

André-Marie Ampè, in André-Marie Ampère: Enlightenment and Electrodynamics http://books.google.co.in/books?id=QWZKQWB-sbQC&pg=PA159, Cambridge University Press, 1996, p. 159

“There is synthesis when, in combining therein judgments that are made known to us from simpler relations, one deduces judgments from them relative to more complicated relations. There is analysis when from a complicated truth one deduces more simple truths.”

André-Marie Ampère (1775–1836) French physicist and mathematician

André-Marie Ampère in: André-Marie Ampère: Enlightenment and Electrodynamics http://books.google.co.in/books?id=QWZKQWB-sbQC&pg=PA158, Cambridge University Press, 1996, p. 158.

“Intellectual culture consists, not chiefly, as many are apt to think, in accumulating information, though this is important, but in building up a force of thought which may be turned at will on any subjects on which we are called to pass judgment. This force is manifested in the concentration of the attention, in accurate, penetrating observation, in reducing complex subjects to their elements, in diving beneath the effect to the cause, in detecting the more subtle differences and resemblances of things, in reading the future in the present, and especially in rising from particular facts to general laws or universal truths. … Oone man talks continually about the particular actions of this or another neighbor; whilst another looks beyond the acts to the inward principle from which they spring, and gathers from them larger views of human nature.”

William Ellery Channing (1780–1842) United States Unitarian clergyman

Self-Culture (1838)

“After this first approximation, the various aspects of the situation undergo a more and more detailed analysis. In contrast to this the second method [for analysis of life space] begins with the life space as a whole and defines its fundamental structure. The procedure in this case is not to add disconnected items but to make the original structure more specific and differentiated. This method therefore proceeds by steps from the more general to the particular and thereby avoids the danger of a "wrong simplification" by abstraction.”

Kurt Lewin (1890–1947) German-American psychologist

Source: 1930s, Principles of topological psychology, 1936, p. 4; partly cited in: Chris Argyris (1952) An introduction to field theory and interaction theory.

“It is abundantly evident, both from history and from present experience, that the instinctive shock, or natural feeling of disgust, caused by the sight of the sufferings of men is not generically different from that which is caused by the sight of the sufferings of animals.”

William Edward Hartpole Lecky (1838–1903) British politician

Source: A History of European Morals from Augustus to Charlemagne (1869), Chapter 2 (2nd edition, Vol. 1, London: Longmans, 1869, p. 294 https://books.google.it/books?id=hdUJs_S3ezwC&pg=PA294)

“It is indeed a matter of great difficulty to discover, and effectually to distinguish, the true motions of particular bodies from the apparent; because the parts of that immovable space, in which those motions are performed, do by no means come under the observation of our senses. Yet the thing is not altogether desperate; for we have some arguments to guide us, partly from the apparent motions, which are the differences of the true motions; partly from the forces, which are the causes and effects of the true motions.”

Isaac Newton book Philosophiae Naturalis Principia Mathematica

Definitions - Scholium
Philosophiae Naturalis Principia Mathematica (1687)

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