“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

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

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Sir William Hamilton, 9th Baronet6

Scottish metaphysician (1788–1856) 1788–1856

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“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

“Science is spectral analysis. Art is light synthesis.”

Karl Kraus (1874–1936) Czech playwright and publicist

Half-Truths and One-And-A-Half Truths (1976)

“Geovisualization integrates approaches from visualization in scientific computing (ViSC), cartography, image analysis, information visualization, exploratory data analysis (EDA), and geographic information systems (GISystems) to provide theory, methods, and tools for visual exploration, analysis, synthesis, and presentation of geospatial data”

Alan MacEachren (1952) American geographer

any data having geospatial referencing
Source: Research challenges in geovisualization (2001), p. 3

“As the analysis of a substantial composite terminates only in a part which is not a whole, that is, in a simple part, so synthesis terminates only in a whole which is not a part, that is, the world.”

Immanuel Kant (1724–1804) German philosopher

Kant's Inaugural Dissertation (1770), Section I On The Idea Of A World In General

“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)

“Man is a synthesis of psyche and body, but he is also a synthesis of the temporal and the eternal. In the former, the two factors are psyche and body, and spirit is the third, yet in such a way that one can speak of a synthesis only when the spirit is posited. The latter synthesis has only two factors, the temporal and the eternal. Where is the third factor? And if there is no third factor, there really is no synthesis, for a synthesis that is a contradiction cannot be completed as a synthesis without a third factor, because the fact that the synthesis is a contradiction asserts that it is not. What, then, is the temporal?”

Sören Kierkegaard (1813–1855) Danish philosopher and theologian, founder of Existentialism

Source: 1840s, The Concept of Anxiety (1844), p. 85

“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

άνάπαλɩν λὐσɩν
The Thirteen Books of Euclid's Elements (1908)

“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.

“But in synthesis, reversing the process, we take as already done that which was last arrived at in the analysis and, by arranging in their natural order as consequences what were before antecedents, and successively connecting them one with another, we arrive finally at the construction of what was sought; and this we call synthesis.”

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

Source: The Thirteen Books of Euclid's Elements (1908), Ch. IX. §6

“There are two general Methods made use of in the Mathematicks, viz. Synthesis and Analysis, which we shall explain, after having acquainted the Reader, that the Method we make use of to resolve a Mathematical Problem, is called Zetetick; and that that Method which determines when, and by what way, and how many different ways a Problem may be resolved, is called Poristick. But in treating of Methods, we will first premise, that in general, a Method is the Art of disposing a Train of Arguments or Consequences in a right Order, either to discover the Truth of a Theorem, which we would find out, or to demonstrate it to others, when found.”

Jacques Ozanam (1640–1718) French mathematician

Source: A Mathematical Dictionary: Or; A Compendious Explication of All Mathematical Terms, 1702, p. 26

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Sir William Hamilton, 9th Baronet6

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