Source: In artem analyticem Isagoge (1591), Ch. 1 as quoted by Douglas M. Jesseph, Squaring the Circle: The War Between Hobbes and Wallis (1999) p. 225
“Now analysis is of two kinds, the one directed to searching for the truth and called theoretical, the other directed to finding what we are told to find and called problematical. (1) In the theoretical kind we assume what is sought as if it were existent and true, after which we pass through its successive consequences, as if they too were true and established by virtue of our hypothesis, to something admitted: then (a), if that something admitted is true, that which is sought will also be true and the proof will correspond in the reverse order to the analysis, but (b), if we come upon something admittedly false, that which is sought will also be false. (2) In the problematical kind we assume that which is propounded as if it were known, after which we pass through its successive consequences, taking them as true, up to something admitted: if then (a) what is admitted is possible and obtainable, that is, what mathematicians call given, what was originally proposed will also be possible, and the proof will again correspond in reverse order to the analysis, but if (b) we come upon something admittedly impossible, the problem will also be impossible.”
Source: The Thirteen Books of Euclid's Elements (1908), Ch. IX. §6
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Pappus of Alexandria 5
Greek mathematician of Antiquity 290–350Related quotes
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The Thirteen Books of Euclid's Elements (1908)
Source: The Thirteen Books of Euclid's Elements (1908), Ch. IX. §6
Books on Religion and Christianity, I am the Truth. Toward a philosophy of Christianity (1996)
Source: Michel Henry, I am the Truth. Toward a Philosophy of Christianity, translated by Susan Emanuel, Stanford University Press, 2003, p. 1
Source: The Tales of Alvin Maker, Seventh Son (1987), Chapter 10.
“But no. There is a difference between the truth and what we wish were true.”
Source: The Slow Regard of Silent Things
“A kiss may not be the truth, but it is what we wish were true.”
As Harris K. Telemacher in "L.A. Story" (1991)
“We can never add more truth to what is true already, nor make that true which is false.”
p, 125
The History of Oracles, and the Cheats of the Pagan Priests (1688)
Source: " The Poet of Pessimism https://www.henrysalt.co.uk/library/essay/the-poet-of-pessimism/", Vegetarian Review, August 1896
Context: We work for an ideal, not because we believe the ideal is destined to be triumphant, but because we are impelled so to work, and cannot, without violence to our best instincts, act otherwise. We protest against cruelty and injustice for the same reason, not merely because we feel that the dawn of a better day is at hand, but because such a protest has to be made, and we know intuitively that we must help to make it. Of the event we can have no absolute assurance—it rests for other minds and other hands than our—but we can at least be assured that we have done what was natural and inevitable to us, and that, whether successful or unsuccessful, there was no other course for a thoughtful man to take.
Source: Guide for the Perplexed (c. 1190), Part III, Ch.21
Context: He fully knows His unchangeable essence, and has thus a knowledge of all that results from any of His acts. If we were to try to understand in what manner this is done, it would be the same as if we tried to be the same as God, and to make our knowledge identical with His knowledge. Those who seek the truth, and admit what is true, must believe that nothing is hidden from God; that everything is revealed to His knowledge, which is identical with His essence; that this kind of knowledge cannot be comprehended by us; for if we knew its method, we would possess that intellect by which such knowledge could be acquired.... Note this well, for I think that this is an excellent idea, and leads to correct views; no error will be found in it; no dialectical argument; it does not lead to any absurd conclusion, nor to ascribing any defect to God. These sublime and profound themes admit of no proof whatever... In all questions that cannot be demonstrated, we must adopt the method which we have adopted in this question about God's Omniscience. Note it.