Hippasus
Hippasus of
Life
Little is known about the life of Hippasus. He may have lived in the late 5th century BC, about a century after the time of Pythagoras. Metapontum in Magna Graecia is usually referred to as his birthplace,[5][6][7][8][9] although according to Iamblichus some claim Metapontum to be his birthplace, while others the nearby city of Croton.[10] Hippasus is recorded under the city of Sybaris in Iamblichus's list of each city's Pythagoreans.[11] He also states that Hippasus was the founder of a sect of the Pythagoreans called the Mathematici (μαθηματικοί) in opposition to the Acusmatici (ἀκουσματικοί);[12] but elsewhere he makes him the founder of the Acusmatici in opposition to the Mathematici.[13]
Iamblichus says about the death of Hippasus:
- It is related to Hippasus that he was a Pythagorean, and that, owing to his being the first to publish and describe the sphere from the twelve pentagons, he perished at sea for his impiety, but he received credit for the discovery, though really it all belonged to HIM (for in this way they refer to Pythagoras, and they do not call him by his name).[14]
According to Iamblichus (ca. 245-325 AD, 1918 translation) in The life of Pythagoras, by Thomas Taylor[15]
- There were also two forms of philosophy, for the two genera of those that pursued it: the Acusmatici and the Mathematici. The latter are acknowledged to be Pythagoreans by the rest but the Mathematici do not admit that the Acusmatici derived their instructions from Pythagoras but from Hippasus. The philosophy of the Acusmatici consisted in auditions unaccompanied with demonstrations and a reasoning process; because it merely ordered a thing to be done in a certain way and that they should endeavor to preserve such other things as were said by him, as divine dogmas. Memory was the most valued faculty. All these auditions were of three kinds; some signifying what a thing is; others what it especially is, others what ought or ought not to be done. (p. 61)
Doctrines
A
Irrational numbers
Hippasus is sometimes credited with the discovery of the existence of
These stories are usually taken together to ascribe the discovery of irrationals to Hippasus, but whether he did or not is uncertain.[24] In principle, the stories can be combined, since it is possible to discover irrational numbers when constructing dodecahedra. Irrationality, by infinite reciprocal subtraction, can be easily seen in the golden ratio of the regular pentagon.[25]
Some scholars in the early 20th century credited Hippasus with the discovery of the irrationality of , the square root of 2. Plato in his Theaetetus,[26] describes how Theodorus of Cyrene (c. 400 BC) proved the irrationality of , , etc. up to , which implies that an earlier mathematician had already proved the irrationality of .[27] Aristotle referred to the method for a proof of the irrationality of ,
In the hands of modern writers this combination of vague ancient reports and modern guesswork has sometimes evolved into a much more emphatic and colourful tale. Some writers have Hippasus making his discovery while on board a ship, as a result of which his Pythagorean shipmates toss him overboard;[31] while one writer even has Pythagoras himself "to his eternal shame" sentencing Hippasus to death by drowning, for showing "that is an irrational number".[32]
References
- ^ Huffman, Carl A. (1993). Philolaus of Croton: Pythagorean and Presocratic. Cambridge University Press. p. 8.
- ^ "Hippasus of Metapontum | Greek philosopher". Encyclopedia Britannica. Retrieved 2021-09-20.
- ^ Iamblichus (1918). The life of Pythagoras (1918 translation ed.). p. 327.
- ^ William Thompson. The Commentary of Pappus on Book X of Euclid's Elements (PDF).
- ^ Aristotle, Metaphysics I.3: 984a7
- ^ a b c Diogenes Laertius, Lives of Eminent Philosophers VIII,84
- ^ Simplicius, Physica 23.33
- ^ Aetius I.5.5 (Dox. 292)
- ^ Clement of Alexandria, Protrepticus 64.2
- ^ Iamblichus, Vita Pythagorica, 18 (81)
- ^ Iamblichus, Vita Pythagorica, 34 (267)
- ^ Iamblichus, De Communi Mathematica Scientia, 76
- ^ Iamblichus, Vita Pythagorica, 18 (81); cf. Iamblichus, In Nic. 10.20; De anima ap. Stobaeus, i.49.32
- ^ Iamblichus, Thomas, ed. (1939). "18". On the Pythagorean Life. p. 88.
- ^ Iamblichus (1918). The life of Pythagoras.
- ^ Aristotle, Metaphysics (English translation)
- ^ Sextus Empiricus, ad Phys. i. 361
- ^ Diogenes Laertius, Lives of Eminent Philosophers, viii. 7
- ^ Scholium on Plato's Phaedo, 108d
- scholiumto the tenth book.
- ^ a b Iamblichus, Vita Pythagorica, 34 (246).
- ^ Iamblichus, Vita Pythagorica, 18 (88), De Communi Mathematica Scientia, 25.
- ^ Iamblichus, Vita Pythagorica, 34 (247).
- ^ Wilbur Richard Knorr (1975), The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and its Significance for Early Greek Geometry, pages 21–22, 50–51. Springer.
- ^ Walter Burkert (1972), Lore and Science in Ancient Pythagoreanism, page 459. Harvard University Press.
- ^ Plato, Theaetetus, 147d ff.
- Thomas Heath(1921) A History of Greek Mathematics, Volume 1, From Thales to Euclid, p. 155.
- ^ Aristotle, Prior Analytics, I-23.
- ^ Thomas Heath (1921) A History of Greek Mathematics, Volume 1, From Thales to Euclid, p. 157.
- ^ a b Thomas Heath (1921) A History of Greek Mathematics, Volume 1, From Thales to Euclid, p. 168.
- ^ Morris Kline (1990), Mathematical Thought from Ancient to Modern Times, page 32. Oxford University Press.
- Fermat's Enigma, p. 50.
External links
- Hippasus of Metapontum at scienceworld.wolfram.com
- Lives of the Eminent Philosophers. Vol. 2:8. Translated by Hicks, Robert Drew(Two volume ed.). Loeb Classical Library.