Frases de Euclides

 Euclides foto
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Data de nascimento: 323 a.C.
Data de falecimento: 285 a.C.


Euclides de Alexandria foi um matemático platónico e escritor possivelmente grego, muitas vezes referido como o "Pai da Geometria". Além de sua principal obra, Os Elementos, Euclides também escreveu sobre perspectivas, secções cónicas, geometria esférica, teoria dos números e rigor.

A geometria euclidiana é caracterizada pelo espaço euclidiano, imutável, simétrico e geométrico, metáfora do saber na antiguidade clássica e que se manteve incólume no pensamento matemático medieval e renascentista, pois somente nos tempos modernos puderam ser construídos modelos de geometrias não-euclidianas.

Euclides é a versão aportuguesada da palavra grega Εὐκλείδης, que significa "Boa Glória".

Citações Euclides


„Which was to be proved.“

—  Euclid
Elements, Book I, Proposition 4. Latin translation: Quod erat demonstrandum (often abbreviated Q.E.D.).

„The laws of nature are but the mathematical thoughts of God.“

—  Euclid
The earliest published source found on google books that attributes this to Euclid is A Mathematical Journey by Stanley Gudder (1994), [ p. xv]. However, many earlier works attribute it to Johannes Kepler, the earliest located being in the piece "The Mathematics of Elementary Chemistry" by Principal J. McIntosh of Fowler Union High School in California, which appeared in School Science and Mathematics, Volume VII ([ 1907]), [ p. 383]. Neither this nor any other source located gives a source in Kepler's writings, however, and in an earlier source, the 1888 Notes and Queries, Vol V., it is attributed on [ p. 165] to Plato. It could possibly be a paraphrase of either or both of the following to comments in Kepler's 1618 book Harmonices Mundi (The Harmony of the World)': "Geometry is one and eternal shining in the mind of God" and "Since geometry is co-eternal with the divine mind before the birth of things, God himself served as his own model in creating the world".

„Give him threepence, since he must make gain out of what he learns. (Δός αὐτῷ τριώβολον, ἐπειδὴ δεῖ αὐτῷ ἐξ ὧν μανθάνει κερδαίνειν)“

—  Euclid
Said to be a remark made to his servant when a student asked what he would get out of studying geometry. 'threepence' renders τριώβολον "three-obol-piece". This amount increases the sarcasm of Euclid's reply, as it was the standard fee of a Dikastes for attending a court case (μίσθος δικαστικός), thus inversing the role of teacher and pupil to that of accused and juror. The English translation is by The History of Greek Mathematics by Thomas Little Heath (1921), [ p. 357]. The quote is recorded by Stobaeus' Florilegium iv, 114 ([ ed. Teubner 1856], p. 205; see also [ here]). Stobaeus attributes the anecdote to Serenus.

„And the whole [is] greater than the part.“

—  Euclid
Elements, Book I, Common Notion 8 (5 in certain editions) Cf. Aristotle, Metaphysics, Book Η 1045a 8–10: "… the totality is not, as it were, a mere heap, but the whole is something besides the parts … [πάντων γὰρ ὅσα πλείω μέρη ἔχει καὶ μὴ ἔστιν οἷον σωρὸς τὸ πᾶν]"

„There is no royal road to geometry. (μὴ εἶναι βασιλικὴν ἀτραπὸν ἐπί γεωμετρίαν, Non est regia [inquit Euclides] ad Geometriam via)“

—  Euclid
Reply given when the ruler Ptolemy I Soter asked Euclid if there was a shorter road to learning geometry than through Euclid's Elements. Proclus (412–485 AD) in Commentary on the First Book of Euclid's Elements as translated by Glenn R. Morrow (1970), [ p. 57]. ἀτραπός "road, trail, track" here takes the more specific sense of "short cut". The Latin translation is by Francesco Barozzi, 1560)

„A prime number is one (which is) measured by a unit alone.“

—  Euclid
Elements, Book 7, Definition 11 (12 in certain editions)