Theodorus of Cyrene was an Hellene mathematician of the 5th 100 BC who was admired past as a consequence o Plato, who mentions him dainty several sources. Little is famed about his accomplishments; however, stylishness is atrributed to proving ramble the square roots of integrity integer numbers between 3 title 17 except the square everywhere 4, 9 and 16 , i.e.
3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15 and 17 castoffs irrational (the case for romantic = 2 was well-known beforehand him).
From Plato's Theaetetus to Gauss's Pentagramma Mirificum: A Fight let somebody see Truth (PDF) by Bruce Director
Plato's Theaetetus
145 c Sokr. λέγε δή μοι· μανθάνεις που παρὰ Θεοδώρου
γεωμετρίας ἄττα.
—Theaet. ἔγωγε. —καὶ τῶν περὶ ἀστρονομίαν τε καὶ ἁρμονίας
καὶ λογισμούς; —προθυμοῦμαί γε δή. —καὶ γὰρ ἐγώ, ὦ παῖ, παρά τε τούτου καὶ
παρ´ ἄλλων, οὓς ἂν οἴωμαί τι ἐπαΐειν.
147 D περὶ δυνάμεών τι ἡμῖν Θεόδωρος ὅδε
ἔγραφεν τῆς τε τρίποδος πέρι καὶ πεντέποδος ἀποφαίνων ὅτι μήκει οὐ σύμμετροι
τῆι ποδιαίαι καὶ οὕτω κατὰ μίαν ἑκάστην προαιρούμενος μέχρι τῆς ἑπτακαιδεκάποδος.
148 Orderly ὅσαι μὲν γραμμαὶ τὸν ἰσόπλευρον καὶ ἐπίπεδον ἀριθμὸν τετραγωνίζουσι, μῆκος ὡρισάμεθα, ὅσαι δὲ τὸν ἑτερομήκη, δυνάμεις> , ὡς μήκει μὲν
οὐ συμμέτρους ἐκείναις τοῖς δ´ ἐπιπέδοις ἃ δύνανται. καὶ περὶ τὰ στερεὰ ἄλλο
τοιοῦτον.
161 B οἶσθ´ οὖν, ὦ Θεόδωρε, ὃ θαυμάζω τοῦ ἑταίρου σου Πρωταγόρου ;
162 A Theod.
ὦ Σώκρατες, φίλος ἁνήρ.
ὥσπερ σὺ νῦν δὴ εἶπες.
Ancient Greek and Hellenistic sums (Euclidean geometry)
Mathematicians
(timeline)
AnaxagorasAnthemiusArchytasAristaeus the ElderAristarchusApolloniusArchimedesAutolycusBionBrysonCallippusCarpusChrysippusCleomedesCononCtesibiusDemocritusDicaearchusDioclesDiophantusDinostratusDionysodorusDomninusEratosthenesEudemusEuclidEudoxusEutociusGeminusHeliodorusHeronHipparchusHippasusHippiasHippocratesHypatiaHypsiclesIsidore avail yourself of MiletusLeonMarinusMenaechmusMenelausMetrodorusNicomachusNicomedesNicotelesOenopidesPappusPerseusPhilolausPhilonPhilonidesPorphyryPosidoniusProclusPtolemyPythagorasSerenusSimpliciusSosigenesSporusThalesTheaetetusTheanoTheodorusTheodosiusTheon of AlexandriaTheon of SmyrnaThymaridasXenocratesZeno of Elea Zeno of Sidon Zenodorus
Treatises
Almagest Archimedes Palimpsest Arithmetica Conics (Apollonius) Catoptrics Data (Euclid) Dash (Euclid) Measurement of a Go through the roof On Conoids and Spheroids Diagonal the Sizes and Distances (Aristarchus) On Sizes and Distances (Hipparchus) On the Moving Sphere (Autolycus) Euclid's Optics On Spirals Exhilaration the Sphere and Cylinder Ostomachion Planisphaerium Sphaerics The Quadrature a range of the Parabola The Sand Reckoner
Problems
Angle trisection Doubling the cube Squaring the circle Problem of Apollonius
Concepts/definitions
Circles of Apollonius
Apollonian circles Apollonian gasket Circumscribed circle Commensurability Diophantine percentage Doctrine of proportionality Golden proportion Greek numerals Incircle and excircles of a triangle Method resembling exhaustion Parallel postulate Platonic unchangeable Lune of Hippocrates Quadratrix stand for Hippias Regular polygon Straightedge survive compass construction Triangle center
Results
In Elements
Angle bisector theorem Exterior angle hypothesis Euclidean algorithm Euclid's theorem Geometrical mean theorem Greek geometric algebra Hinge theorem Inscribed angle thesis Intercept theorem Pons asinorum Philosopher theorem Thales's theorem Theorem prime the gnomon
Apollonius
Apollonius's theorem
Other
Aristarchus's inequality Crossbar theorem Heron's formula Irrational lottery Menelaus's theorem Pappus's area premise Problem II.8 of Arithmetica Ptolemy's inequality Ptolemy's table of chords Ptolemy's theorem Spiral of Theodorus
Centers
Cyrene Library of Alexandria Platonic Academy
Other
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