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Theodorus of Cyrene was an Greek mathematician of the 5th century BC who was admired by Plato, who mentions him in several sources. Little is known about his accomplishments; however, he is atrributed to proving that the square roots of the integer numbers between 3 and 17 except the square numbers 4, 9 and 16 , i.e. 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15 and 17 are irrational (the case for n = 2 was well-known before him).

From Plato's Theaetetus to Gauss's Pentagramma Mirificum: A Fight for 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 A 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 mathematics (Euclidean geometry)
Mathematicians
(timeline)
Anaxagoras Anthemius Archytas Aristaeus the Elder Aristarchus Apollonius Archimedes Autolycus Bion Bryson Callippus Carpus Chrysippus Cleomedes Conon Ctesibius Democritus Dicaearchus Diocles Diophantus Dinostratus Dionysodorus Domninus Eratosthenes Eudemus Euclid Eudoxus Eutocius Geminus Heliodorus Heron Hipparchus Hippasus Hippias Hippocrates Hypatia Hypsicles Isidore of Miletus Leon Marinus Menaechmus Menelaus Metrodorus Nicomachus Nicomedes Nicoteles Oenopides Pappus Perseus Philolaus Philon Philonides Porphyry Posidonius Proclus Ptolemy Pythagoras Serenus Simplicius Sosigenes Sporus Thales Theaetetus Theano Theodorus Theodosius Theon of Alexandria Theon of Smyrna Thymaridas Xenocrates Zeno of Elea Zeno of Sidon Zenodorus
Treatises
Almagest Archimedes Palimpsest Arithmetica Conics (Apollonius) Catoptrics Data (Euclid) Elements (Euclid) Measurement of a Circle On Conoids and Spheroids On the Sizes and Distances (Aristarchus) On Sizes and Distances (Hipparchus) On the Moving Sphere (Autolycus) Euclid's Optics On Spirals On the Sphere and Cylinder Ostomachion Planisphaerium Sphaerics The Quadrature 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 equation Doctrine of proportionality Golden ratio Greek numerals Incircle and excircles of a triangle Method of exhaustion Parallel postulate Platonic solid Lune of Hippocrates Quadratrix of Hippias Regular polygon Straightedge and compass construction Triangle center
Results
In Elements
Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge theorem Inscribed angle theorem Intercept theorem Pons asinorum Pythagorean theorem Thales's theorem Theorem of the gnomon
Apollonius
Apollonius's theorem
Other
Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Menelaus's theorem Pappus's area theorem 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
Ancient Greek astronomy Greek numerals Latin translations of the 12th century Neusis construction

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