26 Ιουλίου · Σαν σήμερα
Dramatized
Τῇδε τῇ ἡμέρᾳ, ὅτε ὁ ἥλιος μέγιστος, καθίζω ἐν τῇ στοᾷ πρὸ τῆς βιβλιοθήκης. Οἱ μαθηταί μου στενάζουσιν ὑπὸ τοῦ καύματος, κἀγὼ λέγω αὐτοῖς: «Ἐὰν μὴ ὑπομείνητε τὴν ἀκρίβειαν, πῶς ὑπομενεῖτε τὴν ἀπόδειξιν;» Σήμερον ἐδίδαξα τὴν πρότασιν τῆς ἰσότητος τῶν ἐναλλάξ γωνιῶν. Ἐν τῇ θέρμῃ, ἡ γωνία φαίνεται πλατυτέρα—ἀλλ᾽ οὐκ ἔστι. Τὸ ὄμμα ἀπατᾷ, ὁ νοῦς δὲ οὔ. Τοῦτο τὸ μάθημα τῆς μεσημβρίας: πίστευε τῷ κανόνι, μὴ τῇ σκιᾷ.
Explain more
Ἡ πρότασις Α΄ 29: αἱ ἐναλλὰξ γωνίαι ἴσαι ἀλλήλαις εἰσίν, ὅταν εὐθεῖα εἰς δύο εὐθείας ἐμπίπτῃ καὶ παράλληλος ᾖ ἡ μία τῇ ἑτέρᾳ. Οὐκ ἔστι δόξα, ἀλλὰ συμπέρασμα ἐξ ὁρισμῶν.
Why it matters
Ὅταν ὁ κόσμος λέγει σοι «ὁρᾷς οὕτως, ἄρα οὕτως ἔχει», ἀνάγκη ἔχεις τὸν κανόνα τῆς διανοίας. Ἡ γεωμετρία διδάσκει ἀντέχειν τῇ ἀληθείᾳ παρὰ τὴν αἴσθησιν.
Try today
Λάβε κάλαμον καὶ σχοῖνον. Σύστησον δύο παραλλήλους ἐν τῷ ἐδάφει τῷ θερινῷ. Μέτρησον τὰς γωνίας ἐναλλάξ. Οὐδὲ ἡ θερμότης αὐτὰς μεταβάλλει.
What is true / dramatized: Dramatized. Educational entertainment — not a primary historical source.
Στοιχεῖα Α΄, πρότασις 29: περὶ παραλλήλων καὶ ἐναλλὰξ γωνιῶν
Difficulty: medium · ~2 min
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