---
title: On Extracting Square Roots
title_greek: Ἀπόσπασμα
author: Diophantus of Alexandria II
eul_wid: rqm-ac
eul_aid: rqm
canonical: "https://eulogikon.org/works/diophantus-alexandria-extracting-square-roots-rqm-ac"
period: Roman
dialect: Technical Koine
domain: History
format: Prose
license: "https://creativecommons.org/publicdomain/mark/1.0/"
---

# On Extracting Square Roots

*Ἀπόσπασμα*

**Author:** Diophantus of Alexandria II

**eul_wid:** `rqm-ac` · [HTML page](https://eulogikon.org/works/diophantus-alexandria-extracting-square-roots-rqm-ac)

## Text

### 2.3.(3)

Ἐκ τῆς ἀριθμητικῆς Διοφάντο υ . Ἀπὸ δύο μεθόδων εὑρίσκεται παντὸς τετραγώνου ἀριθμοῦ πλευρὰ ἤτοι δυνάμεως. καὶ ἡ μὲν μία ἔχει οὕτως· ἀπόγραψαι τοιοῦτον ἀριθμὸν κατὰ τὴν τάξιν τῆς Ἰνδικῆς μεθόδου· εἶτα ἄρξαι ἀπὸ δεξιῶν ἐπὶ ἀριστερά, καθ’ ἕκαστον δὲ στοιχεῖον λέγε· γίνεται· οὐ γίνεται· γίνεται· οὐ γίνεται· ἕως ἂν τελειωθῶσι τὰ στοιχεῖα, καὶ εἰ μὲν τύχῃ τὸ τελευταῖον ὑπὸ τὸ γίνεται, ἄρξαι τοῦ μερισμοῦ ἐκεῖθεν· εἰ δὲ ὑπὸ τὸ οὐ γίνεται, καταλιπὼν τὸ τελευταῖον στοιχεῖον ἄρξαι τοῦ μερισμοῦ ἀπὸ τοῦ μετ’ αὐτὸ στοιχείου τοῦ πρὸς τὰ δεξιά, ἐν ᾧ δηλονότι φθάνει τὸ γίνεται.

## License and provenance

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