KJV - WH Gospel of John - Demo Alignment
Christopher Blackwell /
- Created on 2017-10-26 19:34:09
- Modified on 2018-09-05 21:26:09
- Aligned by Christopher Blackwell
KJV - WH Gospel of John - Demo Alignment. C. Blackwell, Brazil.
English
Ἑλληνική Transliterate
urn:cts:greekLit:tlg0031.tlg001.fukjv:1.1-1.10
urn:cts:greekLit:tlg0031.tlg001.fuwh:1.1-1.10
1 In the beginning was the Word , and the Word was with God , and the Word was God .
2 The same was in the beginning with God .
3 All things were made by him ; and without him was not any thing made that was made .
4 In him was life ; and the life was the light of men .
5 And the light shineth in darkness ; and the darkness comprehended it not .
6 There was a man sent from God , whose name was John .
7 The same came for a witness , to bear witness of the Light , that all men through him might believe .
8 He was not that Light , but was sent to bear witness of that Light .
9 That was the true Light , which lighteth every man that cometh into the world .
10 He was in the world , and the world was made by him , and the world knew him not .
2 The same was in the beginning with God .
3 All things were made by him ; and without him was not any thing made that was made .
4 In him was life ; and the life was the light of men .
5 And the light shineth in darkness ; and the darkness comprehended it not .
6 There was a man sent from God , whose name was John .
7 The same came for a witness , to bear witness of the Light , that all men through him might believe .
8 He was not that Light , but was sent to bear witness of that Light .
9 That was the true Light , which lighteth every man that cometh into the world .
10 He was in the world , and the world was made by him , and the world knew him not .
1
Ἐν
ἀρχῇ
ἦν
ὁ
Λόγος
,
καὶ
ὁ
Λόγος
ἦν
πρὸς
τὸν
Θεόν
,
καὶ
Θεὸς
ἦν
ὁ
Λόγος
.
2 Οὗτος ἦν ἐν ἀρχῇ πρὸς τὸν Θεόν .
3 πάντα δι’ αὐτοῦ ἐγένετο , καὶ χωρὶς αὐτοῦ ἐγένετο οὐδὲ ἕν ὃ γέγονεν .
4 ἐν αὐτῷ ζωὴ ἦν , καὶ ἡ ζωὴ ἦν τὸ φῶς τῶν ἀνθρώπων .
5 καὶ τὸ φῶς ἐν τῇ σκοτίᾳ φαίνει , καὶ ἡ σκοτία αὐτὸ οὐ κατέλαβεν .
6 Ἐγένετο ἄνθρωπος , ἀπεσταλμένος παρὰ Θεοῦ , ὄνομα αὐτῷ Ἰωάννης* ·
7 οὗτος ἦλθεν εἰς μαρτυρίαν , ἵνα μαρτυρήσῃ περὶ τοῦ φωτός , ἵνα πάντες πιστεύσωσιν δι’ αὐτοῦ .
8 οὐκ ἦν ἐκεῖνος τὸ φῶς , ἀλλ’ ἵνα μαρτυρήσῃ περὶ τοῦ φωτός .
9 Ἦν τὸ φῶς τὸ ἀληθινὸν , ὃ φωτίζει πάντα ἄνθρωπον , ἐρχόμενον εἰς τὸν κόσμον .
10 ἐν τῷ κόσμῳ ἦν , καὶ ὁ κόσμος δι’ αὐτοῦ ἐγένετο , καὶ ὁ κόσμος αὐτὸν οὐκ ἔγνω .
2 Οὗτος ἦν ἐν ἀρχῇ πρὸς τὸν Θεόν .
3 πάντα δι’ αὐτοῦ ἐγένετο , καὶ χωρὶς αὐτοῦ ἐγένετο οὐδὲ ἕν ὃ γέγονεν .
4 ἐν αὐτῷ ζωὴ ἦν , καὶ ἡ ζωὴ ἦν τὸ φῶς τῶν ἀνθρώπων .
5 καὶ τὸ φῶς ἐν τῇ σκοτίᾳ φαίνει , καὶ ἡ σκοτία αὐτὸ οὐ κατέλαβεν .
6 Ἐγένετο ἄνθρωπος , ἀπεσταλμένος παρὰ Θεοῦ , ὄνομα αὐτῷ Ἰωάννης* ·
7 οὗτος ἦλθεν εἰς μαρτυρίαν , ἵνα μαρτυρήσῃ περὶ τοῦ φωτός , ἵνα πάντες πιστεύσωσιν δι’ αὐτοῦ .
8 οὐκ ἦν ἐκεῖνος τὸ φῶς , ἀλλ’ ἵνα μαρτυρήσῃ περὶ τοῦ φωτός .
9 Ἦν τὸ φῶς τὸ ἀληθινὸν , ὃ φωτίζει πάντα ἄνθρωπον , ἐρχόμενον εἰς τὸν κόσμον .
10 ἐν τῷ κόσμῳ ἦν , καὶ ὁ κόσμος δι’ αὐτοῦ ἐγένετο , καὶ ὁ κόσμος αὐτὸν οὐκ ἔγνω .
Demo Euclid
Christopher Blackwell /
- Created on 2018-03-16 14:12:51
- Translated by Heath
- Aligned by Christopher Blackwell
Ἑλληνική Transliterate
English
DEFINITIONS .
σημεῖόν ἐστιν , οὗ μέρος οὐθέν .
γραμμὴ δὲ μῆκος ἀπλατές .
γραμμῆς δὲ πέρατα σημεῖα .
εὐθεῖα γραμμή ἐστιν , ἥτις ἐξ ἴσου τοῖς ἐφ᾽ ἑαυτῆς σημείοις κεῖται .
ἐπιφάνεια δέ ἐστιν , ὃ μῆκος καὶ πλάτος μόνον ἔχει .
ἐπιφανείας δὲ πέρατα γραμμαί .
ἐπίπεδος ἐπιφάνειά ἐστιν , ἥτις ἐξ ἴσου ταῖς ἐφ᾽ ἑαυτῆς εὐθείαις κεῖται .
ἐπίπεδος δὲ γωνία ἐστὶν ἡ ἐν ἐπιπέδῳ δύο γραμμῶν ἁπτομένων ἀλλήλων καὶ μὴ ἐπ᾽ εὐθείας κειμένων πρὸς ἀλλήλας τῶν γραμμῶν κλίσις .
ὅταν δὲ αἱ περιέχουσαι τὴν γωνίαν γραμμαὶ εὐθεῖαι ὦσιν , εὐθύγραμμος καλεῖται ἡ γωνία .
ὅταν δὲ εὐθεῖα ἐπ᾽ εὐθεῖαν σταθεῖσα τὰς ἐφεξῆς γωνίας ἴσας ἀλλήλαις ποιῇ , ὀρθὴ ἑκατέρα τῶν ἴσων γωνιῶν ἐστι , καὶ ἡ ἐφεστηκυῖα εὐθεῖα κάθετος καλεῖται , ἐφ᾽ ἣν ἐφέστηκεν .
ἀμβλεῖα γωνία ἐστὶν ἡ μείζων ὀρθῆς .
ὀξεῖα δὲ ἡ ἐλάσσων ὀρθῆς .
ὅρος ἐστίν , ὅ τινός ἐστι πέρας .
σχῆμά ἐστι τὸ ὑπό τινος ἤ τινων ὅρων περιεχόμενον .
κύκλος ἐστὶ σχῆμα ἐπίπεδον ὑπὸ μιᾶς γραμμῆς περιεχόμενον ἣ καλεῖται περιφέρεια , πρὸς ἣν ἀφ᾽ ἑνὸς σημείου τῶν ἐντὸς τοῦ σχήματος κειμένων πᾶσαι αἱ προσπίπτουσαι εὐθεῖαι πρὸς τὴν τοῦ κύκλου περιφέρειαν ἴσαι ἀλλήλαις εἰσίν .
κέντρον δὲ τοῦ κύκλου τὸ σημεῖον καλεῖται .
διάμετρος δὲ τοῦ κύκλου ἐστὶν εὐθεῖά τις διὰ τοῦ κέντρου ἠγμένη καὶ περατουμένη ἐφ᾽ ἑκάτερα τὰ μέρη ὑπὸ τῆς τοῦ κύκλου περιφερείας , ἥτις καὶ δίχα τέμνει τὸν κύκλον .
ἡμικύκλιον δέ ἐστι τὸ περιεχόμενον σχῆμα ὑπό τε τῆς διαμέτρου καὶ τῆς ἀπολαμβανομένης ὑπ᾽ αὐτῆς περιφερείας . κέντρον δὲ τοῦ ἡμικυκλίου τὸ αὐτό , ὃ καὶ τοῦ κύκλου ἐστίν .
σχήματα εὐθύγραμμά ἐστι τὰ ὑπὸ εὐθειῶν περιεχόμενα , τρίπλευρα μὲν τὰ ὑπὸ τριῶν , τετράπλευρα δὲ τὰ ὑπὸ τεσσάρων , πολύπλευρα δὲ τὰ ὑπὸ πλειόνων ἢ τεσσάρων εὐθειῶν περιεχόμενα .
τῶν δὲ τριπλεύρων σχημάτων ἰσόπλευρον μὲν τρίγωνόν ἐστι τὸ τὰς τρεῖς ἴσας ἔχον πλευράς , ἰσοσκελὲς δὲ τὸ τὰς δύο μόνας ἴσας ἔχον πλευράς , σκαληνὸν δὲ τὸ τὰς τρεῖς ἀνίσους ἔχον πλευράς .
ἔτι δὲ τῶν τριπλεύρων σχημάτων ὀρθογώνιον μὲν τρίγωνόν ἐστι τὸ ἔχον ὀρθὴν γωνίαν , ἀμβλυγώνιον δὲ τὸ ἔχον ἀμβλεῖαν γωνίαν , ὀξυγώνιον δὲ τὸ τὰς τρεῖς ὀξείας ἔχον γωνίας .
τῶν δὲ τετραπλεύρων σχημάτων τετράγωνον μέν ἐστιν , ὃ ἰσόπλευρόν τέ ἐστι καὶ ὀρθογώνιον , ἑτερόμηκες δέ , ὃ ὀρθογώνιον μέν , οὐκ ἰσόπλευρον δέ , ῥόμβος δέ , ὃ ἰσόπλευρον μέν , οὐκ ὀρθογώνιον δέ , ῥομβοειδὲς δὲ τὸ τὰς ἀπεναντίον πλευράς τε καὶ γωνίας ἴσας ἀλλήλαις ἔχον , ὃ οὔτε ἰσόπλευρόν ἐστιν οὔτε ὀρθογώνιον : τὰ δὲ παρὰ ταῦτα τετράπλευρα τραπέζια καλείσθω .
παράλληλοί εἰσιν εὐθεῖαι , αἵτινες ἐν τῷ αὐτῷ ἐπιπέδῳ οὖσαι καὶ ἐκβαλλόμεναι εἰς ἄπειρον ἐφ᾽ ἑκάτερα τὰ μέρη ἐπὶ μηδέτερα συμπίπτουσιν ἀλλήλαις .
POSTULATES .
Ἠιτήσθω ἀπὸ παντὸς σημείου ἐπὶ πᾶν σημεῖον εὐθεῖαν γραμμὴν ἀγαγεῖν .
καὶ πεπερασμένην εὐθεῖαν κατὰ τὸ συνεχὲς ἐπ᾽ εὐθείας ἐκβαλεῖν .
καὶ παντὶ κέντρῳ καὶ διαστήματι κύκλον γράφεσθαι .
καὶ πάσας τὰς ὀρθὰς γωνίας ἴσας ἀλλήλαις εἶναι .
καὶ ἐὰν εἰς δύο εὐθείας εὐθεῖα ἐμπίπτουσα τὰς ἐντὸς καὶ ἐπὶ τὰ αὐτὰ μέρη γωνίας δύο ὀρθῶν ἐλάσσονας ποιῇ , ἐκβαλλομένας τὰς δύο εὐθείας ἐπ᾽ ἄπειρον συμπίπτειν , ἐφ᾽ ἃ μέρη εἰσὶν αἱ τῶν δύο ὀρθῶν ἐλάσσονες .
COMMON NOTIONS .
τὰ τῷ αὐτῷ ἴσα καὶ ἀλλήλοις ἐστὶν ἴσα .
καὶ ἐὰν ἴσοις ἴσα προστεθῇ , τὰ ὅλα ἐστὶν ἴσα .
καὶ ἐὰν ἀπὸ ἴσων ἴσα ἀφαιρεθῇ , τὰ καταλειπόμενά ἐστιν ἴσα .
καὶ ἐὰν ἀνίσοις ἴσα προστεθῇ , τὰ ὅλα ἐστὶν ἄνισα .
καὶ τὰ τοῦ αὐτοῦ διπλάσια ἴσα ἀλλήλοις ἐστίν .
καὶ τὰ τοῦ αὐτοῦ ἡμίση ἴσα ἀλλήλοις ἐστίν .
καὶ τὰ ἐφαρμόζοντα ἐπ᾽ ἄλληλα ἴσα ἀλλήλοις ἐστίν .
καὶ τὸ ὅλον τοῦ μέρους μεῖζον ἐστιν .
καὶ δύο εὐθεῖαι χωρίον οὐ περιέχουσιν .
PROPOSITION 1
ἐπὶ τῆς δοθείσης εὐθείας πεπερασμένης τρίγωνον ἰσόπλευρον συστήσασθαι .
ἔστω ἡ δοθεῖσα εὐθεῖα πεπερασμένη ἡ ΑΒ . δεῖ δὴ ἐπὶ τῆς ΑΒ εὐθείας τρίγωνον ἰσόπλευρον συστήσασθαι .
κέντρῳ μὲν τῷ Α διαστήματι δὲ τῷ ΑΒ κύκλος γεγράφθω ὁ ΒΓΔ , καὶ πάλιν κέντρῳ μὲν τῷ Β διαστήματι δὲ τῷ ΒΑ κύκλος γεγράφθω ὁ ΑΓΕ , καὶ ἀπὸ τοῦ Γ σημείου , καθ᾽ ὃ τέμνουσιν ἀλλήλους οἱ κύκλοι , ἐπὶ τὰ Α , Β σημεῖα ἐπεζεύχθωσαν εὐθεῖαι αἱ ΓΑ , ΓΒ .
καὶ ἐπεὶ τὸ Α σημεῖον κέντρον ἐστὶ τοῦ ΓΔΒ κύκλου , ἴση ἐστὶν ἡ ΑΓ τῇ ΑΒ : πάλιν , ἐπεὶ τὸ Β σημεῖον κέντρον ἐστὶ τοῦ ΓΑΕ κύκλου , ἴση ἐστὶν ἡ ΒΓ τῇ ΒΑ . ἐδείχθη δὲ καὶ ἡ ΓΑ τῇ ΑΒ ἴση : ἑκατέρα ἄρα τῶν ΓΑ , ΓΒ τῇ ΑΒ ἐστὶν ἴση .
τὰ δὲ τῷ αὐτῷ ἴσα καὶ ἀλλήλοις ἐστὶν ἴσα : καὶ ἡ ΓΑ ἄρα τῇ ΓΒ ἐστὶν ἴση : αἱ τρεῖς ἄρα αἱ ΓΑ , ΑΒ , ΒΓ ἴσαι ἀλλήλαις εἰσίν .
ἰσόπλευρον ἄρα ἐστὶ τὸ ΑΒΓ τρίγωνον , καὶ συνέσταται ἐπὶ τῆς δοθείσης εὐθείας πεπερασμένης τῆς ΑΒ .
Ἐπὶ τῆς δοθείσης ἄρα εὐθείας πεπερασμένης τρίγωνον ἰσόπλευρον συνέσταται : ὅπερ ἔδει ποιῆσαι .
σημεῖόν ἐστιν , οὗ μέρος οὐθέν .
γραμμὴ δὲ μῆκος ἀπλατές .
γραμμῆς δὲ πέρατα σημεῖα .
εὐθεῖα γραμμή ἐστιν , ἥτις ἐξ ἴσου τοῖς ἐφ᾽ ἑαυτῆς σημείοις κεῖται .
ἐπιφάνεια δέ ἐστιν , ὃ μῆκος καὶ πλάτος μόνον ἔχει .
ἐπιφανείας δὲ πέρατα γραμμαί .
ἐπίπεδος ἐπιφάνειά ἐστιν , ἥτις ἐξ ἴσου ταῖς ἐφ᾽ ἑαυτῆς εὐθείαις κεῖται .
ἐπίπεδος δὲ γωνία ἐστὶν ἡ ἐν ἐπιπέδῳ δύο γραμμῶν ἁπτομένων ἀλλήλων καὶ μὴ ἐπ᾽ εὐθείας κειμένων πρὸς ἀλλήλας τῶν γραμμῶν κλίσις .
ὅταν δὲ αἱ περιέχουσαι τὴν γωνίαν γραμμαὶ εὐθεῖαι ὦσιν , εὐθύγραμμος καλεῖται ἡ γωνία .
ὅταν δὲ εὐθεῖα ἐπ᾽ εὐθεῖαν σταθεῖσα τὰς ἐφεξῆς γωνίας ἴσας ἀλλήλαις ποιῇ , ὀρθὴ ἑκατέρα τῶν ἴσων γωνιῶν ἐστι , καὶ ἡ ἐφεστηκυῖα εὐθεῖα κάθετος καλεῖται , ἐφ᾽ ἣν ἐφέστηκεν .
ἀμβλεῖα γωνία ἐστὶν ἡ μείζων ὀρθῆς .
ὀξεῖα δὲ ἡ ἐλάσσων ὀρθῆς .
ὅρος ἐστίν , ὅ τινός ἐστι πέρας .
σχῆμά ἐστι τὸ ὑπό τινος ἤ τινων ὅρων περιεχόμενον .
κύκλος ἐστὶ σχῆμα ἐπίπεδον ὑπὸ μιᾶς γραμμῆς περιεχόμενον ἣ καλεῖται περιφέρεια , πρὸς ἣν ἀφ᾽ ἑνὸς σημείου τῶν ἐντὸς τοῦ σχήματος κειμένων πᾶσαι αἱ προσπίπτουσαι εὐθεῖαι πρὸς τὴν τοῦ κύκλου περιφέρειαν ἴσαι ἀλλήλαις εἰσίν .
κέντρον δὲ τοῦ κύκλου τὸ σημεῖον καλεῖται .
διάμετρος δὲ τοῦ κύκλου ἐστὶν εὐθεῖά τις διὰ τοῦ κέντρου ἠγμένη καὶ περατουμένη ἐφ᾽ ἑκάτερα τὰ μέρη ὑπὸ τῆς τοῦ κύκλου περιφερείας , ἥτις καὶ δίχα τέμνει τὸν κύκλον .
ἡμικύκλιον δέ ἐστι τὸ περιεχόμενον σχῆμα ὑπό τε τῆς διαμέτρου καὶ τῆς ἀπολαμβανομένης ὑπ᾽ αὐτῆς περιφερείας . κέντρον δὲ τοῦ ἡμικυκλίου τὸ αὐτό , ὃ καὶ τοῦ κύκλου ἐστίν .
σχήματα εὐθύγραμμά ἐστι τὰ ὑπὸ εὐθειῶν περιεχόμενα , τρίπλευρα μὲν τὰ ὑπὸ τριῶν , τετράπλευρα δὲ τὰ ὑπὸ τεσσάρων , πολύπλευρα δὲ τὰ ὑπὸ πλειόνων ἢ τεσσάρων εὐθειῶν περιεχόμενα .
τῶν δὲ τριπλεύρων σχημάτων ἰσόπλευρον μὲν τρίγωνόν ἐστι τὸ τὰς τρεῖς ἴσας ἔχον πλευράς , ἰσοσκελὲς δὲ τὸ τὰς δύο μόνας ἴσας ἔχον πλευράς , σκαληνὸν δὲ τὸ τὰς τρεῖς ἀνίσους ἔχον πλευράς .
ἔτι δὲ τῶν τριπλεύρων σχημάτων ὀρθογώνιον μὲν τρίγωνόν ἐστι τὸ ἔχον ὀρθὴν γωνίαν , ἀμβλυγώνιον δὲ τὸ ἔχον ἀμβλεῖαν γωνίαν , ὀξυγώνιον δὲ τὸ τὰς τρεῖς ὀξείας ἔχον γωνίας .
τῶν δὲ τετραπλεύρων σχημάτων τετράγωνον μέν ἐστιν , ὃ ἰσόπλευρόν τέ ἐστι καὶ ὀρθογώνιον , ἑτερόμηκες δέ , ὃ ὀρθογώνιον μέν , οὐκ ἰσόπλευρον δέ , ῥόμβος δέ , ὃ ἰσόπλευρον μέν , οὐκ ὀρθογώνιον δέ , ῥομβοειδὲς δὲ τὸ τὰς ἀπεναντίον πλευράς τε καὶ γωνίας ἴσας ἀλλήλαις ἔχον , ὃ οὔτε ἰσόπλευρόν ἐστιν οὔτε ὀρθογώνιον : τὰ δὲ παρὰ ταῦτα τετράπλευρα τραπέζια καλείσθω .
παράλληλοί εἰσιν εὐθεῖαι , αἵτινες ἐν τῷ αὐτῷ ἐπιπέδῳ οὖσαι καὶ ἐκβαλλόμεναι εἰς ἄπειρον ἐφ᾽ ἑκάτερα τὰ μέρη ἐπὶ μηδέτερα συμπίπτουσιν ἀλλήλαις .
POSTULATES .
Ἠιτήσθω ἀπὸ παντὸς σημείου ἐπὶ πᾶν σημεῖον εὐθεῖαν γραμμὴν ἀγαγεῖν .
καὶ πεπερασμένην εὐθεῖαν κατὰ τὸ συνεχὲς ἐπ᾽ εὐθείας ἐκβαλεῖν .
καὶ παντὶ κέντρῳ καὶ διαστήματι κύκλον γράφεσθαι .
καὶ πάσας τὰς ὀρθὰς γωνίας ἴσας ἀλλήλαις εἶναι .
καὶ ἐὰν εἰς δύο εὐθείας εὐθεῖα ἐμπίπτουσα τὰς ἐντὸς καὶ ἐπὶ τὰ αὐτὰ μέρη γωνίας δύο ὀρθῶν ἐλάσσονας ποιῇ , ἐκβαλλομένας τὰς δύο εὐθείας ἐπ᾽ ἄπειρον συμπίπτειν , ἐφ᾽ ἃ μέρη εἰσὶν αἱ τῶν δύο ὀρθῶν ἐλάσσονες .
COMMON NOTIONS .
τὰ τῷ αὐτῷ ἴσα καὶ ἀλλήλοις ἐστὶν ἴσα .
καὶ ἐὰν ἴσοις ἴσα προστεθῇ , τὰ ὅλα ἐστὶν ἴσα .
καὶ ἐὰν ἀπὸ ἴσων ἴσα ἀφαιρεθῇ , τὰ καταλειπόμενά ἐστιν ἴσα .
καὶ ἐὰν ἀνίσοις ἴσα προστεθῇ , τὰ ὅλα ἐστὶν ἄνισα .
καὶ τὰ τοῦ αὐτοῦ διπλάσια ἴσα ἀλλήλοις ἐστίν .
καὶ τὰ τοῦ αὐτοῦ ἡμίση ἴσα ἀλλήλοις ἐστίν .
καὶ τὰ ἐφαρμόζοντα ἐπ᾽ ἄλληλα ἴσα ἀλλήλοις ἐστίν .
καὶ τὸ ὅλον τοῦ μέρους μεῖζον ἐστιν .
καὶ δύο εὐθεῖαι χωρίον οὐ περιέχουσιν .
PROPOSITION 1
ἐπὶ τῆς δοθείσης εὐθείας πεπερασμένης τρίγωνον ἰσόπλευρον συστήσασθαι .
ἔστω ἡ δοθεῖσα εὐθεῖα πεπερασμένη ἡ ΑΒ . δεῖ δὴ ἐπὶ τῆς ΑΒ εὐθείας τρίγωνον ἰσόπλευρον συστήσασθαι .
κέντρῳ μὲν τῷ Α διαστήματι δὲ τῷ ΑΒ κύκλος γεγράφθω ὁ ΒΓΔ , καὶ πάλιν κέντρῳ μὲν τῷ Β διαστήματι δὲ τῷ ΒΑ κύκλος γεγράφθω ὁ ΑΓΕ , καὶ ἀπὸ τοῦ Γ σημείου , καθ᾽ ὃ τέμνουσιν ἀλλήλους οἱ κύκλοι , ἐπὶ τὰ Α , Β σημεῖα ἐπεζεύχθωσαν εὐθεῖαι αἱ ΓΑ , ΓΒ .
καὶ ἐπεὶ τὸ Α σημεῖον κέντρον ἐστὶ τοῦ ΓΔΒ κύκλου , ἴση ἐστὶν ἡ ΑΓ τῇ ΑΒ : πάλιν , ἐπεὶ τὸ Β σημεῖον κέντρον ἐστὶ τοῦ ΓΑΕ κύκλου , ἴση ἐστὶν ἡ ΒΓ τῇ ΒΑ . ἐδείχθη δὲ καὶ ἡ ΓΑ τῇ ΑΒ ἴση : ἑκατέρα ἄρα τῶν ΓΑ , ΓΒ τῇ ΑΒ ἐστὶν ἴση .
τὰ δὲ τῷ αὐτῷ ἴσα καὶ ἀλλήλοις ἐστὶν ἴσα : καὶ ἡ ΓΑ ἄρα τῇ ΓΒ ἐστὶν ἴση : αἱ τρεῖς ἄρα αἱ ΓΑ , ΑΒ , ΒΓ ἴσαι ἀλλήλαις εἰσίν .
ἰσόπλευρον ἄρα ἐστὶ τὸ ΑΒΓ τρίγωνον , καὶ συνέσταται ἐπὶ τῆς δοθείσης εὐθείας πεπερασμένης τῆς ΑΒ .
Ἐπὶ τῆς δοθείσης ἄρα εὐθείας πεπερασμένης τρίγωνον ἰσόπλευρον συνέσταται : ὅπερ ἔδει ποιῆσαι .
DEFINITIONS
.
1 A point is that which has no part .
2 A line is breadthless length .
3 The extremities of a line are points .
4 A straight line is a line which lies evenly with the points on itself .
5 A surface is that which has length and breadth only .
6 The extremities of a surface are lines .
7 A plane surface is a surface which lies evenly with the straight lines on itself .
8 A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line .
9 And when the lines containing the angle are straight , the angle is called rectilineal .
10 When a straight line set up on a straight line makes the adjacent angles equal to one another , each of the equal angles is right , and the straight line standing on the other is called a perpendicular to that on which it stands .
11 An obtuse angle is an angle greater than a right angle .
12 An acute angle is an angle less than a right angle .
13 A boundary is that which is an extremity of anything .
14 A figure is that which is contained by any boundary or boundaries .
15 A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another ;
16 And the point is called the centre of the circle .
17 A diameter of the circle is any straight line drawn through the centre and terminated in both directions by the circumference of the circle , and such a straight line also bisects the circle .
18 A semicircle is the figure contained by the diameter and the circumference cut off by it . And the centre of the semicircle is the same as that of the circle .
19 Rectilineal figures are those which are contained by straight lines , trilateral figures being those contained by three , quadrilateral those contained by four , and multilateral those contained by more than four straight lines .
20 Of trilateral figures , an equilateral triangle is that which has its three sides equal , an isosceles triangle that which has two of its sides alone equal , and a scalene triangle that which has its three sides unequal .
21 Further , of trilateral figures , a right-angled triangle is that which has a right angle , an obtuse-angled triangle that which has an obtuse angle , and an acuteangled triangle that which has its three angles acute .
22 Of quadrilateral figures , a square is that which is both equilateral and right-angled ; an oblong that which is right-angled but not equilateral ; a rhombus that which is equilateral but not right-angled ; and a rhomboid that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled . And let quadrilaterals other than these be called trapezia .
23 Parallel straight lines are straight lines which , being in the same plane and being produced indefinitely in both directions , do not meet one another in either direction .
POSTULATES .
1 Let the following be postulated : To draw a straight line from any point to any point .
2 To produce a finite straight line continuously in a straight line .
3 To describe a circle with any centre and distance .
4 That all right angles are equal to one another .
5 That , if a straight line falling on two straight lines make the interior angles on the same side less than two right angles , the two straight lines , if produced indefinitely , meet on that side on which are the angles less than the two right angles .
COMMON NOTIONS .
1 Things which are equal to the same thing are also equal to one another .
2 If equals be added to equals , the wholes are equal .
3 If equals be subtracted from equals , the remainders are equal .
7 Things which coincide with one another are equal to one another .
8 The whole is greater than the part .
PROPOSITION 1
On a given finite straight line to construct an equilateral triangle .
Let AB be the given finite straight line . Thus it is required to construct an equilateral triangle on the straight line AB .
With centre A and distance AB let the circle BCD be described ; [ Post . 3 ] again , with centre B and distance BA let the circle ACE be described ; [ Post . 3 ] and from the point C , in which the circles cut one another , to the points A , B let the straight lines CA , CB be joined . [ Post . 1 ]
Now , since the point A is the centre of the circle CDB , AC is equal to AB . [ Def . 15 ] Again , since the point B is the centre of the circle CAE , BC is equal to BA . [ Def . 15 ] But CA was also proved equal to AB ; therefore each of the straight lines CA , CB is equal to AB .
And things which are equal to the same thing are also equal to one another ; [ C . N . 1 ] therefore CA is also equal to CB . Therefore the three straight lines CA , AB , BC are equal to one another .
Therefore the triangle ABC is equilateral ; and it has been constructed on the given finite straight line AB .
Being what it was required to do .
1 A point is that which has no part .
2 A line is breadthless length .
3 The extremities of a line are points .
4 A straight line is a line which lies evenly with the points on itself .
5 A surface is that which has length and breadth only .
6 The extremities of a surface are lines .
7 A plane surface is a surface which lies evenly with the straight lines on itself .
8 A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line .
9 And when the lines containing the angle are straight , the angle is called rectilineal .
10 When a straight line set up on a straight line makes the adjacent angles equal to one another , each of the equal angles is right , and the straight line standing on the other is called a perpendicular to that on which it stands .
11 An obtuse angle is an angle greater than a right angle .
12 An acute angle is an angle less than a right angle .
13 A boundary is that which is an extremity of anything .
14 A figure is that which is contained by any boundary or boundaries .
15 A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another ;
16 And the point is called the centre of the circle .
17 A diameter of the circle is any straight line drawn through the centre and terminated in both directions by the circumference of the circle , and such a straight line also bisects the circle .
18 A semicircle is the figure contained by the diameter and the circumference cut off by it . And the centre of the semicircle is the same as that of the circle .
19 Rectilineal figures are those which are contained by straight lines , trilateral figures being those contained by three , quadrilateral those contained by four , and multilateral those contained by more than four straight lines .
20 Of trilateral figures , an equilateral triangle is that which has its three sides equal , an isosceles triangle that which has two of its sides alone equal , and a scalene triangle that which has its three sides unequal .
21 Further , of trilateral figures , a right-angled triangle is that which has a right angle , an obtuse-angled triangle that which has an obtuse angle , and an acuteangled triangle that which has its three angles acute .
22 Of quadrilateral figures , a square is that which is both equilateral and right-angled ; an oblong that which is right-angled but not equilateral ; a rhombus that which is equilateral but not right-angled ; and a rhomboid that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled . And let quadrilaterals other than these be called trapezia .
23 Parallel straight lines are straight lines which , being in the same plane and being produced indefinitely in both directions , do not meet one another in either direction .
POSTULATES .
1 Let the following be postulated : To draw a straight line from any point to any point .
2 To produce a finite straight line continuously in a straight line .
3 To describe a circle with any centre and distance .
4 That all right angles are equal to one another .
5 That , if a straight line falling on two straight lines make the interior angles on the same side less than two right angles , the two straight lines , if produced indefinitely , meet on that side on which are the angles less than the two right angles .
COMMON NOTIONS .
1 Things which are equal to the same thing are also equal to one another .
2 If equals be added to equals , the wholes are equal .
3 If equals be subtracted from equals , the remainders are equal .
7 Things which coincide with one another are equal to one another .
8 The whole is greater than the part .
PROPOSITION 1
On a given finite straight line to construct an equilateral triangle .
Let AB be the given finite straight line . Thus it is required to construct an equilateral triangle on the straight line AB .
With centre A and distance AB let the circle BCD be described ; [ Post . 3 ] again , with centre B and distance BA let the circle ACE be described ; [ Post . 3 ] and from the point C , in which the circles cut one another , to the points A , B let the straight lines CA , CB be joined . [ Post . 1 ]
Now , since the point A is the centre of the circle CDB , AC is equal to AB . [ Def . 15 ] Again , since the point B is the centre of the circle CAE , BC is equal to BA . [ Def . 15 ] But CA was also proved equal to AB ; therefore each of the straight lines CA , CB is equal to AB .
And things which are equal to the same thing are also equal to one another ; [ C . N . 1 ] therefore CA is also equal to CB . Therefore the three straight lines CA , AB , BC are equal to one another .
Therefore the triangle ABC is equilateral ; and it has been constructed on the given finite straight line AB .
Being what it was required to do .
Euclid, Elements, Selections
Christopher Blackwell /
- Created on 2018-03-16 15:28:50
- Translated by Heath
- Aligned by Christopher Blackwell
Ἑλληνική Transliterate
English
DEFINITIONS .
σημεῖόν ἐστιν , οὗ μέρος οὐθέν .
γραμμὴ δὲ μῆκος ἀπλατές .
γραμμῆς δὲ πέρατα σημεῖα .
εὐθεῖα γραμμή ἐστιν , ἥτις ἐξ ἴσου τοῖς ἐφ᾽ ἑαυτῆς σημείοις κεῖται .
ἐπιφάνεια δέ ἐστιν , ὃ μῆκος καὶ πλάτος μόνον ἔχει .
ἐπιφανείας δὲ πέρατα γραμμαί .
ἐπίπεδος ἐπιφάνειά ἐστιν , ἥτις ἐξ ἴσου ταῖς ἐφ᾽ ἑαυτῆς εὐθείαις κεῖται .
ἐπίπεδος δὲ γωνία ἐστὶν ἡ ἐν ἐπιπέδῳ δύο γραμμῶν ἁπτομένων ἀλλήλων καὶ μὴ ἐπ᾽ εὐθείας κειμένων πρὸς ἀλλήλας τῶν γραμμῶν κλίσις .
ὅταν δὲ αἱ περιέχουσαι τὴν γωνίαν γραμμαὶ εὐθεῖαι ὦσιν , εὐθύγραμμος καλεῖται ἡ γωνία .
ὅταν δὲ εὐθεῖα ἐπ᾽ εὐθεῖαν σταθεῖσα τὰς ἐφεξῆς γωνίας ἴσας ἀλλήλαις ποιῇ , ὀρθὴ ἑκατέρα τῶν ἴσων γωνιῶν ἐστι , καὶ ἡ ἐφεστηκυῖα εὐθεῖα κάθετος καλεῖται , ἐφ᾽ ἣν ἐφέστηκεν .
ἀμβλεῖα γωνία ἐστὶν ἡ μείζων ὀρθῆς .
ὀξεῖα δὲ ἡ ἐλάσσων ὀρθῆς .
ὅρος ἐστίν , ὅ τινός ἐστι πέρας .
σχῆμά ἐστι τὸ ὑπό τινος ἤ τινων ὅρων περιεχόμενον .
κύκλος ἐστὶ σχῆμα ἐπίπεδον ὑπὸ μιᾶς γραμμῆς περιεχόμενον ἣ καλεῖται περιφέρεια , πρὸς ἣν ἀφ᾽ ἑνὸς σημείου τῶν ἐντὸς τοῦ σχήματος κειμένων πᾶσαι αἱ προσπίπτουσαι εὐθεῖαι πρὸς τὴν τοῦ κύκλου περιφέρειαν ἴσαι ἀλλήλαις εἰσίν .
κέντρον δὲ τοῦ κύκλου τὸ σημεῖον καλεῖται .
διάμετρος δὲ τοῦ κύκλου ἐστὶν εὐθεῖά τις διὰ τοῦ κέντρου ἠγμένη καὶ περατουμένη ἐφ᾽ ἑκάτερα τὰ μέρη ὑπὸ τῆς τοῦ κύκλου περιφερείας , ἥτις καὶ δίχα τέμνει τὸν κύκλον .
ἡμικύκλιον δέ ἐστι τὸ περιεχόμενον σχῆμα ὑπό τε τῆς διαμέτρου καὶ τῆς ἀπολαμβανομένης ὑπ᾽ αὐτῆς περιφερείας . κέντρον δὲ τοῦ ἡμικυκλίου τὸ αὐτό , ὃ καὶ τοῦ κύκλου ἐστίν .
σχήματα εὐθύγραμμά ἐστι τὰ ὑπὸ εὐθειῶν περιεχόμενα , τρίπλευρα μὲν τὰ ὑπὸ τριῶν , τετράπλευρα δὲ τὰ ὑπὸ τεσσάρων , πολύπλευρα δὲ τὰ ὑπὸ πλειόνων ἢ τεσσάρων εὐθειῶν περιεχόμενα .
τῶν δὲ τριπλεύρων σχημάτων ἰσόπλευρον μὲν τρίγωνόν ἐστι τὸ τὰς τρεῖς ἴσας ἔχον πλευράς , ἰσοσκελὲς δὲ τὸ τὰς δύο μόνας ἴσας ἔχον πλευράς , σκαληνὸν δὲ τὸ τὰς τρεῖς ἀνίσους ἔχον πλευράς .
ἔτι δὲ τῶν τριπλεύρων σχημάτων ὀρθογώνιον μὲν τρίγωνόν ἐστι τὸ ἔχον ὀρθὴν γωνίαν , ἀμβλυγώνιον δὲ τὸ ἔχον ἀμβλεῖαν γωνίαν , ὀξυγώνιον δὲ τὸ τὰς τρεῖς ὀξείας ἔχον γωνίας .
τῶν δὲ τετραπλεύρων σχημάτων τετράγωνον μέν ἐστιν , ὃ ἰσόπλευρόν τέ ἐστι καὶ ὀρθογώνιον , ἑτερόμηκες δέ , ὃ ὀρθογώνιον μέν , οὐκ ἰσόπλευρον δέ , ῥόμβος δέ , ὃ ἰσόπλευρον μέν , οὐκ ὀρθογώνιον δέ , ῥομβοειδὲς δὲ τὸ τὰς ἀπεναντίον πλευράς τε καὶ γωνίας ἴσας ἀλλήλαις ἔχον , ὃ οὔτε ἰσόπλευρόν ἐστιν οὔτε ὀρθογώνιον : τὰ δὲ παρὰ ταῦτα τετράπλευρα τραπέζια καλείσθω .
παράλληλοί εἰσιν εὐθεῖαι , αἵτινες ἐν τῷ αὐτῷ ἐπιπέδῳ οὖσαι καὶ ἐκβαλλόμεναι εἰς ἄπειρον ἐφ᾽ ἑκάτερα τὰ μέρη ἐπὶ μηδέτερα συμπίπτουσιν ἀλλήλαις .
POSTULATES .
Ἠιτήσθω ἀπὸ παντὸς σημείου ἐπὶ πᾶν σημεῖον εὐθεῖαν γραμμὴν ἀγαγεῖν .
καὶ πεπερασμένην εὐθεῖαν κατὰ τὸ συνεχὲς ἐπ᾽ εὐθείας ἐκβαλεῖν .
καὶ παντὶ κέντρῳ καὶ διαστήματι κύκλον γράφεσθαι .
καὶ πάσας τὰς ὀρθὰς γωνίας ἴσας ἀλλήλαις εἶναι .
καὶ ἐὰν εἰς δύο εὐθείας εὐθεῖα ἐμπίπτουσα τὰς ἐντὸς καὶ ἐπὶ τὰ αὐτὰ μέρη γωνίας δύο ὀρθῶν ἐλάσσονας ποιῇ , ἐκβαλλομένας τὰς δύο εὐθείας ἐπ᾽ ἄπειρον συμπίπτειν , ἐφ᾽ ἃ μέρη εἰσὶν αἱ τῶν δύο ὀρθῶν ἐλάσσονες .
COMMON NOTIONS .
τὰ τῷ αὐτῷ ἴσα καὶ ἀλλήλοις ἐστὶν ἴσα .
καὶ ἐὰν ἴσοις ἴσα προστεθῇ , τὰ ὅλα ἐστὶν ἴσα .
καὶ ἐὰν ἀπὸ ἴσων ἴσα ἀφαιρεθῇ , τὰ καταλειπόμενά ἐστιν ἴσα .
καὶ ἐὰν ἀνίσοις ἴσα προστεθῇ , τὰ ὅλα ἐστὶν ἄνισα .
καὶ τὰ τοῦ αὐτοῦ διπλάσια ἴσα ἀλλήλοις ἐστίν .
καὶ τὰ τοῦ αὐτοῦ ἡμίση ἴσα ἀλλήλοις ἐστίν .
καὶ τὰ ἐφαρμόζοντα ἐπ᾽ ἄλληλα ἴσα ἀλλήλοις ἐστίν .
καὶ τὸ ὅλον τοῦ μέρους μεῖζον ἐστιν .
καὶ δύο εὐθεῖαι χωρίον οὐ περιέχουσιν .
PROPOSITION 1
ἐπὶ τῆς δοθείσης εὐθείας πεπερασμένης τρίγωνον ἰσόπλευρον συστήσασθαι .
ἔστω ἡ δοθεῖσα εὐθεῖα πεπερασμένη ἡ ΑΒ . δεῖ δὴ ἐπὶ τῆς ΑΒ εὐθείας τρίγωνον ἰσόπλευρον συστήσασθαι .
κέντρῳ μὲν τῷ Α διαστήματι δὲ τῷ ΑΒ κύκλος γεγράφθω ὁ ΒΓΔ , καὶ πάλιν κέντρῳ μὲν τῷ Β διαστήματι δὲ τῷ ΒΑ κύκλος γεγράφθω ὁ ΑΓΕ , καὶ ἀπὸ τοῦ Γ σημείου , καθ᾽ ὃ τέμνουσιν ἀλλήλους οἱ κύκλοι , ἐπὶ τὰ Α , Β σημεῖα ἐπεζεύχθωσαν εὐθεῖαι αἱ ΓΑ , ΓΒ .
καὶ ἐπεὶ τὸ Α σημεῖον κέντρον ἐστὶ τοῦ ΓΔΒ κύκλου , ἴση ἐστὶν ἡ ΑΓ τῇ ΑΒ : πάλιν , ἐπεὶ τὸ Β σημεῖον κέντρον ἐστὶ τοῦ ΓΑΕ κύκλου , ἴση ἐστὶν ἡ ΒΓ τῇ ΒΑ . ἐδείχθη δὲ καὶ ἡ ΓΑ τῇ ΑΒ ἴση : ἑκατέρα ἄρα τῶν ΓΑ , ΓΒ τῇ ΑΒ ἐστὶν ἴση .
τὰ δὲ τῷ αὐτῷ ἴσα καὶ ἀλλήλοις ἐστὶν ἴσα : καὶ ἡ ΓΑ ἄρα τῇ ΓΒ ἐστὶν ἴση : αἱ τρεῖς ἄρα αἱ ΓΑ , ΑΒ , ΒΓ ἴσαι ἀλλήλαις εἰσίν .
ἰσόπλευρον ἄρα ἐστὶ τὸ ΑΒΓ τρίγωνον , καὶ συνέσταται ἐπὶ τῆς δοθείσης εὐθείας πεπερασμένης τῆς ΑΒ .
Ἐπὶ τῆς δοθείσης ἄρα εὐθείας πεπερασμένης τρίγωνον ἰσόπλευρον συνέσταται : ὅπερ ἔδει ποιῆσαι .
σημεῖόν ἐστιν , οὗ μέρος οὐθέν .
γραμμὴ δὲ μῆκος ἀπλατές .
γραμμῆς δὲ πέρατα σημεῖα .
εὐθεῖα γραμμή ἐστιν , ἥτις ἐξ ἴσου τοῖς ἐφ᾽ ἑαυτῆς σημείοις κεῖται .
ἐπιφάνεια δέ ἐστιν , ὃ μῆκος καὶ πλάτος μόνον ἔχει .
ἐπιφανείας δὲ πέρατα γραμμαί .
ἐπίπεδος ἐπιφάνειά ἐστιν , ἥτις ἐξ ἴσου ταῖς ἐφ᾽ ἑαυτῆς εὐθείαις κεῖται .
ἐπίπεδος δὲ γωνία ἐστὶν ἡ ἐν ἐπιπέδῳ δύο γραμμῶν ἁπτομένων ἀλλήλων καὶ μὴ ἐπ᾽ εὐθείας κειμένων πρὸς ἀλλήλας τῶν γραμμῶν κλίσις .
ὅταν δὲ αἱ περιέχουσαι τὴν γωνίαν γραμμαὶ εὐθεῖαι ὦσιν , εὐθύγραμμος καλεῖται ἡ γωνία .
ὅταν δὲ εὐθεῖα ἐπ᾽ εὐθεῖαν σταθεῖσα τὰς ἐφεξῆς γωνίας ἴσας ἀλλήλαις ποιῇ , ὀρθὴ ἑκατέρα τῶν ἴσων γωνιῶν ἐστι , καὶ ἡ ἐφεστηκυῖα εὐθεῖα κάθετος καλεῖται , ἐφ᾽ ἣν ἐφέστηκεν .
ἀμβλεῖα γωνία ἐστὶν ἡ μείζων ὀρθῆς .
ὀξεῖα δὲ ἡ ἐλάσσων ὀρθῆς .
ὅρος ἐστίν , ὅ τινός ἐστι πέρας .
σχῆμά ἐστι τὸ ὑπό τινος ἤ τινων ὅρων περιεχόμενον .
κύκλος ἐστὶ σχῆμα ἐπίπεδον ὑπὸ μιᾶς γραμμῆς περιεχόμενον ἣ καλεῖται περιφέρεια , πρὸς ἣν ἀφ᾽ ἑνὸς σημείου τῶν ἐντὸς τοῦ σχήματος κειμένων πᾶσαι αἱ προσπίπτουσαι εὐθεῖαι πρὸς τὴν τοῦ κύκλου περιφέρειαν ἴσαι ἀλλήλαις εἰσίν .
κέντρον δὲ τοῦ κύκλου τὸ σημεῖον καλεῖται .
διάμετρος δὲ τοῦ κύκλου ἐστὶν εὐθεῖά τις διὰ τοῦ κέντρου ἠγμένη καὶ περατουμένη ἐφ᾽ ἑκάτερα τὰ μέρη ὑπὸ τῆς τοῦ κύκλου περιφερείας , ἥτις καὶ δίχα τέμνει τὸν κύκλον .
ἡμικύκλιον δέ ἐστι τὸ περιεχόμενον σχῆμα ὑπό τε τῆς διαμέτρου καὶ τῆς ἀπολαμβανομένης ὑπ᾽ αὐτῆς περιφερείας . κέντρον δὲ τοῦ ἡμικυκλίου τὸ αὐτό , ὃ καὶ τοῦ κύκλου ἐστίν .
σχήματα εὐθύγραμμά ἐστι τὰ ὑπὸ εὐθειῶν περιεχόμενα , τρίπλευρα μὲν τὰ ὑπὸ τριῶν , τετράπλευρα δὲ τὰ ὑπὸ τεσσάρων , πολύπλευρα δὲ τὰ ὑπὸ πλειόνων ἢ τεσσάρων εὐθειῶν περιεχόμενα .
τῶν δὲ τριπλεύρων σχημάτων ἰσόπλευρον μὲν τρίγωνόν ἐστι τὸ τὰς τρεῖς ἴσας ἔχον πλευράς , ἰσοσκελὲς δὲ τὸ τὰς δύο μόνας ἴσας ἔχον πλευράς , σκαληνὸν δὲ τὸ τὰς τρεῖς ἀνίσους ἔχον πλευράς .
ἔτι δὲ τῶν τριπλεύρων σχημάτων ὀρθογώνιον μὲν τρίγωνόν ἐστι τὸ ἔχον ὀρθὴν γωνίαν , ἀμβλυγώνιον δὲ τὸ ἔχον ἀμβλεῖαν γωνίαν , ὀξυγώνιον δὲ τὸ τὰς τρεῖς ὀξείας ἔχον γωνίας .
τῶν δὲ τετραπλεύρων σχημάτων τετράγωνον μέν ἐστιν , ὃ ἰσόπλευρόν τέ ἐστι καὶ ὀρθογώνιον , ἑτερόμηκες δέ , ὃ ὀρθογώνιον μέν , οὐκ ἰσόπλευρον δέ , ῥόμβος δέ , ὃ ἰσόπλευρον μέν , οὐκ ὀρθογώνιον δέ , ῥομβοειδὲς δὲ τὸ τὰς ἀπεναντίον πλευράς τε καὶ γωνίας ἴσας ἀλλήλαις ἔχον , ὃ οὔτε ἰσόπλευρόν ἐστιν οὔτε ὀρθογώνιον : τὰ δὲ παρὰ ταῦτα τετράπλευρα τραπέζια καλείσθω .
παράλληλοί εἰσιν εὐθεῖαι , αἵτινες ἐν τῷ αὐτῷ ἐπιπέδῳ οὖσαι καὶ ἐκβαλλόμεναι εἰς ἄπειρον ἐφ᾽ ἑκάτερα τὰ μέρη ἐπὶ μηδέτερα συμπίπτουσιν ἀλλήλαις .
POSTULATES .
Ἠιτήσθω ἀπὸ παντὸς σημείου ἐπὶ πᾶν σημεῖον εὐθεῖαν γραμμὴν ἀγαγεῖν .
καὶ πεπερασμένην εὐθεῖαν κατὰ τὸ συνεχὲς ἐπ᾽ εὐθείας ἐκβαλεῖν .
καὶ παντὶ κέντρῳ καὶ διαστήματι κύκλον γράφεσθαι .
καὶ πάσας τὰς ὀρθὰς γωνίας ἴσας ἀλλήλαις εἶναι .
καὶ ἐὰν εἰς δύο εὐθείας εὐθεῖα ἐμπίπτουσα τὰς ἐντὸς καὶ ἐπὶ τὰ αὐτὰ μέρη γωνίας δύο ὀρθῶν ἐλάσσονας ποιῇ , ἐκβαλλομένας τὰς δύο εὐθείας ἐπ᾽ ἄπειρον συμπίπτειν , ἐφ᾽ ἃ μέρη εἰσὶν αἱ τῶν δύο ὀρθῶν ἐλάσσονες .
COMMON NOTIONS .
τὰ τῷ αὐτῷ ἴσα καὶ ἀλλήλοις ἐστὶν ἴσα .
καὶ ἐὰν ἴσοις ἴσα προστεθῇ , τὰ ὅλα ἐστὶν ἴσα .
καὶ ἐὰν ἀπὸ ἴσων ἴσα ἀφαιρεθῇ , τὰ καταλειπόμενά ἐστιν ἴσα .
καὶ ἐὰν ἀνίσοις ἴσα προστεθῇ , τὰ ὅλα ἐστὶν ἄνισα .
καὶ τὰ τοῦ αὐτοῦ διπλάσια ἴσα ἀλλήλοις ἐστίν .
καὶ τὰ τοῦ αὐτοῦ ἡμίση ἴσα ἀλλήλοις ἐστίν .
καὶ τὰ ἐφαρμόζοντα ἐπ᾽ ἄλληλα ἴσα ἀλλήλοις ἐστίν .
καὶ τὸ ὅλον τοῦ μέρους μεῖζον ἐστιν .
καὶ δύο εὐθεῖαι χωρίον οὐ περιέχουσιν .
PROPOSITION 1
ἐπὶ τῆς δοθείσης εὐθείας πεπερασμένης τρίγωνον ἰσόπλευρον συστήσασθαι .
ἔστω ἡ δοθεῖσα εὐθεῖα πεπερασμένη ἡ ΑΒ . δεῖ δὴ ἐπὶ τῆς ΑΒ εὐθείας τρίγωνον ἰσόπλευρον συστήσασθαι .
κέντρῳ μὲν τῷ Α διαστήματι δὲ τῷ ΑΒ κύκλος γεγράφθω ὁ ΒΓΔ , καὶ πάλιν κέντρῳ μὲν τῷ Β διαστήματι δὲ τῷ ΒΑ κύκλος γεγράφθω ὁ ΑΓΕ , καὶ ἀπὸ τοῦ Γ σημείου , καθ᾽ ὃ τέμνουσιν ἀλλήλους οἱ κύκλοι , ἐπὶ τὰ Α , Β σημεῖα ἐπεζεύχθωσαν εὐθεῖαι αἱ ΓΑ , ΓΒ .
καὶ ἐπεὶ τὸ Α σημεῖον κέντρον ἐστὶ τοῦ ΓΔΒ κύκλου , ἴση ἐστὶν ἡ ΑΓ τῇ ΑΒ : πάλιν , ἐπεὶ τὸ Β σημεῖον κέντρον ἐστὶ τοῦ ΓΑΕ κύκλου , ἴση ἐστὶν ἡ ΒΓ τῇ ΒΑ . ἐδείχθη δὲ καὶ ἡ ΓΑ τῇ ΑΒ ἴση : ἑκατέρα ἄρα τῶν ΓΑ , ΓΒ τῇ ΑΒ ἐστὶν ἴση .
τὰ δὲ τῷ αὐτῷ ἴσα καὶ ἀλλήλοις ἐστὶν ἴσα : καὶ ἡ ΓΑ ἄρα τῇ ΓΒ ἐστὶν ἴση : αἱ τρεῖς ἄρα αἱ ΓΑ , ΑΒ , ΒΓ ἴσαι ἀλλήλαις εἰσίν .
ἰσόπλευρον ἄρα ἐστὶ τὸ ΑΒΓ τρίγωνον , καὶ συνέσταται ἐπὶ τῆς δοθείσης εὐθείας πεπερασμένης τῆς ΑΒ .
Ἐπὶ τῆς δοθείσης ἄρα εὐθείας πεπερασμένης τρίγωνον ἰσόπλευρον συνέσταται : ὅπερ ἔδει ποιῆσαι .
DEFINITIONS
.
1 A point is that which has no part .
2 A line is breadthless length .
3 The extremities of a line are points .
4 A straight line is a line which lies evenly with the points on itself .
5 A surface is that which has length and breadth only .
6 The extremities of a surface are lines .
7 A plane surface is a surface which lies evenly with the straight lines on itself .
8 A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line .
9 And when the lines containing the angle are straight , the angle is called rectilineal .
10 When a straight line set up on a straight line makes the adjacent angles equal to one another , each of the equal angles is right , and the straight line standing on the other is called a perpendicular to that on which it stands .
11 An obtuse angle is an angle greater than a right angle .
12 An acute angle is an angle less than a right angle .
13 A boundary is that which is an extremity of anything .
14 A figure is that which is contained by any boundary or boundaries .
15 A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another ;
16 And the point is called the centre of the circle .
17 A diameter of the circle is any straight line drawn through the centre and terminated in both directions by the circumference of the circle , and such a straight line also bisects the circle .
18 A semicircle is the figure contained by the diameter and the circumference cut off by it . And the centre of the semicircle is the same as that of the circle .
19 Rectilineal figures are those which are contained by straight lines , trilateral figures being those contained by three , quadrilateral those contained by four , and multilateral those contained by more than four straight lines .
20 Of trilateral figures , an equilateral triangle is that which has its three sides equal , an isosceles triangle that which has two of its sides alone equal , and a scalene triangle that which has its three sides unequal .
21 Further , of trilateral figures , a right-angled triangle is that which has a right angle , an obtuse-angled triangle that which has an obtuse angle , and an acuteangled triangle that which has its three angles acute .
22 Of quadrilateral figures , a square is that which is both equilateral and right-angled ; an oblong that which is right-angled but not equilateral ; a rhombus that which is equilateral but not right-angled ; and a rhomboid that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled . And let quadrilaterals other than these be called trapezia .
23 Parallel straight lines are straight lines which , being in the same plane and being produced indefinitely in both directions , do not meet one another in either direction .
POSTULATES .
1 Let the following be postulated : To draw a straight line from any point to any point .
2 To produce a finite straight line continuously in a straight line .
3 To describe a circle with any centre and distance .
4 That all right angles are equal to one another .
5 That , if a straight line falling on two straight lines make the interior angles on the same side less than two right angles , the two straight lines , if produced indefinitely , meet on that side on which are the angles less than the two right angles .
COMMON NOTIONS .
1 Things which are equal to the same thing are also equal to one another .
2 If equals be added to equals , the wholes are equal .
3 If equals be subtracted from equals , the remainders are equal .
7 Things which coincide with one another are equal to one another .
8 The whole is greater than the part .
PROPOSITION 1
On a given finite straight line to construct an equilateral triangle .
Let AB be the given finite straight line . Thus it is required to construct an equilateral triangle on the straight line AB .
With centre A and distance AB let the circle BCD be described ; [ Post . 3 ] again , with centre B and distance BA let the circle ACE be described ; [ Post . 3 ] and from the point C , in which the circles cut one another , to the points A , B let the straight lines CA , CB be joined . [ Post . 1 ]
Now , since the point A is the centre of the circle CDB , AC is equal to AB . [ Def . 15 ] Again , since the point B is the centre of the circle CAE , BC is equal to BA . [ Def . 15 ] But CA was also proved equal to AB ; therefore each of the straight lines CA , CB is equal to AB .
And things which are equal to the same thing are also equal to one another ; [ C . N . 1 ] therefore CA is also equal to CB . Therefore the three straight lines CA , AB , BC are equal to one another .
Therefore the triangle ABC is equilateral ; and it has been constructed on the given finite straight line AB .
Being what it was required to do .
1 A point is that which has no part .
2 A line is breadthless length .
3 The extremities of a line are points .
4 A straight line is a line which lies evenly with the points on itself .
5 A surface is that which has length and breadth only .
6 The extremities of a surface are lines .
7 A plane surface is a surface which lies evenly with the straight lines on itself .
8 A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line .
9 And when the lines containing the angle are straight , the angle is called rectilineal .
10 When a straight line set up on a straight line makes the adjacent angles equal to one another , each of the equal angles is right , and the straight line standing on the other is called a perpendicular to that on which it stands .
11 An obtuse angle is an angle greater than a right angle .
12 An acute angle is an angle less than a right angle .
13 A boundary is that which is an extremity of anything .
14 A figure is that which is contained by any boundary or boundaries .
15 A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another ;
16 And the point is called the centre of the circle .
17 A diameter of the circle is any straight line drawn through the centre and terminated in both directions by the circumference of the circle , and such a straight line also bisects the circle .
18 A semicircle is the figure contained by the diameter and the circumference cut off by it . And the centre of the semicircle is the same as that of the circle .
19 Rectilineal figures are those which are contained by straight lines , trilateral figures being those contained by three , quadrilateral those contained by four , and multilateral those contained by more than four straight lines .
20 Of trilateral figures , an equilateral triangle is that which has its three sides equal , an isosceles triangle that which has two of its sides alone equal , and a scalene triangle that which has its three sides unequal .
21 Further , of trilateral figures , a right-angled triangle is that which has a right angle , an obtuse-angled triangle that which has an obtuse angle , and an acuteangled triangle that which has its three angles acute .
22 Of quadrilateral figures , a square is that which is both equilateral and right-angled ; an oblong that which is right-angled but not equilateral ; a rhombus that which is equilateral but not right-angled ; and a rhomboid that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled . And let quadrilaterals other than these be called trapezia .
23 Parallel straight lines are straight lines which , being in the same plane and being produced indefinitely in both directions , do not meet one another in either direction .
POSTULATES .
1 Let the following be postulated : To draw a straight line from any point to any point .
2 To produce a finite straight line continuously in a straight line .
3 To describe a circle with any centre and distance .
4 That all right angles are equal to one another .
5 That , if a straight line falling on two straight lines make the interior angles on the same side less than two right angles , the two straight lines , if produced indefinitely , meet on that side on which are the angles less than the two right angles .
COMMON NOTIONS .
1 Things which are equal to the same thing are also equal to one another .
2 If equals be added to equals , the wholes are equal .
3 If equals be subtracted from equals , the remainders are equal .
7 Things which coincide with one another are equal to one another .
8 The whole is greater than the part .
PROPOSITION 1
On a given finite straight line to construct an equilateral triangle .
Let AB be the given finite straight line . Thus it is required to construct an equilateral triangle on the straight line AB .
With centre A and distance AB let the circle BCD be described ; [ Post . 3 ] again , with centre B and distance BA let the circle ACE be described ; [ Post . 3 ] and from the point C , in which the circles cut one another , to the points A , B let the straight lines CA , CB be joined . [ Post . 1 ]
Now , since the point A is the centre of the circle CDB , AC is equal to AB . [ Def . 15 ] Again , since the point B is the centre of the circle CAE , BC is equal to BA . [ Def . 15 ] But CA was also proved equal to AB ; therefore each of the straight lines CA , CB is equal to AB .
And things which are equal to the same thing are also equal to one another ; [ C . N . 1 ] therefore CA is also equal to CB . Therefore the three straight lines CA , AB , BC are equal to one another .
Therefore the triangle ABC is equilateral ; and it has been constructed on the given finite straight line AB .
Being what it was required to do .
Euclid test: 1.Definitions
Christopher Blackwell /
- Created on 2018-03-19 14:09:36
- Modified on 2018-03-19 14:10:58
- Translated by Heath
- Aligned by Christopher Blackwell
Herodotus 1.35 - Greek :: English
Christopher Blackwell /
- Created on 2018-03-20 17:32:38
- Modified on 2018-03-20 17:46:34
- Translated by Godley
- Aligned by Christopher Blackwell
Ἑλληνική Transliterate
English
Ἔχοντος δέ οἱ ἐν χερσὶ τοῦ παιδὸς τὸν γάμον ἀπικνέεται ἐς τὰς Σάρδις ἀνὴρ συμφορῇ ἐχόμενος καὶ οὐ καθαρὸς χεῖρας , ἐὼν Φρὺξ μὲν γενεῇ , γένεος δὲ τοῦ βασιληίου . Παρελθὼν δὲ οὗτος ἐς τὰ Κροίσου οἰκία κατὰ νόμους τοὺς ἐπιχωρίους καθαρσίου ἐδέετο κυρῆσαι , Κροῖσος δέ μιν ἐκάθηρε . Ἔστι δὲ παραπλησίη ἡ κάθαρσις τοῖσι Λυδοῖσι καὶ τοῖσι Ἕλλησι . Ἐπείτε δὲ τὰ νομιζόμενα ἐποίησε ὁ Κροῖσος , ἐπυνθάνετο ὁκόθεν τε καὶ τίς εἴη , λέγων τάδε · " Ὤνθρωπε , τίς τε ἐὼν καὶ κόθεν τῆς Φρυγίης ἥκων ἐπίστιός μοι ἐγένεο ; Τίνα τε ἀνδρῶν ἢ γυναικῶν ἐφόνευσας ; " Ὁ δὲ ἀμείβετο · " Ὦ βασιλεῦ , Γορδίεω μὲν τοῦ Μίδεω εἰμὶ παῖς , ὀνομάζομαι δὲ Ἄδρηστος , φονεύσας δὲ ἀδελφεὸν ἐμεωυτοῦ ἀέκων πάρειμι ἐξεληλαμένος τε ὑπὸ τοῦ πατρὸς καὶ ἐστερημένος πάντων . " Κροῖσος δέ μιν ἀμείβετο τοῖσδε · " Ἀνδρῶν τε φίλων τυγχάνεις ἔκγονος ἐὼν καὶ ἐλήλυθας ἐς φίλους , ἔνθα ἀμηχανήσεις χρήματος οὐδενὸς μένων ἐν ἡμετέρου συμφορήν τε ταύτην ὡς κουφότατα φέρων κερδανέεις πλεῖστον . "
Then
while
he
was
engaged
about
the
marriage
of
his
son
,
there
came
to
Sardis
a
man
under
a
misfortune
and
with
hands
not
clean
,
a
Phrygian
by
birth
and
of
the
royal
house
.
This
man
came
to
the
house
of
Croesus
,
and
according
to
the
customs
which
prevail
in
that
land
made
request
that
he
might
have
cleansing
;
and
Croesus
gave
him
cleansing
:
now
the
manner
of
cleansing
among
the
Lydians
is
the
same
almost
as
that
which
the
Hellenes
use
.
So
when
Croesus
had
done
that
which
was
customary
,
he
asked
of
him
whence
he
came
and
who
he
was
,
saying
as
follows
:
"
Man
,
who
art
thou
,
and
from
what
region
of
Phrygia
didst
thou
come
to
sit
upon
my
hearth
?
And
whom
of
men
or
women
didst
thou
slay
?
"
And
he
replied
:
"
O
king
,
I
am
the
son
of
Gordias
,
the
son
of
Midas
,
and
I
am
called
Adrastos
;
and
I
slew
my
own
brother
against
my
will
,
and
therefore
am
I
here
,
having
been
driven
forth
by
my
father
and
deprived
of
all
that
I
had
.
"
And
Croesus
answered
thus
:
"
Thou
art
,
as
it
chances
,
the
offshoot
of
men
who
are
our
friends
and
thou
hast
come
to
friends
,
among
whom
thou
shalt
want
of
nothing
so
long
as
thou
shalt
remain
in
our
land
:
and
thou
wilt
find
it
most
for
thy
profit
to
bear
this
misfortune
as
lightly
as
may
be
.
"
So
he
had
his
abode
with
Croesus
.
Euclid 1.proposition.1
Christopher Blackwell /
- Created on 2018-03-23 13:21:22
- Translated by Heath
- Aligned by Christopher Blackwell
Euclid Book 1 Proposition 1
Ἑλληνική Transliterate
English
urn:cts:greekLit:tlg1799.tlg001.heiberg:1.prop.1
urn:cts:greekLit:tlg1799.tlg001.heath:1.prop.1
PROPOSITION 1
ἐπὶ τῆς δοθείσης εὐθείας πεπερασμένης τρίγωνον ἰσόπλευρον συστήσασθαι .
ἔστω ἡ δοθεῖσα εὐθεῖα πεπερασμένη ἡ ΑΒ . δεῖ δὴ ἐπὶ τῆς ΑΒ εὐθείας τρίγωνον ἰσόπλευρον συστήσασθαι .
κέντρῳ μὲν τῷ Α διαστήματι δὲ τῷ ΑΒ κύκλος γεγράφθω ὁ ΒΓΔ , καὶ πάλιν κέντρῳ μὲν τῷ Β διαστήματι δὲ τῷ ΒΑ κύκλος γεγράφθω ὁ ΑΓΕ , καὶ ἀπὸ τοῦ Γ σημείου , καθ᾽ ὃ τέμνουσιν ἀλλήλους οἱ κύκλοι , ἐπὶ τὰ Α , Β σημεῖα ἐπεζεύχθωσαν εὐθεῖαι αἱ ΓΑ , ΓΒ .
καὶ ἐπεὶ τὸ Α σημεῖον κέντρον ἐστὶ τοῦ ΓΔΒ κύκλου , ἴση ἐστὶν ἡ ΑΓ τῇ ΑΒ : πάλιν , ἐπεὶ τὸ Β σημεῖον κέντρον ἐστὶ τοῦ ΓΑΕ κύκλου , ἴση ἐστὶν ἡ ΒΓ τῇ ΒΑ . ἐδείχθη δὲ καὶ ἡ ΓΑ τῇ ΑΒ ἴση : ἑκατέρα ἄρα τῶν ΓΑ , ΓΒ τῇ ΑΒ ἐστὶν ἴση .
τὰ δὲ τῷ αὐτῷ ἴσα καὶ ἀλλήλοις ἐστὶν ἴσα : καὶ ἡ ΓΑ ἄρα τῇ ΓΒ ἐστὶν ἴση : αἱ τρεῖς ἄρα αἱ ΓΑ , ΑΒ , ΒΓ ἴσαι ἀλλήλαις εἰσίν .
ἰσόπλευρον ἄρα ἐστὶ τὸ ΑΒΓ τρίγωνον , καὶ συνέσταται ἐπὶ τῆς δοθείσης εὐθείας πεπερασμένης τῆς ΑΒ .
Ἐπὶ τῆς δοθείσης ἄρα εὐθείας πεπερασμένης τρίγωνον ἰσόπλευρον συνέσταται : ὅπερ ἔδει ποιῆσαι .
ἐπὶ τῆς δοθείσης εὐθείας πεπερασμένης τρίγωνον ἰσόπλευρον συστήσασθαι .
ἔστω ἡ δοθεῖσα εὐθεῖα πεπερασμένη ἡ ΑΒ . δεῖ δὴ ἐπὶ τῆς ΑΒ εὐθείας τρίγωνον ἰσόπλευρον συστήσασθαι .
κέντρῳ μὲν τῷ Α διαστήματι δὲ τῷ ΑΒ κύκλος γεγράφθω ὁ ΒΓΔ , καὶ πάλιν κέντρῳ μὲν τῷ Β διαστήματι δὲ τῷ ΒΑ κύκλος γεγράφθω ὁ ΑΓΕ , καὶ ἀπὸ τοῦ Γ σημείου , καθ᾽ ὃ τέμνουσιν ἀλλήλους οἱ κύκλοι , ἐπὶ τὰ Α , Β σημεῖα ἐπεζεύχθωσαν εὐθεῖαι αἱ ΓΑ , ΓΒ .
καὶ ἐπεὶ τὸ Α σημεῖον κέντρον ἐστὶ τοῦ ΓΔΒ κύκλου , ἴση ἐστὶν ἡ ΑΓ τῇ ΑΒ : πάλιν , ἐπεὶ τὸ Β σημεῖον κέντρον ἐστὶ τοῦ ΓΑΕ κύκλου , ἴση ἐστὶν ἡ ΒΓ τῇ ΒΑ . ἐδείχθη δὲ καὶ ἡ ΓΑ τῇ ΑΒ ἴση : ἑκατέρα ἄρα τῶν ΓΑ , ΓΒ τῇ ΑΒ ἐστὶν ἴση .
τὰ δὲ τῷ αὐτῷ ἴσα καὶ ἀλλήλοις ἐστὶν ἴσα : καὶ ἡ ΓΑ ἄρα τῇ ΓΒ ἐστὶν ἴση : αἱ τρεῖς ἄρα αἱ ΓΑ , ΑΒ , ΒΓ ἴσαι ἀλλήλαις εἰσίν .
ἰσόπλευρον ἄρα ἐστὶ τὸ ΑΒΓ τρίγωνον , καὶ συνέσταται ἐπὶ τῆς δοθείσης εὐθείας πεπερασμένης τῆς ΑΒ .
Ἐπὶ τῆς δοθείσης ἄρα εὐθείας πεπερασμένης τρίγωνον ἰσόπλευρον συνέσταται : ὅπερ ἔδει ποιῆσαι .
PROPOSITION
1
On a given finite straight line to construct an equilateral triangle .
Let AB be the given finite straight line . Thus it is required to construct an equilateral triangle on the straight line AB .
With centre A and distance AB let the circle BCD be described ; [ Post . 3 ] again , with centre B and distance BA let the circle ACE be described ; [ Post . 3 ] and from the point C , in which the circles cut one another , to the points A , B let the straight lines CA , CB be joined . [ Post . 1 ]
Now , since the point A is the centre of the circle CDB , AC is equal to AB . [ Def . 15 ] Again , since the point B is the centre of the circle CAE , BC is equal to BA . [ Def . 15 ] But CA was also proved equal to AB ; therefore each of the straight lines CA , CB is equal to AB .
And things which are equal to the same thing are also equal to one another ; [ C . N . 1 ] therefore CA is also equal to CB . Therefore the three straight lines CA , AB , BC are equal to one another .
Therefore the triangle ABC is equilateral ; and it has been constructed on the given finite straight line AB .
Being what it was required to do .
On a given finite straight line to construct an equilateral triangle .
Let AB be the given finite straight line . Thus it is required to construct an equilateral triangle on the straight line AB .
With centre A and distance AB let the circle BCD be described ; [ Post . 3 ] again , with centre B and distance BA let the circle ACE be described ; [ Post . 3 ] and from the point C , in which the circles cut one another , to the points A , B let the straight lines CA , CB be joined . [ Post . 1 ]
Now , since the point A is the centre of the circle CDB , AC is equal to AB . [ Def . 15 ] Again , since the point B is the centre of the circle CAE , BC is equal to BA . [ Def . 15 ] But CA was also proved equal to AB ; therefore each of the straight lines CA , CB is equal to AB .
And things which are equal to the same thing are also equal to one another ; [ C . N . 1 ] therefore CA is also equal to CB . Therefore the three straight lines CA , AB , BC are equal to one another .
Therefore the triangle ABC is equilateral ; and it has been constructed on the given finite straight line AB .
Being what it was required to do .
Hdt. 8.22
Christopher Blackwell /
- Created on 2019-02-13 05:54:48
- Aligned by Christopher Blackwell
Ἑλληνική Transliterate
English
urn:cts:greekLit:tlg0016.tlg001.grc:8.22
urn:cts:greekLit:tlg0016.tlg001.grc:8.22
Ἀθηναίων δὲ νέας τὰς ἄριστα πλεούσας ἐπιλεξάμενος Θεμιστοκλέης ἐπορεύετο περὶ τὰ πότιμα ὕδατα , ἐντάμνων ἐν τοῖσι λίθοισι γράμματα , τὰ Ἴωνες ἐπελθόντες τῇ ὑστεραίῃ ἡμέρῃ ἐπὶ τὸ Ἀρτεμίσιον ἐπελέξαντο . Τὰ δὲ γράμματα τάδε ἔλεγε · " Ἄνδρες Ἴωνες , οὐ ποιέετε δίκαια ἐπὶ τοὺς πατέρας στρατευόμενοι καὶ τὴν Ἑλλάδα καταδουλούμενοι . Ἀλλὰ μάλιστα μὲν πρὸς ἡμέων γίνεσθε · εἰ δὲ ὑμῖν ἐστι τοῦτο μὴ δυνατὸν ποιῆσαι , ὑμεῖς δὲ ἔτι καὶ νῦν ἐκ τοῦ μέσου ἡμῖν ἕζεσθε καὶ αὐτοὶ καὶ τῶν Καρῶν δέεσθε τὰ αὐτὰ ὑμῖν ποιέειν · εἰ δὲ μηδέτερον τούτων οἷόν τε γίνεσθαι , ἀλλ᾽ ὑπ᾽ ἀναγκαίης μέζονος κατέζευχθε ἢ ὥστε ἀπίστασθαι . ὑμεῖς δὲ ἐν τῷ ἔργῳ , ἐπεὰν συμμίσγωμεν , ἐθελοκακέετε , μεμνημένοι ὅτι ἀπ᾽ ἡμέων γεγόνατε καὶ ὅτι ἀρχῆθεν ἡ ἔχθρη πρὸς τὸν βάρβαρον ἀπ᾽ ὑμέων ἡμῖν γέγονε . " Θεμιστοκλέης δὲ ταῦτα ἔγραφε , δοκέειν ἐμοί , ἐπ᾽ ἀμφότερα νοέων , ἵνα ἢ λαθόντα τὰ γράμματα βασιλέα Ἴωνας ποιήσῃ μεταβαλεῖν καὶ γενέσθαι πρὸς ἑωυτῶν , ἢ ἐπείτε ἂν ἀνενειχθῇ καὶ διαβληθῇ πρὸς Ξέρξην , ἀπίστους ποιήσῃ τοὺς Ἴωνας καὶ τῶν ναυμαχιέων αὐτοὺς ἀπόσχῃ .
Themistocles
however
selected
those
ships
of
the
Athenians
which
sailed
best
,
and
went
round
to
the
springs
of
drinking-water
,
cutting
inscriptions
on
the
stones
there
,
which
the
Ionians
read
when
they
came
to
Artemision
on
the
following
day
.
These
inscriptions
ran
thus
:
"
Ionians
,
ye
act
not
rightly
in
making
expedition
against
the
fathers
of
your
race
and
endeavouring
to
enslave
Hellas
.
Best
of
all
were
it
that
ye
should
come
and
be
on
our
side
;
but
if
that
may
not
be
done
by
you
,
stand
aside
even
now
from
the
combat
against
us
and
ask
the
Carians
to
do
the
same
as
ye
.
If
however
neither
of
these
two
things
is
possible
to
be
done
,
and
ye
are
bound
down
by
too
strong
compulsion
to
be
able
to
make
revolt
,
then
in
the
action
,
when
we
engage
battle
,
be
purposely
slack
,
remember
that
ye
are
descended
from
us
and
that
our
quarrel
with
the
Barbarian
took
its
rise
at
the
first
from
you
.
"
Odyssey 9.105-110 corrected
Christopher Blackwell /
- Created on 2019-02-14 18:04:56
- Modified on 2019-02-20 17:07:45
- Aligned by Christopher Blackwell
English
Ἑλληνική
English
" Thence we sailed on , grieved at heart , and we came to the land of the Cyclopes , an overweening and lawless folk , who , trusting in the immortal gods , plant nothing with their hands nor plough ; but all these things spring up for them without sowing or ploughing , wheat , and barley , and vines , which bear the rich clusters of wine , and the rain of Zeus gives them increase . Neither assemblies nor council have they , nor appointed laws , but they dwell on the peaks of lofty mountains in hollow caves , and each one is lawgiver to his children and his wives , and they reck nothing one of another . "
ἔνθεν δὲ προτέρω πλέομεν ἀκαχήμενοι ἦτορ :
Κυκλώπων δ᾽ ἐς γαῖαν ὑπερφιάλων ἀθεμίστων
ἱκόμεθ᾽ , οἵ ῥα θεοῖσι πεποιθότες ἀθανάτοισιν
οὔτε φυτεύουσιν χερσὶν φυτὸν οὔτ᾽ ἀρόωσιν ,
ἀλλὰ τά γ᾽ ἄσπαρτα καὶ ἀνήροτα πάντα φύονται ,
πυροὶ καὶ κριθαὶ ἠδ᾽ ἄμπελοι , αἵ τε φέρουσιν
οἶνον ἐριστάφυλον , καί σφιν Διὸς ὄμβρος ἀέξει .
τοῖσιν δ᾽ οὔτ᾽ ἀγοραὶ βουληφόροι οὔτε θέμιστες ,
ἀλλ᾽ οἵ γ᾽ ὑψηλῶν ὀρέων ναίουσι κάρηνα
ἐν σπέσσι γλαφυροῖσι , θεμιστεύει δὲ ἕκαστος
παίδων ἠδ᾽ ἀλόχων , οὐδ᾽ ἀλλήλων ἀλέγουσιν .
Κυκλώπων δ᾽ ἐς γαῖαν ὑπερφιάλων ἀθεμίστων
ἱκόμεθ᾽ , οἵ ῥα θεοῖσι πεποιθότες ἀθανάτοισιν
οὔτε φυτεύουσιν χερσὶν φυτὸν οὔτ᾽ ἀρόωσιν ,
ἀλλὰ τά γ᾽ ἄσπαρτα καὶ ἀνήροτα πάντα φύονται ,
πυροὶ καὶ κριθαὶ ἠδ᾽ ἄμπελοι , αἵ τε φέρουσιν
οἶνον ἐριστάφυλον , καί σφιν Διὸς ὄμβρος ἀέξει .
τοῖσιν δ᾽ οὔτ᾽ ἀγοραὶ βουληφόροι οὔτε θέμιστες ,
ἀλλ᾽ οἵ γ᾽ ὑψηλῶν ὀρέων ναίουσι κάρηνα
ἐν σπέσσι γλαφυροῖσι , θεμιστεύει δὲ ἕκαστος
παίδων ἠδ᾽ ἀλόχων , οὐδ᾽ ἀλλήλων ἀλέγουσιν .
We sailed on , our morale sinking ,
And we came to the land of the Cyclopes ,
Lawless savages who leave everything
Up to the gods . These people neither plow nor plant ,
But everything grows for them unsown :
Wheat , barley , and vines that bear
Clusters of grapes , watered by rain from Zeus .
They have no assemblies or laws but live
In high mountain caves , ruling their own
Children and wives and ignoring each other .
And we came to the land of the Cyclopes ,
Lawless savages who leave everything
Up to the gods . These people neither plow nor plant ,
But everything grows for them unsown :
Wheat , barley , and vines that bear
Clusters of grapes , watered by rain from Zeus .
They have no assemblies or laws but live
In high mountain caves , ruling their own
Children and wives and ignoring each other .
Greek120-OdysseyAlignment
Christopher Blackwell /
- Created on 2019-02-15 14:51:41
- Modified on 2019-02-15 15:21:55
- Aligned by Christopher Blackwell
English
Ἑλληνική
English
Thence we sailed on , grieved at heart , and we came to the land of the Cyclopes , an overweening and lawless folk , who , trusting in the immortal gods , plant nothing with their hands nor plough ; but all these things spring up for them without sowing or ploughing , wheat , and barley , and vines , which bear the rich clusters of wine , and the rain of Zeus gives them increase . Neither assemblies nor council have they , nor appointed laws , but they dwell on the peaks of lofty mountains in hollow caves , and each one is lawgiver to his children and his wives , and they reck nothing one of another .
ἔνθεν δὲ προτέρω πλέομεν ἀκαχήμενοι ἦτορ :
Κυκλώπων δ᾽ ἐς γαῖαν ὑπερφιάλων ἀθεμίστων
ἱκόμεθ᾽ , οἵ ῥα θεοῖσι πεποιθότες ἀθανάτοισιν
οὔτε φυτεύουσιν χερσὶν φυτὸν οὔτ᾽ ἀρόωσιν ,
ἀλλὰ τά γ᾽ ἄσπαρτα καὶ ἀνήροτα πάντα φύονται ,
110πυροὶ καὶ κριθαὶ ἠδ᾽ ἄμπελοι , αἵ τε φέρουσιν
οἶνον ἐριστάφυλον , καί σφιν Διὸς ὄμβρος ἀέξει .
τοῖσιν δ᾽ οὔτ᾽ ἀγοραὶ βουληφόροι οὔτε θέμιστες ,
ἀλλ᾽ οἵ γ᾽ ὑψηλῶν ὀρέων ναίουσι κάρηνα
ἐν σπέσσι γλαφυροῖσι , θεμιστεύει δὲ ἕκαστος
115παίδων ἠδ᾽ ἀλόχων , οὐδ᾽ ἀλλήλων ἀλέγουσιν .
Κυκλώπων δ᾽ ἐς γαῖαν ὑπερφιάλων ἀθεμίστων
ἱκόμεθ᾽ , οἵ ῥα θεοῖσι πεποιθότες ἀθανάτοισιν
οὔτε φυτεύουσιν χερσὶν φυτὸν οὔτ᾽ ἀρόωσιν ,
ἀλλὰ τά γ᾽ ἄσπαρτα καὶ ἀνήροτα πάντα φύονται ,
110πυροὶ καὶ κριθαὶ ἠδ᾽ ἄμπελοι , αἵ τε φέρουσιν
οἶνον ἐριστάφυλον , καί σφιν Διὸς ὄμβρος ἀέξει .
τοῖσιν δ᾽ οὔτ᾽ ἀγοραὶ βουληφόροι οὔτε θέμιστες ,
ἀλλ᾽ οἵ γ᾽ ὑψηλῶν ὀρέων ναίουσι κάρηνα
ἐν σπέσσι γλαφυροῖσι , θεμιστεύει δὲ ἕκαστος
115παίδων ἠδ᾽ ἀλόχων , οὐδ᾽ ἀλλήλων ἀλέγουσιν .
We sailed on , our morale sinking ,
And we came to the land of the Cyclopes ,
Lawless savages who leave everything
Up to the gods . These people neither plow nor plant ,
But everything grows for them unsown :
Wheat , barley , and vines that bear
Clusters of grapes , watered by rain from Zeus .
They have no assemblies or laws but live
In high mountain caves , ruling their own
Children and wives and ignoring each other .
And we came to the land of the Cyclopes ,
Lawless savages who leave everything
Up to the gods . These people neither plow nor plant ,
But everything grows for them unsown :
Wheat , barley , and vines that bear
Clusters of grapes , watered by rain from Zeus .
They have no assemblies or laws but live
In high mountain caves , ruling their own
Children and wives and ignoring each other .
Fighting: Iliad 5.655–5.667
Christopher Blackwell /
- Created on 2019-02-22 14:05:11
- Modified on 2019-02-22 14:24:04
- Aligned by Christopher Blackwell
English
Ἑλληνική
English
Thus spoke Sarpedon , and Tlepolemos upraised his spear . They threw at the same moment , and Sarpedon struck his foe in the middle of his throat ; the spear went right through , and the darkness of death fell upon his eyes . Tlepolemos ' spear struck Sarpedon on the left thigh with such force that it tore through the flesh and grazed the bone , but his father as yet warded off destruction from him . His comrades bore Sarpedon out of the fight , in great pain by the weight of the spear that was dragging from his wound . They were in such haste and stress [ ponos ] as they bore him that no one thought of drawing the spear from his thigh so as to let him walk uprightly .
ὣς φάτο Σαρπηδών , ὃ δʼ ἀνέσχετο μείλινον ἔγχος
Τληπόλεμος · καὶ τῶν μὲν ἁμαρτῇ δούρατα μακρὰ
ἐκ χειρῶν ἤϊξαν · ὃ μὲν βάλεν αὐχένα μέσσον
Σαρπηδών , αἰχμὴ δὲ διαμπερὲς ἦλθʼ ἀλεγεινή ·
τὸν δὲ κατʼ ὀφθαλμῶν ἐρεβεννὴ νὺξ ἐκάλυψε .
Τληπόλεμος δʼ ἄρα μηρὸν ἀριστερὸν ἔγχεϊ μακρῷ
βεβλήκειν , αἰχμὴ δὲ διέσσυτο μαιμώωσα
ὀστέω ἐγχριμφθεῖσα , πατὴρ δʼ ἔτι λοιγὸν ἄμυνεν .
οἳ μὲν ἄρʼ ἀντίθεον Σαρπηδόνα δῖοι ἑταῖροι
ἐξέφερον πολέμοιο · βάρυνε δέ μιν δόρυ μακρὸν
ἑλκόμενον · τὸ μὲν οὔ τις ἐπεφράσατʼ οὐδὲ νόησε
μηροῦ ἐξερύσαι δόρυ μείλινον ὄφρʼ ἐπιβαίη
σπευδόντων · τοῖον γὰρ ἔχον πόνον ἀμφιέποντες .
Τληπόλεμος · καὶ τῶν μὲν ἁμαρτῇ δούρατα μακρὰ
ἐκ χειρῶν ἤϊξαν · ὃ μὲν βάλεν αὐχένα μέσσον
Σαρπηδών , αἰχμὴ δὲ διαμπερὲς ἦλθʼ ἀλεγεινή ·
τὸν δὲ κατʼ ὀφθαλμῶν ἐρεβεννὴ νὺξ ἐκάλυψε .
Τληπόλεμος δʼ ἄρα μηρὸν ἀριστερὸν ἔγχεϊ μακρῷ
βεβλήκειν , αἰχμὴ δὲ διέσσυτο μαιμώωσα
ὀστέω ἐγχριμφθεῖσα , πατὴρ δʼ ἔτι λοιγὸν ἄμυνεν .
οἳ μὲν ἄρʼ ἀντίθεον Σαρπηδόνα δῖοι ἑταῖροι
ἐξέφερον πολέμοιο · βάρυνε δέ μιν δόρυ μακρὸν
ἑλκόμενον · τὸ μὲν οὔ τις ἐπεφράσατʼ οὐδὲ νόησε
μηροῦ ἐξερύσαι δόρυ μείλινον ὄφρʼ ἐπιβαίη
σπευδόντων · τοῖον γὰρ ἔχον πόνον ἀμφιέποντες .
So spake Sarpedon , and Tlepolemus lifted on high his ashen spear , and the long spears sped from the hands of both at one moment . Sarpedon smote him full upon the neck , and the grievous point passed clean through , and down upon his eyes came the darkness of night and enfolded him . And Tlepolemus smote Sarpedon upon the left thigh with his long spear , and the point sped through furiously and grazed the bone ; howbeit his father as yet warded from him destruction . Then his goodly companions bare godlike Sarpedon forth from out the fight , and the long spear burdened him sore , as it trailed , but no man marked it or thought in their haste to draw forth from his thigh the spear of ash , that he might stand upon his feet ; such toil had they in tending him .