KJV - WH Gospel of John - Demo Alignment

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

( 116 ) 67% ENG
( 58 ) 33% ENG - GRC

( 52 ) 33% ENG - GRC
( 105 ) 67% GRC

Antigone, Second Stasimon

Francesco Mambrini / Antigone, Second Stasimon (583-625). Trans. by E.R. Dodds (1951: 49-50)
  • Created on 2017-07-02 16:07:42
  • Modified on 2017-07-02 20:14:35
  • Aligned by Francesco Mambrini
Translated by E.R. Dodds (1951). The Greek text is tentatively identified with the OCT edition of Pearson
English
Ἑλληνική Transliterate
εὐδαίμονες οἷσι κακῶν ἄγευστος αἰών .
οἷς γὰρ ἂν σεισθῇ θεόθεν δόμος , ἄτας
οὐδὲν ἐλλείπει γενεᾶς ἐπὶ πλῆθος ἕρπον ·
ὅμοιον ὥστε πόντιον
οἶδμα δυσπνόοις ὅταν
Θρῄσσῃσιν ἔρεβος ὕφαλον ἐπιδράμῃ πνοαῖς ,
κυλίνδει βυσσόθεν κελαινὰν
θῖνα καὶ δυσάνεμοι
στόνῳ βρέμουσι ἀντιπλῆγες ἀκταί .

ἀρχαῖα τὰ Λαβδακιδᾶν οἴκων ὁρῶμαι
πήματα φθιμένων ἐπὶ πήμασι πίπτοντʼ ,
οὐδʼ ἀπαλλάσσει γενεὰν γένος , ἀλλʼ ἐρείπει
θεῶν τις , οὐδʼ ἔχει λύσιν .
νῦν γὰρ ἐσχάτας ὕπερ
ῥίζας ἐτέτατο φάος ἐν Οἰδίπου δόμοις ·
κατʼ αὖ νιν φοινία θεῶν τῶν
νερτέρων ἀμᾷ κοπίς ,
λόγου τʼ ἄνοια καὶ φρενῶν Ἐρινύς .

τεάν , Ζεῦ , δύνασιν τίς ἀνδρῶν ὑπερβασία κατάσχοι ;
τὰν οὔθʼ ὕπνος αἱρεῖ ποθʼ παντoγήρως ,
οὔτ ' ἀκάματοι θεῶν
μῆνες , ἀγήρως δὲ χρόνῳ δυνάστας
κατέχεις Ὀλύμπου
μαρμαρόεσσαν αἴγλαν .
τό τʼ ἔπειτα καὶ τὸ μέλλον
καὶ τὸ πρὶν ἐπαρκέσει
νόμος ὅδʼ · οὐδὲν ἕρπει
θνατῶν βιότῳ πάμπολύ γʼ ἐκτὸς ἄτας .

γὰρ δὴ πολύπλαγκτος ἐλπὶς πολλοῖς μὲν ὄνασις ἀνδρῶν ,
πολλοῖς δʼ ἀπάτα κουφονόων ἐρώτων ·
εἰδότι δʼ οὐδὲν ἕρπει ,
πρὶν πυρὶ θερμῷ πόδα τις προσαύσῃ .
σοφίᾳ γὰρ ἔκ του
κλεινὸν ἔπος πέφανται ,
τὸ κακὸν δοκεῖν ποτʼ ἐσθλὸν
τῷδʼ ἔμμεν ὅτῳ φρένας
θεὸς ἄγει πρὸς ἄταν ·
πράσσει δʼ ὀλίγιστον χρόνον ἐκτὸς ἄτας .

( 80 ) 28% ENG
( 207 ) 72% ENG - GRC

( 162 ) 78% ENG - GRC
( 47 ) 22% GRC

Sophocles' Ajax

Daniel Libatique /
  • Created on 2018-01-29 05:41:58
  • Translated by Daniel Libatique
  • Aligned by Daniel Libatique
First speech of Athena in Sophocles' Ajax.
Ἑλληνική Transliterate
English
urn:cts:greekLit:tlg0011.tlg003.1st1K-grc1

( 39 ) 38% GRC
( 65 ) 62% GRC - ENG

( 85 ) 66% GRC - ENG
( 44 ) 34% ENG

Athenazde 13b part 1

Kendra Hayes / Athenazde 13b
  • Created on 2018-01-29 13:04:29
  • Translated by kendra.hp
  • Aligned by Kendra Hayes
Ἑλληνική Transliterate
English

( 21 ) 23% GRC
( 69 ) 77% GRC - ENG

( 92 ) 88% GRC - ENG
( 13 ) 12% ENG

IG I3.104.1-10, AIO trans.

Katharine Shields /
  • Created on 2018-01-29 16:27:02
  • Modified on 2018-01-30 13:53:28
  • Aligned by Katharine Shields
Ἑλληνική Transliterate
English

( 5 ) 6% GRC
( 75 ) 94% GRC - ENG

( 93 ) 92% GRC - ENG
( 8 ) 8% ENG

Euclid, Elements, Selections.

jordan mcneill /
  • Created on 2018-03-19 05:43:36
  • Modified on 2018-03-20 14:21:01
  • Aligned by jordan mcneill
Ἑλληνική Transliterate
English
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 , μῆκος καὶ πλάτος μόνον ἔχει .



ἐπιφανείας δὲ πέρατα γραμμαί .



ἐπίπεδος ἐπιφάνειά ἐστιν , ἥτις ἐξ ἴσου ταῖς ἐφ᾽ ἑαυτῆς εὐθείαις κεῖται .



ἐπίπεδος δὲ γωνία ἐστὶν 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 γωνία .



ὅταν δὲ εὐθεῖα ἐπ᾽ εὐθεῖαν σταθεῖσα τὰς ἐφεξῆς γωνίας ἴσας ἀλλήλαις ποιῇ , ὀρθὴ ἑκατέρα τῶν ἴσων γωνιῶν ἐστι , καὶ ἐφεστηκυῖα εὐθεῖα κάθετος καλεῖται , ἐφ᾽ ἣν ἐφέστηκεν .



ἀμβλεῖα γωνία ἐστὶν μείζων ὀρθῆς .



ὀξεῖα δὲ ἐλάσσων ὀρθῆς .



ὅρος ἐστίν , τινός ἐστι πέρας .



σχῆμά ἐστι τὸ ὑπό τινος τινων ὅρων περιεχόμενον .



κύκλος ἐστὶ σχῆμα ἐπίπεδον ὑπὸ μιᾶς γραμμῆς περιεχόμενον 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 , 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 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 , ἰσόπλευρόν τέ ἐστι καὶ ὀρθογώνιον , ἑτερόμηκες δέ , ὀρθογώνιον μέν , οὐκ ἰσόπλευρον δέ , ῥόμβος δέ , ἰσόπλευρον μέν , οὐκ ὀρθογώνιον δέ , ῥομβοειδὲς δὲ τὸ τὰς ἀπεναντίον πλευράς τε καὶ γωνίας ἴσας ἀλλήλαις ἔχον , 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᾽ 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 δοθεῖσα εὐθεῖα πεπερασμένη ΑΒ . δεῖ δὴ ἐπὶ τῆς ΑΒ εὐθείας τρίγωνον ἰσόπλευρον συστήσασθαι .



κέντρῳ μὲν τῷ Α διαστήματι δὲ τῷ ΑΒ κύκλος γεγράφθω ΒΓΔ , καὶ πάλιν κέντρῳ μὲν τῷ Β διαστήματι δὲ τῷ ΒΑ κύκλος γεγράφθω ΑΓΕ , καὶ ἀπὸ τοῦ Γ σημείου , καθ᾽ 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 ΑΓ τῇ ΑΒ : πάλιν , ἐπεὶ τὸ Β σημεῖον κέντρον ἐστὶ τοῦ ΓΑΕ κύκλου , ἴση ἐστὶν ΒΓ τῇ ΒΑ . ἐδείχθη δὲ καὶ ΓΑ τῇ ΑΒ ἴση : ἑκατέρα ἄρα τῶν ΓΑ , ΓΒ τῇ ΑΒ ἐστὶν ἴση .



τὰ δὲ τῷ αὐτῷ ἴσα καὶ ἀλλήλοις ἐστὶν ἴσα : καὶ 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 .



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 .

( 748 ) 92% GRC
( 64 ) 8% GRC - ENG

( 101 ) 10% GRC - ENG
( 890 ) 90% ENG

Iliad XXII, 188-213

Chiara Palladino / Homer, Iliad, 21.1-53
  • Created on 2018-02-24 22:28:58
  • Modified on 2018-04-05 17:59:03
  • Translated by Samuel Butler
  • Aligned by Chiara Palladino
Ἑλληνική Transliterate
English
Ἕκτορα δʼ ἀσπερχὲς κλονέων ἔφεπʼ ὠκὺς Ἀχιλλεύς .
ὡς δʼ ὅτε νεβρὸν ὄρεσφι κύων ἐλάφοιο δίηται
ὄρσας ἐξ εὐνῆς διά τʼ ἄγκεα καὶ διὰ βήσσας ·
τὸν δʼ εἴ πέρ τε λάθῃσι καταπτήξας ὑπὸ θάμνῳ ,
ἀλλά τʼ ἀνιχνεύων θέει ἔμπεδον ὄφρά κεν εὕρῃ ·
ὣς Ἕκτωρ οὐ λῆθε ποδώκεα Πηλεΐωνα .
ὁσσάκι δʼ ὁρμήσειε πυλάων Δαρδανιάων
ἀντίον ἀΐξασθαι ἐϋδμήτους ὑπὸ πύργους ,
εἴ πως οἷ καθύπερθεν ἀλάλκοιεν βελέεσσι ,
τοσσάκι μιν προπάροιθεν ἀποστρέψασκε παραφθὰς
πρὸς πεδίον · αὐτὸς δὲ ποτὶ πτόλιος πέτετʼ αἰεί .
ὡς δʼ ἐν ὀνείρῳ οὐ δύναται φεύγοντα διώκειν ·
οὔτʼ ἄρʼ τὸν δύναται ὑποφεύγειν οὔθʼ διώκειν ·
ὣς τὸν οὐ δύνατο μάρψαι ποσίν , οὐδʼ ὃς ἀλύξαι .
πῶς δέ κεν Ἕκτωρ κῆρας ὑπεξέφυγεν θανάτοιο ,
εἰ μή οἱ πύματόν τε καὶ ὕστατον ἤντετʼ Ἀπόλλων
ἐγγύθεν , ὅς οἱ ἐπῶρσε μένος λαιψηρά τε γοῦνα ;
λαοῖσιν δʼ ἀνένευε καρήατι δῖος Ἀχιλλεύς ,
οὐδʼ ἔα ἱέμεναι ἐπὶ Ἕκτορι πικρὰ βέλεμνα ,
μή τις κῦδος ἄροιτο βαλών , δὲ δεύτερος ἔλθοι .
ἀλλʼ ὅτε δὴ τὸ τέταρτον ἐπὶ κρουνοὺς ἀφίκοντο ,
καὶ τότε δὴ χρύσεια πατὴρ ἐτίταινε τάλαντα ,
ἐν δʼ ἐτίθει δύο κῆρε τανηλεγέος θανάτοιο ,
τὴν μὲν Ἀχιλλῆος , τὴν δʼ Ἕκτορος ἱπποδάμοιο ,
ἕλκε δὲ μέσσα λαβών · ῥέπε δʼ Ἕκτορος αἴσιμον ἦμαρ ,
ᾤχετο δʼ εἰς Ἀΐδαο , λίπεν δέ Φοῖβος Ἀπόλλων .
Achilles was still in full pursuit of Hektor , as a hound chasing a fawn which he has started from its covert on the mountains , and hunts through glade and thicket . The fawn may try to elude him by crouching under cover of a bush , but he will scent her out and follow her up until he gets her - even so there was no escape for Hektor from the fleet son of Peleus . Whenever he made a set to get near the Dardanian gates and under the walls , that his people might help him by showering down weapons from above , Achilles would gain on him and head him back towards the plain , keeping himself always on the city side . As a man in a dream who fails to lay hands upon another whom he is pursuing - the one cannot escape nor the other overtake - even so neither could Achilles come up with Hektor , nor Hektor break away from Achilles ; nevertheless he might even yet have escaped death had not the time come when Apollo , who thus far had sustained his strength and nerved his running , was now no longer to stay by him . Achilles made signs to the Achaean host , and shook his head to show that no man was to aim a dart at Hektor , lest another might win the glory of having hit him and he might himself come in second . Then , at last , as they were nearing the fountains for the fourth time , the father of all balanced his golden scales and placed a doom in each of them , one for Achilles and the other for Hektor . As he held the scales by the middle , the doom of Hektor fell down deep into the house of Hades - and then Phoebus Apollo left him .

( 62 ) 28% GRC
( 163 ) 72% GRC - ENG

( 237 ) 73% GRC - ENG
( 86 ) 27% ENG

Euclid, Elements, 1.definitions (test1)

Christopher Blackwell / Euclid
  • Created on 2018-03-15 17:03:44
  • Modified on 2018-03-15 17:23:58
  • Translated by Heath
  • Aligned by Christopher Blackwell
Ἑλληνική Transliterate
English
urn:cts:greekLit:tlg1799.tlg001.heiberg:1.def
urn:cts:greekLit:tlg1799.tlg001.heath:1.def
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 , μῆκος καὶ πλάτος μόνον ἔχει .
ἐπιφανείας δὲ πέρατα γραμμαί .
ἐπίπεδος ἐπιφάνειά ἐστιν , ἥτις ἐξ ἴσου ταῖς ἐφ᾽ ἑαυτῆς εὐθείαις κεῖται .
ἐπίπεδος δὲ γωνία ἐστὶν 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 γωνία .
ὅταν δὲ εὐθεῖα ἐπ᾽ εὐθεῖαν σταθεῖσα τὰς ἐφεξῆς γωνίας ἴσας ἀλλήλαις ποιῇ , ὀρθὴ ἑκατέρα τῶν ἴσων γωνιῶν ἐστι , καὶ ἐφεστηκυῖα εὐθεῖα κάθετος καλεῖται , ἐφ᾽ ἣν ἐφέστηκεν .
ἀμβλεῖα γωνία ἐστὶν μείζων ὀρθῆς .
ὀξεῖα δὲ ἐλάσσων ὀρθῆς .
ὅρος ἐστίν , τινός ἐστι πέρας .
σχῆμά ἐστι τὸ ὑπό τινος τινων ὅρων περιεχόμενον .
κύκλος ἐστὶ σχῆμα ἐπίπεδον ὑπὸ μιᾶς γραμμῆς περιεχόμενον 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 , 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 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 , ἰσόπλευρόν τέ ἐστι καὶ ὀρθογώνιον , ἑτερόμηκες δέ , ὀρθογώνιον μέν , οὐκ ἰσόπλευρον δέ , ῥόμβος δέ , ἰσόπλευρον μέν , οὐκ ὀρθογώνιον δέ , ῥομβοειδὲς δὲ τὸ τὰς ἀπεναντίον πλευράς τε καὶ γωνίας ἴσας ἀλλήλαις ἔχον , 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 .
A point is that which has no part .
A line is breadthless length .
The extremities of a line are points .
A straight line is a line which lies evenly with the points on itself .
A surface is that which has length and breadth only .
The extremities of a surface are lines .
A plane surface is a surface which lies evenly with the straight lines on itself .
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 .
And when the lines containing the angle are straight , the angle is called rectilineal .
urn : cts : greekLit : tlg1799 . tlg001 . heath : 1 . def . 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 .
An obtuse angle is an angle greater than a right angle .
An acute angle is an angle less than a right angle .
A boundary is that which is an extremity of anything .
A figure is that which is contained by any boundary or boundaries .
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 ;
And the point is called the centre of the circle .
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 .
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 .
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 .
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 .
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 .
urn : cts : greekLit : tlg1799 . tlg001 . heath : 1 . def . 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 .
urn : cts : greekLit : tlg1799 . tlg001 . heath : 1 . def . 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 .

( 381 ) 86% GRC
( 62 ) 14% GRC - ENG

( 83 ) 14% GRC - ENG
( 504 ) 86% ENG

Euclid, Elements, 1.definitions (test2)

Christopher Blackwell / Euclid
  • Created on 2018-03-15 17:13:14
  • Modified on 2018-03-19 13:52:53
  • Translated by Heath
  • Aligned by Christopher Blackwell
Euclid. Elements. Book 1. Defintions.
Ἑλληνική Transliterate
English
urn:cts:greekLit:tlg1799.tlg001.heiberg:1.def
urn:cts:greekLit:tlg1799.tlg001.heath:1.def
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 , μῆκος καὶ πλάτος μόνον ἔχει .

ἐπιφανείας δὲ πέρατα γραμμαί .

ἐπίπεδος ἐπιφάνειά ἐστιν , ἥτις ἐξ ἴσου ταῖς ἐφ᾽ ἑαυτῆς εὐθείαις κεῖται .

ἐπίπεδος δὲ γωνία ἐστὶν 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 γωνία .

ὅταν δὲ εὐθεῖα ἐπ᾽ εὐθεῖαν σταθεῖσα τὰς ἐφεξῆς γωνίας ἴσας ἀλλήλαις ποιῇ , ὀρθὴ ἑκατέρα τῶν ἴσων γωνιῶν ἐστι , καὶ ἐφεστηκυῖα εὐθεῖα κάθετος καλεῖται , ἐφ᾽ ἣν ἐφέστηκεν .

ἀμβλεῖα γωνία ἐστὶν μείζων ὀρθῆς .

ὀξεῖα δὲ ἐλάσσων ὀρθῆς .

ὅρος ἐστίν ,