A history of Greek mathematics Vol.II from Aristarchus to Diophantus by Heath, Thomas Little, Sir, 1921
MACEDONIA is GREECE and will always be GREECE- (if they are desperate to steal a name, Monkeydonkeys suits them just fine) ΚΑΤΩ Η ΣΥΓΚΥΒΕΡΝΗΣΗ ΤΩΝ ΠΡΟΔΟΤΩΝ!!! ΦΕΚ,ΚΚΕ,ΚΝΕ,ΚΟΜΜΟΥΝΙΣΜΟΣ,ΣΥΡΙΖΑ,ΠΑΣΟΚ,ΝΕΑ ΔΗΜΟΚΡΑΤΙΑ,ΕΓΚΛΗΜΑΤΑ,ΔΑΠ-ΝΔΦΚ, MACEDONIA,ΣΥΜΜΟΡΙΤΟΠΟΛΕΜΟΣ,ΠΡΟΣΦΟΡΕΣ,ΥΠΟΥΡΓΕΙΟ,ΕΝΟΠΛΕΣ ΔΥΝΑΜΕΙΣ,ΣΤΡΑΤΟΣ, ΑΕΡΟΠΟΡΙΑ,ΑΣΤΥΝΟΜΙΑ,ΔΗΜΑΡΧΕΙΟ,ΝΟΜΑΡΧΙΑ,ΠΑΝΕΠΙΣΤΗΜΙΟ,ΛΟΓΟΤΕΧΝΙΑ,ΔΗΜΟΣ,LIFO,ΛΑΡΙΣΑ, ΠΕΡΙΦΕΡΕΙΑ,ΕΚΚΛΗΣΙΑ,ΟΝΝΕΔ,ΜΟΝΗ,ΠΑΤΡΙΑΡΧΕΙΟ,ΜΕΣΗ ΕΚΠΑΙΔΕΥΣΗ,ΙΑΤΡΙΚΗ,ΟΛΜΕ,ΑΕΚ,ΠΑΟΚ,ΦΙΛΟΛΟΓΙΚΑ,ΝΟΜΟΘΕΣΙΑ,ΔΙΚΗΓΟΡΙΚΟΣ,ΕΠΙΠΛΟ, ΣΥΜΒΟΛΑΙΟΓΡΑΦΙΚΟΣ,ΕΛΛΗΝΙΚΑ,ΜΑΘΗΜΑΤΙΚΑ,ΝΕΟΛΑΙΑ,ΟΙΚΟΝΟΜΙΚΑ,ΙΣΤΟΡΙΑ,ΙΣΤΟΡΙΚΑ,ΑΥΓΗ,ΤΑ ΝΕΑ,ΕΘΝΟΣ,ΣΟΣΙΑΛΙΣΜΟΣ,LEFT,ΕΦΗΜΕΡΙΔΑ,ΚΟΚΚΙΝΟ,ATHENS VOICE,ΧΡΗΜΑ,ΟΙΚΟΝΟΜΙΑ,ΕΝΕΡΓΕΙΑ, ΡΑΤΣΙΣΜΟΣ,ΠΡΟΣΦΥΓΕΣ,GREECE,ΚΟΣΜΟΣ,ΜΑΓΕΙΡΙΚΗ,ΣΥΝΤΑΓΕΣ,ΕΛΛΗΝΙΣΜΟΣ,ΕΛΛΑΔΑ, ΕΜΦΥΛΙΟΣ,ΤΗΛΕΟΡΑΣΗ,ΕΓΚΥΚΛΙΟΣ,ΡΑΔΙΟΦΩΝΟ,ΓΥΜΝΑΣΤΙΚΗ,ΑΓΡΟΤΙΚΗ,ΟΛΥΜΠΙΑΚΟΣ, ΜΥΤΙΛΗΝΗ,ΧΙΟΣ,ΣΑΜΟΣ,ΠΑΤΡΙΔΑ,ΒΙΒΛΙΟ,ΕΡΕΥΝΑ,ΠΟΛΙΤΙΚΗ,ΚΥΝΗΓΕΤΙΚΑ,ΚΥΝΗΓΙ,ΘΡΙΛΕΡ, ΠΕΡΙΟΔΙΚΟ,ΤΕΥΧΟΣ,ΜΥΘΙΣΤΟΡΗΜΑ,ΑΔΩΝΙΣ ΓΕΩΡΓΙΑΔΗΣ,GEORGIADIS,ΦΑΝΤΑΣΤΙΚΕΣ ΙΣΤΟΡΙΕΣ, ΑΣΤΥΝΟΜΙΚΑ,ΦΙΛΟΣΟΦΙΚΗ,ΦΙΛΟΣΟΦΙΚΑ,ΙΚΕΑ,ΜΑΚΕΔΟΝΙΑ,ΑΤΤΙΚΗ,ΘΡΑΚΗ,ΘΕΣΣΑΛΟΝΙΚΗ,ΠΑΤΡΑ, ΙΟΝΙΟ,ΚΕΡΚΥΡΑ,ΚΩΣ,ΡΟΔΟΣ,ΚΑΒΑΛΑ,ΜΟΔΑ,ΔΡΑΜΑ,ΣΕΡΡΕΣ,ΕΥΡΥΤΑΝΙΑ,ΠΑΡΓΑ,ΚΕΦΑΛΟΝΙΑ, ΙΩΑΝΝΙΝΑ,ΛΕΥΚΑΔΑ,ΣΠΑΡΤΗ,ΠΑΞΟΙ
MACEDONIA is GREECE and will always be GREECE- (if they are desperate to steal a name, Monkeydonkeys suits them just fine)
ΚΑΤΩ Η ΣΥΓΚΥΒΕΡΝΗΣΗ ΤΩΝ ΠΡΟΔΟΤΩΝ!!!
ΦΕΚ,ΚΚΕ,ΚΝΕ,ΚΟΜΜΟΥΝΙΣΜΟΣ,ΣΥΡΙΖΑ,ΠΑΣΟΚ,ΝΕΑ ΔΗΜΟΚΡΑΤΙΑ,ΕΓΚΛΗΜΑΤΑ,ΔΑΠ-ΝΔΦΚ, MACEDONIA,ΣΥΜΜΟΡΙΤΟΠΟΛΕΜΟΣ,ΠΡΟΣΦΟΡΕΣ,ΥΠΟΥΡΓΕΙΟ,ΕΝΟΠΛΕΣ ΔΥΝΑΜΕΙΣ,ΣΤΡΑΤΟΣ, ΑΕΡΟΠΟΡΙΑ,ΑΣΤΥΝΟΜΙΑ,ΔΗΜΑΡΧΕΙΟ,ΝΟΜΑΡΧΙΑ,ΠΑΝΕΠΙΣΤΗΜΙΟ,ΛΟΓΟΤΕΧΝΙΑ,ΔΗΜΟΣ,LIFO,ΛΑΡΙΣΑ, ΠΕΡΙΦΕΡΕΙΑ,ΕΚΚΛΗΣΙΑ,ΟΝΝΕΔ,ΜΟΝΗ,ΠΑΤΡΙΑΡΧΕΙΟ,ΜΕΣΗ ΕΚΠΑΙΔΕΥΣΗ,ΙΑΤΡΙΚΗ,ΟΛΜΕ,ΑΕΚ,ΠΑΟΚ,ΦΙΛΟΛΟΓΙΚΑ,ΝΟΜΟΘΕΣΙΑ,ΔΙΚΗΓΟΡΙΚΟΣ,ΕΠΙΠΛΟ, ΣΥΜΒΟΛΑΙΟΓΡΑΦΙΚΟΣ,ΕΛΛΗΝΙΚΑ,ΜΑΘΗΜΑΤΙΚΑ,ΝΕΟΛΑΙΑ,ΟΙΚΟΝΟΜΙΚΑ,ΙΣΤΟΡΙΑ,ΙΣΤΟΡΙΚΑ,ΑΥΓΗ,ΤΑ ΝΕΑ,ΕΘΝΟΣ,ΣΟΣΙΑΛΙΣΜΟΣ,LEFT,ΕΦΗΜΕΡΙΔΑ,ΚΟΚΚΙΝΟ,ATHENS VOICE,ΧΡΗΜΑ,ΟΙΚΟΝΟΜΙΑ,ΕΝΕΡΓΕΙΑ, ΡΑΤΣΙΣΜΟΣ,ΠΡΟΣΦΥΓΕΣ,GREECE,ΚΟΣΜΟΣ,ΜΑΓΕΙΡΙΚΗ,ΣΥΝΤΑΓΕΣ,ΕΛΛΗΝΙΣΜΟΣ,ΕΛΛΑΔΑ, ΕΜΦΥΛΙΟΣ,ΤΗΛΕΟΡΑΣΗ,ΕΓΚΥΚΛΙΟΣ,ΡΑΔΙΟΦΩΝΟ,ΓΥΜΝΑΣΤΙΚΗ,ΑΓΡΟΤΙΚΗ,ΟΛΥΜΠΙΑΚΟΣ, ΜΥΤΙΛΗΝΗ,ΧΙΟΣ,ΣΑΜΟΣ,ΠΑΤΡΙΔΑ,ΒΙΒΛΙΟ,ΕΡΕΥΝΑ,ΠΟΛΙΤΙΚΗ,ΚΥΝΗΓΕΤΙΚΑ,ΚΥΝΗΓΙ,ΘΡΙΛΕΡ, ΠΕΡΙΟΔΙΚΟ,ΤΕΥΧΟΣ,ΜΥΘΙΣΤΟΡΗΜΑ,ΑΔΩΝΙΣ ΓΕΩΡΓΙΑΔΗΣ,GEORGIADIS,ΦΑΝΤΑΣΤΙΚΕΣ ΙΣΤΟΡΙΕΣ, ΑΣΤΥΝΟΜΙΚΑ,ΦΙΛΟΣΟΦΙΚΗ,ΦΙΛΟΣΟΦΙΚΑ,ΙΚΕΑ,ΜΑΚΕΔΟΝΙΑ,ΑΤΤΙΚΗ,ΘΡΑΚΗ,ΘΕΣΣΑΛΟΝΙΚΗ,ΠΑΤΡΑ, ΙΟΝΙΟ,ΚΕΡΚΥΡΑ,ΚΩΣ,ΡΟΔΟΣ,ΚΑΒΑΛΑ,ΜΟΔΑ,ΔΡΑΜΑ,ΣΕΡΡΕΣ,ΕΥΡΥΤΑΝΙΑ,ΠΑΡΓΑ,ΚΕΦΑΛΟΝΙΑ, ΙΩΑΝΝΙΝΑ,ΛΕΥΚΑΔΑ,ΣΠΑΡΤΗ,ΠΑΞΟΙ
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THE TEXT OF THE CONICS 127<br />
The edition <strong>of</strong> Eu<strong>to</strong>cius suffered interpolations which were<br />
probably made in the ninth century when, under the auspices<br />
<strong>of</strong> Leon, mathematical studies were revived at Constantinople ;<br />
for it was at that date that the uncial manuscripts were<br />
written, <strong>from</strong> which our best manuscripts, V (= Cod. Vat. gr.<br />
206 <strong>of</strong> the twelfth <strong>to</strong> thirteenth century) for the Conies, and<br />
W (= Cod. Vat. gr. 204 <strong>of</strong> the tenth century) for Eu<strong>to</strong>cius,<br />
were copied.<br />
Only the first four Books survive in <strong>Greek</strong> ; the eighth<br />
Book is al<strong>to</strong>gether lost, but the three Books V-V<strong>II</strong> exist in<br />
Arabic. It was Ahmad and al-Hasan, two sons <strong>of</strong> Muh. b.<br />
Musa b. Shakir, who first contemplated translating the Conies<br />
in<strong>to</strong> Arabic. They were at first deterred <strong>by</strong> the bad state <strong>of</strong><br />
their manuscripts ; but afterwards Ahmad obtained in Syria<br />
a copy <strong>of</strong> Eu<strong>to</strong>cius's edition <strong>of</strong> Books I-IV and had them<br />
translated <strong>by</strong> Hilal b. Abi Hilal al-Himsi (died 883/4).<br />
Books V-V<strong>II</strong> were translated, also for Ahmad, <strong>by</strong> Thabit<br />
b. Qurra ( 826-901) <strong>from</strong> another manuscript. Naslraddm's<br />
recension <strong>of</strong> this translation <strong>of</strong> the seven Books, made in 1248,<br />
is represented <strong>by</strong> two copies in the Bodleian, one <strong>of</strong> the year<br />
1301 (No. 943) and the other <strong>of</strong> 1626 containing Books V-V<strong>II</strong><br />
only (No. 885).<br />
A Latin translation <strong>of</strong> Books I-IV was published <strong>by</strong><br />
Johannes Baptista Memus at Venice in 1537 ; but the first<br />
important edition was the translation <strong>by</strong> Commandinus<br />
(Bologna, 1566), which included the lemmas <strong>of</strong> Pappus and<br />
the commentary <strong>of</strong> Eu<strong>to</strong>cius, and was the first attempt <strong>to</strong><br />
make the book intelligible <strong>by</strong> means <strong>of</strong> explana<strong>to</strong>ry notes.<br />
For the <strong>Greek</strong> text Commandinus used Cod. Marcianus 518<br />
and perhaps also Vat. gr. 205, both <strong>of</strong> which were copies <strong>of</strong> V,<br />
but not V itself.<br />
The first published version <strong>of</strong> Books V-V<strong>II</strong> was a Latin<br />
translation <strong>by</strong> Abraham Echellensis and Giacomo Alfonso<br />
Borelli (Florence, 1661) <strong>of</strong> a reproduction <strong>of</strong> the Books written<br />
in 983 <strong>by</strong> Abu 1 Fath al-Isfahanl.<br />
The editio princeps <strong>of</strong> the <strong>Greek</strong> text is the monumental<br />
work <strong>of</strong> Halley (Oxford, 1710). The original intention was<br />
that Gregory should edit the four Books extant in <strong>Greek</strong>, with<br />
Eu<strong>to</strong>cius's commentary and a Latin translation, and that<br />
Halley should translate Books V-V<strong>II</strong> <strong>from</strong> the Arabic in<strong>to</strong><br />
128 APOLLONIUS OF PERGA<br />
Gregory, however, died while the work was proceeding,<br />
Latin.<br />
and Halley then under<strong>to</strong>ok responsibility for the whole. The<br />
<strong>Greek</strong> manuscripts used were two, one belonging <strong>to</strong> Savile<br />
and the other lent <strong>by</strong> D. Baynard ;<br />
their whereabouts cannot<br />
apparently now be traced, but they were both copies <strong>of</strong> Paris,<br />
gr. 2356, which was copied in the sixteenth century <strong>from</strong> Paris,<br />
gr. 2357 <strong>of</strong> the sixteenth century, itself a copy <strong>of</strong> V. For the<br />
three Books in Arabic Halley used the Bodleian MS. 885, but<br />
also consulted (a) a compendium <strong>of</strong> the three Books <strong>by</strong> 'Abdelmelik<br />
al-Shirazi (twelfth century), also in the Bodleian (913),<br />
(b) Borelli's edition, and (c) Bodl. 943 above mentioned, <strong>by</strong> means<br />
<strong>of</strong> which he revised and corrected his translation when completed.<br />
Halley's edition is still, so far as I know, the only<br />
available source for Books V-V<strong>II</strong>, except for the beginning <strong>of</strong><br />
Book V (up <strong>to</strong> Prop. 7) which was edited <strong>by</strong> L. Nix (Leipzig,<br />
1889).<br />
The <strong>Greek</strong> text <strong>of</strong> Books I-IV is now available, with the<br />
commentaries <strong>of</strong> Eu<strong>to</strong>cius, the fragments <strong>of</strong> Apollonius, &c,<br />
in the definitive edition <strong>of</strong> Heiberg (Teubner, 1891-3).<br />
Apollonius's own account <strong>of</strong> the Conies.<br />
A general account <strong>of</strong> the contents <strong>of</strong> the great work which,<br />
according <strong>to</strong> Geminus, earned for him the title <strong>of</strong> the ' great<br />
geometer' cannot be better given than in the words <strong>of</strong> the<br />
writer himself. The prefaces <strong>to</strong> the several Books contain<br />
interesting his<strong>to</strong>rical details, and, like the prefaces <strong>of</strong> Archimedes,<br />
state quite plainly and simply in what way the<br />
treatise differs <strong>from</strong> those <strong>of</strong> his predecessors, and how much<br />
in it is claimed as original. The strictures <strong>of</strong> Pappus (or<br />
more probably his interpola<strong>to</strong>r), who accuses him <strong>of</strong> being a<br />
braggart and unfair <strong>to</strong>wards his predecessors, are evidently<br />
unfounded. The prefaces are quoted <strong>by</strong> v. Wilamowitz-<br />
Moellendorff as specimens <strong>of</strong> admirable <strong>Greek</strong>, showing how<br />
perfect the style <strong>of</strong> the great mathematicians could be<br />
when they were free <strong>from</strong> the trammels <strong>of</strong> mathematical<br />
terminology.<br />
Book I. General Preface.<br />
Apollonius <strong>to</strong> Eudemus, greeting.<br />
If you are in good health and things are in other respects<br />
as you wish, it is well ; with me <strong>to</strong>o things are moderately