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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

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