Geminus wrote about the Egyptian calendar during the 1st century B.C. in a work that is known by the title Elements of Astronomy. He comments about the nature of the Egyptian calendar, how it differed from Greek practices, and how it moved with respect to the seasons.
This work is significant with respect to claims made by moderns that Christian holy days and practices were taken from particular dates in use by ancient pagan Egypt. Geminus gives us an example in the 1st
century B.C. of how very unlikely direct influence from any Egyptian civil calendar celebration would have been on the primary holy days of Christianity.
About Geminus
We know almost nothing about Geminus himself. He is often called Geminus of Rhodes though we do not know if that was his birthplace. He at least did some of his work there according to the text his Elements of Astronomy. We can say at least that he was a mathematician and astronomer. We know of three works penned by him. Through citations and mentions in other authors we know about a mathematical work by Geminus and about a commentary he wrote on Posidonius' writing On Meteorology.
About Elementa Astronomiae
His ΕΙΣΑΓΩΓΗ ΕΙΣ ΤΑ ΦΑΙΝΟΜΕΝΑ Introduction to the Phenomena, also called Elements of Astronomy survives to us in manuscripts that come mainly from the 15th century.
About the text and translation presented here
The Greek text here come from the critical edition of Karl Manitius in the 1898 Teubner edition.
Geminus, Eisagōgē eis ta phainomena, Ed. and Tr. Karl Manitius, Bibliotheca scriptorum Graecorum et Romanorum Teubneriana, 1898
This edition is available on Google Books at
https://books.google.com/books?id=M3I7AQAAMAAJ
and on Google Play at
https://play.google.com/books/reader?id=M3I7AQAAMAAJ&pg=GBS.PA106&hl=en
The text was scanned through Google Play and then visually corrected. Critical notes and line numbers are not included in this transcription. Greek numerals did not scan well. These have been corrected according to the printed text. However, the letter koppa used to indicate the number 90 is signified by an older, non-Byzantine form ϙ. I was unable to find a Byzantine UTF glyph.
The translation is an edited and corrected machine translation through Google Translate based on the Greek text and on Manitius’ German translation.
Any corrections or suggestions are more than welcome.
Elementa Astronomiae 8.16-31
16 Οἱ μὲν γὰρ Αἰγύπτιοι τὴν ἐναντίαν διάληψιν καὶ πρόθεσιν ἐσχήκασι τοῖς Ἕλλησιν. οὔτε γὰρ τοὺς ἐνιαυτοὺς ἄγουσι καθ' ἥλιον, οὔτε τοὺς μῆνας καὶ τὰς ἡμέρας κατὰ σελήνην, ἀλλ᾿ ἰδίᾳ τινὶ ὑποστάσει κεχρημένοι εἰσί. |
16 The Egyptians had the exact opposite conception and intention to the Greeks. They neither counted the years according to the sun, nor the months and days according to the moon, but followed a very peculiar principle. |
17 βούλονται γὰρ τὰς θυσίας τοῖς θεοῖς μὴ κατὰ τὸν αὐτὸν καιρὸν τοῦ ἐνιαυτοῦ γίνεσθαι, ἀλλὰ διὰ πασῶν τῶν τοῦ ἐνιαυτοῦ ὡρῶν διελθεῖν καὶ γίνεσθαι τὴν θερινὴν ἑορτὴν καὶ χειμερινὴν καὶ τὴν φθινοπωρινὴν καὶ ἐαρινήν. |
17 They wanted that the sacrifices should not be offered at the same time of the year, but should run through all the seasons, i.e. the summer festival should also be a winter festival and the autumn festival a spring festival. |
18 ἄγουσι γὰρ τὸν ἐνιαυτὸν ἡμερῶν τξε'· ιβ' γὰρ μῆνας ἄγουσι τριακονθημέρους καὶ πέντε ἐπαγομένας· τὸ δὲ δον οὐκ ἐπάγουσι διὰ τὴν προειρημένην αἰτίαν, ἵνα αὐτοῖς ἵνα αὐτοῖς ἀναποδίζωνται αἱ ἑορταί. |
18 They reckon the year to be 365 days, for they have 12 months of 30 days and 5 additional days. They do not take the quarter day into account for the reason stated above, so that their festivals may be counted backwards. |
19 ἐν γὰρ τοῖς τέσσαρσιν ἔτεσι μιᾷ ἡμέρᾳ ὑστεροῦσι παρὰ τὸν ἥλιον, ἐν δὲ τοῖς μ' ἔτεσι δέκα ἡμέραις ὑστερήσουσι παρὰ τὸν τοῦ ἡλίου ἐνιαυτόν, ὥςτε καὶ τοσαύταις ἡμέραις ἀναποδίσουσιν αἱ ἑορταὶ πρὸς τὸ μὴ γίνεσθαι κατὰ τὰς αὐτὰς ὥρας τοῦ ἐνιαυτοῦ. ἐν δὲ τοῖς ρκ' ἔτεσι μηνιαῖον ἔσται τὸ παράλλαγμα καὶ πρὸς τὸν τοῦ ἡλίου ἐνιαυτὸν καὶ πρὸς τὰς κατὰ τὸ ἔτος ὥρας. |
19 In 4 years they will be one day 19 behind the sun, but in 40 years they will be 10 days behind the solar year, so that their festivals will also be delayed by that many days, in accordance with the intention that they should not take place in the same seasons. Thus, over 120 years the difference with the solar year, i.e. also with the seasons, will be a whole month. |
20 Δι᾿ ἣν αἰτίαν καὶ τὸ περιφερόμενον ἁμάρτημα παρὰ τοῖς Ἕλλησιν ἐκ πολλῶν χρόνων παραδοχῆς ἠξιωμένον μέχρι τῶν καθ᾿ ἡμᾶς χρόνων πεπίστευται. ὑπολαμβάνουσι γὰρ οἱ πλεῖστοι τῶν Ἑλλήνων ἅμα τοῖς Ισίοις κατ' Αίγυπτίους καὶ κατ᾿ Εὔδοξον εἶναι χειμερινὰς τροπάς, ὅπερ ἐστὶ παντάπασι ψεῦδος· μηνὶ γὰρ ὅλῳ παραλλάσσει τὰ Ἴσια πρὸς τὰς χειμερινὰς τροπάς. |
20 (In this very gradual increase) we can also see the reason why a common error, sanctioned by a long-standing tradition, has been accepted in good faith by the Greeks up to our times. The overwhelming majority of Greeks are of the opinion that the winter solstice takes place at the same time as the Isis festival, both according to the Egyptian calendar and according to (the calendar of) Eudoxus. But this is quite wrong, because the Isis festival differs from the winter solstice by a whole month. |
21 ἐρρύη δὲ τὸ ἁμάρτημα ἀπὸ τῆς προειρημένης αἰτίας. πρὸ γὰρ ρκ' ἐτῶν συνέπεσε κατ᾽ αὐτὰς τὰς χειμερινὰς τροπὰς ἄγεσθαι τὰ Ἴσια. ἐν ἔτεσι δὲ τέσσαρσι μιᾶς ἡμέρας ἐγένετο παράλλαγμα. τοῦτο οὖν οὐκ αἰσθητὴν ἔσχε παραλλαγὴν πρὸς τὰς κατ᾽ ἔτος ὥρας. ἐν ἔτεσι δὲ μ' ἡμερῶν δέκα ἐγένετο παράλλαγμα. οὐδ᾽ οὕτως αἰσθητὴν εἶναι συμβαίνει τὴν παραλλαγήν. |
21 The error crept in for the reason given above. 120 years ago, it was the case that the Isis festival was celebrated at the winter solstice; but after just four years, the difference was one day. This was not, however, a noticeable difference with the season. After 40 years, the difference was 10 days. But even then, the difference would not be particularly noticeable. |
22 νυνὶ μέντοι γε μηνιαίας γινομένης παραλλαγῆς ἐν ρκ' ἔτεσιν, ὑπερβολὴν οὐκ ἀπολείπουσιν ἀγνοίας οἱ διαλαμβάνοντες ἐν τοῖς Ἰσίοις κατʼ Αἰγυπτίους καὶ κατ᾽ Εὔδοξον τὰς χειμερινὰς τροπὰς εἶναι. μιᾷ μὲν γὰρ ἡμέρᾳ ἢ δυσὶ διενεχθῆναι ἐνδεχόμενόν ἐστι, μηνιαῖον δὲ παράλλαγμα ἀδύνατόν ἐστι λαθεῖν. |
22 But now, when after 120 years the difference is a whole month, the assumption that the winter solstice takes place on the Isis festival according to both the Egyptian calendar and the calendar of Eudoxus leaves nothing to be desired in terms of ignorance. A difference of one day, or at most two days, is acceptable, but a difference of one month cannot possibly go unnoticed. |
23 καὶ γὰρ τὰ μεγέθη τῶν ἡμερῶν ἐλέγχειν δύναται μεγάλην ἔχοντα παραλλαγὴν πρὸς τὰς χειμερινὰς τροπάς, καὶ αἱ τῶν ὡρολογίων καταγραφαὶ ἐκδήλους ποιοῦσι τὰς κατὰ ἀλήθειαν γινομένας τροπάς, καὶ μάλιστα παρ' Αἰγυπτίοις ἐν παρατηρήσει γενομένοις. |
23 The length of the days, can serve as a guide, which, compared with the time of the winter solstice, shows a great difference; the hour dials of the sundials also make the actual occurrence of the solstice clearly noticeable, especially among the Egyptians, who were such good observers. |
24 ὅθεν τὰ Ἴσια πρότερον μὲν ἤγετο κατά τὰς χειμερινὰς τροπάς, καὶ πρότερον δ᾽ ἔτι κατὰ τὰς θερινὰς τροπάς, ὡς καὶ Ἐρατοσθένης ἐν τῷ περὶ τῆς ὀκταετηρίδος ὑπομνήματι μνημονεύει, καὶ ἀχθήσεται πάλιν κατὰ φθινόπωρον καὶ κατὰ τὰς θερινὰς τροπὰς καὶ κατὰ τὸ ἔαρ καὶ πάλιν κατὰ τὰς χειμερινὰς τροπάς. ἐν ἔτεσι γὰρ αυξ' ἅπασαν ἑορτὴν διελθεῖν δεῖ διὰ πασῶν τῶν τοῦ ἐνιαυτοῦ ὡρῶν καὶ πάλιν ἀποκατασταθῆναι ἐπὶ τὸν αὐτὸν καιρὸν τοῦ ἔτους. |
24 So the Isis festival once fell on the winter solstice, and even earlier on the summer solstice, as Eratosthenes also mentions in his treatise on the eight-year period, and will in future be celebrated in autumn, at the summer solstice, in spring, and then again at the winter solstice. For in 1460 years every festival must pass through all the seasons and return again at the same time of the year. |
25 Οἱ μὲν οὖν Αἰγύπτιοι κατὰ τὴν ἰδίαν ὑπόστασιν κεκρατήκασι τοῦ προκειμένου τέλους, οἱ δὲ Ἕλληνες τὴν ἐναντίαν γνώμην ἔχοντες τοὺς μὲν ἐνιαυτοὺς καθ᾿ ἥλιον ἄγουσι, τοὺς δὲ μῆνας καὶ τὰς ἡμέρας κατὰ σελήνην. |
25 The Egyptians therefore set about solving the problem we are now dealing with according to this peculiar principle, while the Greeks, following the opposite view, reckoned the years according to the sun, but the months and days according to the moon. |
26 οἱ μὲν οὖν ἀρχαῖοι τοὺς μῆνας τριακονθημέρους ἦγον, τοὺς δὲ ἐμβολίμους παρʼ ἐνιαυτόν. ταχέως δ᾽ἐπὶ τοῦ φαινομένου ἐλεγχομένης τῆς ἀληθείας διὰ τὸ τὰς ἡμέρας καὶ τοὺς μῆνας μὴ συμφωνεῖν τῇ σελήνῃ, τοὺς δὲ ἐνιαυτοὺς μὴ στοιχεῖν τῷ ἡλίῳ, ὅθεν ἐζήτουν περίοδον, ἥτις κατὰ μὲν τοὺς ἐνιαυτοὺς τῷ ἡλίῳ συμφωνήσει , κατὰ δὲ τοὺς μῆνας καὶ τὰς ἡμέρας τῇ σελήνῃ, περιέχει δὲ ὁ τῆς περιόδου χρόνος ὅλους μῆνας καὶ ὅλας ἡμέρας καὶ ὅλους ἐνιαυτούς. |
26 As for the ancients, they had months consisting of 30 days each, and added the intercalary months one year after the other. But because the correctness of this procedure was soon called into question by the celestial phenomena, in that the days and months did not correspond with the moon and the years did not progress with the sun, they sought a period which should correspond with the sun as regards the years, and with the moon as regards the months and days, and which should contain whole months, whole days and whole years. |
27 πρώτην δὲ συνεστήσαντο τὴν περίοδον τῆς ὀκταετηρίδος, ἥτις περιέχει μὲν μῆνας ϙθ', ἐν οἷς ἐμβολίμους τρεῖς, ἡμέρας δὲ βϡκβ', ἔτη δὲ ὀκτώ. συνεστήσαντο δὲ τὴν ὀκταετηρίδα τὸν τρόπον τοῦτον. |
27 The first period which they established was the eight-year period; it comprises 99 months, including three intercalary months, or 2922 days, that is, eight years. They arrived at the establishment of this period in the following manner. |
28 ἐπεὶ γὰρ ὁ καθ ' ἥλιον ἐνιαυτὸς ἡμερῶν ἐστι τξε' δον, ὁ δὲ κατὰ σελήνην ἐνιαυτός ἐστιν ἡμερῶν τνδ', ἔλαβον τὴν ὑπεροχήν, ἣν ὑπερέχει ὁ καθ' ἥλιον ἐνιαυτὸς τοῦ κατὰ σελήνην. εἰσὶ δὲ ἡμέραι ια' δον. |
28 Since the solar year has 365 ¼ days and the lunar year has only 354 days, they took the surplus of the solar year over the lunar year, which is 11 1/4 days. |
29 ἐὰν ἄρα κατὰ σελήνην ἄγωμεν τοὺς μῆνας ἐν τῷ ἐνιαυτῷ, ὑστερήσομεν ἡμέρας παρὰ τὸν τοῦ ἡλίου ἐνιαυτὸν ια΄ δον. ἐζήτησαν οὖν, ποσάκις αὗται αἱ ἡμέραι πολυπλασιασθεῖσαι ἀποτελοῦσιν ὅλας ἡμέρας καὶ ὅλους μῆνας. ὀκτάκις δὲ πολυπλασιασθεῖσαι ἀποτελοῦσιν ὅλας ἡμέρας καὶ ὅλους μῆνας, ἤγουν ἡμέρας μὲν ϙʹ, μῆνας δὲ τρεῖς. |
29 If we therefore reckon the months in the year according to the lunar year, we shall be 11 1/4 days behind the solar year. They then sought the number by which this number of days must be multiplied in order to obtain whole days and whole months. This result is obtained by multiplying by eight: it is 90 days or three months. |
30 ἐπεὶ οὖν ἐν τῷ ἐνιαυτῷ παρὰ τὸν ἥλιον ὑστεροῦμεν ἡμέρας ια' δον, φανερὸν ὅτι ἐν τοῖς ὀκτὼ ἔτεσιν ὑστερήσομεν παρὰ τὸν ἥλιον ἡμέρας ϙ', ὅπερ εἰσὶ μῆνες τρεῖς. |
30 Since we are 114 days behind in a solar year, it is clear that in eight years we will be 90 days, or three months, behind the sun. |
31 δι᾽ ἣν αἰτίαν καθ᾿ ἑκάστην οκταετηρίδα τρεῖς ἄγονται μῆνες ἐμβόλιμοι, ἵνα τὸ καθ᾽ ἕκαστον ἐνιαυτὸν γινόμενον ἔλλειμμα πρὸς τὸν ἥλιον ἀναπληρωθῇ καὶ πάλιν ἐξ ἀρχῆς διελθόντων τῶν ὀκτὼ ἐτῶν συμφωνῶσιν αἱ ἑορταί πρὸς τὰς κατ᾽ ἔτος ὥρας. γινομένου γὰρ τούτου αἱ θυσίαι τοῖς θεοῖς διὰ παντὸς ἐπιτελεσθήσονται κατὰ τὰς αὐτὰς ὥρας τοῦ ἐνιαυτοῦ. |
31 For this reason, three leap months are inserted in every eight-year period, so that the annual loss of light from the sun is balanced out, and so that once the eight years have elapsed, the festivals will fall in the same seasons. If this happens, the sacrifices to the gods will always be made at the same times of year. |
