Anatolius of Alexandria

“ For although the moon of the 20th does not fill the whole night, yet, rising as it does in the second watch, it illumines the greater part of the night. Certainly if the rising of the moon should be delayed on to the end of two watches, that is to say, to midnight, the light would not then exceed the darkness, but the darkness the light. But it is clear that in the Paschal feast it is not possible that any part of the darkness should surpass the light; for the festival of the Lord’s resurrection is one of light, and there is no fellowship between light and darkness. ”

“ But our predecessors, men most learned in the books of the Hebrews and Greeks,—I mean Isidore and Jerome and Clement,—although they have noted similar beginnings for the months just as they differ also in language, have, nevertheless, come harmoniously to one and the same most exact reckoning of Easter, day and month and season meeting in accord with the highest honour for the Lord’s resurrection. ”

“ As we are about to speak on the subject of the order of the times and alternations of the world, we shall first dispose of the positions of diverse calculators; who, by reckoning only by the course of the moon, and leaving out of account the ascent and descent of the sun, with the addition of certain problems, have constructed diverse periods, [2] self-contradictory, and such as are never found in the reckoning of a true computation ”

“ From Jerome [1] we learn that Anatolius flourished in the reign of Probus and Carus, that he was a native of Alexandria, and that he became bishop of Laodicea. Eusebius gives a somewhat lengthened account of him, [2] and speaks of him in terms of the strongest laudation, as one surpassing all the men of his time in learning and science. He tells us that he attained the highest eminence in arithmetic, geometry, and astronomy, besides being a great proficient also in dialectics, physics, and rhetoric. ”

“ What is mathematics?
Aristotle thinks that all philosophy consisted of theory and practice, [2] and divides the practical into ethical and political, and the theoretic again into the theological, the physical, and the mathematical. And thus very clearly and skilfully he shows that mathematics is (a branch of) philosophy.
The Chaldæans were the originators of astronomy, and the Egyptians of geometry and arithmetic.... ”

“ In fifteen days and half an hour, the sun ascending by so many minutes, that is, by four in one day, from the eighth day before the Kalends of January, i.e., 25th December, to the eighth before the Kalends of April, i.e., 25th March, an hour is taken up; [1] at which date there are twelve hours and a twelfth. On this day, towards evening, if it happen also to be the moon’s fourteenth, the lamb was sacrificed among the Jews. ”

“ For we believe that nothing is impossible to your power of prayer, and to your faith. Strengthened, therefore, by this confidence, we shall set bashfulness aside, and shall enter this most deep and unforeseen sea of the obscurest calculation, in which swelling questions and problems surge around us on all sides. ”

“ Seven days shall there be no leaven found in your houses.” From this they maintain that it is quite permissible to celebrate the Passover on the twenty-first day of the moon; understanding that if the twenty-second day were added, there would be found eight days of unleavened bread. A thing which cannot be found with any probability, indeed, in the Old Testament, as the Lord, through Moses, gives this charge: “Seven days ye shall eat unleavened bread.” [2] Unless perchance the fourteenth day is not reckoned by them among the days of unleavened bread with the celebration of the feast ”

“ These writers, in solving some questions which are raised with respect to Exodus, say that all alike ought to sacrifice the Passover [4] after the vernal equinox in the middle of the first month. And that is found to be when the sun passes through the first segment of the solar, or, as some among them have named it, the zodiacal circle. ”

“ Following their example up to the present time all the bishops of Asia—as themselves also receiving the rule from an unimpeachable authority, to wit, the evangelist John, who leant on the Lord’s breast, and drank in instructions spiritual without doubt—were in the way of celebrating the Paschal feast, without question, every year, whenever the fourteenth day of the moon had come, and the lamb was sacrificed by the Jews after the equinox was past ”

“ And although the outset of four nights begins to be dark, that is, the 17th and 18th and 19th and 20th, yet the moon of the 20th, which rises before that, does not permit the darkness to extend on even to midnight. ”

“ For every day in the reckoning of the moon does not end in the evening as the same day in respect of number, as it is at its beginning in the morning. For the day which in the morning, that is up to the sixth hour and half, is numbered the 13th day of the month, is found at even to be the 14th. ”

“ Computation and theoretical music have a closer affinity than others with arithmetic; for this department, being one also of quantity and ratio, approaches it in number and proportion. [17] Optics and geodesy, again, are more in affinity with geometry. And mechanics and astrology are in general affinity with both.
As to mathematics having its principles [18] in hypothesis and about hypothesis. Now, the term hypothesis is used in three ways, or indeed in many ways. For according to one usage of the term we have the dramatic revolution ”

“ But this again is held by other wise and most acute men to be an impossibility, because within that narrow and most contracted limit of a cycle of nineteen years, a thoroughly genuine Paschal time, that is to say, one held on the Lord’s day and yet after the equinox, cannot occur. ”

“ According to a second meaning, we have the investigation of matters in the special in rhetoric; and in this sense the Sophists say that a hypothesis must be proposed. And, according to a third signification, the beginning of a proof is called a hypothesis, as being the begging of certain matters with a view to the establishment of another in question. ”

“ For it is one thing to act in accordance with the precept given by the apostle, yea, by the Lord Himself, and be sad with the sad, and suffer with him that suffers by the cross, His own word being: “My soul is exceeding sorrowful, even unto death;” [2] and it is another thing to rejoice with the victor as he triumphs over an ancient enemy, and exults with the highest triumph over a conquered adversary, as He Himself also says: “Rejoice with Me ”

“ And therefore we have said that those parties have committed no trivial offence who have ventured either on anticipating or on going beyond this number, which is given us in the divine Scriptures themselves. ”

“ For Agathobulus, the philosopher, flourished in the times of Adrian, as Eusebius writes in his Chronicon, and after him Georgius Syncellus.—Vales.↑ ̓Αριστοβούλου τοῦ πάνυ—Rufinus erroneously renders it Aristobulum ex Paneade, Aristobulus of Paneas. ”

“ His reputation was so great among the Alexandrians that they are said to have requested him to open a school for teaching the Aristotelian philosophy in their city. [3] He did great service to his fellow-citizens in Alexandria on their being besieged by the Romans in a.d. ”

“ And he (Archytas) gave them this name, because he found science [4] in them, and that in a manner suitable to man’s study. [5] For they (the Pythagoreans) perceived that these studies dealt with things eternal and immutable and perfect, [6] in which things alone they considered that science consisted. ”