"He was more careful in observing the unlucky days of the Egyptians than they are themselves, and maintained a personal fast on certain days through revelation. For he went without food on every 'old and new,' not even having dined the previous day, just as indeed he also performed conspicuous and holy rituals at the new moons." - Marinus, Proclus, or on Happiness 19 (trans. Mark Edwards)

It seems the Greek here is somewhat ambiguous, but according to the translations of Thomas Taylor and Mark Edwards, Proclus fasted on the last day of the month (Guthrie's translation suggests it was on the first). According to Edwards, 'old and new' was the Athenian term for the last day of the lunar month and does not mean "last and first days of the months." Marinus does not provide detail about the rituals Proclus performed on the new moon, but there are various statements in the literature about new moon practices, such as libations to the moon (see note 206 in Edwards).

The next new moon is on the thirtieth of May.

"By paying honor and respect to one’s kinfolk and all who share in the worship of the gods of the tribe and who also share descent and blood, a person will also enjoy the favor of the gods of the household who will be well disposed toward his own begetting of children."

Plato, Laws 729c

[The daimonic] interprets and conveys things from humans to gods and things from gods to humans, that is, the requests and sacrifices of the humans and the orders and returns for sacrifices of the gods. Being between both it fills (the void) so that everything is bound together. Through the daimonic all divination proceeds and the craft of the priests who are concerned with sacrifices, rituals, chants, and all divination and sorcery. God does not mix with human, but through the daimonic is all association and discussion for gods with humans, both when humans are awake and asleep ... These daimones are numerous and of all kinds, and Eros is one of these.

Plato, Symposium 202e-203a

You'll have to excuse the length of this post, but I thought it was worth sharing since it is one of the more detailed denoscriptions of ancient sacrifice in Europe.

"[The ox] is sacrificed if it makes a deep bow to Hestia. The kings' share-receiver makes the sacrifice and provides the offerings and offers in addition a half hekteus of offerings. He takes his share, the skin and a leg, the hieropoioi take a leg, and the remaining meat belongs to the city.

The heralds lead the ox selected for Zeus to the agora. After reaching the agora, the owner of the ox or the person deputizing for him calls out: 'For the people of Cos I am providing the ox; let the Coans give the price to Hestia.' And let the chief magistrates immediately take an oath and make a valuation; when a valuation has been made, let the herald announce how much the valuation was. Then they drive the ox to Hestia Hetaeraea and make the sacrifice. The priest puts a ribbon upon the ox and pours a cup of wine mixed with water as a libation in front of the ox. Then they lead the ox away, together with the burnt offering, seven cakes, honey, and the ribbon. As they leave, they call for respectful silence. At this point they untie the ox and begin the sacrificial ritual with olive and laurel. The heralds burn a pig and its entrails upon the altar, pouring on libations of honey and milk. After washing the intestines, they burn them beside the altar. And once they are burnt without wine, let him pour upon them a libation of honey and milk.

Let the herald announce that they are celebrating the annual festival as a feast for Zeus Polieus. Let the priest make an additional offering together with the intestines, incense, and cakes, libations mixed and unmixed, and a ribbon. Then let the priest and herald go to the hieropoioi at the public building, and let the hieropoioi entertain the priest and the herald during this night. And let the heralds choose whoever they want from their own number as slaughterer of the ox and let whoever of them wishes to proclaim the choice to the person chosen.

On the same day: to Dionysius Scyllites, a pig and a kid. The pig meat is not to be taken away [from the sanctuary]. The priest makes the sacrifice and provides the offerings. As perquisites, he takes the skin and leg.

On the twentieth: the selected ox is sacrificed to Zeus Polieus. What has to be wrapped is wrapped in the skin. On the hearth a sacrifice is made of half a hekteus of barley, two half-hekteus loaves, one shaped like a cheese, and things wrapped in skin. On these the priest pours a libation of three mixing bowls of wine. Perquisites from the ox: for the priest the skin and a leg (the priest provides the offerings) and half of the breast and half the stomach; for the incense-bearer the hip-end of the leg given to the hieropoioi; for the heralds, a double portion of meat from the back, shoulder meat, a three-spit share of blood meat; for the Nestoridae, a double portion of meat from the back; for the doctors, meat; for the flute-player, meat; to the smiths and potters, the brain. The rest of the meat is for the city. All of these are not taken out of the city.

On the same day: to Athena Polias, a pregnant sheep. The priest makes the sacrifice and provides the offerings. As perquisites, he takes the skin and a leg. On the twenty-first: to Dionysius Scyllites a pig and a kid: the meat of the pig is not to be taken away. The priest makes the sacrifice and provides the offerings. As perquisites he takes the skin and a leg."

A denoscription of sacrifice in Cos to Zeus Polieus (of the City) from an innoscription on a fourth century BCE calendar. Quoted from Greek Religion: A Sourcebook by Valerie Warrior p. 67.

As we train ourselves to deal with sophistical questioning, so we should also train ourselves each day to deal with impressions, because they too put questions to us.

'The son of So-and-so has died.' - Reply: That lies outside the sphere of choice, it is nothing bad.
'So-and-so has been disinherited by his father.' - That lies outside the sphere of choice, it is nothing bad.
'Caesar has condemned him' - That lies outside the sphere of choice, it is nothing bad.
'He has been distressed by these things.' - That lies within the sphere of choice, it is something bad.
'He has endured it nobly.' - That lies within the sphere of choice, it is something good.

If we adopt this habit, we'll make progress, because we'll never give our assent to anything unless we get a convincing impression.

'His son has died.' - What has happened? - 'His son has died.' - Nothing more than that? - 'Nothing more.'
'His ship has gone down.' - What has happened? His ship has gone down.
'He has been taken off to prison.' - What has happened? He has been taken off to prison. But the observation 'Things have gone badly for him' is something that each person adds for himself.

Epictetus, Discourses 3.8

As for the famous judgment of the goddesses that the myths say was performed by Paris, following the ancient account, it is not to be believed that there was truly strife among the goddesses themselves and that they were judged by a [particular] barbarian. Rather, this is to be interpreted as meaning that the choices of lives – to which Plato testifies in many passages – are likewise carried out under the watchful eye of the gods who supervise souls.

Plato himself indeed clearly teaches the same thing in the Phaedrus, saying that the regal life belongs to Hera, the philosophical to Zeus, and the erotic to Aphrodite. Thus souls, when many kinds of lives are offered them out of the universe, accept some and reject others, following their own judgment, while the myths, transferring to the gods themselves the specific qualities of the lives, say that those who preside over the variation in them, form by form, are "judged" by those choosing the lives.

This is the sense in which Paris is said to have been made the judge of Athena, Hera, and Aphrodite: three lives were offered him, and he chose the erotic, not after due thought, but rushing after the beauty of the world of appearances and pursuing the phantom of the beauty grasped by the mind. He whose life is truly devoted to Eros sets intelligence and wisdom before him and contemplates the true and the apparent beauty through these and has no less to do with Athena than with Aphrodite. But he who pursues only the erotic form of life, in and for itself and through the passions, departs from true beauty and goodness and out of stupidity and greed leaps upon the phantom of the beautiful and lies there on it, failing to attain that balanced perfection commensurate with the erotic. The truly erotic individual, who is the concern of Aphrodite, is drawn up to the divine beauty itself, looking beyond the beauties of the senses, but since there are Aphrodisian daemons presiding over the beauty that is visible and has its existence in matter, for this reason, of course, even he who pursues the phantom is said to have Aphrodite as his helper.

- Proclus, On the Republic 6

'It is fitting' for each of us to do these things 'according to the customs of one's country'. For God is always simultaneously present everywhere, with all of his divine powers. But we are limited to one form among those many forms produced by God, the human form, and within the human form are limited to one form of life for now and one choice of life, and are divided up into a little portion of the universe and of the earth itself. So different people partake in a different instance of divine goodness, and they do so in a different way at different times and places. You can at least see that when it is day with us, it is night for others, and when it is winter in one place, it is summer in another, and that these sorts of flora and fauna prevail here, and elsewhere other sorts: the earth and the things on it partake of divine goodness in a divided way.

Simplicius, On Epictetus' Handbook 94.8-21

The most important thing is not life, but the good life.

Plato, Crito 48b

But all things desire the Good, and each attains it through the mediation of its own proximate cause: therefore each has appetition of its own cause also. Through that which gives it being it attains its well-being; the source of its well-being is the primary object of its appetites; and the primary object of its appetite is that upon which it reverts.

Proclus, The Elements of Theology 31

This is just what I was getting at when I said I knew of a way to put into effect this law of ours which permits the sexual act only for its natural purpose, procreation, and forbids not only homosexual relations, in which the human race is deliberately murdered, but also the sowing of seeds on rocks and stone, where it will never take root and mature into a new individual; and we should also have to keep away from any female 'soil' in which we'd be sorry to have the seed develop.

Plato, Laws 838e-839a

Likewise I advise those who cherish the ways of freedom and shun the yoke of slavery as something evil, to beware lest by an excessive and ill-timed thirst for freedom they fall into the affliction of their ancestors, the excessive anarchy they experienced as a result of their unmeasured passion for liberty. For the Sicilians before the reign of Dionysius and Hipparinus lived happily, as they thought, faring sumptuously and ruling their rulers; they it was who, without any legal judgment, stoned to death the ten generals who preceded Dionysius, in order not to be subject to any master, not even justice and the law, but to be altogether and absolutely free. This is why tyranny came upon them. Both servitude in excess and liberty in excess are very great evils, but in due measure both are great goods. Due measure is found in obedience to God, the absence of measure in obedience to men. And the god of wise men is the law; of foolish men, pleasure.

Plato(?), Letter VIII 354d-e

But souls that live according to virtue shall, in other respects, be happy; and when separated from the irrational nature, and purified from all body, shall be conjoined with the gods, and govern the whole world, together with the deities by whom it was produced.

Sallust, On the Gods and the World Chapter 21

On the day after the conference it is prudent to honour the anniversary of the death of both the divine emperor Julian and the Inspired Gemistus Plethon. May the high gods accept them and may we share in their wisdom and courage

Or haven’t you remembered that in that life alone, when he looks at Beauty in the only way that Beauty can be seen - only then will it become possible for him to give birth not to images (because he’s in touch with no images), but to true virtue (because he is in touch with the true Beauty). The love of the gods belongs to anyone who has given birth to true virtue and nourished it, and if any human being could become immortal, it would be he.

Plato, Symposium 212a

If pagans are motivated by destruction, we are motivated by an evil impulse. We must be motivated by love and a desire to improve the spiritual condition of our people.

The consequences of the undermining of Christianity in the West have been overwhelmingly negative. That’s because, despite Christianity’s numerous shortcomings, it was, on balance, a force for good and a source of unity among Europeans.

As pagans, we should lovingly correct the failures of Christianity and seek to guide the living spiritual tradition of the West back to its purer and better (i.e., pagan) form rather than aid the destroyers of it.

It is of paramount importance that pagans understand this, as difficult as it might be for some to accept.

And this Aphrodite who belongs to the universe and is not only soul nor simply soul gave birth to the Love who is in this world and who from the start concerned himself with marriages and to the degree to which he is personally linked to the desire for what is above, moves the souls of the young and turns back the soul to which he is attached insofar as it is itself naturally disposed to recall the things above. For every soul desires the Good, both the mixed soul and the soul of the individual, since it follows on from and is derived from the higher soul.

Plotinus, Enneads 3.5.3.31-38

Consider that what I said before about anger has also been said about the other diseases of the soul. First, we must not leave the diagnosis of these passions to ourselves but we must entrust it to others; second, we must not leave this task to anyone at all but to older men who are commonly considered to be good and noble — men to whom we ourselves have given full approval because, on many occasions, we have found them free from these passions. We must further show that we are grateful to these men and not annoyed with them when they mention any of our faults. Furthermore, one should remind oneself of these things each day. It would be better to do this many times, but otherwise at least in the morning, before starting with your business, and in the evening, before going to rest. I in any case am accustomed first to read those exhortations circulating in Pythagoras’s name [i.e., The Golden Verses] twice during the day, and to say them out loud later. It is not enough for us to practice self-control over our anger; we must also cleanse ourselves of voluptuous eating, carnal lust, drunkenness, excessive curiosity, and envy. Let someone else keep watch over us to see that we are not seen greedily filling ourselves with food as dogs do, or, as do those who are on fire with a nonintermittent fever, that we do not lift the drink to our lips more greedily than becomes a man of dignity.

Galen, On the Diagnosis and Cure of the Passions in One's Soul 6.10-11

Only he knows how to pay honour [to divinities] who does not confuse the worth of those being honoured and who renders above all himself as a sacrifice, crafting his own soul into a divine sculpture and making his own intellect a temple for the reception of the divine light.

Hierocles of Alexandria, Commentary on the Pythagorean Golden Verses

Detail from an oversized statue of the goddess Hygeia

Archaeological Museum of ancient Feneos, Greece

Every manifold in some way participates unity.

For suppose a manifold in no way participating unity. Neither this manifold as a whole nor any of its several parts will be one; each part will itself be a manifold of parts, and so to infinity; and of this infinity of parts each, once more, will be infinitely manifold; for a manifold which in no way participates any unity, neither as a whole nor in respect of its parts severally, will be infinite in every way and in respect of every part. For each part of the manifold - take which you will - must be either one or not-one; and if not-one, then either many or nothing. But if each part be nothing, the whole is nothing, if many, it is made up of an infinity of infinities. This is impossible: for, on the one hand, nothing which is is made up of an infinity of infinities (since the infinite cannot be exceeded, yet the single part is exceeded by the sum); on the other hand, nothing can be made up of parts which are nothing. Every manifold, therefore, in some way participates unity.

Proclus, Elements of Theology 1