Quotations about:
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The first rule is, to keep an untroubled spirit; for all things must bow to Nature’s law, and soon enough you must vanish into nothingness, like Hadrian and Augustus. The second is to look things in the face and know them for what they are, remembering that it is your duty to be a good man. Do without flinching what man’s nature demands; say what seems to you most just — though with courtesy, modesty, and sincerity.

[Τὸ πρῶτον μὴ ταράσσου: πάντα γὰρ κατὰ τὴν τοῦ ὅλου φύσιν καὶ ὀλίγου χρόνου οὐδεὶς οὐδαμοῦ ἔσῃ, ὥσπερ οὐδὲ Ἁδριανὸς οὐδὲ Αὔγουστος. ἔπειτα ἀτενίσας εἰς τὸ πρᾶγμα ἴδε αὐτὸ καὶ συμμνημονεύσας ὅτι ἀγαθόν σε ἄνθρωπον εἶναι δεῖ καὶ τί τοῦ ἀνθρώπου ἡ φύσις ἀπαιτεῖ, πρᾶξον τοῦτο ἀμεταστρεπτὶ καὶ εἰπέ, ὡς δικαιότατον φαίνεταί σοι: μόνον εὐμενῶς καὶ αἰδημόνως καὶ ἀνυποκρίτως.]

Marcus Aurelius (AD 121-180) Roman emperor (161-180), Stoic philosopher

Meditations [To Himself; Τὰ εἰς ἑαυτόν], Book 8, ch. 5 (8.5) (AD 161-180) [tr. Staniforth (1964)]
    (Source)

This translation was adapted (and significantly shortened) by Norman Vincent Peale in You Can If You Think You Can (1974): "The first rule is to keep an untroubled spirit. The second is to look things in the face and know them for what they are."

Peale's paraphrase significantly changes the meaning (by removing the fatalism and the sense of duty in the face of the actions of great men from the past, and turning it into a general call for calm and clarity). Nonetheless, Peale's version of this translation shows up all over the place, and generally without reference to him.

Original Greek. Alternate translations:

First; let it not trouble thee. For all things both good and evil come to pass according to the nature and general condition of the universe, and within a very little while, all things will be at an end; no man will be remembered: as now of Africanus (for example) and Augustus it is already come to pass. Then secondly; fix thy mind upon the thing itself; look into it, and remembering thyself, that thou art bound nevertheless to be a good man, and what it is that thy nature requireth of thee as thou art a man, be not diverted from what thou art about, and speak that which seemeth unto thee most just: only speak it kindly, modestly, and without hypocrisy.
[tr. Casaubon (1634), 8.4]

In the first place , keep your self easie, for all things are govern'd by the Laws, and Order of Providence: Besides, you'l quickly go the way of all Flesh, as Augustus, Adrian, and the rest of the Emperours have done before you. Farther, Examine the matter to the bottom , and remember, that the top of your business is to be a Good Man : Therefore whatever the Dignity of Humane Nature requires of you, set about it presently , without Ifs, or Ands : And speak always according to your Conscience , but let it be done in the Terms of Good Nature and Civility.
[tr. Collier (1701)]

In the first place, be not disturbed or put into confusion. All things happen according to the nature of the whole. In a little time you shall be gone, as Hadrian, and Augustus. And, then, attentively consider the nature of what occurs to you: Remember you must persist in the purpose of being a good man. Act, then, inflexibly what suits the nature of a man, and speak always what appears to you just, and yet with calm good-nature and modesty; and without Hypocrisy.
[tr. Hutcheson/Moor (1742)]

Let it be a principal part of your philosophy to preserve your tranquility: for all things come to pass by the direction of Providence. And, in a few years, you yourself must leave this world, as Hadrian and Augustus have done before you.
In the next place, consider the affair in its proper light, and you will find, that your whole business here is to be a good man. Whatever teh nature of man therefore requires of you, perform it strenuously and with assiduity; and whatever justice dictates on every occasion, speak it boldly, but with good-nature, modesty, and sincerity.
[tr. Graves (1792)]

This is the chief thing: Be not perturbed, for all things are according to the nature of the universal; and in a little time thou wilt be nobody and nowhere, like Hadrianus and Augustus. In the next place, having fixed thy eyes steadily on thy business, look at it, and at the same time remembering that it is thy duty to be a good man, and what man's nature demands, do that without turning aside; and speak as it seems to thee most just, only let it be with a good disposition and with modesty and without hypocrisy.
[tr. Long (1862)]

In the first place, keep yourself easy, for all things are governed by the universal nature. Besides, you'll quickly go the way of all flesh, as Augustus and Hadrian have done before you. Farther, examine the matter from top to bottom, and remember that your business is to be a good man. Therefore, whatever the dignity of human nature requires of you, set about it at once, without "ifs" or "ands"; and speak always according to your conscience, but let it be done in the terms of good nature and modesty and sincerity.
[tr. Collier/Zimmern (1887)]

First and foremost, keep unperturbed. For all things follow the law of Nature: and in a little while you will vanish and be nought, even as are Hadrian and Augustus. Secondly, face facts open-eyed, bearing in mind that it is your duty to be a man and to do good; what man's nature demands, that you do without swerving; so speak, as seems to you most just; only be it considerately, modestly, and with sincerity.
[tr. Rendall (1898)]

Before all things, be not perturbed. Everything comes to pass as directed by universal Nature, and in a little time you will be departed and gone, like Hadrianus and Augustus. Then, scan closely the nature of what has befallen, remembering that it is your duty to be a good man. Do unflinchingly whatever man’s nature requires, and speak as seems most just, yet in kindliness, modesty, and sincerity.
[tr. Hutcheson/Chrystal (1902)]

Firstly, fret not thyself, for all things are as the Nature of the Universe would have them, and within a little thou shalt be non-existent, and nowhere, like Hadrianus and Augustus. Secondly, look steadfastly at the thing, and see it as it is and, remembering withal that thou must be a good man, and what the Nature of man calls for, do this without swerving, and speak as seemeth to thee most just, only be it graciously, modestly, and without feigning.
[tr. Haines (Loeb) (1916)]

In the first place, be not troubled; for all things are according to Universal Nature, and in a little while you will be no one and nowhere, even as Hadrian and Augustus are no more. Next, looking earnestly at the question, perceive its essence, and reminding yourself that your duty is to be a good man, and what it is that man's nature demands, do that without swerving, and speak the thing that appears to you to be most just, provided only that it is with kindness and modesty, and without hypocrisy
. [tr. Farquharson (1944)]

First of all, be untroubled in your mind; for all things come about as universal nature would have them, and in a short while you will be no one and nowhere, as are Hadrian and Augustus. And next, keep your eyes fixed on the matter in hand and observe it well, remembering that it is your duty to be a good person, and that whatever human nature demands, you must fulfil without the slightest deviation and in the manner that seems most just to you; only do so with kindness and modesty, and without false pretences.
[tr. Hard (1997 ed.), Hard (2011 ed.)]

The first step: Don't be anxious. Nature controls it all. And before long you'll be no one, nowhere -- like Hadrian, like Augustus. The second step: Concentrate on what you have to do. Fix your eyes on it. Remind yourself that your task is to be a good human being; remind yourself what nature demands of people. Then do it, without hesitation, and speak the truth as you see it. But with kindness. With humility. Without hypocrisy.
[tr. Hays (2003)]

First, do not be upset: all things follow the nature of the Whole, and in a little while you will be no one and nowhere, as is true now even of Hadrian and Augustus. Next, concentrate on the matter in hand and see it for what it is. Remind yourself of your duty to be a good man and rehearse what man’s nature demands: then do it straight and unswerving, or say what you best think right. Always, though, in kindness, integrity, and sincerity.
[tr. Hammond (2006)]