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doubt, but that those things which are most right are most conducive to our happiness.” (Cicero, Letters to Friends.) ↩

Quis hoc statuit, quod æquum sit in Quinctium, id iniquum esse in Nævium? “Who has decreed that what is equitable with regard to Quinctius, should be unjust with respect to Nævius?” (Cicero, For Publius Quinctius.) ↩

That question in Plato, Τί ἄν τις ἔχοι τεκμήριον ἀποδεῖξαι, εἴ τις ἔροιτο νῦν οὕτως ἐν τῷ παρόντι, πότερον καθεύδομεν καὶ πάντα ἃ διανοούμεθα ὀνειρώττομεν, κ.τ.λ., “If anyone should affirm that all our thoughts are only mere dreams, and that we are now asleep, what demonstrative proof could be brought to the contrary?” may have place among the velitations of philosophers: but a man can scarce propose it seriously to himself. If he does, the answer will attend it. (Theaetetus.) ↩

= a. ↩

= e. ↩

= ae. ↩

See André Tacquet’s Elementa Geometriæ 1.5, page 3, Number XII. But the thing appears from the bare inspection of these quantities: b, ab, aeb, aeib, aeiob, etc. ↩

“Things that are equal to the same thing, are equal to one another,” and “things that are each equal to a third thing, are also equal to each other” (versions of Euclid’s first postulate). If men, in their inferences, or in comparing their ideas, do many times not actually make use of such maxims; yet the thing is really the same. For what these maxims express, the mind sees without taking notice of the words. ↩

Under the word “reason” I comprehend the intuition of the truth of axioms. For certainly to discern the respect which one term bears to another, and from thence to conclude the proposition necessarily true, is an act of reason, though performed quick, or perhaps all at once. ↩

If many believed, according to Socrates (in Lucian’s Halcyon) that ὅσην ἔχει τὸ μέγεθος τοῦ κόσμου τὴν ὑπεροχὴν πρὸς τὸ Σωκράτους ἢ Χαιρεφῶντος εἶδος, τηλικοῦτον καὶ τὴν δύναμιν αὐτοῦ, καὶ τὴν φρόνησιν, καὶ διάνοιαν ἀνάλογον διαφέρειν τῆς περὶ ἡμᾶς διαθέσεως, “so much as the magnitude of the world exceeds the bulk of Socrates and Chærophon; so far are their powers, reason, and understanding beyond the capacity of one of us,” what may we think of the God of the world? Therefore Cicero seems to express himself too boldly where he writes, Est⁠ ⁠… homini cum Deo rationis societas. Inter quos autem ratio, inter eosdem etiam recta ratio communis est: “That God and man are allied to each other by reason. And where reason is in common to any persons, right reason is so likewise.” (De Legibus.) ↩

Upon this account it is, that I add the word “given” at the end of my description of reason. ↩

Simplex et nuda veritas est luculentior; quia satis ornata per se est: adeoque ornamentis extrinsecus additis fucata corrumpitur: mendacium verò specie placet alienâ, etc.: “Pure and naked truth is so much the clearer, because it has ornaments enough of its own; and therefore, when it is daubed over with external additional ornaments, it is corrupted by them, so that a lie is therefore pleasing, because it appears in the shape that is not its own, etc.” (Lactantius, Divine Institutes.) ↩

That way, which some Sceptics take to prove the inexistence of truth, has nothing in it, unless it be a contradiction. If anything, say they, is demonstrated to be true, how shall it be known that that demonstration is true? Εἰ ἐξ ἀποδείξεως, ζητηθήσεται πάλιν, πῶς ὅτι καὶ τοῦτο ἀληθές ἐστι, καὶ οὕτως εἰς ἄπειρον: “If by another demonstration, how shall we know that this is true? and so on forever.” (Sextus Empiricus, Against the Logicians.) Nor do I well comprehend St. Chrysostom’s meaning, when he says, Τὸ λογισμοῖς ἀποδεχθέν, κᾄν ἀληθὲς ᾖ, οὐδέπω πληροφορίαν τῇ ψυχῇ παρέχει καὶ πίστιν ἱκανήν: “That what is demonstrated by reasoning, though it may indeed be true, yet it does not afford sufficient proof or conviction to the mind.” (Against the Anomoeans.) For as no man truly believes anything, unless he has a reason for believing it: so no reason can be stronger than demonstration. ↩

Haud alio fidei proniore lapsu, quàm ubi falsæ rei gravis autor existit: “Men being never more easily drawn into a wrong belief, than when the author of a falsity is a grave person.” (Pliny the Elder, Natural History.) ↩

That manner of demonstration, in which it has been pretended truth is deduced directly from that which is false, is only a way of showing that an assertion is true, because its contradictory is false; founded in that known rule, Contradictoriæ nec simul veræ, nec simul falsæ esse possunt, etc., “That contradictory propositions can neither be true at the same time, nor false at the same time, etc.” ↩

Cujus [summi rectoris et domini] ad naturam apta ratio vera illa et summa lex à philosophis dicitur: “The reason [of the supreme lord and governor] which is accommodated to the nature of things, is, by philosophers, called the true and chief law.” (Cicero, De finibus bonorum et malorum.) Νόμος ἀψευδὴς ὁ ὀρθὸς λόγος, οὐχ ὑπὸ τοῦ δεῖνος ἢ τοῦ δεῖνος, θνητοῦ φθαρτός, ἐν χαρτιδίοις ἢ στήλαις, ἄψυχος ἀψύχοις, ἀλλ᾿ ὑπ᾿ ἀθανάτου φύσεως ἄφθαρτος ἐν ἀθανάτῳ διανοίᾳ τυπωθείς: “Right reason is an unerring law, not to be defaced by any mortal man, as if it were a lifeless thing written upon paper or pillars which must decay: but it proceeds from an immortal being, and is itself immortal,

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