The opposition of the _analytical_ and _synthetical_ methods we find already indicated by Aristotle, yet perhaps first distinctly described by Proclus, who says quite correctly: “Μεθοδοι δε παραδιδονται; καλλιστη μεν ἡ δια της αναλυσεως επ᾽ αρχην ὁμολογουμενην αναγουσα το ζητουμενον; ἡν και Πλατων, ὡς φασι, Λαοδαμαντι παρεδωκεν. κ.τ.λ.” (_Methodi traduntur sequentes: pulcherrima quidem ea, quæ per analysin quæsitum refert ad principium, de quo jam convenit; quam etiam Plato Laodamanti tradidisse dicitur._) “_In Primum Euclidis Librum_,” L. iii. Certainly the analytical method consists in referring what is given to an admitted principle; the synthetical method, on the contrary, in deduction from such a principle. They are therefore analogous to the επαγωγη and απαγωγη explained in chapter ix.; only the latter are not used to establish propositions, but always to overthrow them. The analytical method proceeds from the facts; the particular, to the principle or rule; the universal, or from the consequents to the reasons; the other conversely. Therefore it would be much more correct to call them _the inductive and the deductive methods_, for the customary names are unsuitable and do not fully express the things. If a philosopher tries to begin by thinking out the methods in accordance with which he will philosophise, he is like a poet who first writes a system of æsthetics in order to poetise in accordance with it. Both of them may be compared to a man who first sings himself a tune and afterwards dances to it. The thinking mind must find its way from original tendency. Rule and application, method and achievement, must, like matter and form, be inseparable. But after we have reached the goal we may consider the path we have followed. Æsthetics and methodology are, from their nature, younger than poetry and philosophy; as grammar is younger than language, thorough bass younger than music, and logic younger than thought.