'but can never feize or lay hold of it."" When they dispute however from principles which are better founded than the dreams and hypothefes of Aristotle, logicians would do well to recollect that in Physical Syllogifms the minor Propofitions are not general but particular, a circumstance which, philofophically weighed, might put a short period to their Difputations, however tenacious men attached to forms and difciplines may be of their ancient privileges, and however willing to wreft every thing to them and them to every thing, and to confider their ufe and application as universal. BUT, though the common fyllogiftic Logic can lend no useful affiftance to Phyfical learning, either in its advancement or com * Hoc vero fciant homines pro certo, omnem fubtilitatem difputationum et difcurfuum mentis, fi adhibeatur tantum poft axiomata inventa, feram effe et præpofteram ; et fubtilitatis tempus verum ac proprium, aut faltem præcipuum, verfari in penfitanda experientia, et inde conftituendis axiomatibus: Nam illa altera fubtilitas naturam prenfat et captat, fed nunquam apprehendit, aut capit. Nov. Org. lib. i. Áph. 121. munication; K 2 munication; as there is, perhaps, nothing in Nature without rule and measure, if philofophers can find them out, MATHEMATIC is its moft ufeful friend and handmaid. The fubject of pure Mathematics are the ideal Forms of Quantity separated from body by an act of mind. The fubject of Phyfics are the Qualities, Caufes and Affections of things as they exist in body, and produce, by that existence, various Phænomena and Effects. To account for thefe Phænomena and Effects, as a science, by reducing them under the general Laws of Nature, Phyfics from Experiments by Induction derives its general Forms, and from them erects philofophical Axioms: and it is in the application of the Forms of Quantity to the Forms of Quality, wherever they are capable of accurate menfuration, that Mathematical fo advantageously applies to the elucidation and promotion of Phyfical learning. In all these cafes it is of moft effential ufe both in the act of deriving the general Laws and Principles of Phyfics from Experiments and Pha nomena; nomena; and also, after they are established, it is equally useful in calculating all their particular Operations and Effects, which are the other Phænomena, and in adopting them, with the utmost address and ingenuity, to the ufe as well as elegance of civil, focial, and domeftic life. MOTION is a general Form of great influence and extent in the wonderful mechanifm and œconomy of nature, to which the Forms of Number and Figure apply, as an affection of various fubjects, and capable of various mensuration. They begin with the moving power confidered as a fecond Caufe (for with the First ftupendous Cause natural Philofophy has no direct concern ;) or, if the phyfical Cause cannot be properly ascertained from experiment and obfervation, which too often happens, they take a general Phænomenon established on their authority, which will fufficiently fupply its place. Naturæ vires legefque virium fimpliciores ex felectis quibufdam phænomenis per Analyfin deducunt, ex quibus deinde per Synthefin reliquorum conftitutionem tradunt. Cotefii Præf. in Newtonii Princip. с Upon this experimental foundation, they calculate the force, or the quantity of motion produced; they account for the different kinds of that motion; they fhew how their are mixed and compounded, what direction and velocity they will confequently have; and they demonftrate the times and periods in which they are refpectively performed. From this application of Geometry and Numbers to the Motion of bodies on the furface of the earth, we derive the philofophy of Mechanics: By their application to the Motion of the heavenly bodies, we rife to the philofophy of Aftronomy: And to their application to the Motion of various founds, we are indebted for the fundamental part of the philofophy of Mufic-All which useful and liberal departments of learning, with fome • Mechanica rationalis erit fcientia Motuum quæ ex Viribus quibufcumque refultant, et Virium quæ ad motus quofcunque requiruntur, accurate propofita, et demonftrata. Newtoni Præf. in Princip. τα 4 Τὰ ὀπτικὰ πρὸς γεωμετρίαν, καὶ τὰ μηχανικὰ πρὸς σερεωμετρίαν, καὶ τὰ αρμονικὰ πρὸς ἀριθμητικὴν, καὶ τὰ φαινόμενα πρὸς ἀτρολογικήν. Ariftot. Analyt. Poft. lib. i, cap. 13. others, others, fo far as the Forms of Quantity are concerned, may be allowed to partake of the nature and precision of Mathematical science. Thus we fee with pleasure and advantage thefe two kindred fciences, both of which are originally derived from Body, meeting together in a kind of connubial union,' and producing a Philofophy which conftitutes the richest and brightest gem in the crown of human learning. • Mixta habet pro subjecto axiomata et portiones phy. ficas : Quantitatem autem confiderat, quatenus eft ad ea elucidanda, et demonftranda, et actuanda, auxiliaris. Multæ fiquidem naturæ partes, nec fatis fubtiliter com. prehendi, nec fatis perfpicue demonftrari, nec fatis dextere et certo ad ufum accommodari poffint, fine ope et interventu mathematicæ, Cujus generis funt perspectiva, mufica, aftronomia, commographia, archite&tura, machinaria et nonnullæ aliæ. Baconus de Augm. Sc. lib. iii. cap. 6. * Δηλοῖ δὲ καὶ τὰ φυσικώτερα την μαθεματικὴν, οἷον ὀπτικὴ, καὶ αρμονικὴ, καὶ ἀερολογία· ἀνάπαλιν γὰρ τρόπον τινὰ ἔχουσι τῇ γεωμετρίᾳ· ἀλλὰ ἡ μὲν γεωμετρία περὶ γραμμῆς φυσικῆς σκοπεῖν ἀλλ' ἐχ ᾗ φυσική· ἡ δὲ ὀπτικὴ, μαθηματικὴν μὴν γραμμήν, ἀλλ' ἐχ ᾗ μαθηματική, αλλ ᾗ φυσική. Ἐπειδὴ δὲ ἡ φύσις διχῶς, τό, τε εἶδος καὶ ἡ ὕλη, ὡς ἂν εἴ περὶ σιμότητος τί ἐςι σκοποῦμεν, ὅτω θεωρητέον. ὥστ ̓ ἔτ ̓ ἄνευ ὕλης τὰ τοιαῦτα, ἔτε κατὰ τὴν ὕλην. Καὶ γὰρ δὴ καὶ περὶ τούτου διχῶς ἀπορήσειεν ἄν τις, ἐπεὶ δύο |