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but can never seize or lay hold of it.' When they dispute however from principles which are better founded than the dreams and hypotheses of Aristotle, logicians would do well to recollect that in Physical Syllogisms the minor Propositions are not general but particular, a circumstance which, philosophically weighed, might put a short period to their Disputations, however tenacious men attached to forms and disciplines may be of their ancient privileges, and however willing to wrest every thing to them and them to every thing, and to consider their use and application as universal.

BUT, though the common syllogistic Logic can lend no useful assistance to Physical learning, either in its advancement or com

• Hoc vero sciant homines pro certo, omnem fubtilitatem disputationum et discursuum mentis, fi adhibeatur tantum poft axiomata inventa, seram esse et præpofteram; et subtilitatis tempus verum ac proprium, aut faltem præcipuum, versari in pensitanda experientia, et inde conftituendis axiomatibus : Nam illa altera subiilitas naturam preosat et captat, sed nunquam apprehendit aut capit. Nov. Org. lib. i. Aph. 121.

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munication ; as there is, perhaps, nothing in Nature without rule and measure, if philosophers can find them out, MATHEMATIC is its most useful friend and handmaid.

The subject of pure Mathematics are the ideal Forms of Quantity separated from body by an act of mind. The subject of Physics are the Qualities, Causes and Affections of things as they exist in body, and produce, by that existence, various Pbænomena and Effects. To account for these Phænomena and Effects, as a science, by reducing them under the general Laws of Nature, Physics from Experiments by Induction derives its general Forms, and from them erects philosophical Axioms : and it is in the application of the Forms of Quantity to the Forms of Quality, wherever they are capable of accurate mensuration, that Mathematical so advantageously applies to the elucidation and promotion of Physical learning. In all these cases it is of most effential use both in the act of deriving the general Laws and Principles of Physics from Experiments and Phæ


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 use as well as elegance of civil, social, and domestic life.

Motion is a general Form of great influence and extent in the wonderful mechanism and economy of nature, to which the Forms of Number and Figure apply, as an affection of various subjects, and capable of various mensuration. They begin with the moving power considered as a second Cause (for with the First stupendous Cause natural Philosophy has no direct concern ;) or, if the physical Cause cannot be properly ascertained from experiment and observation, which too often happens, they take a general Phænomenon established on their authority, which will sufficiently supply its place.

Naturæ vires legesque virium simpliciores ex selectis quibusdam phænomenis per Analysin deducunt, ex quibus deinde per Synthesin reliquorum constitutionem tradunt, Cotesii Præf. in Newtonii Princip.

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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 demonstrate the times and periods in which they are respectively performed.

From this application of Geometry and Numbers to the Motion of bodies on the surface of the earth, we derive the philosophy of Mechanics: By their application to the Motion of the heavenly bodies, we rise to the philosophy of Astronomy : And to their application to the Motion of various sounds, we are indebted for the fundamental part of the philosophy of Music_All which useful and liberal departments of learning, with some

Mechanica rationalis erit scientia Motuum quæ ex Viribus quibuscumque resultant, et Virium quæ ad motus quoscunque requiruntur, accurate proposita, et demonstrata. Newtoni Pref. in Princip.

« Τα οπτικα προς γεωμετρίαν, και τα μηχανικά προς Siswetgíax, vai tā apuovxż wpós cipoguntiņu, xxi tä canvóleva após cscono yıxúv. Aristot. Analyt. Poft. lib. i, cap. 13.


others, so far as the forms of Quantity are concerned, may be allowed to partake of the dature and precision of Mathematical science.

Thus we fee with pleasure and advantage these two kindred sciences, both of which are originally derived from Body, meeting together in a kind of connubial union, and producing a Philofophy which constitutes 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 satis subtiliter com. prehendi, nec fatis perspicue demonstrari, nec satis dextere et certo ad ufum accommodari poffint, fine ope et interventu mathematicæ, Cujus generis sunt perspectiva, mufica, astronomia, cosmographia, architectura, machinaria et nonnullæ aliæ. Baconus de Augm. Sc. lib. iii. cap. 6.

* Δηλοί δε και τα φυσικώτερα την μαθεματικήν, οίον οπική, και αρμονική, και ατρολογία ανάπαλιν γαρ τρόπον τινα έχουσι τη γεωμετρία αλλά μέν γεωμετρία σερί γραμμης φυσικής σκοπει'. αλλ' έχ ή φυσική" η δε οπτική, μαθηματικών μην γραμμής, αλλ' έχ ή μαθηματική, αλλά ή φυσική. Επειδή δε η φύσις διχώς, τό, τε είδος και η ύλη, ως αν εί περί σιμότητος τί έξι σκοπούμεν, έτω θεωρητέον. έτ' έτάνευ ύλης τα τοιαύτα, έτε κατα την ύλην. Και γαρ δή και σερί τούτου διχως απορήσειεν άν τις, έπει δύο

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