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times before: for it is only by trying many and different roads to Knowledge that men can find out the right one to her temple.

Sensible bow great, how various, how extensive, the work I undertake will be j fearful of degrading, by mixtures of human weakness, that ineffable Wisdom, part of which I am attempting to display; and conscious, as I am, of my own defects* I feel the task I have set before me too heavy for my abilities alone to support me under it—«* O send Her out of thy holy heavens "and from the throne of thy glory, that '• being present she may labour with me!— ** for She knoweth and understandeth all *« things: and she shall lead me soberly in "my doings and preserve me in her pow•• Pr." t

* Wisdom.


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Of the Logic of Mathematics.

P V E R Y thing that is the subject of ■*—J human knowledge belongs either to Mind or Body.

The two parts of learning, MetaphySic and Logic, which have been touched in a summary way in the preceeding pages, treat more immediately of Mind, its powers and operations, its acts and energies. The former, producing by peculation the general "Principles of all other parts of knowledge, or at least affecting to produce them, is the universal Scienee-, and the -latter, descending more fraflically to the particular

investiinvestigation and establishment of the Principles of each as they exist in nature and affect the mind, and then pursuing them, in a just and rational way, into all their different effects, is the universal Art: in which Universality, as well as in many other respects, they have a close connection and affinity with each other.* All the other Sciences and Arts, as has been before observed, apply to particular Subjects," which are of different kinds and various extent.

Physics is the Science which treats more immediately of Body, or matter organized, its properties and affections, its motions and operations, its qualities, and internal structure.

Between these Sciences of Mind and Body lies one, which is intermediate and which partakes of both, taking its subject from the

• See Aristot. Metaph. lib. iv. cap. 2.

Morn St « nPHTH *IA02O*lA 39 n' AIAAEKTIK.H urox»f*i»w \yei is-xvrx T* SVra. Philoponus in 1 Post. Analyt.

» EKASTH pb EniSTHMH Tt$ h Ti ywoc xaray'nrou. Ibid.

sensible sensible qualities of Body, bat having it perfectly separated from it and made abstract by an act of Mind/ This intermediate

1 Aristotle distinguishes the three Sciences thus, v/Aw $ $TEIKH Tvici d^ugif* (Av, ot^'axaxiWa' -r»f{ Si MA~ OHMATIKH2 tvtx Tb-eji axivnla [*.hy « yu^x Si Hiro?, «XA.'«f h \)\x' n Si IIPX2TH xal wjg» ym^x 1^ dxirStt' Aristot. Metaph. lib. vi. cap. i. Which is thus explained by Duval—Physica quidem versatur circa substantiam mobilem et materialem: Mathematicæ puræ agunt de rebus reipsa mobilibus, et a materia senfibili re inseperabilibus, fed tamen ea ratione qua siint immobiles, et cogitatione separatae; vel, quod idem est, prout in sui consideratione materiam sensibilem non includunt. Ut ergo Physica, mobilium et inseperabilium ; Mathematica vero, velut immobilium et separabilium; sic Metaphysica est revera immobilium, æternorum, separabilium, etdivinorum contcmplatrix. Doct. Peripat. Synop. p. 22. And again Aristotle distinguishes Mathematics from both Physics and Metaphysical Ferms, ?t» Si zragx rx AI20HTA x*» T<* EIAH, Ta MA0HMATIKA Twk ■a-^xy^xrm ilvxi Qxei

fUTX%U, OKXIpiCOVTX T«V fJ.\v OAcSriTUV, TW xii'iX XXI XY.'l-' HIT* UVXl' T«» S' tlSuil, TU TX fAiV -GTOXX' Xt\x OfMIX SlWl,

S\ nSct Auto, txxrmi pivov. Metaph. lib. i. cap. vi. which is thus explained by another commentator.—Indicat Aristoteles Platonem aliud adhuc genus rerum possuisse [principalium] a rebus scnsibilibus et ab ipfis ideis diversum. Nam, præ'ter sensibilia et suas sormas, res mathematicas constituit, quas media* eflc dixit inter res sensiles et inter ideas; et difFerunt asenfibilibus, quod sempiterna siint et immobilia entia mathematicæ, sicut ideæ quoque suntj a formis autem et ideis distant, quod pleraque . . mathe

Science is MATHEMATICS, which, as it is related to both, is the connecting link by which they are united in the grand fyftem of knowledge: and the transition from Metaphyfics and general Logic, to the particular Logic of Pbyjics and the other parts of learning, will be aptly and advantageously made through Mathematics.

This Science is entirely confined to the predicament of Quantity, which being of two kinds Magnitude and Multitude, that is Quantity continuous and Quantity discrete., the first bounded and defined by Figure, the second bounded and defined by Number, k accordingly divides with these different subjects into two collateral correspondent branches— Geometry and Arithmetic* And, as they are the simplest in their Prin

mathematics fimilia Cunt inter fe, hoe est, quod plura fint ejusdem speciei individua, ut plures trianguli æquum latcrum, plura quadrata, et sic deinceps. Forma au tern ipsa et idea unaquæque unum quoddam fit tantum. Ita ut res mathematics fint inter res senfiles et inter idea*, quia de utrisque aliquid commune habent, et tamen ab utrisque rursus differunt. Joan. Ludor. Haver. Comment. in locum.

* See Aristot. Catcg. cap. vi.

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