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sensible qualities of Body, but having it perfe&ly separated from it and made abstract by an act of Mind. This intermediate

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Aristotle diftinguishes the three Sciences thus, ý užr SOTEIKH wapi azúc15a pèv, ám'>x asívnao tñs og MAΘΗΜΑΤΙΚΗΣ ένια σερί ακίνηλα μεν, και χωρισα δε ίσως, ára is in 'n mo na ME DIPS2TH xai wspi gwerscă sj axivnice 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 reipla mobilibus, et a materia fenfibili re inseperabilibus, fed tamen ea ratione qua funt immobiles, et cogitatione separatæ ; vel, quod idem eft, prout in sui consideratione materiam senfibilem non includunt. Ut ergo Phyfica, mobilium et inseperabilium ; Mathematica yero, velut immobilium et separabilium ; fic Metaphysica est revera immobilium, æternorum, feparabilium, et divinorum contemplatrix. Doct. Peripat. Synop. p. 27. And again Aristotle distinguishes Mathematics from both Physics and Metaphysical Forms, što dñ wapa ta AIEOHTA xai oce ΕΙΔΗ, τα ΜΑΘΗΜΑΤΙΚΑ των πραγμάτων είναι φασι μεταξύ, διαφέροντα των μεν αισθητών, το αίδια και ακίνητα είναι των δ' ειδών, τω τα μεν πολλ’ άτια όμοια είναι, di sidos aútė,' Ê éxasov pórov. Metaph. lib. i. cap. vi. which is thus explained by another commentator.-Indi. cat Aristoteles Platonem aliud adhuc genus rerum poffuiffe (principalium] a rebus fenfibilibus et ab ipfis ideis diversum. Nam, præter sensibilia et suas formas, res mathematicas constituit, quas medias esse dixit inter res sensiles et inter ideas; et differunt a sensibilibus, quod fempiterna sunt et immobilia entia mathematicæ, ficut ideæ quoque sunt; a formis autem et ideis diftant, quod pleraque


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Science is MATHEMATICS, which, as it is related to both, is the connecting link by which they are united in the grand fystem of knowledge: and the transition from Metaphysics and general Logic, to the particular Logic of Physics 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 difcrete, the first bounded and defined by Figure, the second bounded and defined by Number, it saccordingly divides with these different fabjects into two collateral correspondent branches --GEOMETRY and ARITHMETIC, And, as they are the simplest in their Prin

mathematicæ fimilia sunt inter fe, hoc eft, quod plura fint ejusdem speciei individua, ut plures trianguli æquum laterum, plura quadrata, et fic deinceps. Forma autem ipfa et idea unaquæque unum quoddam fit tantum. Ita ut res mathematicæ fint inter res sensiles et inter ideas, quia de utrisque aliquid commune habent, et tamen ab utrisque rurfus differunt. Joan. Ludov. Haver. Comment. in locum.

See Ariftot. Categ. cap. vi.


ciples, the clearest in their Reasoning, and the most convincing in their Truth, the Logic of them will be properly introductory to that of the other parts of Learning, which are more complicated in their nature, and more involved in their construction,

SECT. 1.

Of Mathematical PRINCIPLES.

FXTERNAL Nature is the archetype L and original of all our sensations, and of many of our ideas : and the EVIDENCE of the EXTERNAL Senses exercised upon the superficial properties of innumerable bodies with which they are familiarly and perpetually conversant, as their Length, Breadth and Depth and other exterior qualities, and

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again as familiarly and incessantly employed upon many different objects, which they cannot avoid distinguishing as Individuals or Monades, is undoubtedly the PRIMARY PRINCIPLE of Mathematical learning in both its branches.

This is every where the doctrine of Ariftotle, who, as well as Plato, has very philosophically remarked, that, whereas many of the properties of Body are confined to particular senses, those few, which are the subject of Mathematics, are common to all the senses.

These external and obvious properties of Natural Body conftitute the qualities of what is called MATHEMATICAL Body, if we may be allowed to give the name of body to that which is ideal : for, all the other qualities and attributes of Natural Body being abstracted and taken away by an act of the Mind, they are conceived to be left alone, and to exist feparate and independent of the bodies from which they are originally taken, constituting what are properly and logically termed ideas. These separate and abstract ideas are Units or Monades, Points, Lines, Angles, Circles, Superficies, Solids, Equality and Inequality and some more, which are otherwise denominated Universal Forms ; and the Abstraction, by which they are collected from the Senses exercised upon many individual objects, is performed in a way so perfectly obvious and familiar, and with so much ease and perspicuity, that they seem to present themselves to the mind imme

gieo xessa xác vị ve si, xiv, tác g" xa gety ozoiest, ódi yivetes figūdos xofi SávTWv. Aristot. Nat. Ausc. lib. ii. cap. ii.

See Metaph. lib. xi. cap. i, 2, 3. 8 Kosvaxívnous, netuia, dipoques, cxñuchy péyeθοςτα γαρ τοιαύτα εδεμιάς έσιν ίδια, αλλά κοινά πάσαις. Aristot. De Anima, lib. ii. cap. vi.


duttive Reafoning."

* Το μεν γαρ σεριτίον έςαι και το άρτιον, και το ευθύ xa và xau-TuAoy' về vai desubs, xa: Yeovun, xa rx puce õveu xıvýGEWS. Aristot. Nat. Ausc. lib. ii. cap. 2.

1 λανθάνεσι δε τετο σοιέντες, και οι τας ιδέας λέγοντες. Τα γαρ φυσικα ψωρίζεσιν ήτίον όλα χωριςα των μαGruotix@y. Aristot. Nat. Ausc. lib. ii. cap. 2.

* Ertau ta gãe só prèv Őti, tū aicIntixūv sidérase rò δε διότι, των μαθεμαλικών» έτοι γαρ έχoισι των αιτίων τας



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