fenfible qualities of BODY, but having it perfectly feparated from it and made abstract by an act of MIND. This intermediate

• Ariftotle diftinguilhes the three Sciences thus, ἡ μὲν * ΦΥΣΙΚΗ περὶ ἀχώρισα μὲν, ἀλλ ̓ ἐκ ακίνητα τῆς δὲ ΜΑ ΘΗΜΑΤΙΚΗΣ ἔνια περὶ ακίνητα μὲν, ε χωριςὰ δὲ ἴσως, ἀλλ' ὡς ἐν ὕλη ἡ δὲ ΠΡΩΤΗ καὶ περὶ χωριςὰ καὶ ἀκίνητα Ariftot. Metaph. lib. vi. cap. i. Which is thus explained by Duval-Phyfica quidem verfatur circa fubftantiam mobilem et materialem: Mathematicæ puræ agunt de rebus reipfa mobilibus, et a materia fenfibili re infeperabilibus, fed tamen ea ratione qua funt immobiles, et cogitatione feparata ; vel, quod idem eft, prout in fui confideratione materiam fenfibilem non includunt. Ut ergo Phyfica, mobilium et infeperabilium ; Mathematica vero, velut immobilium et feparabilium; fic Metaphyfica eft revera immobilium, æternorum, feparabilium, et divinorum contemplatrix. Doct. Peripat. Synop. p. 22. And again Ariftotle diftinguishes Mathematics from both Phyfics and Metaphyfical Forms, ἔτι δὴ παρὰ τὰ ΑΙΣΘΗΤΑ καὶ τὰ ΕΙΔΗ, τα ΜΑΘΗΜΑΤΙΚΑ τῶν πραγμάτων εἶναί φασι μεταξύ, διαφέροντα τῶν μὲν αἰσθητῶν, τῷ αΐδια καὶ ακί νητα εἶναι· τῶν δ ̓ εἰδῶν, τῷ τὰ μὲν πολλ ̓ ἄτα ὅμοια εἶναι, τὸ δὲ εἶδος αὐτὸ, ἓν ἕκασον μόνον. Metaph. lib. i. cap. vi. which is thus explained by another commentator.-Indicat Ariftoteles Platonem aliud adhuc genus rerum poffuiffe [principalium] a rebus fenfibilibus et ab ipfis ideis diverfum. Nam, præter fenfibilia et fuas formas, res mathematicas conftituit, quas medias effe dixit inter res fenfiles et inter ideas; et differunt a fenfibilibus, quod fempiterna funt et immobilia entia mathematicæ, ficut ideæ quoque funt; a formis autem et ideis diftant, 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 system of knowledge and the tranfition from Metaphyfics and general Logic, to the particular Logic of Phyfics 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 fecond bounded and defined by Number, it accordingly divides with these different fubjects into two collateral correfpondent branches-GEOMETRY and ARITHMETIC, And, as they are the fimpleft in their Prin

mathematicæ fimilia funt inter fe, hoc eft, quod plura fint ejufdem fpeciei 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 fenfiles et inter ideas, quia de utrifque aliquid commune habent, et tamen ab utrifque rurfus differunt. Joan. Ludov. Haver. Comment. in locum.

• See Ariftot. Categ. cap. vi.

ciples,

ciples, the cleareft in their Reafoning, and the moft 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 conftruction.

SECT. I.

Of Mathematical PRINCIPLES.

EXTE

XTERNAL Nature is the archetype and original of all our fenfations, and of many of our ideas: and the EVIDENCE of the EXTERNAL SENSES exercised upon the fuperficial properties of innumerable bodies with which they are familiarly and perpetually converfant, as their Length, Breadth and Depth and other exterior qualities, and

ων

* Καὶ γὰρ ἐπίπεδα καὶ σερεὰ ἔχει τὰ φισικὰ σώματα, καὶ μήκη, καὶ σιγμᾶς, περὶ ὧν σκοπεῖ ὁ μαθηματικός. ἀλλ' ἐκ ᾗ φυσικά σώματος πέρας ἕκασον· ἐδὲ τὰ συμπ βεβηκότα θεωρεῖ ἡ τοιέτοις ἔσι συμβέβηκε· Διὸ καὶ χω

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again as familiarly and inceffantly 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 philofophically remarked, that, whereas many of the properties of Body are confined to particular fenfes, thofe few, which are the fubject of Mathematics, are common to all the Senfes.

Thefe 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

ρίζει χωριςὰ γὰρ τῇ νοήσει, κινήσεως ἐςι· καὶ ἐδὲν διαφέ PEL, ἐδὲ γίνεται ψεῦδος χωριζόντων. Ariftot. Nat. Aufce lib. ii. cap. ii.

See Metaph. lib. xi. cap. i, 2, 3.

8 Κοινὰ δὲ, κίνησις, ἠρεμία, αριθμός, σχήμα, μέγε θος· τὰ γὰρ τοιαῦτα ἐδεμιᾶς ἐςιν ἴδια, ἀλλὰ κοινὰ πάσαις. Ariftot. De Anima, lib. ii. cap. vi.

abstracted

abstracted and taken away by an act of the Mind, they are conceived to be left alone, and to exist separate and independent of the bodies from which they are originally taken, conftituting 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 fome more, which are otherwise denominated Univerfal Forms; and the Abstraction, by which they are collected from the Senfes exercifed upon many individual objects, is performed in a way so perfectly obvious and familiar, and with fo much ease and perfpicuity, that they seem to present themselves to the mind immediately, and without the application of Inductive Reasoning.*

* Τὸ μὲν γὰρ περιπὸν ἔςαι καὶ τὸ ἄρτιον, καὶ τὸ εὐθὺ καὶ τὸ καμπύλον· ἔτι δὲ καὶ ἀριθμὸς, καὶ γραμμὴ, καὶ oxñμa äveυ XIVŃGews. Ariftot. Nat. Aufc. lib. ii. cap. 2.

1 Λανθάνεσι δὲ τἔτο ποιέντες, καὶ οἱ τὰς ἰδέας λέγοντες. Τὰ γὰρ φυσικὰ ψωρίζεσιν ἦτον ὅλα χωριςὰ τῶν μα Snuari. Ariftot. Nat. Aufc. lib. ii. cap. 2.

k Ενταύθα γὰρ τὸ μὲν ὅτι, τῶν αἰσθητικῶν εἰδέναι τὸ δὲ διότι, τῶν μαθεματικῶν· ἔτοι γὰρ ἔχοισι τῶν αἰτίων τας G 2

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