Monitio logica, or, An abstract and translation of Burgersdicius his logick by a gentleman.

CHAP. V. Of Quantity.

Ax. 1. AN Accident is a being inherent in a Substance.

That is, so as that it can no ways exist separate from it. Hence follows, that,

I. An Accident cannot exist without a Subject.

II. Cannot pass from one Subject to another.

III. Cannot inhere in another Accident. Of which more is to be philosophiz'd in the Me∣taphysicks.

Ax. 2. Quantity is an Accident which hath by it self Part out of Part.

In which three things are attributed to Quan∣tity: 1st. To have Parts; and therefore God, An∣gels, Human Souls, Points, Unites, &c. are nei∣ther Quantity, nor Parts of Quantity, because not consisting of Parts. 2dly. To have Part out of Part; that is, to have Parts not in Essence only, but also in Scite and Space different: For there are two kinds of Parts: Some together, and mutually penetrating each the other; as Matter and Form: Others not, but are different in Scite, as Head, Breast, Body, Limbs, &c. And such as these are re∣quir'd in Quantity. I said Part out of Part, rather than Parts, because Quantity may have but two, as in the Number Two. 3dly. To have Part out of Part by it self. Because a Corporeal Substance, and every Accident inhering in it, hath Part out of Part; but by reason of Quantity, not by it self: But, Quantity, as Magnitude, and Number, and Time, have Part out of Part, and that by themselves.

Ax. 3. Quantity is either continu'd or discrete.

Ax. 4. Continu'd is that whose Parts are con∣nected together by one common Term.

Ax. 5. Discrete, whose Parts are not connected by one common Term, and is nothing else but Number.

Number uses to be divided into Number num∣bering, and Number numbred. Number number∣ing is nothing else but Number in the Abstract, or a Collection of Unities it self, as two, three, &c. Number numbred is only Number in the con∣crete, or the things that are to be numbred, as Two Men, Three Horses, &c.

Ax. 6. Quantity continu'd, is either Magnitude or Time.

Ax. 7. Magnitude is a Permanent Quantity.

Ax. 8. Time a Fluent.

Ax. 9. Its Term is a Moment, or 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉.

That Quantity is said to be permanent which consists of Parts having a Position amongst them∣selves, or whose Parts exist together, and of which each may be shewn, where seated, and to which of the other Parts it sticks or coheres. But the Parts of Magnitude exist together, and each of them may be shewn where it is seated, and to which of the other Parts it coheres. But the Parts of Time have no Scite, because they consist in a continual Flux. Nor have the Parts of Number any Position, because they are no where seated, neither do they cohere. Yet the Parts both of Time and Number have an Or∣der amongst themselves, by which some are be∣fore others, &c.

Ax. 10. Magnitude is either a Line, or a Super∣ficies, or a Body.

Ax. 11. A Line is a Magnitude one way divisible.

Ax. 12. Its Term is a Point.

Ax. 13. A Superficies is a Magnitude, and two ways divisible.

Ax. 14. Its Term is a Line.

Ax. 15. A Body is a Magnitude three ways di∣visible.

Ax. 16. Its Term is a Superficies.

Ax. 17. A Term is an Extremity or Bound.

A Line is said to be one way divisible, be∣cause it is a meer Length without Breadth or Depth, as an Ell, a Furlong, a Mile. A Superficies two, because Length and Breadth, without Depth; as an Acre of Land. A Body three; that is, into Length, Breadth, and Thickness; as a Cube, a Sphere, &c. For altho' a Body elsewhere signifies a Substance compos'd of Matter and Form, yet in this place it denotes nothing else, but Mag∣nitude or Quantity every way divisible in the Abstract.

Nor are we yet to imagine a Longitude is to be found without Breadth, or a Breadth without Thickness: For these things are not really sepa∣rate, but distinct only in the Mind.

Ax. 18. To Superficies is reduc'd Place.

Place is the next Superficies of the Body con∣taining, as the next Superficies of the Cask is the place of Wine, &c.

Ax. 19. The Notes of Quantity are these Three: First, Quantity has not its Contrary.

That is, By it self: For if Quantity be said to be contrary to Quantity, it is because of its Quality adjoined; as when the Winter Season is said to be contrary to the Summer, because of the Cold and Heat.

Ax. 20. Secondly, Quantity receives not more and less.

That is, Is not intended or remitted; but it is extended and contracted.

Ax. 21. Thirdly, Things are said by Quantity to be equal or unequal.

I. For Equality and Inequality are Relations a∣greeing to things on the account of Quantity.

II. Hitherto of Quantity, properly so call'd, which, because contain'd in this one Category, is wont to be call'd Praedicamental. There is also another Quantity improperly so call'd, which con∣sists not in the Extension of Parts, but in the Perfection and Vertue of every thing. Hence uses it to be call'd, The Quantity of Perfection, and Quantity of Vertue. For the Essential Perfections of Things and Vertues are compos'd of divers De∣grees, as, the Quantity of a Heap or Mole of several Parts. This, because diffus'd almost through all the Categories, uses to be call'd a Transcendental Quantity.

III. To these may be added the Precepts which Aristotle gives us, Book IV. of his Metaphysicks, Cap. 13. Of Quantities, says he, some are by themselves, others by Accident. Those are said to be Quan∣tities by themselves, in whose Definition is put Quantity. And these are either Quantities, 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, that is, according to their Essence, as Line, Superficies, and those other things which we have before-mention'd: Or 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, that is, Affecti∣ons of those things which may be call'd Quan∣tities according to their Essence, as Multum, Parum, Magnum, Parvum; that is, Much, Little, Great, Small, &c. And the like if taken 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, that is, absolutely. For if 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, that is, compared one with another, they belong to the Catego∣ry of Relation.

IV. Quantities by Accident are said two ways, First, those which are said to be Quantities upon the account of the Quantity in which they are, whether extended with the extension of the Sub∣ject, as, Whiteness in the Wall; Or not, as, Musick in a Man. Secondly, Those whose Divisibility arises from the Divisibility of other things, as that of Motion, &c.