The arte of logick Plainely taught in the English tongue, according to the best approued authors. Very necessary for all students in any profession, how to defend any argument against all subtill sophisters, and cauelling schismatikes, and how to confute their false syllogismes, and captious arguments. By M. Blundevile.

CHAP. IX.

Of Quantitie.

WHat is quantitie, and how is it diuided?

Quantitie is that which comprehendeth the greatnesse and number or multitude of things, and is diuided into two kindes, that is, whole and broken.

What is whole quantitie?

Whole quantitie, called in Latine, quantitas continua, is that whose parts are ioined together with some common bound or limit, which is the ending of one part, and the beginning of ano∣ther, as the parts of the line here set downe in the margent, mar∣ked with the letters a. c. are coupled together with the middle* 1.1 point b. which point is the ending of a. b. and the beginning of b. c.

How many kindes of whole quantitie be there?

Of whole quantitie there be three kindes, that is, linea, superfi∣cies, and corpus.

Shew how they are defined and diuided.

Linea (in English, a line) is a length without either bredth or thicknesse, which is either right, or crooked; •…•…ight, as a yard, an ell, or pole; crooked, as a hoope, or circle.

Superficies (which wee may properly interprete to be the vp∣per face of any thing) is a length and bredth without depth or thicknesse; and that is either plaine, or bowing; plaine, as a plaine or smooth floore; bowing or compassing, as a vault or ouen, whereof the outward side is called conu•…•…x, and the inward side concaue or hollow.

Corpus (which is as much to say as a body) is that which hath both length, bredth, and depth, and that is either round, or with angles; round, as a bowle or ball; with a•…•…gles or co•…•…ners, as a square die, or such like thing. All which three kindes of quantitie are to be considered onely with the minde mathematically. as things abstract, and separated from all k•…•…nde of matter, t•…•…at is to say as things that haue no being •…•…t al, but imaginatiuely▪ and yet so nec•…•…ssarily inuented by man, as nothing can be measured with∣out

them. To these three kindes of whole quantitie may be also added two other kindes, that is to say, mouing, and time, being taken for the measure, space, or distance of place or time wherein any thing is moued.

How many kindes of this mouing be there, and which be they?

Of this mouing there be three kindes, that is, right, circular, and mixt. The right belongeth to the foure elements, and to bo∣dies without life: for their natuall mouing is either right vpward, or else right downeward, as the fire, whose proper mouing is al∣waies to ascend right vp, and the mouing of a stone, or such like heauie thing, is to fall right downeward: for (according to the rules of philosophie) all light things doe moue vpward, and all heauie things downeward. Circular, or round mouing, belongeth to the heauens, and celestiall bodies, which doe turne round like a Cart wheele. The mixt mouing (that is to say, partly right, and partly round) belongeth to all liuing beasts, that goe sometime forward, sometime backward, or sidelong, sometime vpward, and sometime downeward.

How is time diuided?

Time is diuided into three kindes, that is, into time past, time present, and time to come: and vnder time are comprehended yeares, moneths, weekes, daies, houres, and all other words sig∣nifying distance or difference of time.

What is broken quantitie?

Broken quantitie, called of the Latines, quantitas discreta, is that, whose parts are not ioined with any common bound or li∣mit, but be loose and seuerall one from another; which quantitie is diuided into two kindes, that is, number and speech.

What is number, and how is it diuided?

Number is a multitude or summe of vnities or ones gathered together: and such number is either simple, respectiue, or figura∣tiue: Simple, as, two, three, foure, fiue, &c. Respectiue, as halfe, double, treble, quadruble, and such like: Figuratiue, as a three∣square or foure-square number, like to these here figured ∴ :: and such like.

What things are comprehended vnder broken quantitie?

All names of measures, whereby we measure any thing, either

drie or liquid, as gallon, quart; pint, bushell, pecke, pound, dram, scruple, graine, &c.

How is speech here taken?

Speech is taken here for the measure or quantitie of syllables, whereof some be long, and some be short: and such quantitie is to be considered either in harmonie, in rythme, or verse; of which things, the generall and speciall kindes, together with the rest that haue beene said touching quantitie, are orderly set forth in the Table of quantitie here following.

What, and how many properties doe belong to quantitie?

To quantitie belong three properties: First, to haue no con∣trarietie; for great and small be not of themselues contrarie, but only by way of comparison. Secondly, to be greater or lesser, but not more or lesse, spoken aduerbially; for a little quantitie is a quantitie as well as the greatest quantitie of all. The third and chiefest propertie of quantitie, is, to be equall or vnequall.

The Table of Quantitie.

• Quantitie is either
• ...
  • Whole, if it bee whole, it is either
  • ...
    • permanent, if it be per∣manent, it is either
    • ...
      • A line, which is either
      • ...
        • Right, as a yard, an ell. Or crooked, as a hoope, or bow, &c.
      • A superficies, which is either
      • ...
        • Plaine, as a smooth floore, &c.
        • Or bowing, as a vault, or ouen, &c.
      • Or a body, which is ei∣ther
      • ...
        • Round, as a bowle or ball.
        • Or with corners, as a square die, &c.
    • Or mouea∣ble, if it bee moueable, it is either
    • ...
      • Motion, which is either
      • ...
        • Right,
        • Circular,
        • Or Mixt.
      • Or time, and that is either
      • ...
        • Time past,
        • Time present,
        • Or time to come.
  • Or broken: if it be bro∣ken quanti∣tie, it is ei∣ther
  • ...
    • Number, which is either
    • ...
      • Simple, as euen or odde, &c.
      • Respectiu•…•…, as double, treble, &c.
      • Or figuratiue, as three-cornered, foure-cornered, &c.
    • Or measure of speech, which consisteth either
    • ...
      • In composition of syllables, as Dactilus, Spon∣de•…•…s, &c.
      • In harmonie, as a third, a fist, &c.
      • In rythme, as charme, harme.
      • Or in verse, as hexamiter, pen∣tami•…•…er, Iam∣bicke.

Notes

• * 1.1

  b a—c