that of Heidelberg, 137.
Hetruscus, that of Tuscan, in Italie, 138.
Sedanensis, of Sedan in France, 139.
Romanus, that of Rome in Italy, 144.
Atticus, of Athens in Greece, 150.
Anglicus, of England, 152.
Parisinus, of Paris in France, 160.
Syriacus, of Syria, 166.
Ægyptiacus, of Egypt, 171.
Hebraicus, that of Iudæa, 180.
Babylonius, that of Babylon, 200.
Looke of what parts Pes Romanus, the foote of Rome, (which is all one with the foote of Rheinland) is 1000. of such parts is the foote of
Toledo, in Spaine, 864.
Mechlin, in Brabant, 890.
Strausburgh, in Germany, 891.
Amsterdam, in Holland, 904.
Antwerpe, in Brabant, 909.
Bavaria, in Germany, 924.
Coppen-haun, in Denmarke, 934.
Goes, in Zeland, 954.
Middleburge, in Zeland, 960.
London, in England, 968.
Noremberge, in Germany, 974.
Ziriczee, in Zeland, 980.
The ancient Greeke, 1042.
Dort, in Holland, 1050.
Paris, in France, 1055.
Briel, in Holland, 1060.
Venice, in Italy, 1101.
Babylon, in Chaldæa, 1172.
Alexandria, in Egypt, 1200.
Antioch, in Syria, 1360.
Of all other therefore our English foote commeth neerest unto that used by the Greekes: And the learned Master Ro. Hues, was not much amisse, who in his booke or Treatise De Globis, thus writeth of it Pedem nostrum Angli cum Græcorum pedi æqualem invenimus, comparatione facta cum Græcorum pede, quem Agricola & alij ex antiquis monumentis tradiderunt.
Now by any one of these knowne and compared with ours, to all English men well knowne the rest may easily be proportioned out.
2. The thing proposed to bee measured is a Magnitude.
Magnitudo, a Magnitude or Bignesse is the subject about which Geometry is busied. For every Art hath a proper subject about which it doth employ al his rules and precepts: And by this especially they doe differ one from another. So the subject of Grammar was speech; of Logicke, reason; of Arithmeticke, numbers; and so now of Geometry it is a magnitude, all whose kindes, differences and affections, are hereafter to be declared.
3. A Magnitude is a continuall quantity.
A Magnitude is quantitas continua, a continued, or continuall quantity. A number is quantitas discreta, a disjoined quantity: As one, two, three, foure; doe consist of one, two, three, foure unities, which are disjoyned and severed parts: whereas the parts of a Line, Surface, and Body are contained and continued without any manner of disjunction, separation, or distinction at all, as by and by shall better and more plainely appeare. Therefore a Magnitude is here understood to be that whereby every thing to be measured is said to bee great: As a Line from hence is said to be long, a Surface broade, a Body solid: Wherefore Length, Breadth, and solidity are Magnitudes.
4. That is continuum, continuall, whose parts are contained or held together by some common bound.
This definition of it selfe is somewhat obscure, and to be understand onely in a geometricall sense: And it dependeth especially of the common bounde. For the parts (which here are so called) are nothing in the whole, but in a potentia or powre: Neither indeede may the whole magnitude bee conceived, but as it is compact of his parts, which notwithstanding wee may in all places assume or take as conteined and continued with a common bound, which Aristotle nameth a Common limit; but Euclide a Common section, as in a line, is a Point, in a surface, a Line: in a body, a Surface.
5. A bound is the outmost of a Magnitude.
Terminus, a Terme, or Bound is here understood to bee that which doth either bound, limite, or end actu, in deede; as in the beginning and end of a magnitude: Or potentia, in powre or ability, as when it is the common bound of the continuall magnitude. Neither is the Bound a parte of the bounded magnitude: For the thing bounding is one thing, and the thing bounded is another: For the Bound is one distance, dimension, or degree, inferiour to the thing bounded: A Point is the bound of a line, and it is lesse then a line by one degree, because it cannot bee divided, which a line may. A Line is the bound of a surface, and it is also lesse then a surface by one distance or dimension, because it is only length, wheras a surface hath both length and breadth. A Surface is the bound of a body, and it is lesse likewise then it is by one dimension, because it is onely length and breadth, whereas as a body hath both length, breadth, and thickenesse.
Now every Magnitude actu, in deede, is terminate, bounded and finite, yet the geometer doth desire some time to have an infinite line granted him, but no otherwise infinite or farther to bee drawane out then may serve his turne.
6. A Magnitude is both infinitely made, and continued, and cut or divided by those things wherewith it is bounded.
A line, a surface, and a body are made gemetrically by the motion of a point, line, and surface: Item, they are conteined, continued, and cut or divided by a point, line, and surface. But a Line is bounded by a point: a surface, by a line: And a Body by a surface, as afterward by their severall kindes shall be understood.
Now that all magnitudes are cut or divided by the same wherewith they are bounded, is conceived out of the definition of Continuum, e. 4. For if the common band to containe and couple together the parts of a Line, surface, & Body, be a Point, Line, and Surface, it must needes bee that a section or division shall be made by those common bandes: And that to bee dissolved which they did containe and knitt together.
7. A point is an undivisible signe in a magnitude.
A Point, as here it is defined, is not naturall and to bee perceived by sense; Because sense onely perceiveth that which is a body; And if there be any thing lesse then other to be perceived by sense, that is called a Point. Wherefore a Point is no Magnitude: But it is onely that which in a Magnitude is conceived and imagined to bee undivisible. And although it be voide of all bignesse or Magnitude, yet is it the beginning of all magnitudes, the beginning I meane potentiâ, in powre.
8. Magnitudes commensurable, are those which one and the same measure doth measure: Contrariwise, Magnitudes incommensurable are those, which the same measure cannot measure. 1, 2. d. X.
Magnitudes
