The elements of geometrie of the most auncient philosopher Euclide of Megara. Faithfully (now first) translated into the Englishe toung, by H. Billingsley, citizen of London. Whereunto are annexed certaine scholies, annotations, and inuentions, of the best mathematiciens, both of time past, and in this our age. With a very fruitfull præface made by M. I. Dee, specifying the chiefe mathematicall scie[n]ces, what they are, and wherunto commodious: where, also, are disclosed certaine new secrets mathematicall and mechanicall, vntill these our daies, greatly missed

* 1.13 The endes or limites of a lyne, are pointes.

For a line hath his beginning from a point, and likewise endeth in a point: so that by this also it is manifest, that pointes, for their simplicitie and lacke of composition, are neither quantitie, nor partes of quantitie, but only the termes and endes of quantitie. As the pointes A, B, are onely the endes of the line AB, and no partes thereof. And herein differeth a poynte in quantitie,* 1.2 from vnitie in number••

[illustration]

for that although vnitie be the beginning of nombers, and no number (as a point is the beginning of quantitie, and no quan∣titie) yet is vnitie a part of number.* 1.3 For number is nothyng els but a collection of vnities, and therfore may be deuided into them, as into his partes. But a point is no part of quantitie,* 1.4 or of a lyne•• neither is a lyne composed of pointes, as number is of vnities. For things indiuisible being neuer so many added together, can neuer make a thing diuisible, as an instant in time, is neither tyme, nor part of tyme, but only the beginning and end of time, and coupleth & ioyneth partes of tyme together.

Notes

• * 1.1

  The endes of a line.
• * 1.2

  Difference of a point fr•• ••nity.
• * 1.3

  Vnitie is a part of number.
• * 1.4

  A poynt is no part of quan∣titie.