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

An other more briefe demonstration after Flussates.

* 1.1Suppose that from vnitie be nūbers in cō••••nuall proportion how many so euer, namely, A, B, C, D. And let some prime nūber, namely, •• measure the last nūber which is D. Thē I say that th•• same E mea∣sureth A which is the next number vnto vnitie. For if E doo not measure A, then are they prime the one to the other by the 31. of the seuenth. And forasmuch as A, B, C, D, are proportionall from vnitie,

therefore A multiplying himselfe produceth B. Wherfore B and E ar•• prim••.

[illustration]

numbers (by the 27. of the seuenth). And forasmuch as A multiplying B produceth C, therefore C is to E also a prime number by the 26. of the se∣uenth. And likewise infinitely A multiplying C produceth D: wherefore D and E are prime numbers the one to the other (b•• 〈◊〉〈◊〉 same ••6. of th•• s••∣uenth•• Wherefore E measureth not D as it was supposed, which is absurd, wherefore the prime number E measureth A, whiche is nexte vnto vnities which was required to be proued.

Notes

• * 1.1

  An other de∣monstratiō a••∣ter Flussates.