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 addition of Pelitarius.

* 1.1Vnto a right lyne which cutteth a circle, to drawe a parallel line which shall touch the circle.

S••ppose that the right lyne AB do out the circle ABC in the poyntes A and B. It is required to drawe vnto the line AB a parallel lyne

[illustration]

which shall touche the circle. Let the centre of the circle be the point D. And deuide the lyne AB into two equall partes in the point E. And by the point E and by the centre D, draw the diameter CDEF. And from the point F (which is the ende of the dia∣meter) rayse vp (by the 11. of the first) vnto the dia∣meter CF a perpendicular line GFH. Then I say that the lyne GFH (which by the correllary of the 16. of this booke toucheth the circle) is a parallel vnto the line AB.* 1.2 For forasmuch as the right line CF fallyng vpon either of these lines AB & GH ma∣keth all the angles at the point •• right angles (by the 3. of this boke) and the two angles at the point Fare supposed to be right angles: therfore (by the 29. of the first) the lines AB and GH are parallels: which was required to be done. And this Probleme is very commodious for the inscribing or circumscribing of figures in or about circles.

Notes

• * 1.1

  An addition of Pelitarius.
• * 1.2

  This Pro∣bleme commo∣dious for the inscribing and circumscri∣bing of figures in or abou•• circles.