The pathvvay to knowledg containing the first principles of geometrie, as they may moste aptly be applied vnto practise, bothe for vse of instrumentes geometricall, and astronomicall and also for proiection of plattes in euerye kinde, and therefore much necessary for all sortes of men.

Example.

[illustration] diagram

The circle is A. B. C. D. E. H, and his centre is F, the diame∣ter is A. E, in whiche diameter I haue taken a certain point di∣staunt from the centre, and that pointe is G, from whiche I haue drawen .iiij. lines to the circum∣ference, beside the two partes of the diameter, whiche maketh vp vi. lynes in all. Nowe for the diuersitee in quantitie of these lynes, I saie accordyng to the Theoreme, that the line whiche goeth by the centre is the longest line, that is to saie, A. G, and the reside we of the same diameter beeyng G. E, is the shortest lyne. And of all the other that lyne is longest, that is neerest vnto that parte of the diameter whiche gooeth by the centre, and that is shortest, that is farthest distant from it, wherefore I saie, that G. B, is longèr then G. C, and therfore muche more longer then G. D, sith G. C, also is longer then G. D, and by this maie you soone perceiue, that it is not possible to drawe .ij. lynes on any one side of the diameter, whiche might be equall in lengthe together, but on the one side of the diameter maie you easylie make one lyne equall to an other, on the other side of the same diameter, as you see in this example G. H, to bee equall to G.B, betweene whiche the lyne G. E, (as the shortest in all the circle) doothe stande euen distaunte from eche of them, and that is the precise knoweledge of their equalitee, if they be equally distaunt from one halfe of the diameter. Where as contrary waies if the one be neerer to any one halfe of the diameter then the other is, it is not possible that they two may be equall in lengthe, namely if they dooe ende bothe in the circumference of the

circle, and be bothe drawen from one poynte in the dia∣meter, so that the saide poynte be (as the Theoreme doeth suppose) somewhat distaunt from the centre of the said cir∣cle. For if they be drawen from the centre, then must they of necessitee be all equall, howe many so euer they bee, is the definition of a circle dooeth importe, withoute any regarde how neere so euer they be to the diameter, or how distante from it. And here is to be noted, that in this The∣oreme, by neerenesse and distaunce is vnderstand the nere∣nesse and distaunce of the extreeme partes of those lynes where they touche the circumference. For at the other end they do all meete and touche.