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

14 The centre of a Sphere is that poynt which is also the centre of the se∣micircle.* 1.1

This definition of the centre of a Sphere is geuen as was the other definition of the axe, namely, hauing a relation to the definition of a Sphere here geuen of Euclide: where it was sayd that a Sphere is made by the reuolution of a semicircle, whose diameter abideth fixed. The diameter of a circle and of a semicrcle is all one. And in the diameter either of a circle or of a semicircle is contayned the center of either of them, for that they diameter of eche euer passeth by the centre. Now (sayth Euclide) the poynt which is the center of the semicircle, by whose motion the Sphere was described, is also the centre of the Sphere. As in the example there geuen, the poynt D is the centre both of the semicircle & also of the Sphere. Theodosius geueth as other definition of the centre of a Sphere which is thus.* 1.2 The centre of a Sphere is a poynt with in the Sphere, from which all lines drawen to the superficies of the Sphere are equall. As in a circle being a playne figure there is a poynt in the middest, from which all lines drawen to the circum∣frence are equall, which is the centre of the circle: so in like maner with in a Sphere which is a solide and bodely figure, there must be conceaued a poynt in the middest thereof, from which all lines drawen to the superficies thereof are equall. And this poynt is the centre of the Sphere by this definition of Theodosius. Flussas in defining the centre of a Sphere comprehendeth both those definitions in one, after this sort. The centre of a Sphere is a poynt assigned in a Sphere, from which all the lines drawen to the superfi∣cies are equall, and it is the same which was also the centre of the semicircle which described the Sphere.* 1.3 This defi∣nition is superfluous and contayneth more thē nedeth. For either part thereof is a full and sufficient dif∣finition, as before hath bene shewed. Or ells had Euclide bene insufficient for leauing out the one part, or Theodosius for leauing out the other. Paraduenture Flussas did it for the more explication of either, that the one part might open the other.

Notes

• * 1.1

  Fourtenth diffinition.
• * 1.2

  Theodosius diffinition of the center of a sphere.
• * 1.3

  Flussas diffi∣nition of the center of a sphere.