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

* 1.119 The axe of a cilinder is that right line which abydeth fixed, about which the parallelogramme is moued. And the bases of the cilinder are the circles described of the two opposite sides which are moued about.

Euen as in the description of a Sphere the line fastened was the axe of the Sphere pro••uced: and in the description of a cone, the line fastened was the axe of the cone brought forth: so in this descripti∣on of a cilinder the line abiding, which was fixed, about which the rectangle parallelogramme was mo∣ued is the axe of that cilinder. As in this example is the line AB. The bases of the cilinder ••••c. In the reuo∣lution of a parallelogramme onely one side is fixed, therefore the three other sides are moued about: of which the two sides which with the axe make right angles, and which also are opposite sides, in their motion describe eche of them a circle, which two circles are called the bases of the cilinder. As ye see in the figure before put two circles described of the motiō of the two opposit lines AD and BC, which are the bases of the Cilinder.

* 1.2The other line of the rectangle parallelogramme moued, by his motion describeth the round su∣perficies about the Cilinder. As the third line or side of a rectangle triangle by his motion described the round Conical superficies about the Cone. And as the circūferēce of the semicircle described the round sphericall superficies about the Sphere. In this example it is the superficies described of the line DC.

* 1.3By this definition it is playne that the two circles, or bases of a cilinder are euer equall and paral∣lels: for that the lines moued which produced them remayned alwayes equall and parallels. Also the axe of a cilinder is euer an erected line vnto either of the bases. For with all the lines described in the bases, and touching it, it maketh right angles,

* 1.4Campane, Vitell••o, with other later writers, call this solide or body a round Column•• or piller. And Campane addeth vnto this definition this, as a corrollary. That of a round Columne, of a Sphere, and

of a circle the cētre is one and the selfe same.* 1.5 That is (as he him selfe declareth it & proueth the same) where the Columne, the Sphere, and the circle haue one diameter.

Notes

• * 1.1

  Ninetenth diffinition.
• * 1.2

  A cillindricall superficies.
• * 1.3

  Corollary.
• * 1.4

  A round•• Co∣lumne or sphere.
• * 1.5

  A Corollary added by Cam¦pane.