As in the figure underwritten are ae, ai, ao. It is called the Diagonius, when it passeth from corner to corner. In solids it is called the Axis, as hereafter we shall heare.
Therefore,
6. The diameters in the same figure are infinite.
Although of an infinite number of unequall lines that be only the diameter, which passeth by or through the center
notwithstanding by the center there may be divers and sundry. In a circle the thing is most apparent: as in the Astrolabe the index may be put up and downe by all the points of the periphery. So in a speare and all rounds the thing is more easie to be conceived, where the diameters are equall: yet notwithstanding in other figures the thing is the same. Because the diameter is a right line inscribed by the center, whether from corner to corner, or side to side, the matter skilleth not. Therefore that there are in the same figure infinite diameters, it issueth out of the difinition of a diameter.
And
7. The center of the figure is in the diameter.
As here thou seest a, e, i this ariseth out of the definition of the diameter. For because the diameter is inscribed into the figure by the center: Therefore the Center of the figure must needes be in the diameter thereof: This is by Archimedes assumed especially at the 9, 10, 11, and 13 Theoreme of his Isorropicks, or Æquiponderants.
