2. I affirme that there are very high Mountaines in the Moone. _Keplar_ and _Galilæus_ thinke that they are higher than any which are upon our earth. But I am not of their opinion in this, because I suppose they goe upon a false ground whilst they conceive that the highest mountaine upon the earth is not above a mile perpendicular.
Whereas 'tis the common opinion and found true enough by observation, that _Olympus_, _Atlas_, _Taurus_ and _Enius_, with many others are much above this height. _Tenariffa_ in the Canary Ilands is proved by computation to bee above 8 miles perpendicular, and about this height is the mount _Perjacaca_ in _America_. Sr. _Walter Rawleigh_ seemes to thinke, that the highest of these is neere 30 miles upright: nay _Aristotle_[1] speaking of _Caucasus_ in _Asia_, affirmes it to bee visible for 560 miles, as some interpreters finde by computation, from which it will follow, that it was 78 miles perpendicularly high, as you may see confirmed by _Jacobus Mazonius_,[2] and out of him in _Blancanus_ the Jesuite.[3] But this deviates from the truth more in excesse then the other doth in defect. However though these in the moone are not so high as some amongst us, yet certaine it is they are of a great height, and some of them at the least foure miles perpendicular. This I shall prove from the observation of _Galilæus_, whose glasse can shew this truth to the senses, a proofe beyond exception and certaine that man must needs be of a most timerous faith who dares not believe his owne eye.
[Sidenote 2: _Comparatio Arist. cum Platone, Sect. 3. c. 5._]
[Sidenote 3: _Exposi. in loc. Math. Artis. loc. 148._]
By that perspective you may plainely discerne some enlightned parts (which are the mountaines) to be distant from the other about the twentieth part of the diameter. From whence it will follow, that those mountaines must necessarily be at the least foure Italian miles in height.
For let BDEF be the body of the moone, ABC will be a ray or beame of the Sunne, which enlightens a mountaine at A and _B_ is the point of contingency, the distance betwixt A and B must bee supposed to be the twentieth part of the diameter which is an 100 miles, for so far are some enlightened parts severed from the common terme of illumination. Now the aggregate of the quadrate from A _B_ a hundred, and _B_ _G_ a 1000 will bee 1010000, unto which the quadrate arising from A G must be equall according to the 47th proposition in the first booke of elements. Therefore the whole line _A_ _G_ is somewhat more than 104, and the distance betwixt H A must be above 4 miles, which was the thing to be proved.