But to this I answere:
1. You must consider the height of the Mountaines is but very little, if you compare them to the length of their shadowes. Sr. Walter Rawleigh Hist. l. 1. c. 7. § 11. observes that the Mount Athos now called Lacas casts its shadow 300 furlongs, which is above 37 miles, and yet that Mount is none of the highest, nay Solinus Poly. histor. c. 21. (whom I should rather believe in this kinde) affirmes that this Mountaine gives his shadow quite over the Sea, from Macedon to the Ile of Lemnos which is 700 furlongs or 84 miles, and yet according to the common reckoning it doth scarce reach 4 miles upwards, in its perpendicular height.
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 Emus[4], 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 Meteor. l. 1. c. 11. 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, Comparatio Arist. cum Platone, Sect. 3. c. 5.
Exposi. in loc. Math. Artis. loc. 148. and out of him in Blancanus the Jesuite. 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.
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.[5]
But it may be againe objected, if there be such rugged parts, and so high mountaines, why then cannot wee discerne them at this distance, why doth the moone appeare unto us so exactly round, and not rather as a wheele with teeth?
I answere, by reason of too great a distance, for if the whole body appeare to our eye so little, then those parts which beare so small a proportion to the whole will not at all be sensible.
But it may be replied, if there were any such remarkeable hils, why does not the limbe of the moone appeare like a wheele with teeth to those who looke upon it through the great perspective on whose witnesse you so much depend? or what reason is there that she appeares as exactly round through it as shee doth to the bare eye? certainely then either there is no such thing as you imagine, or else the glasse failes much in this discovery.