Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/186

 is, fifteen first minutes of a degree, in one first minute of an hour; that is, fifteen seconds of a degree, in one second of an hour; and because one second is the time of the shot, therefore in this time the Western horizon riseth fifteen seconds of a degree, and so much likewise the mark; and therefore fifteen seconds of that circle, whose semidiameter is five hundred paces (for so much the distance of the mark from the Piece was supposed.) Now let us look in the table of Arches and Chords (see here is Copernicus his book) what part is the chord of fifteen seconds of the semidiameter, that is, five hundred paces. Here you see the chord (or subtense) of a first minute to be less than thirty of those parts, of which the semidiameter is an hundred thousand. Therefore the chord of a second minute shall be less then half of one of those parts, that is less than one of those parts, of which the semidiameter is two hundred thousand; and therefore the chord of fifteen conds shall be less than fifteen of those same two hundred thousand parts; but that which is less than (a) fifteen parts of two hundred thousand, is also more than that which is four centesmes of five hundred; therefore the ascent of the mark in the time of the balls motion is lesse than four centesmes, that is, than one twenty fifth part of a pace; it shall be therefore (b) about two inches: And so much consequently shall be the variation of each Western shot, the Earth being supposed to have a diurnal motion. Now if I shall tell you, that this variation (I mean of falling two inches short of what they would do in case the Earth did not move) upon triall doth happen in all shots, how will you convince me Simplicius, shewing me by an experiment that it is not so? Do you not see that it is impossible to confute me, unless you first find out a way to shoot at a mark with so much exactnesse, as never to misse an hairs bredth? For whilst the ranges of great shot consist of different numbers of paces, as de facto they do, I will affirm that in each of those variations there is contained that of two inches caused by the motion of the Earth.

Pardon me, Salviatus, you are too liberal. For I would tell the Peripateticks, that though every shot should hit the very centre of the mark, that should not in the least disprove the motion of the Earth. For the Gunners are so constantly imployed in levelling the sight and gun to the mark, as that they can hit the same, notwithstanding the motion of the Earth. And I say, that if the Earth should stand still, the shots would not prove true; but the Occidental would be too low, and the Oriental too high: now let Simplicius disprove me if he can.

This is a subtilty worthy of Sagredus: But whether this variation be to be observed in the motion, or in the rest of the Earth, it must needs be very small, it must needs be swallowed up