( 269 )
Now this premised, We are next, with him, to suppose the Earth carried about with a double motion; The one Annual, as (Fig. 1.) in B E C the great Orb, in which the Center of the Earth B, is supposed to move about the Sun A.
The other Diurnal, whereby the whole moves upon its own Axis, and each point in its surface describes a Circle, as D E F G.
It is then manifest, that if we suppose, that the Earth moved but by any one of these motions, and that regularly, (with an equal swiftness;) the Water, having once attained an equal Impetus thereunto, would still hold equal space with it: there being no occasion, from the Quickening or Slackening of the Earths motion, (in that part where the Water lyeth) for the Water thereon either to be cast Forward or fall Backward, and thereby to accumulate on the other parts of the Water: But the true motion of each part of the Earths surface being compounded of those two motions, the Annual and Diurnal; (the Annual in B E C being, as Galilæo there supposeth, about three times as fast as a diurnal motion in a great Circle, as D E F;) while a Point in the Earths surface moves about its Center B. from G. to D. and E. and at the same time, its Center B. be carried forwards to C; the true motion of that Point forwards, is made up of both those motions; to wit, of B to C, and of G to E; but while G moves by D to E, B moves backward by F to G, contrary to the motion of B to C; so that the true motion of E, is but the difference of B C, and E G; (for, beside the motion of B. above the Center; G is also[errata 1] put forward as much as from G to E; and E put backward as much as from E to G:) so that the diurnal motion, in that part of the Earth, which is next the Sun, as E F G, doth abate the progress of the Annual, (and most of all at F;) and in the other part, which is from the Sun, as G D E, it doth increase it, (and most of all at D.) that is, in the day time there is abated, in the night time is added to the Annual motion, about as much as is G E, the Earths Diameter. Which would afford us a Cause of two Tides in twenty four hours; the One upon the greatest Acceleration of motion, the Other upon its greatest Retardation.
And thus far Galilæo's Discourse holds well enough; But then
