“ Now supposing the Earth and Moon, joyntly as one Body, carried about by the Sun in the great Orb of the Annual motion; this motion is to be estimated, (according to the Laws of Staticks, in other cases,) by the motion of the common Center of Gravity of both Bodies. For we use in Staticks, to estimate a Body, or Aggregate of Bodies, to be moved upwards, downwards, or otherwise, so much as its Common Center of Gravity is so moved, howsoever the parts may change places amongst themselves. ”

“ And consequently, supposing the Sea to be but as a loose Body, carried about with the Earth, but not so united to it, as necessarily to receive the same degree of Impetus with it, as its fixed parts do; The acceleration or retardation in the motion of this or that part of the Earth, will cause (more or less, according to the proportion of it) such a dashing of the Water, or rising at one part, with a falling at another, as is that, which we call the Flux and Reflux of the Sea ”

“ For, since that Galilæo, and (after him) Torricellio, and others, have applied Mechanick Principles to the salving of Philosophical difficulties; Natural Philosophy is well known to have been rendered more intelligible, and to have made a much greater progress in less than an hundred years, than before for many ages.
The Seas Ebbing and Flowing, hath so great a connexion with the Moons motion, that in a manner all Philosophers (whatever other Causes they have joyned with it) have attributed much of its cause to the Moon ”

“ And you find, that other Astronomers have been seen to bring in (some upon one supposition, some upon another) some kind of Menstrual Æquation, to solve the inequalities of the Moon's motion, according to her Synodical Revolution, or different Aspects (of New-moon, Full Moon, &c.) beside what concerns her own Periodical motion. ”

“ And I find them generally agreed, by their constant Observations, (and Experience dearly bought) that their times of danger are about the beginning of February and of November: that is, at those Spring Tides which happen near those times; to which they give the names of Candlemass-stream and Allhallond-stream: And if they scape those Spring-titles, they apprehend themselves out of Danger for the rest of the year. And as for March and September (the two Æquinoxes) they are as little solicitous of them, as of any other part of the year. ”

“ The Earth being undeniably the greater Body of the two (whereof there is no doubt to be made) it cannot be thought probable, that this should be carried about by the Moon, lesser than it self: The contrary being seen, not onely in the Sun, which is bigger than any of the Planets, which it carryes about; but in Jupiter, bigger than any of his Satellites; and Saturne, bigger than his. ”

“ The Periods of Tides (to say nothing of the greatness of them near the New-moon and Full-moon) so constantly waiting on the Moon's motion, that it may be well presumed, that either the one is governed by the other, or at least both from some common cause.
But the first that I know of, who took in the consideration of the Earth's motion, (Diurnal and Annual) was Galilæo ”

“ Objection, That the Spring-Tydes happen not, with us, just at the Full and Change, but two or three daies after. I should with the more confidence attempt an Answer, were I certain, whether it be so in the Open Seas, or onely in our Channels. For the Answers will not be the same in both cases. If onely in our Channels, where the Tydes find a large in-draught; but not in the Open Seas: we must seek the reason of it from the particular position of these places. But if it be so generally in the wide Open Seas: We must then seek a reason of it from the general Hypothesis. ”

“ As the Sun by it's motion about it's own Axis, is with good reason judged to be the Physical cause of the Primary Planets moving about it; So there is the like reason to believe, that Jupiter and Saturne moving about their Axes, are the Physical cause of their Satellites moving about them, which motion of Jupiter hath been of late discover'd, by the help of a fixed Spot discern'd in him ”

“ And moreover attempting to give an account of the Menstrual Periods from the Earths carrying the Moon about it self, as Jupiter doth his Satellites; which together with them is carryed about by the Sun, as one Aggregate; (and that the Earth with its Moon is to be supposed in like manner to be carried about by the Sun, as one Aggregate, cannot be reasonably doubted, by those who entertain the Copernican Hypothesis, and do allow the same of Jupiter and his Satellites.) ”

“ Æquinoctial hours, (which is indeed taken to be performed in equal times,) but increases by so much, as answers to that part of the Sun's (or Earths,) Annual motion as is performed in that time. For, when that part of the Æquinoctial, which (with the Sun) was at the Meridian yesterday at noon, is come thither again to day, it is not yet Noon (because the Sun is not now at the place where yesterday he was, but is gone forward about one degree, more or less) but we must stay till that place, where the Sun now is, comes to the Meridian before it be now Noon. ”

“ But it is now, the best part of twenty years, since I have had frequent occasions to converse with some Inhabitants of Rumney-marsh in Kent; where the Sea being kept out with great Earthen walls, that it do not at high water overflow the Levell; and the Inhabitants livelyhood depending most on grazing, or feeding Sheep; they are (as you may believe they have reason to be) very vigilant and observant, at what times they are most in danger of having their Lands drowned. ”

“ That a Body in motion is apt to continue its motion, and that in the same degree of celerity, unless hindred by some contrary Impediment; (like as a Body at rest, to continue so, unless by some sufficient mover, put into motion:) And accordingly (which daily experience testifies) if on a Board or Table, some loose incumbent weight, be for some time moved, & have thereby contracted an Impetus to motion at such a rate ”

“ That though Euclid's Σημογ, which we translate, a Point, be not indeed Nomen Quanti; yet cannot this be actually represented by any thing, but what will have some Magnitude; nor can a Painter, no not Apelles himself; draw a Line so small, but that it will have some Breadth; nor can Thread be spun so Fine, but that it will have some Bigness; (pag. 2, 3, 19, 21.) is nothing to the Business; For Euclide doth not speak either of such Points, or of such Lines. ”

“ So that in pursuance of Galilæo's Notion, the Menstrual adding to or detracting from the Annual motion, should either leave behinde, or cast forward the loose waters incumbent on the Earth, (and thereby cause a Tide, or accumulation of Waters;) and most of all at the Full-moon and New-moon, where those Accelerations or Retardations are greatest. ”

“ Like as a loose thing, lying on a moving body; if the body be thrust suddainly forward, that loose thing is cast back, or rather left behind, not having yet obtained an equal impetus with that of the body, on which it lyes ”

“ That it appears not how two Bodies, that have no tye can have one common Center of Gravity: that is (for so I understand the intendment of the objection) can act or be acted in the same manner, as if they were connected: I shall onely answer, that it is harder to shew How they have, than That they have it. ”

“ Rook's, in confutation of Mr. Hobs's Duplication of the Cube: Which when he had repeated, pag. 43. He doth then (that it might seem absurd) change those words, æquales quator cubis dv; (pag. 43 line 33.) into these (p. 44. l. 5.) aqualia quator Lineis, nempe quadruplus recta dv: And would thence perswade you, that Mr. Rook had assigned a Solide, equal to a Line. But Mr. Rook's Demonstration was clear enough without [errata 6] Mr. Hobse's Comment. Nor do I know any Mathematician (unless you take Mr. Hobs to be one) who thinks that a Line multiplyed by a Number will make a Square ”