Center of Force acting upon them, do both lie in immovable Planes, and are proportional to the Times; and fo in any given Time are every where equal; the Velocity of Motion in the leffer Distance, and the Slowness thereof in the greater fo tempering the Description of the Area's, that from thofe various Distances no Difference of the Spaces run over in the given Time doth ever arise.

XVI. Every Body which is mov'd in a Curve. Line, and doth by a Radius drawn to fome Point, either immovable, or going forwards, uniformly with a Rectilineal Motion, defcribe Area's about that Point proportional to the Times; is urged or imprefs'd by a centripetal Force tending to the fame Point.

XIX. If a Body be mov'd in an Ellipfis about the Center of the fame, the centripetal Force will be directly as the Distance of the Body from the fame Center..

XX. If a Body be mov'd in a Spiral Line, which cuts all the Radii in the fame Angle, the centripetal Force will be reciprocally as the Cube of the Distance from the Center of the Spiral.

XXI. If a Body be mov'd in an Ellipfis or Parabola, or Hyperbola, about its Focus, the centripetal Force will be every where in the duplicate Proportion of the Distance from the fame Focus reciprocally.

XXII. The Velocity of a Body moving in a Parabola about a Body placed in the Focus, the Force whereof is in the reciprocal duplicate Proportion of the Distances, is every where to the Velocity of a Body revolving in a Circle in the fame time, in the fubduplicate Proportion of

the

the Number, Two to Unity; or as the Diagonal of a Square to its Side; that is, as 10 to 7 nearly.

XXVII. Two Bodies attracting one another, defcribe like Figures both about the Common Center of Gravity, and about one another; that is, whilft they really defcribe like Figures about the Common Center of Gravity, the Eye being placed in either of the two, and not perceiving its own Motion, or that of the Center of Gravity, a Figure like to the fame will thereby feem to it to be defcrib'd.

XXXI. If a primary Planet revolving about the Sun carry a Moon along with it, this will be fo mov'd about the Primary, that it will perpetually be accelerated from the Quadrature with the Sun, unto the Conjunction or Oppofition next following; but from the Conjunction to the Quadrature, it will be retarded; and confequently will be carried more fwiftly about the Conjunction and Oppofition, but more flowly about the Quadratures.

XXXVIII. The abfolute Force of the Sun in the disturbing the Secondary Planets, and the Effects thereof, in divers Diftances from the Sun, is in the triplicate Proportion of those Distances inverfly.

XLI. If a Fluid be contain'd in a Channel form'd in the Surface of any Planet, Primary or Secondary, and be uniformly revolv'd together" with the Planet with a diurnal periodic Motion; each Part of this Fluid will be accelerated and retarded by turns; in its Conjunction and Oppofition, or at Noon-day and Midnight, it will be fwifter; in the Quadratures, or at the 6th Hour Evening and Morning, it will be flower

than

than the contiguous Surface of the Globe; and thus there will be a flux and reflux in the Channel, by turns perpetually.

XLII. If a Solid Ring be put about a Globe perfectly spherical, at the Equator of the fame, and ftick to it; there will indeed be no Motion of Flux and Reflux, but the vibrating Motion of Inclination, and the Preceffion of the Nodes, will remain. Let the Globe have the fame Axis with the Ring, and compleat its Revolution in the fame time; and with its Surface touch the Ring inwardly, and cleave to it; by its participating of the Motion thereof, the whole Frame will vibrate to and fro, and the Nodes will go back.

XLIV. If towards each equal Points of a Spherical Physical Surface of equal Thickness every where, but which Thickness is fo fmall that it is not to be regarded, there be a Tendency of equal Centripetal Forces decreafing in the duplicate Proportion of the Distances from the fame Points; any Corpufc placed any where within this Surface, will not be attracted unto any Part by the said Force; but will either rest, or continue that Motion which is begun without any Disturbance, and in the fame manner as if it were acted upon with no Force at all from that Surface: And the cafe is the fame in any Spherical concave Space within a folid Sphere, about its Center.

XLVII. If unto each Point of fome given Sphere, which is Homogeneous, or of equal Denfity every where, there be a Tendency of equal Centripetal Force decreafing in the duplicate Proportion of the Distances from the points; a Corpufcle placed within the Sphere, is attracted.

with a Force proportional to its Distance from the Center thereof.

LIX. If the Denfity of a Fluid compos'd of Particles which do flee from each other, be as the Compreffion; fo that if the preffing Force be two, or four, or eightfold, the Denfity thence, arifing is fo likewife; the Centrifugal Force of the Particles is reciprocally proportional to the Distances from the Center: And, vice versâ, where the faid Force is reciprocally proportional to the Distances from their Centers, the Particles which flee from each other compose an elas ftic Fluid, the Denfity whereof is proportional to the Compreffion.

LX. The Quantity of Matter in all Bodies,. iş exactly proportional to their Weight.

LXII. Bodies mov'd with an unequal Velocity in a very Subtle Fluid, are refifted by the Fluid in the Duplicate Proportion of their Velocity.

LXIV. As the Refiftance of Fluids in divers Velocities is in the duplicate Proportion of the Velocity; fo in divers Denfities the Velocity being given, it is in the direct Proportion of the Density it felf; but the Density and Velocity being given, in the duplicate Proportion of the Diameters; and confequently the Refiftance in general is in a Proportion compounded of the duplicate Proportion of the Velocity, and the duplicate Proportion of Diameters, and the fimple Proportion of the Density of the Medium directly.

LXVII. If a folid Cylinder, infinitely long, be revolv'd in an uniform and infinite Fluid about its own Axis, the Pofition whereof is given, and the Fluid be mov'd round by the Im pulfe

4

pulfe of this Cylinder only; and every Part of the Fluid perfeveres uniformly in its Motion; the periodic Times of the Fluid will be as their Distances from the Axis of the Cylinder directly; and the Velocities will be every where equal.

LXVIII. If a folid Sphere, in an uniform and infinite Fluid, be revolv'd uniformly about its own Axis, the Pofition whereof is given; and by the Impulfe of this alone the Fluid be turned round, and every part of the Fluid perfeveres uniformly in its Motion; the periodic Times of the Parts of the Fluid will be as the Squares of the Distances from the Center of the Sphere.

LXIX. The Velocities of all the Planets, whether Primary or Secondary, about their Central Bodies, by being in the reciprocal fubduplicate Proportion of the Distances from their Centers, do wholly overthrow the Cartefian Hypothefis of Vortices.

LXX. The Six Primary Planets, each with its own Satellites, where they have any, encompass the Sun with their Orbs, and revolve about it.

LXXI. The periodic Times of the fix Primary Planets, are in the fefqui-alteral Proportion of their mean Distances from the Sun.

LXXII. The fix Primary Planets do always, by Rays drawn to the Sun, defcribe equal Areas in equal Times, and in genéral Areas proportional to the Times.

LXXIII. The Moon, by Rays drawn to the Center of the Earth, defcribes in equal Times Areas almost equal; and in general, Areas almoft proportional to the Times.

LXXIV. The