The mathematical principles of natural philosophy, Volume 1Printed for H.D. Symond, 1803  Celestial mechanics 
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Common terms and phrases
ABFD accelerative altitude angle VCP apsides attracting body bisected body describes body revolving centre of force centre of gravity centripetal force tending circle common centre conic section conjunctly corpuscle curve line curvilinear cycloid decrease demonstrated diameter diminished direction distance draw drawn duplicate ratio earth ellipsis evanescent fame ratio fame thing figure fince focus given by position given points given ratio globe greater hyperbola immovable insinitely inversely latus rectum LEMMA let fall lower apsis manisest meeting mutually nodes orbit ordinate parabola parallel parallelogram particles perpendicular plane principal vertex PROBLEM prop quadratures quantity radii radius reciprocally proportional rectangle rectilinear right lines given SCHOLIUM similar triangles space sphærical sphere square subducted subduplicate ratio superficies suppose syzygies tangent THEOREM touch trajectory trapezium triangles ultimate ratio upper apsis velocity Wherefore whole
Popular passages
Page 6  Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.
Page 11  The effects which distinguish absolute from relative motion are the forces of receding from the axis of circular motion. For there are no such forces in a circular motion purely relative, but in a true and absolute circular motion they are greater or less, according to the quantity of the motion.
Page xxviii  Therefore the retardation is proportional to the motion communicated, and the communicated motion, when the velocity of the moving body is given, is as the density of the fluid; and therefore the retardation or resistance will be as the same density of the fluid; nor can it be taken away, unless the fluid, coming about to the hinder parts of the body, restore the motion lost.
Page 10  A property near akin to the preceding is this, that if a place is moved, whatever is placed therein moves along with it; and therefore a body which is moved from a place in motion partakes also of the motion of its place. Upon which account all motions, from places in motion, are no other than parts of entire and absolute motions; and every entire motion is composed of the motion of the body out of its first place and the motion of this place out of its place; and...
Page 3  ... line to the distance of two miles before it falls to the ground; the same, if the resistance of the air were taken away, with a double or decuple velocity, would fly twice or ten times as far.
Page 47  ... increased or diminished in the ratio of the same length to the radius of the circle; that is, as the square of that length applied to the radius; and therefore the polygon, by having its sides diminished in infinitum, coincides with the circle, as the square of the arc described in a given time applied to the radius. This is the centrifugal force, with which the body impels the circle; and to which the contrary force, wherewith the circle continually repels the body towards the centre, is equal.
Page 46  From the same demonstration it likewise follows that the arc which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time is a mean proportional between the diameter of the circle and the space which the same body falling by the same given force would descend through in the same given time.
Page 2  This force consists in the action only and remains no longer in the body when the action is over. For a body maintains every new state it acquires, by its inertia only. Impressed forces are of different origins, as from percussion, from pressure, from centripetal force.
Page 13  And thus we might find both the quantity and the determination of this circular motion, even in an immense vacuum, where there was nothing external or sensible with which the globes could be compared.
Page 27  ... both. But the one extreme part HKI will with its whole weight bear upon and press the middle part towards the other extreme part EGF; and therefore the force with which EGI, the sum of the parts HKI and EGKH, tends towards the third part EGF, is equal to the weight of the part HKI, that is, to the weight of the third part EGF. And therefore the weights of the two parts EGI and EGF, one towards the other, are equal, as I was to prove. And indeed if those weights were not equal, the whole earth...