The Mathematical Principles of Natural Philosophy, Volume 1, Issue 1 (Google eBook)H.D. Symonds, 1803  Mechanics 
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Common terms and phrases
ABFD altitude angle VCP apsides attracting body bisected body describes body revolving centre of force centre of gravity centripetal force 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 focus given by position given points given ratio globe greater hyperbola immovable infinitely inversely latus rectum LEMMA let fall lower apsis meeting move 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 sine 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 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 xxxvi  To make an estimate what might be the degree of this diminution, he considered with himself that, if the moon be retained in her orbit by the force of gravity, no doubt the primary planets are carried round the sun by the like power. And, by comparing the periods of the...
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.
Page 26  ... of a hammer) is (as far as I can perceive) certain and determined, and makes the bodies to return one from the other with a relative velocity, which is in a given ratio to that relative velocity with which they met.
Page 13  ... to another, as the fixed stars do in our regions, we could not indeed determine from the relative translation of the globes among those bodies, whether the motion did belong to the globes or to the bodies. But if we observed the cord, and found that its tension was that very tension which the motions of the globes required, we might conclude the motion to be in the globes, and the bodies to be at rest...
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 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...