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A D E accelerating force acquired acts angle attraction axes axis becomes body calculus central centre of force centripetal force chord circle constant continually curve descended described determine diameter difference differential diminished direction distance dividing draw drawn earth ellipse equal equation expressed falling feet flows fluxion focus follows force acting function given gravity greater height Hence increase increment independent infinitely small quantity infinitesimal initial integrating inversely less limit London magnitude maximum mean measured method miles motion move multiplied orbit parabola parallel planet portion position produced projected proportional radius ratio rectangle represent respectively solid space space described square sun's suppose surface tangent triangle ultimate uniform vanish varies velocity whence
עמוד 5 - ... calculus must have been in the hands of its inventor, did not permit him to resolve completely the difficult problems which the theory of the system of the world presents ; and he was often obliged to give conjectures, uncertain till they have been since verified by a rigorous calculation. Notwithstanding these inevitable defects, the importance and extent of his discoveries, the great number of original and profound conceptions, which have been the germ of the most brilliant theories of the...
עמוד 5 - Notwithstanding these unavoidable defects, the number and generality of his discoveries relative to this system, and many of the most interesting points of the Physico-mathematical sciences, the multitude of original and profound views, which have been the germ of the most brilliant theories of the geometers of the last century, all of which were presented with much elegance, will assure to the Principia a preeminence above all the other productions of the human intellect.
עמוד 8 - The part 2az, which is independent of h, is therefore the limit of the ratio of the increment of the function to that of the variable.
עמוד 11 - EF, of equal triangles; and these bases are reciprocally as the perpendiculars let fall upon them. COR. 2. If the chords AB, BC of two arcs, successively described in equal times by the same body, in spaces void of resistance, are completed into a parallelogram ABCV, and the diagonal BV of this parallelogram, in the position which it ultimately acquires when those arcs are diminished in infinitum, is produced both ways, it will pass through the centre of force COR.
עמוד 14 - IF A BODY REVOLVES IN A SPIRAL PQS, CUTTING ALL THE RADII SP, SQ, &C., IN A GIVEN ANGLE; IT IS PROPOSED TO FIND THE LAW OF THE CENTRIPETAL FORCE TENDING TO THE CENTRE OF THAT SPIRAL.
עמוד 16 - ... inversely as the square of the distance of the body from the center, but a body or particle in the interior with a force varying directly as its distance from the center.
עמוד 11 - III.) their ultimate perimeter ADF will be a curve line: and therefore the centripetal force, by which the body is perpetually drawn back from the tangent of this curve, will act continually...
עמוד 16 - We know that by the law of gravitation, the force with which one body attracts another varies directly as its mass, and inversely as the square of its distance...
עמוד 11 - The velocity of a body attracted towards an immovable centre, in spaces void of resistance, is reciprocally as the perpendicular let fall from that centre on the right line that touches the orbit. For the velocities in those places A, B, C, D, E, are as the bases AB, BC, CD, DE, EF, of equal triangles; and these bases are reciprocally as the perpendiculars let fall upon them.
עמוד 18 - ... perpendicularly at a distance from its middle equal to 3 cos i 4 (4 + TT sin i) of its breadth, and gives for the amount of this force in gravitation measure, where A denotes the area of one side of the blade, and P the weight of a column of the fluid of unit cross-sectional area, and of height equal to the height from which a body must fall to acquire a velocity equal to V. § 22. The assumption (§ 11) on which this investigation is founded admits no velocity of fluid motion, relatively to...