## Miscellanea curiosa mathematica: or, The literary correspondence of some eminent mathematicians in Great Britain & Ireland. Containing a choice collection of mathematical essays & dissertations on what is most valuable & really useful, not only in algebra, trigonometry, the doctrine of chances, astronomy, chronology, geometry, gunnery, infinite series, fluxions, fluents, exponentials, the quadrature of curves, &c. but likewise a curious collection of 160 new problems, with their solutions, in most branches of the mathematics ..., Volume 1 |

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Page 62 - ... the angle of reflection is always equal to the angle of incidence, the image for any point can be seen only in the reflected ray prolonged.

Page 1 - ... be always, proportional to the velocity of the motion. If the force were as the square of the velocity, all that part of the force, which was above the proportion of the velocity, would arise out of nothing.

Page 97 - IN a plain triangle, the fum of any two fides is to their difference, as the tangent of half the fum of the angles at the bafe, to the tangent of half their difference. Let ABC be a...

Page 291 - ... fine of double the latitude, or, which comes to the fame thing, as the fquare of the right fine of the latitude. And the arcs of the degrees of' latitude in the meridian, increafe nearly in the fame proportion.

Page 2 - ... by a greater number of particles in the same time ; and again, in proportion to its velocity, it is resisted by the same particles singly with a greater force, as being to be moved out of their places with greater velocity. What I have thus demonstrated concerning any force, considered as the cause producing an effect, and concerning the time, during which the force operates, is on all hands acknowledged to be true concerning velocity. And, therefore, velocity and force, in this case, are one...