...generated in a given time, such increments or decrements will represent the fluxions. f * Sir I8AAC NEWTON, in the Introduction to his Quadrature of Curves,...motion of bodies. And after this manner, the .ancients, b) drawing moveable right lines along immoveable right lines, taught the genesis of rectangles." •f...

...generated in a given time, such increments or decrements will represent the fluxions.t * Sir ISAAC NEWTOS, in the Introduction to his Quadrature• of Curves,...observes, that " these geneses really take place in ihe nature of things, and are daily seen in the motion of bodies. And after this manner, the ancients,...

...the rotation of their sides, time by a continual flowing, and so in other things. These generations really take place in the nature of things, and are daily seen in the motion of bodies. The prime or ultimate ratios of maganudes, thus generated, are investigated by ob»ervtng their finite...

...rotation of the sides ; portions of time by continual flax : and so on in other quantities. These geueses really take place in the nature of things, and are daily seen in the motion of bodies. . . . "Fluxions are, as near as we please (quam proxime), as the increments of fluents generated in...

...by the rotation of the sides ; portions of time by continual flux : and so on in other quantities. These geneses really take place in the nature of things, and are daily seen in the motion of bodies. . . . "Fluxions are, as near as we please (quam proxime), as the increments of fluents generated in...

...angles by the rotation, of sides; portions of time by continual flux: and so on in other quantities. These geneses really take place in the nature of things and are daily seen iu the motion of bodies." He then goes on to define fluxions, or as we would now call them, differentials:...

...sacrifice of objectivity. These modern pure mathematicians cannot say with Newton: "These generations really take place in the nature of things and are daily seen in the motion of bodies." This modern limit-theory cannot be recommended to beginners of the calculus. The physical notion of...

...and thereby generated, not by the apposition of parts but by the continued motion of points. . . . These geneses really take place in the nature of things, and are daily seen in the motion of bodies." Gradually the terms and symbolism for the various types of functions represented by these curves were...

...as described by a continuous motion.' Curves, in fact, are generated by continuously moving points: 'These geneses really take place in the nature of...things, and are daily seen in the motion of bodies.' Names he had previously invented for the variable ('fluent') and its changes ('fluxion'), now, as his...

...angles by the rotation of the sides; portions of time by continual flux: and so on in other quantities. These geneses really take place in the nature of things, and are dally seen in the motion of bodies. . . . "Fluxions are, as near as we please (quam peoxime), as the...