Fluxions, and the Idea of Time

Excerpts

• Fluxions, and the Idea of Time

  Here we want a new word, which has not been invented for the world at large, since none but mathematicians consider the subject; which word, if the change considered were change of place, depending upon change of time, would be *velocity*.

• Fluxions, and the Idea of Time

  Imagine the diameter of a circle divided into a million of equal parts, from each of which a perpendicular is drawn meeting the circle.

• Fluxions, and the Idea of Time

  We may answer that the notion of time is only necessary, inasmuch as we are not able to consider more than one thing at a time.

• Fluxions, and the Idea of Time

  But we, who cannot consider all these perpendiculars at once, are obliged to take one after another.

• Fluxions, and the Idea of Time

  and succession, disguise it as we may, is the identical idea of time introduced in Newton’s Method of Fluxions.

• Fluxions, and the Idea of Time

  who should never take it for granted that because he has made some progress in a science, he understands the first principles, which are often, if not always, the last to be learned well.

• Fluxions, and the Idea of Time

  The number which represents this line (reference being made to a given linear unit) is in a corresponding state of increase or decrease, and so is every function of this number, or every algebraical expression in the formation of which it is required.

• Fluxions, and the Idea of Time

  This not being the case, it is a cause of embarrassment to the student, that he is introduced at once to a definition so refined as that of the limiting ratio which the increment of a function bears to the increment of its variable.

Equations

Problems

No exercises in this chapter.