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Literary notes about Differential (AI summary)

The term "differential" has been employed with a surprising range of meanings in literature, largely centered on its technical application in mathematics and physics yet occasionally venturing into more figurative territory. In many texts, it is used in the context of calculus and differential equations—appearing in discussions of exact differentials, the integration of equations of various orders, and even in the representation of geometrical and physical phenomena ([1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]). Its mathematical use extends further to mechanical contexts, such as in references to differential wheels and screws ([12], [13], [14]). Meanwhile, some authors have played with the term’s connotations; for instance, Sinclair Lewis contrasts a "generator" with a "differential" in a more colloquial sense ([15]), and Ralph Waldo Emerson employs it metaphorically to describe nature's subtle capacity to measure divine sentiment ([16]). This versatility illustrates not only the technical precision the word has acquired but also its potential as a literary device to bridge scientific precision with broader, imaginative expression.
  1. Integration of the equation M dx + N dy = 0 when its first member is an exact differential.
    — from The Declaration of Independence of the United States of America by Thomas Jefferson
  2. Differential equations of the motion in vacuo.
    — from The Declaration of Independence of the United States of America by Thomas Jefferson
  3. Integration of Differential Equations of the First Order.
    — from The Declaration of Independence of the United States of America by Thomas Jefferson
  4. Differential equations of the same deduced from their characteristic geometrical properties.
    — from The Declaration of Independence of the United States of America by Thomas Jefferson
  5. Differential equations of the motion.
    — from The Declaration of Independence of the United States of America by Thomas Jefferson
  6. Integration of Differential Equations of Orders superior to the First.
    — from The Declaration of Independence of the United States of America by Thomas Jefferson
  7. Partial Differential Equations.
    — from The Declaration of Independence of the United States of America by Thomas Jefferson
  8. Symbolical formula for representing the total differential of the n th order of a function of several independent variables.
    — from The Declaration of Independence of the United States of America by Thomas Jefferson
  9. Solution of various problems in geometry which lead to differential equations of the first order.
    — from The Declaration of Independence of the United States of America by Thomas Jefferson
  10. Solution of various problems in geometry which conduct to differential equations of the second order.
    — from The Declaration of Independence of the United States of America by Thomas Jefferson
  11. Differential equations of the motion of the gases, of the projectile, and of the gun.
    — from The Declaration of Independence of the United States of America by Thomas Jefferson
  12. Idea of differential wheels.
    — from The Declaration of Independence of the United States of America by Thomas Jefferson
  13. Simple and differential wheel and axle moved by cords.
    — from The Declaration of Independence of the United States of America by Thomas Jefferson
  14. Left and right handed screws; differential screw of Prony, called the micrometric screw.
    — from The Declaration of Independence of the United States of America by Thomas Jefferson
  15. “You—why, my good woman, you don't know a generator from a differential.”
    — from Babbitt by Sinclair Lewis
  16. Man is fallen; nature is erect, and serves as a differential thermometer, detecting the presence or absence of the divine sentiment in man.
    — from Essays by Ralph Waldo Emerson by Ralph Waldo Emerson

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