### Indivisibles and Infinitesimals

The concept 'indivisible' appeared for the first time as the word 'indivision' in the 15th century in the book '

*On Learned Ignorance*' by Nicholas of Cusa.(See Book I, Ch. Ten) The word indivision was used by Cusa to show that the greatest Oneness, which is God, and is not other than indivision, distinctness, and union. If God contracts His Oneness by plurality and finitude, a Universe of finite things appear.

The work of Cusa on indivisibles was known by Galileo because, in the 16th century, the book by Galileo on '

*Dialogues Concerning Two New Sciences*' appeared. (click) In this book, Galileo uses 'indivisibles' to extend all of the divisible bodies that God created for the Universe.

In the 17th century, Gottfried Leibniz developed the indivisibles. He called them indivisibks the 'true atoms.' In his work on indivisibles, Leibniz says that the Greeks developed monads in which some were active entelcchies. In his work, Leibniz also develops the infinitesimal calculus, which is used in all high schools today.

Now look at the book '

*A Source Book In Mathematics*"' by David Eugene Smith. This book includes the paper '

*On the Hypotheses Which Lie At he Foundations of Geometry*' by Bernhard Riemann. In the footnote on page 425 says that 'g

**eometry ought to start from the infinitesimal, and depend upon integration for statements about finite lengths, areas, or volume. This requires, inter alis, the replacement of the straight line by the geodesic:**' ...

In 1997, K. D. Stroyan posted his latest book on '

*Mathematical Background: Foundations of Infinitesimal Calculus.*Stroyan tells high school students that '

**We**

**want you to reason with mathematics**.' He also says that the pointwise approach most books give to the theory of derivatives spoils the subject. The result of the pointwise approach is that instructors feel they have to either be dishonest with students or disclaim good intuitive approximations. This is sad because it makes a clear subject seem obscure. This book shows how to bridge the gap between intuition and technical rigor.

Unless the U.S. government rejects atheism and materialism and opens the thoughts of the persons above, the USA will continue to degenerate in many ways.

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