In arithmetic the question is given; in algebra the answer is given; in calculus neither is given. As an example:

y = 3x² + 2x + 1

In arithmetic x is given; in algebra y is given; in calculus neither is given. In its most general form, the original equation says:

(    ) = 3(    )² + 2(    ) + 1

If a small amount of x is added to x to one side of the equation then a small amount of y should be added to y on the other side of the equation such that:

(y + y) = 3(x + x)² + 2(x + x) + 1 i.e.       (y + y) = 3(x² + 2xx + x²) + 2(x + x) + 1             [y] + y = [3x²] + 6xx + 3x² + [2x] + 2x + [1]

x and y are small amounts of x and y. Quantities in [   ]'s cancel out according to the original equality. What remains is:

y = 6xx + 3x² + 2x

Dividing both sides by x:		= 6x + 3x + 2
In the "limit" as x0:		= 6x + 2	or		= 6x + 2

6x + 2 is the derivative of 3x² + 2x + 1. x cannot be equal to 0 because then y would be divided by zero. The definition of the derivative can be found using the same method as above. The formula for the derivative is:

Starting with y = f(x), plug in <y + y> for <y> and <x + x> for <x>, subtract the old equation from the new and then divide both sides by x.

-- Bigger yet Smaller: Newton used a very small thing to solve a very large thing. The small thing used was the infinitesimal. The large thing solved was the path length of the orbits of the planets.
-- An infinitesimal is as a quantity that approaches zero but never actually reaches zero. When zero is reached, the thing that is large becomes universal.
-- Re: the philosophy of the derivative: one can derive something from a relation when there is an equality.
-- Re: the philosophy of integration: it's the little things that add up.
-- A philosophical discussion of the derivative can be found at: http://www.friesian.com/calculus.htm.
-- The word "calculus" comes from "rock", and also means a stone formed in a body http://soucc.southern.cc.oh.us/home/jdavidso/MathAdvising/AboutCalculus.html.

Trigonometry: Sine is associated with rise; cosine is associated with run. Tangent = sin/cos = opp/adj = rise/run = slope = dy/dx.

"Newton, who died in 1727, won immortality for formulating the law of gravity, but he was also a theologian who wrote well over a million words on biblical subjects and was influenced by Hebrew scripture, according to academic articles on his work.

The BBC statement said he studied the Bible for more than 50 years, trying to unravel what he believed were God's secret laws of the universe." Feb. 23 2003 - http://www.ctv.ca/servlet/ArticleNews/story/CTVNews/1046029105331_30?hub=SciTech.

End Times Now - Second Coming - by same author

600, 60 and 6 extend a progression. A zero date has been reached.

0-date = black hole. Go to full site. All content original.

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As is evident in the definition of an infinitesimal, mathematics is as a language that never stops "talking" even when the answer is reached. Making the switch from the language of data processing to the language of word processing is as a continuation of Newton's work. Newton's seat = judgement seat.