to complete the sentences, and there are no blanks in the sentences ( as there would be for
Sentence Completion Questions).
1.
Before you attack the questions, skim the passage about Newton and Leibniz
below. Take 4 minutes and make a passage map. Time yourself.
2.
Before comparing your passage map to the one in the Answer Key, consider the
following questions:
a.
What is the main idea of each paragraph?
b.
What did you put in your passage map?
c.
What is the main idea of the passage?
Passage 1 - Who Discovered Calculus - Newton or Leibniz?
Born in 1643 in Lincolnshire, Isaac Newton is best known for his contribution to
physics, as he was the first to define many of the fundamental concepts that form
the basis of this field. Newton pioneered the study of optics, the properties of light
detectable by the human eye, with his insight that white light is made up of the
same spectrum of colour as a rainbow. Newton was also the first to demonstrate that
gravity was a universal physical force, applied to everything in the universe, in his
groundbreaking 1687 study,
Mathematical Principles of Natural Philosophy.
Newton
furthered the study of physics in this same work by explaining the three fundamental
laws of classical mechanics for the first time. Newton always wrote in Latin, as this was
the accepted scientific language of the time.
Following from insights developed by mathematicians over several centuries, Isaac Newton
was the first to elucidate the fundamental theorem of calculus and the first to explore
differential calculus, as well as its relation to integral calculus. Newton originally developed
these concepts of calculus in a 1666 treatise that was not published in full until 1704.
There are two reasons that Newton's discovery of calculus remained unknown for so
long. First, publishers in the 17th century were wary of texts in the field of theoretical
maths, which were so unprofitable that they drove one specialist publisher to bankruptcy.
Second, Newton was extremely tight-lipped about his highly original work in 'the method
of fluxions and fluents' (as he called calculus), not mentioning it in print until a brief
reference in
Mathematical Principles of Natural Philosophy.
What Newton called a fluxion
is known today as a derivative of a function, one of the basic concepts of calculus.
A derivative describes the way that the slope of a function changes over time, so it is
focused on the differences in the graph of the function. This approach is known today as
differential calculus.
Reading Chapter 3
I
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109

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Part Three: Reading
110
After commencing study of differential calculus in the 1670s, Gottfried Leibniz, a German
mathematician, developed many of the principles of calculus independently of Newton,
and was initially given credit for its discovery, with a 1684 publication. Leibniz's work was
very analytical, whereas Newton's was more geometrical. Leibniz focused on sequences of
extremely similar values, which could then be integrated (added up) to find, for example, the
area under the graph of a function. Integral calculus, as the approach developed by Leibniz

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