History of Mathematics: From the 17th Century to Key Developments

This essay provides an overview of the history of mathematics, beginning in the 17th century with the emergence of key mathematicians and the development of scientific theories. It traces the evolution of geometry and algebra, the introduction of mathematical notations, and the contributions of figures like Galileo, who focused on Euclidean geometry and challenged Aristotelian views. The essay explores the development of notations, including the use of plus and minus signs, and the contributions of mathematicians like Vieta, who perfected algebraic symbolism. It further discusses the contributions of Simon Stevin and John Napier, who introduced decimal fractions and logarithms, respectively. The essay also covers the contributions of Brahe, Kepler, and Descartes, who played key roles in developing analytic geometry and solving algebraic equations. The essay concludes by highlighting the contributions of Newton and the development of geometry by Desargues and Poncelet.

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History of mathematics 2
History of mathematics
The knowledge and emergence of mathematics started in the seventeenth century. At this
age, different mathematicians emerged. Their main aim was to spread the knowledge by
developing different theories. The growth of science was a key pillar of the mathematics
development. Therefore, mathematics history can be traced back to William Gilbert’s DE
Magnete in 1600 and Isaac Newton’s Opticks in 1704 (Courant and Herbert, 1996). All these
materials focused on developing experimentation of scientific facts. Other mathematician and
scientist followed and developed their own materials which later led to the renaissance of
mathematics. Geometry and algebra were able to emerge in connection with the different
researches. Moreover, further researched led to other mathematical concentrations on topics such
as probability, trigonometry, arithmetic, logarithms, calculus among others.
Galileo is one of the major figures in the history of mathematics and science. His
telescopic observation has been used to explain different scientific and mathematical
formulations. In the mathematical area, Galileo was able to concentrate on geometry of Euclid
(Cook, 2005). In the end, he was able to show that bodies of the same material and with different
weights fall with equal speed. This was through an open challenge. His invention of telescope
was able to bring out a lot of fame and led to disapproving of Aristotelian view of earth.
The next era of mathematics focused on mathematical notations. The notations were able to form
different basis of writing mathematical equations and representations. The first notations were +
and – which appeared on Johann Widmann’s Mercantile Arithmetic in 1489. Different
mathematician were as well involved in formulation of different mathematical notations such as
equal, multiplication, division, greater, less among others. Franc¸ois Vi`eta was able to get

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involved in perfecting of algebraic symbolism (Fauvel, Flood and Wilson, 2000). The
mathematician was able to show that letters can be used in place of numbers to form equations.
The literal notations were able to make it possible to form general theory of equations (Anglin,
1994). In addition, other mathematician who played a key role in symbolism of mathematics
includes Diophantus and Descartes. These mathematicians were able to formulate the use of
different notations in mathematics.
In addition, Simon Stevin was able to play a key role in formulation of decimal fractions
in arithmetic. In addition, Franc¸ois Vi`eta was able to play a key role in development of
different rules of operating the decimal fractions. In addition, Stevin was able to develop
different notations which proved to be important in decimal fractions. Moreover, another key
mathematician in the history of mathematics is John Napier, who was able to bring out the idea
of logarithms (Philip’s, 2000). In mathematics, Napier was able to concentrate with practicalities
of computations. His development of numbering rods was able to play an important role in quick
calculation of partial products. In addition, other important mathematicians who played key role
in the history of mathematics include Brahe and Kepler. Kepler was able to formulate the area of
circle when he formulated and imagined that a circle was made of infinite number of triangles.
Moreover, he was able to develop a key model of relating planetary spheres and regular
geometric solids.
In addition, writings of Descartes are able to play a key role in mathematics today. Rene
Descartes was able to play an important role in formulating different mathematical interventions.
Rene was able to play a key role in inventing of Cartesian geometry. In the inventions, Rene was
able to form a critical role in algebra to geometry. In addition, in geometry, Descartes was able to
bring out the three crucial notations of x, y and z (Boyer, 1991). He went further to define that

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any square is able to represent area and cubic represent volumes. In addition, the mathematician
was able to use the La Geometrie theme in generalization of three and four line problems which
had been developed by Pappus. In addition, Descartes played a crucial role in formulation for
finding a normal. In his Book II, he was able to devise a pure algebraic method for finding a
solution to the normal at any point of a curve.
In addition, in his last book, Descartes was able to focus on solving algebraic equations
and their aspects in mathematics. The major recommendation of geometric aspect was that all the
expression should be taken to one side and then equated to zero. He highlighted that every
equations must have different distinct roots. In addition, to solve these problems, Descartes noted
that every root must be able to appear in the corresponding linear factor of (x-a) (Philip’s, 2000).
In addition, Descartes was able to develop Principia Philosophiae in the aim to transfer the
methods of mathematical thoughts. Descartes was critical in analytic geometry. The
mathematician was able to develop key formulations in solving algebraic equations to different
curves. In addition, in his research, Descartes was able to formulate the working of the solar
systems in understandable terms. The experimental theories were able to include the Kepler’s aw
of motions and showed that planets were not circular but elliptical. In addition, Newton was able
to enhance the formulation of mathematics through the invention of gravitational pulls
discoveries.
In addition, in the geometry perspective, Desargues and Poncelet were able to enhance
the development of different mathematical perspectives. Descartes was able to bring out the
ideas of asymptotes of hyperbola and its tangents. In addition, Poncelet in Traite, was able to
made extensive use if controversial principle of geometric continuity. Poncelet was able to
exploit the law of duality in projecting planes (Gary, 2002). The idea was to relate the valid

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statements of points and lines. The first valid statement of relating a point and line is able to give
rise to second valid statement when the point and lines are interchanged. The dual of Desargue’s
theorem is critical in finding the solution when points and lines are interchanged. Poncelet was
able to generate key geometric issues and solutions in different situations. Poncelet was able to
aid in formulating solutions for different algebraic equations.

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References
Anglin, W. S. (1994). Mathematics: A Concise History and Philosophy. New York: Springer-
Verlag.
Boyer, C. B. (1991). A History of Mathematics. 2d ed. New York: John Wiley.
Cook, R. (2005). The History of Mathematics: A Brief Course. 2d ed. New York: Wiley.
Courant, R. and Herbert R. (1996). What is Mathematics? An Elementary Approach to Ideas and
Methods. 2nd ed. Revised by Ian Stewart. Oxford: Oxford University Press.
Fauvel, J., Flood, R., and Wilson, R., eds. (2000). Significant Figures: A History of Mathematics
at Oxford. Oxford: Oxford University Press.
Gary, B. (2002). The Honors Class: Hilbert’s Problems and Their Solvers. Natick, Mass.: A. K.
Peters.
Phillip’s, G. (2000). Two Millenia of Mathematics: From Archimedes to Gauss. New York:
Springer-Verlag.