A Short History of the Cartesian Coordinates
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Transcript of A Short History of the Cartesian Coordinates
The first intent
of formalizing
the geometry
concepts and
knowledge came
from Euclid’s
Elements (c. 300
BC).
Elements is probably a
collection of theorems
previously proved by
other mathematicians
that predated Euclid
with some original
work; among them
Pythagoras.
However, geometry
became analytic
with the
publication of
René Descartes'
(1596–1650)
masterpiece in
1637: Discourse on
the Method.
In an appendix to the
Discourse, titled La
Gèomètrie, he
included applications
of algebra to
geometry, giving a
push to the use of
geometry to solve some
algebraic problems.
But some authors claim
that the discovery of
the coordinate system
should be attributed
to Pierre de Fermat
(1601–1665), because
Fermat had more
geometrical insight
than Descartes.
“But as his work of about
1629 was not
communicated to others
until 1636, and was
published posthumously
only in 1679, it could
not be possibly have
influenced Descartes in
his own invention, and
Fermat never hinted that
it had.”
James Newman,
expressing his
thought about to
whom should be
attributed the
'modern' use of the
coordinate system
states:
“Fermat may have preceded
Descartes in stating
problems of maxima and
minima; but Descartes went
far past Fermat in the use
of symbols, in
"arithmetizing" analytic
geometry., in extending it
to equations of higher
degree.”
But… in order to
develop a useful
geometric coordinate
system to solve
mathematical problems
related to geometry and
physics two important
steps are needed:
The number zero has no
zero-history, on the
contrary, its uses,
manipulations and
rejections has been
traced as far as the
beginning of
civilization itself.
Some form of acceptance
can be found in Greece,
India, Babylon.
With the acceptance
of the negative
numbers the story is
similar: some
mathematicians
argued against the
existence of numbers
"below zero". Other
considered that
subtraction from zero
was "nonsense".
Descartes used only an
X-axis and did not
refers to a Y-axis. For
each value of x he
computed the
corresponding y from
the equation, thus
getting the coordinates
x and y.
Bell again: “The use of two
axes obviously is not a
necessity but a
convenience. In our
terminology, he used the
equivalent of both
rectangular and oblique
axes”. “In Descartes' work
every thing was measured
with positive distances.”
The earliest use of
negative coordinates
is attributed to Isaac
Newton (1642–1727) in a
collection of figures
and graphs of
polynomials of the
third degree of his
book ...
In fact, in some of the
figures he used the
capital letter X to label
the horizontal axis, the
capital letter Y for the
vertical axis, and even
the capital letter O to
label the point of
intersection of both
axes.
References:
[1] Bell E. T. (1945). Development of Mathematics.
2nd. ed. McGraw-Hill Book Company. New York.
[2] Descartes, Rene. (1956). The Geometry. In James R.
Newman (Ed.) The World of Mathematics. Vol. 1. (pp.
235-253). Simon and Schuster. New York.
[3] Newton, Sir Isaac. (c. 1760). Enumeration Of
Lines Of The Third Order, Generation Of Curves By
Shadows, Organic Description Of Curves, And
Construction, Of Equations By Curves. Retrieved
2007 from the digital version at Google Book
Search at http://books.google.com/books?
id=6I97byFB3v0C&dq=newton+enumeration+curves.
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