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History of logrithms mid unit assignment
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- MHF4U
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- 12th Grade
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The original logarithms were invented by John Napier. In 1624 Briggs and Napier wereworking together on a certain task and they discovered natural logarithms which they thought
were accidental variations of John’s discoveries. The concept was worked out by Gregoire de
Saint-Vincent and Alphonse Antonio de Sarasa before 1649. Both of these mathematicians' work
involved quadrature of the hyperbola with the equation xy=1. This was done by determining the
area of hyperbolic sectors. The possibility of defining logarithms as exponents was discovered in
1985 by John Wallis and then in 1694 by Johann Bernoulli (Heimduo, 2020).
John Napiers began working on logarithms before 1954. He stated that creating all the
entries from which he selected proper values probably took about 20 years from before his work
was published (Clark, 2021). John slowly began improving his computational system where
roots, products and quotients could be found quickly from a table. This table showed powers of a
fixed number used as a base. Logarithms were invented in the 17th century to serve as a tool of
calculation (Heinduo, 2020). John Napiers published his findings in 1614. He shared his findings
in a book with the title “Mirifici Logarithmorum Canonis Descriptio" which translates to
“Description of the wonderful rule of logarithms”. The book contained 57 pages filled with
explanations and 90 pages of tables that are related to natural logarithms (Heinduo, 2020). There
was also another book that was published two years after John’s death. This book was titled
“Miricifi logarithmorum canonis constructio” which translates to “Construction of the marvelous
canon of logarithms. In this book, the steps which led to the invention of logarithms were
outlined (Britannica, 2023).
Logarithms were invented by John Napier as a tool for calculations. The purpose of this
invention was to help people in multiplication of quantities that were called sines back then
(Heinduo, 2023). John Napier, like any other mathematician, was very aware of the issues of
computation and John knew he had to create solutions to the problems that others encountered.
An example is recognizing the potential of recent developments in math, decimal fractions and
symbolic index arithmetic to help solve the issues that were associated with reducing
computation. Practitioners who had very hard work at computations used tools in the context of
trigonometry. John Napier did not develop just a logarithmic relation, he also set it in a
trigonometric way so that others could use it (Heinduo, 2023).
The location of logarithms invention is not shared however there is a statement that says
“the first table based on the concept of connecting sequences of geometry and arithmetic was
shared in Prague by Joost Burgi who is a mathematician from swiss. He published the table in
1620 which is 6 years after John Napier shared his findings (Britannica, 2023). We can assume
that John Napier may have created logarithms in Prague becuase he stayed in one place for a
very long time (Britanica, 2023).
There were connections between the techniques of prosthaphaeresis and sequences but
Napier decided that roots of logarithms can be found in a kinematic framework. There were
many historians in math that did not realize why Napier took this approach. Napier envisioned 2
particles moving along 2 lines that are never going to meet (Clark, 2021). The first line had no
length and the second line’s length was restricted. Napier envisioned both particles starting from
the same position horizontally at the same time and the same velocity. The location of the first
particle was on the infinite line where it covered the same distances at the same time. The
location of the second particle was on the line which had restricted length (Clark, 2021). Napier
made sure that the velocity of the second particle was proportional to the distance that was left
from the particle to the end point of the line. To explain in further detail, the distance the second
particle on the second line did not cover yet was the sine. The distance the first particle crossed
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