# Journey of understaning logarithms

2024-06-25T16:56:41+00:00

Finally, I got a grip on logarithms. Why they came into being. First, I watched this video, from James Tanton - Logarithms: Brief History and Brief Mat.

• How logarithms relate to `power`
• Multiplying `3.156 * 3.456 * 2.876` by hand is very tedious

How they Invented Logarithms

• Introduces Jost who also contributed to logarithms

This book should have changed mathematics forever

• Jost Burgi’s Book

Series

• One method originating in the late sixteenth century that was used extensively to save computation was the technique called `prosthaphaeresis`, a compound constructed from the Greek terms prosthesis (addition) and aphaeresis (subtraction). This relation transformed long multiplications and divisions into additions and subtractions via trigonometric identities.
• their application specifically for multiplication first appeared in print in 1588 in a work by Nicolai Reymers Ursus

From History Victor Katz observed that Napier developed logarithms “for use in the extensive plane and spherical trigonometrical calculations necessary for astronomy

From https://locomat.loria.fr/napier/napier1619construction.pdf

• Mirifici logarithmorum canonis constructio
• Napier introduced a new notion of numbers and called them `artificial numbers`
• Napier took as origin the value 10^7(10 million) and defined its logarithm to be 0. Any smaller value x was given a logarithm corresponding to the ratio between 107 and x.
• Napier first published his work on logarithms in 1614 under the title Mirifici logarithmorum canonis descriptio, which translates literally as A Description of the Wonderful Table of Logarithms.
• Napier grounded his conception of the logarithm in a kinematic framework.
• To complete the tables, Napier computed almost `ten million entries` from which he selected the appropriate values. Napier himself reckoned that computing this many entries had taken him `twenty years`, which would put the beginning of his endeavors as far back as 1594.
• `The motivation behind this approach is still not well understood by historians of mathematics`