**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

- 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.

From Logarithms: The Early History of a Familiar Function - John Napier Introduces Logarithms

- 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`

https://www.youtube.com/watch?v=habHK6wLkic&t=73s story of natural logarithms

https://www.youtube.com/watch?v=uMfnJ6TJinc

- where sin, cos came from
- SOHCAHTOA