Definition:Prosthaphaeresis/Logarithms

Definition

The logarithmic technique of prosthaphaeresis is based on the rule of the Sum of Logarithms:

$\log_b x y = \log_b x + \log_b y$

Any base $b$ can be used.

The original tecnhique used Napierian logarithms where the base was $0.9999999$

In due course the common (base $10$) logarithm was used, as developed by Henry Briggs, called Briggsian logarithms.

Linguistic Note

The word prosthaphaeresis or prosthapheiresis is a neologism coined some time in the $16$th century from the two Greek words:

prosthesis, meaning addition

aphaeresis or apheiresis, meaning subtraction.

With the advent of machines to aid the process of arithmetic, this word now has only historical significance.

Ian Stewart, in his Taming the Infinite from $2008$, accurately and somewhat diplomatically describes the word as "ungainly".

Sources

• 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $5$: Eternal Triangles: Base ten logarithms