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You can spell the possessive form "Eratosthenes's" if you wish, but it makes for a rather clumsy sound. It is quite common, in British English anyway, to omit the 's' following the apostrophe after a name or other noun that ends in 's', for reasons of euphony.

The two accepted forms for possessive singular nouns ending in s are:

Add an apostrophe (') after the existing s at the end of the word: Eratosthenes'

Add an apostrophe s ('s) after the existing s at the end of the word: Eratosthenes's

Examples:

Eratosthenes' life was devoted to science.

Eratosthenes's life was devoted to science.

Note: The -s's is the most commonly used form, but if you are a student, use the form that is preferred by your teacher.

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