Hello, in textbooks on mathematics, I have encountered different usages of the definite article. Suppose there is a formula or a theorem named after a mathematician, say Newton. Which of the following are correct?
1. By the Newton's formula, it follows...
2. By the Newton formula, it follows...
3. By Newton's formula, it follows...
4. By Newton formula, it follows...
Thank you!
(2) and (3) are both possible. Which is used depends on convention in a particular case. For example, in UK public finance we have something called "the Barnett formula", which is always called that, and never "Barnett's formula".
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(2) and (3) are both possible. Which is used depends on convention in a particular case. For example, in UK public finance we have something called "the Barnett formula", which is always called that, and never "Barnett's formula". However, (3) is more general-purpose, so in situations where (2) is not an established convention, use (3).
(1) and (4) are not correct.