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Note: this was original an example question, posted by neizod. As I mentioned in meta, it would be nice if we could get the example questions asked on the site. neizod did not commit to the site and has not yet joined, so I will place it here. I can make this post community wiki if the community feels this is the right thing to do. I have also rephrased it, as per the suggestion on area51 of @J.W.Perry.

Who invented the Haversine formula (or at least the oldest paper in which it was cited)?

The relevant Wikipedia page.

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  • $\begingroup$ Your question contains the answer: the Wikipedia article on which you refer says correctly that it was introduced by Jose de Mendoza y Rios in 1801. I have his book on navigation and can confirm this. $\endgroup$
    – Alexandre Eremenko
    Nov 12, 2014 at 0:29
  • $\begingroup$ @AlexandreEremenko Well, can you write that into an answer - but not using Wikipedia? I wanted to completely avoid that, and use other sources. I simply put the page there for anyone who was curious. Does the question really warrant a downvote? $\endgroup$
    – HDE 226868 ♦
    Nov 12, 2014 at 0:30
  • $\begingroup$ This time I did not object using Wikipedia. But if you are using it in your question, it is natural to expect that you READ YOURSELF the article you mention before posting the question. $\endgroup$
    – Alexandre Eremenko
    Nov 12, 2014 at 0:43
  • $\begingroup$ @AlexandreEremenko I did read it, but chose to disregard it. I normally only mention Wikipedia articles if I've been able to access their sources and have seen that they're okay. Here, I wasn't able to look at the sources, and I didn't expect that anyone else would have easy access to them - I was obviously wrong! $\endgroup$
    – HDE 226868 ♦
    Nov 12, 2014 at 0:45
  • $\begingroup$ If you are affiliated with a university, it is possible that they have a subscription to the database called JSTOR. If so, this makes the Proceeding of the Royal Society accessible to you on your computer from the time of inception. Which is a real treasure containing all papers of Newton, Hooke, Boyle, etc. $\endgroup$
    – Alexandre Eremenko
    Nov 12, 2014 at 0:54

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Don Josef de Mendoza y Rios, F.R.S. Recherches sur les principaux Problemes de l'Astronomie Nautique, Proc. Royal Soc., Dec 22, 1796.

He himself calls this sinus-verse and cosinus-verse.

Wikipedia article which you cite in your question contains a reference on Mendoza y Rios, but on a slightly later paper of 1801.

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  • $\begingroup$ I apologize for not accepting this answer before now; I completely forgot about the question! $\endgroup$
    – HDE 226868 ♦
    Dec 4, 2014 at 16:16

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