# Maclaurin and the Lituus spiral

Lots of books and web sites claim that the lituus was first defined by Roger Cotes (correct) but named by Maclaurin in his "Harmonia mensurarum" in 1722. I believe the latter is incorrect on two accounts: 1) Cotes was the first to use the word lituus, not Maclaurin; 2) Harmonia mensurarum (1722) was the book by Cotes where the lituus was defined, and Maclaurin never wrote a book with that title. The Wikipedia artcle on the lituus does not make this error.

My question is why Maclaurin has been pulled into this story? Did Maclaurin ever write about the lituus at all? Or was he somehow involved with the publishing of Cotes' Harmonia mensurarum?

I think that a possible source of error is the following entry (dated : Jan.1997) of the authoritative web -site of MacTutor History of Mathematics archive:

Lituus : The lituus curve originated with Cotes in 1722. Lituus means a crook, for example a bishop's crosier. Maclaurin used the term in his book Harmonia Mensurarum in 1722. The lituus is the locus of the point $P$ moving in such a manner that the area of a circular sector remains constant.

But MacTutor list of Maclaurin's publications does not list Harmonia mensurarum, while it is named as Cotes' posthumous work.

See Scholium, page 85 :

quam Litui Figuram appello propter formae similitudinem.

This source can explain why the mistake is repeated into many recent books and web-pages (see e.g. Wolfram MathWorld's entry, with explicit reference to MacTutor Archive).

We can comapre it with some "old" source, like :

• Thanks, yes some get it right as you say, like Wikipedia and the book by Gowing, but the Maclaurin story is all around. My question is why Maclaurin has entered the picture here at all. Has Maclaurin said anything about the lituus? Or is it a random error? – Ø. Hammer Dec 7 '15 at 13:05
• Yes yes, all well and good, I know that Cotes invented and named the lituus. But what is the story with Maclaurin? :-) – Ø. Hammer Dec 7 '15 at 21:25