# What is the meaning of 'comminuent'

I have only seen this word in the book "Differential and Integral Calculus" by Augustus De Morgan and in letters relating to this book. e.g.

On page 108 of the above book, (lines 8, 9, 10 from the top) : "By [the integral of] UdV we mean ... p. 102. where the values of ΔV in the several terms are different. but comminuent."

Thus I might suggest it is a mathematical word, yet I cannot immediately make sense of it as an adjective derived from the Latin comminuō.

Edit: The book was wrongly named as 'Elementary Illustrations of the differential and integral calculus' - thanks go to @MetaEd for the correction

• en.wiktionary.org/wiki/comminuent probably Latin. See related English here merriam-webster.com/dictionary/comminute – NVZ Aug 29 '16 at 19:41
• @NVZ while I found both the above articles, neither seem to easily give rise to an adjective that makes sense in the context above. – Somniare Aug 29 '16 at 19:45
• Even one look dictionary finds nothing: onelook.com/?w=comminuent&ls=a&loc=2osdf – Helmar Aug 29 '16 at 21:57
• This passage is not from the Elementary Illustrations of the Differential and Integral Calculus of 1899. It is from the Differential and Integral Calculus of 1836 by the same author. "By ∫UdV we mean the limit of ∑(UΔV), obtained in the same manner as in p. 102, where the values of ΔV in the several terms are different, but comminuent." [emphasis added] – MetaEd Aug 29 '16 at 23:54

The word comminuent is a coinage by the author. On page 66 of the Differential and Integral Calculus of 1836, he gives a footnote to the term:

* To avoid the tedious repetition of “a quantity which diminishes without limit when Δx diminishes without limit,” I have coined this word. If ever the constant recurrence of a long phrase justified a new word, here is a case. There are sufficient analogies for the derivation, or at any rate we must not want words because Cicero did not know the Differential Calculus. Hence we add to our dictionary as follows :—To comminute two quantities, is to suppose them to diminish without limit together : comminution, the corresponding substantive ; comminuents, quantities which diminish without limit together. To comminute has been used in the sense of to pulverize, and is therefore recognised English.

source

• How did you find this? (and thank you!) – Somniare Aug 30 '16 at 7:22
• @Somniare A title search with Google located a reproduction of the 1899 Elementary Illustrations at Internet Archive (archive.org). When I did not find the passage, I did a title search there for other editions. This located a reproduction combining in one volume the 1836 Differential and Integral Calculus and the 1899 Elementary Illustrations. Sensing confusion, I turned to page 108 in the 1836 work and found your passage. A keyword search within the reproduction located the footnote on page 66. – MetaEd Aug 30 '16 at 17:04

I can't find the passage in an online copy of DeMorgan's work. If you can point me to the passage, I'll take a look. It's likely however, that the discussion is about a proof of an integral formula. These types of proofs generally concern statements about limits, and these statements can contain expressions involving delta terms (e.g, ΔV) that represent infinitesimal changes in a variable or variables (here the variable V). It would seem that this particular infinitesimal term ΔV appears in several terms, but should not be taken to be constant across all the terms in which it appears. In other words ΔV is actually a function of the term in which it appears, but in all the terms the ΔV's are made sufficiently small (in DeMorgans's phrasing they're comminuent) that the differences between them do not affect the validity of the proof of the limit.

## comminute

is a recognized verb and its adjectival form, comminuted, is especially used in the field of medicine. Nowadays, comminuted fracture is perhaps its most common usage.

verb (used with object), comminuted, comminuting.
1. to pulverize; triturate.