More than what was asked, but below is a near-copy of an etymological answer I left on math.SE a while ago, on the etymological origin of the words "zero", "cipher", and "nought". (Sources: Online Etymology Dictionary and Oxford English Dictionary.)
zero: circa 1600, (either from Middle Latin zephirum, or French zéro or its source Italian zero, for *zefiro) in any case from Arabic sifr "cipher", itself a translation of Sanskrit śūnya "empty place, desert, naught".
cipher: late 14th century, from Arabic sifr, "zero", literally "empty, nothing", from safara "to be empty", loan-translation of Sanskrit śūnya "empty". The word "cipher" came to Europe with Arabic numerals. Originally meant "zero", then "any numeral", then (c. 1520s) "coded message". OED: "The Arabic was simply a translation of the Sanskrit name śūnya, literally ‘empty’."
nought: variant of naught which means "nothing". The meaning of "zero, cipher" is only from the early 15th century. (?c1425 Crafte Nombrynge in R. Steele The Earliest Arithmetics in English. (1922) 20: "A 0 is noȝt, And twyes noȝt is but noȝt.")
So these sources seem to agree that:
- In Sanskrit, the word for "empty" (śūnya) was used for zero.
- Correspondingly when translating into Arabic, the word sifr based on the word safara, meaning "to be empty", was used for zero.
- For the number in English, cipher and zero were imported from Arabic, but also, similar to the passing from Sanskrit to Arabic, the existing word for "nothing" (nought) was used.
Abbreviations and contractions of words follow many conventions, take for example the word continued I have seen it abbreviated/shortened/contracted or clipped in three ways.
Mathematics can be similarly contracted
- math
- math.
- (math's) maths
Perhaps, originally, the written form with the apostrophe, math's, was more common in Great Britain but over time the apostrophe became obsolete. In fact the apostrophe in math's has no effect on its pronunciation. Unfortunately, I don't have access to the Oxford English Dictionary to confirm my suspicion that the term math's was ever used.
The Online Etymology Dictionary instead states that the American math first appeared in 1890 while the British maths is attested from 1911.
Wikipedia has this to say on contractions:
An abbreviation is a shortening by any method; a contraction is a
reduction of size by the drawing together of the parts. A contraction
of a word is made by omitting certain letters or syllables and
bringing together the first and last letters or elements; an
abbreviation may be made by omitting certain portions from the
interior or by cutting off a part. A contraction is an abbreviation,
but an abbreviation is not necessarily a contraction.
Further on, Wikipedia explains
In British English, according to Hart's Rules, the general rule is
that abbreviations (in the narrow sense that includes only words with
the ending, and not the middle, dropped) terminate with a full stop,
whereas contractions (in the sense of words missing a middle part) do
not.
Curious to see whether I could find the apostrophe version, I turned to Google Books and found to my surprise that math's existed in the US, this example is dated 1836, and predates Word Detective's claim that the first instance of math appeared in 1847.
Larry Trask who was professor of Linguistics in Sussex University (UK) mentions the most common shortened forms where the apostrophe still survives.
A few words which were contractions long ago are still conventionally
written with apostrophes, even though the longer forms have more or
less dropped out of use. There are so few of these that you can easily learn them all. Here are the commonest ones, with their original longer forms:
- o'clock, of the clock
- Hallowe'en, Halloweven
- fo'c's'le, forecastle
- cat-o'-nine-tails, cat-of-nine-tails
- ne'er-do-well, never-do-well
- will-o'-the-wisp, will-of-the-wisp
EDIT
Published in Richmond USA by William F. Richie, 1853-54, The Merit Roll of the Cadets of the Virginia Military Institute, July 1853 lists math's as the shortened form for mathematics twice!
Personal Reflections
As demonstrated in the excerpts I provided, it seems clear that the spelling convention for contracted words i.e., the use of the apostrophe for showing the omission of letters, was also used in the US. The shortened form math's was necessary in order to save space but for some reason the superfluous apostrophe and the letter -S were kept despite logic demanding that the word math was shorter. The question also arises whether this contracted word was ever actually spoken by Americans? My guess? Probably not, they chose not to say maths /maθs/ because it sounded plural and therefore opted for the clipped form, math /maθ/ in speech. The British, being renowned traditionalists, decided to keep the "silent" apostrophe in speech and thus favoured the longer form maths.
Best Answer
The mathematical meaning of ratio comes from the mathematical meaning of rational, which in turn comes from the mathematical meaning of irrational.
The OED says that we get the word irrational from the Latin word irrationalis, which was used in Latin for both the mathematical and the non-mathematical sense of irrational. It appears that the mathematical senses of both ratio and rational are backformations from irrational.
Euclid called irrational numbers ἄλογος (alogos). Since the word logos in Greek means either word or reason, this would have meant either unsayable numbers or unreasonable numbers. I expect the name originally was intended to mean unsayable numbers; the ancient Greeks used rationals to identify numbers, so an irrational number would have been a number without a name. Furthermore, the word for the mathematical sense of irrational in modern Greek is άρρητος (arretos), which also means unsayable.
Anyway, the word ἄλογος was translated into Latin as irrationalis, and according to the OED, the mathematical sense of irrational is first attested in English in 1551, and the mathematical sense of rational in 1570. The mathematical sense of ratio is first attested in English in 1660, so it seems that the mathematical meaning of ratio was a backformation from rational. The word ratio means both reason and calculation in Latin, but I haven't found any evidence it was used to mean ratio, i.e., one quantity divided by another. One of the meanings of the related adjective rata, as in pro rata, does seem to have been in ratio, so the choice of ratio to mean this was not too unreasonable.
The backformation from rational to ratio presumably happened in English, because the French word ratio (same meaning as in English) was borrowed from English and not Latin (see this link to le trésor de la langue française informatisé).
The backformation from irrationalis to rationalis happened in Latin.