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Why does the word analogous have an extra letter o after the g in comparison to the word analogue?

How is their origin related to one another?

According to The American Heritage Dictionary of the English Language, 4th edition, analogue has the following origin:

French, analogous, analogue, from Medieval Latin analogus, from Greek analogos, proportionate; see analogous. (see wordlink.)

And analogous has similar origins:

From Latin analogus, from Greek analogos, proportionate : ana-, according to; see ana- + logos, proportion; see leg- in Indo-European roots. (see wordlink.)

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The two terms entered the English languages in different periods, analogue, retained the French spelling from which the different suffixes.

Analogous:

  • "corresponding (to some other) in particulars," 1640s, from Latin analogus, from Greek analogos "proportionate, according to due proportion," from ana "throughout; according to" (see ana-) + logos "ratio, proportion," a specialized use (see Logos). Used with to or with.

Ethymonline

Analogue:

  • The newer [analogue came directly from French around 1800, bearing the word’s French sense and spelling. The newer spelling, analog, developed in the U.S. around the early 20th century and is now preferred in the U.S. and to a lesser extent in Canada.

The Grammarist

As for the use of the suffix -ous of terms like analogous:

  • a suffix forming adjectives that have the general sense “possessing, full of” a given quality (covetous; glorious; nervous; wondrous); -ous, and its variant -ious, have often been used to Anglicize Latin adjectives with terminations that cannot be directly adapted into English (atrocious; contiguous; garrulous; obvious; stupendous). As an adjective-forming suffix of neutral value, it regularly Anglicizes Greek and Latin adjectives derived without suffix from nouns and verbs; many such formations are productive combining forms in English, sometimes with a corresponding nominal combining form that has no suffix.

(Random House Dictionary)

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It's not an “extra” o. It’s there because the English suffix is ‑ous not ‑us.

The OED notes the following as part of a very much longer etymological note:

Classical Latin stressed long ō /oː/ passed, via close /o/, into a diphthong /ou/ in early Old French, which was variously written o or u, less commonly ou; hence Latin adjectives in -ōsus, which either came down in popular use, or were adopted at an early date, had in Old French forms in -os, or -us (-ous), e.g. coveitos, coveitus, doleros, dolerus, envios, envius, glorios, glorius, religios, religius.

In the 12th cent. the vowel-sound changed in Central French (via 11th-cent. /eu/ and later /øu/) to /ø/, written eu, so that the suffix had now the form -eus (covoiteus, dolereus, envieus, glorieus, etc.); and this still later was written in the masculine -eux (convoiteux, envieux, glorieux, with feminine however in -euse), as still in modern French.

In Anglo-Norman the forms were the same as in early Old French (coveitos, coveitus, envios, envius, glorios, glorius), but in English the vowel was soon identified with Old English and Middle English long ū, and like it written ou (covetous, envious, glorious), the spelling ever since retained, though the sound has passed through /uːs/, /us/, /ʊs/ to /ʌs/, /əs/ (there is some evidence from early modern English orthoepists that where secondary stress fell on the suffix, Middle English long ū was sometimes retained as the diphthong /ʌu/, and that under low stress the final -s could be voiced to /z/: see E. J. Dobson Eng. Pronunc. 1500–1700 (ed. 2, 1968) II. §281, §363).

This -ous, having thus become the form of the suffix in all words from Norman French, became the established type for all those of later introduction, whether adaptations of French adjectives in -eus, -eux, or Latin adjectives in -ōsus (but see -ose suffix¹), or new formations on the analogy of these, from French, Latin, or other elements.

And later also:

This tendency to represent a Latin adjective by an English form in -ous may have been strengthened by the fact that the canonical form of the Latin adjective entered in dictionaries is the nominative singular masculine, and that this in the majority of adjectives ends in -us, the English pronunciation of which is the same as that of the English word in -ous, so that the latter to the cursory observer appears to be merely an English spelling of the Latin.

So all such words have the -ous; it’s not just analogous that merits is and so it somehow special.

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