What does the root "ject" mean? It occurs in words such as "subject", "object", "project", "injection", "surjection", "bijection". As far as I know these words came to English from French and, in turn, from Latin. Prefixes "ob-", "sub-", "pro-" also came from Latin as Wiktionary says.
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The root is Latin iaciō (throw, cast), whose supine is iactum.
Because of Latin ablaut (vowel change), prefixes like sub-, ob-, pro- trigger a vowel change to *-iectum.
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More grammatical terms (many used in mathematics as well) and their Latin derivations are available here. – jlawler Aug 25 '14 at 15:36
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This isn't ablaut, as the term is usually used, but unstressed vowel weakening. – TKR Aug 25 '14 at 17:23
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I'm not actually sure what the literature calls it -- possibly vowel mutation. But it's not called unstressed vowel weakening -- for one, the changed vowel in proiectum is actually stressed... – jogloran Aug 26 '14 at 4:49
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Naturally, it's not ablaut, no prefix triggers it, it's the very fact of derivation that does, it's just a historical vowel alternation. The rule for this a > e change is: Short ă in a closed non-final and in a closed final syllable of a multi-syllable word changes to short ĕ. E. g.: Princĕps < *prim-căp-s (primus + căpio 'first taking'), here in a closed final syllable ă > ĕ. – Yellow Sky Aug 26 '14 at 13:07
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All of these “rules” are not so straight-forward. You have prō-icio, -iēcī, -iectus, but capio, cēpī, captus. – fdb Aug 27 '14 at 11:44
