In the middle of the nineteenth century, following the great strides made in philology, the teaching of Latin in schools began to use a reconstructed “Classical” Latin pronunciation. This ‘restored’ the long and short vowel sounds of Latin to /iː, ɪ, eɪ, e, æ, ɑː, ɒ, ɔː, ʊ, uː/ and the diphthongs AE, AU, OE to /aɪ, aʊ, ɔɪ/. Among the consonants, C became always /k/, G was always /g/, consonantal I~J became /j/, and consonantal U~V, /w/. S was now to be pronounced /s/ wherever it occurred, and not as /z/ in final position or intervocalically, as it had been previously (See John Wells’ posts). This pronunciation has been taught in English schools ever since.
As if this was not sufficient confusion, the Roman Catholic Church uses a third version, the so-called “Italianate” pronunciation. In this, the vowels are the same as the reconstructed “Classical” pronunciation, but two of the diphthongs are treated differently: AE and OE become /eɪ/. Among the consonants, C is /k/ before consonants or A, O, U, but /tʃ/ before AE, E, I, or OE. Similarly, G is /g/ before A, O, U, but /dʒ/before AE, E, I, or OE. Consonantal I or J is always /j/, but consonantal U or V is /v/. Intervocalic S is /z/, but final S varies between /s/ and /z/. T before I and another vowel (e.g. penitentiam) is affricated to /ts/.
No wonder there is confusion in the minds of English-speaking people when they have a Latin phrase or name to pronounce. Consistency is almost impossible. In the BBC TV series “I, Claudius”, the familiar names – Claudius, Nero, Caligula, Caesar, etc. were anglicised in the old way: /ˈklɔːdɪəs, ˈnɪərəʊ, kəˈlɪgjʊlə, ˈsiːzər/, but less famous names were pronounced in a more ‘Latin’ way: Agrippina, Messalina /ægrɪˈpiːnə, mesəˈliːnə/.
Minutiae is a complete mixture – the most frequent pronunciation that I hear is /maɪˈnjuːʃiaɪ/, while a full-blooded traditional pronunciation would be /maɪˈnjuːʃiiː/ and a reconstructed ‘Latin’ one would be /mɪˈnuːtɪai/.
Veni, vidi, vici:
traditional: /ˈviːnaɪ, ˈvaɪdaɪ, ˈvaɪsaɪ/
reconstructed: /ˈweɪni, ˈwiːdi, ˈwiːki/
Italianate: /ˈveɪni, ˈviːdi, ˈviːtʃi/
All three as spoken with English phonology, of course.