XIV. The reasons are: (1) the promise of the covenant pertains no less to infants than to adults, since God promises that he will be "the God of Abraham and of his seed" (Gen. 17:7) and the promise is said to have been made "with the fathers and their children" (Acts 2:39). Therefore also the blessings of the covenant (such as "remission of sins" and "sanctification") ought to pertain to them (according to Jer. 31 and 32) and are communicated to them by God according to their state. In this sense (as some think), the children of believers are called "holy" by Paul (1 Cor. 7:14). This may with more propriety be referred to the external and federal holiness which belongs to them, according to which (because they are born of covenanted and Christian parents—at least of one) they are also considered to be begotten in "holiness" (i.e., in Christianity, and not in heathenism, which was a state of uncleanness [akatharsias] and impurity).(source for English, including the other paragraphs of this question)
The above is taken from Turretin's Institutes, Volume 2, 15th Topic, 14th Question, 14th paragraph. One unfortunate error in Dennison's edition of Turretin's Institutes (in English) is that "Patribus et Liberis" has been placed in quotation marks (see English version above), when - in fact - it is not a quotation from Acts 2:39, but rather the sense of the text.
This is mostly being posted for a friend who wants the Latin, rather than to spark conversation (although, of course, if someone wants to comment on the faith that infants can have, they are welcome to do so).