In 1557, the Italian antitrinitarian Giovanni Valentino Gentile took refuge in Geneva with other Italian exiles, some of whom held antitrinitarian views. Gentile and fellow Italian exile Nicola Gallo were charged with heresy in 1558. Gentile would eventually be executed, under Bern’s authority, for his antitrinitarian views in 1566. In the final 1559/60 edition of his Institutes, Calvin takes up Gentile’s antitrinitarian argument; Gentile had cited a number of church fathers to defend his views, including Tertullian. Calvin writes in Institutes 1.13.28:

They are no more honest when they claim Tertullian as their patron, for, despite his occasionally harsh and prickly rhetorical style, he still unequivocally teaches the substance of the doctrine we are defending, namely, that, while there is one God, nonetheless by dispensation or economy there is his Word;that God is one through the unity of substance, and nevertheless that unity is disposed into a trinity by the mystery of dispensation; that there are three, not in status, but in rank;[1] not in substance, but in form; not in power, but in order.

Except that is not what Tertullian says.

Tertullian says that there are three, not in status, but in rank, not in substance, but in form, not in power, but in species. “Tres autem non statu, sed gradu; nec substantia, sed forma; nec potestate, sed specie…” (Adv. Prax. 2; Migne PL 2: 157). Calvin’s Latin reads nec potestate, sed serie, to which the 1560 French corresponds (non pas en puissance, mais en ordre). Battles, following the Opera Selecta (3: 149 note a) presumes this is just a simple error; and Opera Selecta corrects Calvin’s serie to specie. 

But was it just a simple error? Tertullian’s original phrasing is problematic in terms of later Trinitarian orthodoxy. In fact, English theologian Herbert Thorndike (1598-1672) observed that both Robert Bellarmine and his fellow Jesuit Gregory de Valentia read this phrase from Tertullian in the works of Bullinger, who did not clearly attribute it to Tertullian, and promptly accused him of Arianism. See The Theological works of Herbert Thorndike, 6 vols. in 10 (Oxford: J.H. Parker, 1844-1856), 3: 294-295. The work in question is Bullinger’s Ad Ioannes Cochlei de canonicae scripturae et Catholicae ecclesiae authoritate libellum, appended to an edition of his De scripturae sanctae authoritate, certitudine, firmitate et absoluta perfectione, etc. (Zurich: Froschauer, 1544), fol. 16v.  

It is possible that Calvin, more or less consciously, corrected Tertullian’s orthodoxy at this point, since the term species often refers to a visible or sensible form or manifestation, which is problematic in describing the Trinity, which is spiritual and invisible. In addition, an understanding that relates essence and persons as genus and species would also be problematic in the context of later, more developed Trinitarian orthodoxy. Calvin had earlier criticized Servetus’s opinion that the persons were only external manifestations (species) of ideas, in 1.13.22. So, Calvin was already on guard against seeing the persons as species.

In any case, this section of the Institutes was based on documents from the controversy and trial. Calvin later published the materials related to the controversy and trial: Impietas Valentini Gentilis detecta, et palam traducta, qui Christum non sine sacrilega blasphemia Deum essentiatum esse fingit, etc. ([Geneva,] 1561), CO 9: 361-420. In this document, Tertullian’s words are correctly reproduced.

So we are left with a few mysteries. Why did Calvin replace specie with serie in the quotation from Tertullian? And how exactly would Calvin have interpreted Tertullian’s problematic phrasing? And, going back further, what did Tertullian himself mean when he applied the term species to the distinction of Trinitarian persons? I am not sure that any of these can be answered with any certainty.