Afterwards (chap. so) proceeding to the opposition of propositions, he adds the form called tertii adjacentis, in a passage which is the first appearance, or rather adumbration, of the verb of being as a copula.
In the form secundi adjacentis we only get oppositions, such as the following: - man is - man is not not - man is - not - man is not In the form tertii adjacentis the oppositions, becoming more complex, are doubled, as follows: man is just - man is not just man is non-just - man is not non-just not-man is just - not-man is not just not-man is non-just - not-man is not non-just.
The words introducing this form (6Tav bE TO '&TL Tptrov irpoo-KaTnyopijTac, chap. so, s 9 b s 9), which are the origin of the phrase tertii adjacentis, disengage the verb of being (g un) partially but not entirely, because they still treat it as an extra part of the predicate, and not as a distinct copula.
But even the normal proposition in the syllogistic form tertii adjacentis, with subject, predicate and copula, is seldom a complete expression of the judgment.
To this work were added two treatises, entitled Tractatus duo de speciebus et magnitudine figurarum curvilinearum, the one bearing the title Tractatus de Quadratura Curvarum, and the other Enumeratio linearum tertii ordinis.
The next important work, founded on the Geometric, was Sir Isaac Newton's Enumeratio linearum tertii ordinis (1706), establishing a classification of cubic curves founded chiefly on the nature of their infinite branches, which was in some details completed by James Stirling (1692-1770), Patrick Murdoch (d.