[7] Brentano, Bedeutung des Seienden nach A., pp. 148-178.
[8] For detailed examination of the Stoic categories, see Prantl, Ges. d. Logik, i. 428 sqq.; Zeller, Ph. d. Griech. iii. 1, 82, sqq,; Trendelenburg, Kateg. p. 217.
[9] It does not seem necessary to do more than refer to the slight alterations made on Kant’s Table of Categories by J.G. von Herder (in the Metakritik), by Solomon Malmon (in the Propadeutik zu einer neuen Theorie des Denkens), by J.F. Fries (in the Neue Kritik der Vernunft), or by Schopenhauer, who desired to reduce all the categories to one—that of Causality. We should require a new philosophical vocabulary even to translate the extraordinary compounds in which K.C.F. Krause expounds his theory of the categories. Notices of the changes introduced by Antonio Rosmini-Serbati, and of Vincenzo Gioberti’s remarkable theory, will be found in Ragnisco’s work referred to below.
[10] System der Metaphysik (1844).
[11] Logische Untersuchungen, i. 376-377.
[12] Essais de critique générale (2nd ed.), La Logique, i. pp. 184, 190, 207-225.
[13] Discussions, p. 577.
[14] Logic, i. 83; cf. Bain, Ded. Log., App. C.
CATENARY (from Lat. catena, a chain), in mathematics, the curve assumed by a uniform chain or string hanging freely between two supports. It was investigated by Galileo, who erroneously determined it to be a parabola; Jungius detected Galileo’s error, but the true form was not discovered until 1691, when James Bernoulli published it as a problem in the Acta Eruditorum. Bernoulli also considered the cases when (1) the chain was of variable density, (2) extensible, (3) acted upon at each point by a force directed to a fixed centre. These curves attracted much attention and were discussed by John Bernoulli, Leibnitz, Huygens, David Gregory and others.