[241] Diog. 78: συλλογιστικοὶ [λόγοι] μὲν οὖν εἰσιν οἱ ἤτοι ἀναπόδεικτοι ὄντες ἢ ἀναγόμενοι ἐπὶ τοὺς ἀναποδείκτους κατά τι τῶν θεμάτων ἢ τινά. According to Galen, Hipp. et Plat. ii. 3, p. 224, Chrysippus had taken great pains in resolving the composite forms of inference (Diog. 190 and 194). Antipater suggested still simpler modes. [242] Sext. 229–243, borrowing the example used by Ænesidemus, but no doubt following the Stoic treatment. Prantl, 479. Such a composite inference is that mentioned by Sextus l.c. 281. [243] Sext.; Prantl, p. 478. [244] Alex. on Anal. Pr. i. 25, 42, b, 5, after speaking of the Sorites, continues (p. 94, b): ἐν τῇ τοιαύτῃ τῶν προτάσεων συνεχείᾳ τό τε συνθετικόν ἐστι θεώρημα ... καὶ οἱ καλούμενοι ὑπὸ τῶν νεωτέρων ἐπιβάλλοντές τε καὶ ἐπιβαλλόμενοι. The συνθετικὸν θεώρημα (or chain-argument), the meaning of which is next investigated, must be a Peripatetic expression. The same meaning must attach to ἐπιβάλλοντές τε καὶ ἐπιβαλλόμενοι, which are to be found ἐν ταῖς συνεχῶς λαμβανομέναις προτάσεσι χωρὶς τῶν συμπερασμάτων· for instance, A is a property of B, B of C, C of D; ∴ A is a property of D. ἐπιβαλλόμενος means the inference, the conclusion of which is omitted; ἐπιβάλλων, the one with the omitted premiss. These inferences may be in either of the three Aristotelian figures κατὰ τὸ παραδεδομένον συνθετικὸν θεώρημα. ὃ οἱ μὲν περὶ Ἀριστοτέλην τῇ χρείᾳ παραμετρήσαντες παρέδοσαν, ἐφ’ ὅσον αὐτὴ ἀπῇτει, οἱ δὲ ἀπὸ τῆς τοῦ [στοᾶς] παρ’ ἐκείνων λαβόντες καὶ διελόντες ἐποίησαν ἐξ αὐτοῦ τὸ καλούμενον παρ’ αὐτοῖς δεύτερον καὶ τρίτον θέμα καὶ τέταρτον, ἀμελήσαντες μὲν τοῦ χρησίμου, πᾶν δὲ τὸ ὁπωσοῦν δυνάμενον λέγεσθαι ἐν τῇ τοιαύτῃ θεωρίᾳ κἂν ἄχρηστος ᾖ, ἐπεξελθόντες τε καὶ ζηλώσαντες. Reference is made to the same thing in Simpl. De Cœlo; Schol. in Arist. 483, b, 26: ἡ δὲ τοιαύτη ἀνάλυσις τοῦ λόγου, ἡ τὸ συμπέρασμα λαμβάνουσα καὶ προσλαμβάνουσα ἄλλην πρότασιν, κατὰ τὸ τρίτον λεγόμενον παρὰ τοῖς Στωϊκοῖς θέμα περαίνεται, the rule of which is, that when a third proposition can be drawn from the conclusion of an inference and a second proposition, that third proposition can be drawn also from the premisses of the inference and the second proposition. Both these passages appear to have escaped the notice of Prantl in his summing up, otherwise so accurate. Or else the πρῶτον, δεύτερον, τρίτον and τέταρτον θέμα mentioned by Galen, Hipp. et Plat. ii. 3, vol. v. 224; Alex. Anal. Pr. 53, b, would hardly suggest to him the various forms of the ἀναπόδεικτοι instead of the formulæ for the resolution of composite conclusions. The expressions διὰ δύο τροπικῶν, διὰ τριῶν τροπικῶν, and the title of a treatise of Chrysippus περὶ τοῦ διὰ τριῶν (sc. τροπικῶν or λημμάτων conf. p. 117, 3) in Diog. vii. 191; (Galen, l.c.; Sext. Pyrrh. ii. 2), appear to refer to such composite inferences.