will be shown in the account; for the two and a half cubits of the diameter measure the 15 six times, and the 10 four times, and the 30 twelve times, and the 20 eight times; and as 6 is to 4, so is 30 to 20; and as 15 is to 6, so is 10 to 4; and 6 is one and a half times 4; for it contains 4 and its half; therefore 15 is also one and a half times 10; and 15 is two and a half times 6; 266 therefore 10 is also two and a half times 4; so that the measurement of the diameter of the wheels is also found to be in harmony with the construction of its size, as they preserve the same ratio in proportion to the things being measured. And the diagram has been drawn below. This same tube will become more effective for a siege, if its front opening were larger in size, and it had its exit through two closing doors, so as to admit two armed men, standing one beside the other, who are about to mount the wall together. Let the doors of this tube's opening be made startling on the outside by means of conspicuous carving and multi-colored painting, along with the front part of the tube, bearing the fire-breathing bust of a dragon or a lion, approaching to the astonishment and fear of the enemy, so that even before the assault the defenders on the wall might be terrified and flee from the spaces between the towers. And it is necessary 267 to know that if the tube, lying on the upright timbers at an equal height, approaches the wall in a straight line, it will also indicate the base in a straight line; but if it is found to be placed higher than the wall, having been lowered a little at the front and having bent down it will perform its function; but if it should happen to be lower than the height of the wall, having been extended further forward and brought up straight, being pulled down from the smaller rear part by the chain and having projected slightly upwards toward the wall, it will also fulfill the need for those wishing to mount to the greater height. And the diagram has been drawn below. The Athenian says that the machines brought up from ships, which some call sambucas, named metaphorically from the musical instruments, being similar in their arched construction to the aforementioned tube, have nothing worthy of writing about because they are well-known and obvious to all. But it is preferable for them 268 often not to be made at all than to be constructed illogically and asymmetrically. For those in the siege of Chios, having missed their target by conjecture and having brought up sambucas that were higher than the towers, caused those who had mounted them to be destroyed by fire, being unable to get onto the towers from that height; and it was not possible to lower them in any way; otherwise, the ships would have been capsized, with the weight of the load placed on top being carried off balance. Therefore he also adds that those who are going to use such machines must not be inexperienced in the treatise on Optics; and that whenever some of the engineers choose to take a coastal city, having yoked two ships together they place the machine up to a height, and in calm seas they are accustomed to bring it to the walls. But if the ships are caught by a contrary wind and a breaking wave comes under them, the machine fixed upon the ships bobs up and is overturned, being pulled against itself; for the ships do not always make the same and similar motion, but one of them at times happens to be at the crest of the wave, and the other at its 269 trough; from which the machines, being pulled against by the self-destructive device, are torn apart and shattered, and it puts the enemy into a state of greater boldness and courage. And since there is agility in the human soul, we must not only know the things well discovered by others, but also ourselves find something additional that contributes to utility, we have taken pride in inventing for the support of the machine that the so-called ‘ape’ be fitted in the middle of the yoke of the two ships, being a certain weight similar in size to the shape, but being suspended from below and weighing down for the sake of balance, so that while the sea's surge tosses and drives from all sides
ἐν λόγῳ δειχθήσονται· καὶ γὰρ οἱ δύο ἥμισυ πήχεις τῆς διαμέτρου ἑξάκις μὲν τὸν ˉιˉε μετροῦσι, τετράκις δὲ τὸν ˉι, καὶ δωδεκάκις μὲν τὸν ˉλ, τὸν δὲ ˉκ ὀτάκις· καὶ ἔστιν ὡς ὁ ˉ πρὸς ˉδ, οὕτως ὁ ˉλ πρὸς ˉκ· καὶ ὡς ˉιˉε πρὸς τὸν ˉ, οὕτως ὁ ˉι πρὸς τὸν ˉδ· ἡμιόλιος δὲ ὁ ˉ τοῦ ˉδ· ἔχει γὰρ τὸν ˉδ καὶ τὸ ˉ#ˉ1ˉ7ˉ2 αὐτοῦ· ἡμιόλιος ἄρα καὶ ὁ ˉιˉε τοῦ ˉι· διπλασιεφήμισυς δὲ ὁ ˉιˉε τοῦ ˉ· διπλα266 σιεφήμισυς ἄρα καὶ ὁ ˉι τοῦ ˉδ· ὥστε καὶ ἡ τῆς διαμέτρου τῶν τροχῶν καταμέτρησις σύμφωνος πρὸς τὴν τοῦ μεγέθους κατασκευὴν εὑρίσκεται, ὡς τὸν αὐτὸν τοῖς μετρουμένοις κατὰ ἀναλογίαν σώζουσι λόγον. Καὶ τὸ σχῆμα [δὲ] καταγέγραπται. Ὁ δὲ αὐτὸς αὐλὸς ἐνεργέστερος πρὸς πολιορκίαν γενήσεται, εἰ μεῖζον κατὰ μέγεθος ἐπὶ τὸ ἔμπροσθεν στόμιον εἴη, καὶ ὑπὸ δύο κλειομένων θυρίδων τὴν ἐξέλευσιν ἔχοι, ὥστε καὶ δύο ἐνόπλους ἄνδρας τοὺς τῷ τείχει ὁμοῦ ἐπιβαίνειν μέλλοντας παρὰ μέρος ἑστῶτας ἐπ' ἀλλήλους εἰσδέχεσθαι. Αἱ δὲ τοῦ αὐτοῦ στομίου θύραι ἔξωθεν καταπληκτικαὶ διὰ γλυφῆς ἐκφανοῦς καὶ πολυχρώμου γραφῆς σὺν τῷ ἔμπροσθεν μέρει τοῦ αὐλοῦ γινέσθωσαν, δράκοντος ἢ λέοντος πυροφόρον ἐπιφερόμεναι προτομὴν εἰς κατάπληξιν καὶ φόβον τῶν ἐναντίων προσερχομένην, ὅπως καὶ πρὸ τῆς ἐπιβάσεως πτοηθέντες οἱ τῷ τείχει προεστῶτες ἀπὸ τῶν μεταπυργίων ἐκφύγωσι. Καὶ δεῖ 267 εἰδέναι ὅτι, εἰ μὲν ἐπ' εὐθείας ἰσοϋψὴς ὁ αὐλὸς ἐπὶ τοῖς ὀρθίοις κείμενος ξύλοις τῷ τείχει προσέρχεται, ἐπ' εὐθείας καὶ τὴν βάσιν δηλώσει· εἰ δὲ ἀνώτερος τοῦ τείχους ἐπιθέσει εὑρίσκεται, μικρὸν καταχθεὶς ἔμπροσθεν καὶ ἐπικύψας τὴν ἐνέργειαν τελέσει· εἰ δὲ ταπεινότερος τοῦ τείχους ἐπὶ τὸ ὕψος τύχῃ, παρεκβληθεὶς ἐπὶ πλέον ἔμπροσθεν καὶ προσαχθεὶς πάρορθος, ἐκ τοῦ ἐλάσσονος καὶ ὄπισθεν μέρους ὑπὸ τῆς ἁλύσεως καταγόμενος ἀνωφερῶς τε μικρὸν προκύψας ἐπὶ τὸ τεῖχος, καὶ τὴν πρὸς τὸ μεῖζον ὕψος τοῖς βουλομένοις ἐπιβαίνειν ἀναπληρώσει χρείαν. Καὶ τὸ σχῆμα ὑπογέγραπται. Τὰς ἐκ τῶν πλοίων ἀγομένας μηχανάς φησιν ὁ Ἀθηναῖος, ἅς τινες σαμβύκας καλοῦσιν ἐκ μεταφορᾶς τῶν μουσικῶν ἐσχηματισμένας ὀργάνων, ἐμφερεῖς οὔσας ἐπὶ τῇ καμαρικῇ κατασκευῇ τῷ προειρημένῳ αὐλῷ, μὴ ἔχειν τι ἄξιον γραφῆς διὰ τὸ πᾶσιν εὐγνώστους εἶναι καὶ φανεράς. Αἱρετώτερον δέ ἐστι μηδὲ γενέσθαι 268 πολλάκις αὐτὰς ἢ παραλόγως καὶ ἀσυμμέτρως κατασκευασθῆναι. Καὶ γὰρ οἱ ἐν τῇ περὶ Χίον πολιορκίᾳ εἰκαστικῶς τοῦ σκοποῦ ἀστοχήσαντες καὶ ὑψηλοτέρας τῶν πύργων τὰς σαμβύκας προσενεγκόντες, τοὺς ἐπ' αὐτὰς ἀναβάντας ὑπὸ τοῦ πυρὸς ἀπολέσθαι ἐποίησαν, μὴ δυνηθέντας ἐκ τοῦ ὕψους τοῖς πύργοις ἐπιβῆναι· χαλάσαι τε οὐκ ἦν δυνατὸν οὐδενὶ τρόπῳ· εἰ δὲ μή, κατεστρέφετο τὰ πλοῖα, ἔξω βάρους τοῦ ἄνωθεν ἐπικειμένου φορτίου φερομένου. ∆ιὸ καὶ ἐπάγει μὴ ἀπείρους τῆς Ὀπτικῆς εἶναι πραγματείας τοὺς ταῖς τοιαύταις μηχαναῖς χρῆσθαι μέλλοντας· καὶ ὅτι, ἐπάν τινες τῶν ἀρχιτεκτόνων ἐνθάλασσον ἑλεῖν προαιρῶνται πόλιν, ὑποζυγώσαντες δυσὶ πλοίοις πρὸς ὕψος τιθέασι τὸ μηχάνημα, καὶ ἐν ταῖς γαλήναις εἰώθασιν αὐτὸ τοῖς τείχεσι προσάγειν. Ἀλλ' εἰ μὲν ὑπ' ἐναντίου ἀνέμου τὰ πλοῖα καταληφθῶσι καὶ τεθραυμένον ὑποδύῃ πρὸς αὐτὰ κῦμα, ἀναδύνει καὶ περιτρέπεται ἀνθελκόμενον τὸ στηριχθὲν ἐπὶ τὰ πλοῖα μηχάνημα· τὰ γὰρ πλοῖα οὐ τὴν αὐτὴν καὶ ὁμοίαν ἀεὶ ποιοῦνται κίνησιν, ἀλλὰ τὸ μὲν αὐτῶν πρὸς τῇ τοῦ κύματος κορυφώσει ἐνίοτε τυγχάνει, τὸ δὲ ἐπὶ τῇ κατα269 δύσει· ὅθεν σπαρασσόμενα ἐνθραύονται τὰ μηχανήματα ὑπὸ τῆς αὐτεπιβουλεύτου μηχανῆς ἀνθελκόμενα, τοὺς δὲ πολεμίους πρὸς εὐτολμίαν μᾶλλον καὶ θάρσος καθίστασι. Καὶ ἐπείπερ ἐστὶν εὐκινησία περὶ τὴν ἀνθρωπίνην ψυχὴν, οὐ μόνον τὰ καλῶς ὑφ' ἑτέρων εὑρημένα δεῖ ἡμᾶς εἰδέναι, ἀλλὰ καὶ αὐτούς τι προσευρίσκειν τῶν εἰς ὠφέλειαν συντεινόντων, πεφιλοτιμήμεθα πρὸς τὴν τοῦ μηχανήματος ὑποστήριξιν ἐφευρόντες τοῦ ἐφαρμόζεσθαι κατὰ μέσον τῆς ἐπιζεύξεως τῶν δύο πλοίων τὸ λεγόμενον πιθήκιον, βάρος τι ὂν κατὰ μὲν μέγεθος ἐμφερὲς τῷ σχήματι, ἐκκρεμὲς δὲ κάτωθεν ὂν καὶ ἐπιβρῖθον διὰ τὸ ἰσόρρωπον, ὅπως τοῦ θαλασσίου κλύδωνος πάντοθεν σαλεύοντος καὶ κλονοῦντος