they made; and on all they always set aside from the top the fifth part of the base. But Apollodorus, constructing the tower more impressively at its feet, declares it to be one and a half times the 60 cubits and four-wheeled, showing a height of 60 feet; whence he himself made each side around the base 10 feet in length, without the one-foot projection at the ends, of a width of one foot and four fingers, and a thickness of 12 fingers, making the lower beams double, where the wheels are towards the middle, and the middle-posts are to be inserted on the projections. These two and two beams he placed in thickness, and separating them width-wise with an interval for each of 12 240 fingers or even greater, he inserts the upright middle-posts at the ends coming down to the ground, which some have named the legs of the tower, being 10 feet each in height, of a width of one foot and four fingers, and a thickness of 12 fingers each; these are secured to the laid double beams by means of straight collars and sockets, that is, hemispheres hollowed out around the middle and cut out like some fists, similar to those placed on the hinges of doors, around the nailing, so that they may remain upright. To these upright legs, being middle-posts, he placed other timbers of equal length as cross-beams, from the laid double beams to the opposite double beams, forming the framework of the tower into an equal-sided square, that is, bounding the base equally, so that the said four middle-posts might be equally distant from each other on all sides; and next to each of the four he placed two timbers, being 8 in number, of the same width and thickness as these, 9 feet each in height, standing upon and beside the middle-posts on either side on the laid double beams and these too nailed securely (as said before) both to the beams and the middle-posts; and thus he joined the three in the arrangement of a single upright, with the middle one projecting. And these eight let them be called side-posts. And since both the middle-posts and the side-posts are hard to find because of the magnitude of their width, it is necessary to follow 241 the school of Diades and Charias and to make the legs below square of 12 fingers each, and smaller above; but especially the side-posts, and especially being symmetrical for the construction of a tower of such a size. And to these again, from above, the aforesaid Apollodorus placed beams and cross-beams similarly to the lower ones, smaller in length by up to a foot, and up to the highest story he subtracted a foot at a time from those being placed both in length and width, so that the tower might acquire a tapering from above, lest being top-heavy it should topple, but have a secure stance from the width of the seat below. And of the stories, let some be covered all around, and others having walkways around them of a width of about three feet; for they are useful for helping against incendiaries. And in the space by which the lower beams that received the middle-posts are separated in width, in the aforementioned intervals of twelve fingers or even greater, showing the craftsman, he orders him to insert wheels pierced through by well-turned axles and bound with iron plates hammered cold, having a diameter, that is, a height, of about four and a half feet; and that the same wheels are sometimes pierced also through short iron axles, both because of the weight placed upon them and the bulk of their size; and that two of them are secured to each of the two timbers alone, and the remaining two to the opposite timbers facing them, lifting from the ground and 242 holding up the double timbers, so that the wheels may roll easily and without obstruction and move the whole structure of the tower together. Thus, then, with the construction being put together, the first middle-posts were found projecting on the upper story by a third part of their own length. Whence he again placed side-posts upon the upper beams, extending beyond the middle-post, and to it another one joined by the side-posts, and thus on every story, weaving the tower together in four parts, he strengthened it. And the first middle-post not

ἐποίουν· ἐπὶ πάντας δὲ ἀεὶ τὸ τῆς βάσεως πέμπτον μέρος ἄνωθεν ἀπετίθουν. Ὁ δὲ Ἀπολλόδωρος, σεμνότερον πρὸς πόδας κατασκευάζων τὸν πύργον, ὑφημιόλιον αὐτὸν τῶν ˉξ πηχῶν καὶ τετράτροχον δηλοῖ, ποδῶν πρὸς ὕψος ἐμφαίνων ˉξ· ὅθεν καὶ αὐτὸς ἑκάστην τὴν περὶ τὴν βάσιν πλευρὰν κατὰ μῆκος ποδῶν ἐποίει ˉιˉ, δίχα τῆς ποδιαίας ἐπὶ τὰ ἄκρα παρεξοχῆς, πλάτους ποδὸς ἑνὸς καὶ δακτύλων τεσσάρων, κατὰ δὲ πάχος δακτύλων ˉιˉβ, διπλᾶ τὰ κάτω ζυγὰ ποιῶν, ὅπου οἱ τροχοὶ πρὸς τὸ μέσον, οἱ δὲ μεσοστάται ἐπὶ ταῖς παρεξοχαῖς ἐμβάλλεσθαι μέλλουσι. Ταῦτα τὰ δύο καὶ δύο ζυγὰ κατὰ πάχος ἐτίθει, καὶ μεταξὺ πρὸς ἕκαστα ˉιˉβ 240 δακτύλων μεσόχωρον εἴτε καὶ μεῖζον ἐπὶ τὰ πλάτη διϊστῶν, ὀρθοὺς ἐπὶ τὰ ἄκρα τοὺς μεσοστάτας ἐμβάλλει μέχρι τοῦ ἐδάφους κατερχομένους, οὕς τινες σκέλη τοῦ πύργου ὠνόμασαν, ποδῶν πρὸς ὕψος ἀνὰ ˉιˉ ὄντα, πλάτους ποδὸς ἑνὸς καὶ δακτύλων τεσσάρων, κατὰ δὲ πάχος ἀνὰ δακτύλων ˉιˉβ· ταῦτα πρὸς τοῖς κειμένοις διπλοῖς διὰ κανονίων περιστομίδων τε καὶ χελωνίων, ἤτοι ἡμισφαιρίων περὶ τὸ μέσον ἐγγεγλυμμένων καὶ ὡς γρονθαρίων τινῶν ἐκκεκομμένων, παρομοίων τοῖς ἐπὶ τῶν στροφίγγων τῶν θυρῶν τιθεμένοις, περὶ τὴν προσήλωσιν ἀσφαλίζεται, ἵνα μένωσιν ὀρθά. Τοῖς ὀρθίοις τούτοις σκέλεσι μεσοστάταις οὖσιν ἀπὸ τῶν κειμένων διπλῶν ἐπὶ τὰ ἀντικείμενα διπλᾶ ἕτερα ξύλα ἴσα ὄντα κατὰ μῆκος ὡς ἀντιζυγίδας ἐτίθει, ἰσοτετράγωνον τὸ τοῦ πύργου σχηματίζων ἐσχάριον, ἤτοι τὴν βάσιν ἐξ ἴσου περιορίζων, ἵνα οἱ ῥηθέντες τέσσαρες μεσοστάται ἴσον ἀπ' ἀλλήλων πανταχόθεν ἀπέχωσιν· ἐφ' ἑκάστῳ δὲ τῶν τεσσάρων δύο παρίστανε ξύλα ἀριθμῷ ὄντα ˉη, ἰσοπλατῆ τούτων καὶ ἰσοπαχῆ, ὕψους ἀνὰ ποδῶν ˉθ, ἐφεστῶτα δὲ καὶ παριστάμενα τῶν μεσοστατῶν ἐφ' ἑκάτερα ἐπὶ τὰ κείμενα διπλᾶ καὶ προσηλούμενα καὶ αὐτὰ ἀσφαλῶς (ὡς προείρηται) πρός τε τὰ ζυγὰ καὶ τοὺς μεσοστάτας· καὶ οὕτως τὰ τρία συνίστανεν ἐν τάξει ὀρθοστάτου ἑνὸς κατὰ μέσον ὑπερανέχοντος. Ταῦτα δὲ τὰ ὀκτὼ παραστάται καλείσθωσαν. Καὶ ἐπεὶ δυσεύρετοί εἰσι διὰ τὸ τοῦ πλάτους μέγεθος οἵ τε μεσοστάται καὶ παραστάται, ἀνάγκη τοῖς περὶ ∆ιάδην καὶ Χαρίαν ἕπε241 σθαι καὶ ἰσοτετράγωνα ἀνὰ ˉιˉβ δακτύλων τὰ σκέλη κάτωθεν ποιεῖν, ἄνωθεν δὲ ἐλάσσονα· ἐξαιρέτως δὲ τὰ παριστάμενα, καὶ μάλιστα πρὸς κατασκευὴν μεγέθους τοιούτου πύργου σύμμετρα τυγχάνοντα. Πρὸς αὐτὰ δὲ πάλιν ἄνωθεν ὁ προρρηθεὶς Ἀπολλόδωρος ὁμοίως τοῖς κάτω ζυγὰ καὶ ἐπιζυγίδας ἐτίθει ἐλάσσονας τῷ μήκει ποδὸς ἄχρι, καὶ ἕως τῆς ἀνωτάτω στέγης πρός τε μῆκος καὶ πλάτος ἐκ τῶν τιθεμένων ἀνὰ πόδα ἀφῄρει, ἵνα συναγωγὴν ἄνωθεν ὁ πύργος λάβῃ, μήπως ἀκροβαρήσας περινεύσῃ, ἀλλ' ἀσφαλῆ τὴν στάσιν ἐκ τοῦ κάτωθεν πλάτους τῆς ἕδρας ἕξῃ. Τῶν δὲ στεγῶν αἱ μὲν περίπτεροι ἔστωσαν, αἱ δὲ περιδρόμους κύκλῳ ἔχουσαι πλάτους ὡσεὶ ποδῶν τριῶν· χρειώδεις γάρ εἰσιν εἰς τὴν τῶν ἐμπρησμῶν ἐκβοήθησιν. Καθ' ὃ δὲ διέστηκεν ἐπὶ τὰ πλάτη τὰ κάτω ζυγὰ τὰ τοὺς μεσοστάτας δεξάμενα ἐπὶ τὰ ῥηθέντα δωδεκαδάκτυλα ἢ καὶ μείζονα μεσόχωρα, τῷ τεχνίτῃ ἐμφαίνων ἐντέλλεται τροχοὺς ἐμβάλλειν δι' ἐξευτόνων ἀξόνων συμπεπερονημένους καὶ σιδηροῖς πετάλλοις ψυχρηλάτοις συνδεδεμένους, τὴν διάμετρον ἔχοντας ἤτοι τὸ ὕψος ποδῶν ὡσεὶ τεσσάρων ἥμισυ· συμπερονᾶσθαι δὲ ὁτὲ τοὺς αὐτοὺς τροχοὺς καὶ διὰ σιδηρῶν βραχέων ἀξόνων, διά τε τὸ ἐπικείμενον βάρος καὶ τὸ ἔξογκον τοῦ μεγέθους· καὶ τοὺς μὲν δύο πρὸς ἕκαστα μόνα τὰ δύο ξύλα ἀσφαλίζεσθαι, τοὺς δὲ λοιποὺς δύο πρὸς τὰ ἐξ ἐναντίας ἀντικείμενα αἴροντας ἀπὸ τῆς γῆς καὶ 242 ἀνέχοντας τὰ διπλᾶ ξύλα, ἵνα εὐστρόφως οἱ τροχοὶ καὶ ἀπαρεμποδίστως κυλίωνται καὶ ὅλον συγκινῶσι τὸ τοῦ πύργου σύμπηγμα. Οὕτως οὖν τῆς κατασκευῆς συνισταμένης εὑρίσκοντο οἱ πρῶτοι μεσοστάται τρίτῳ ἑαυτῶν μήκους μέρει ἐπὶ τῇ ἀνωτέρᾳ στέγῃ ἀνέχοντες. Ὅθεν παραστάτας ἐπὶ τὰ ἀνώτερα ζυγὰ πάλιν ἐπετίθει ὑπερέχοντας τοῦ μεσοστάτου, καὶ πρὸς αὐτὸν ἄλλον συνεχόμενον ὑπὸ τῶν παραστατῶν, καὶ οὕτως κατὰ πᾶσαν στέγην τετραμερῶς συμπλέκων τὸν πύργον ἐστήριξεν. Καὶ τὸν μὲν πρῶτον μεσοστάτην οὐκ