De strategematibus

 in this book for both construction and use, proceeding in order, we have set it forth, having written it down systematically. And let no nitpicker of

 it is necessary first to go through and inspect the positions of the cities accurately, and having made the protection of one's own people unharmed ab

 from a weaving of freshly-cut willow rods or of tamarisk or linden, these also being pointed at the front up to the ridge at the top. And the so-calle

 to have in exchange. But if we wish to take the city by a theft in the night, with the citizens being ignorant of our arrival and unprepared, when win

 with slender and close-set posts, rather than thick and widely-spaced ones, with a plank placed above and below, so that the posts, giving way at the

 entering under and turning back upon the so-called socket-plate or a kind of headpiece, with a rule lying on the ground which brings 221 it forward an

 concerning their limbs and the suspensions belonging to the single timbers at intervals on both ram-bearing tortoises and towers and double ladders, a

 to be brought forward easily and constructed from small pieces of wood, and not one very large one, because it is made from large and hard-to-find tim

 the movement. If we wish to ascertain the thickness of the walls and to observe the actions of the enemy and to survey the host from behind, to see th

 Let them be 30 each and at the height of 20 let them receive the pin and 20 is two-thirds of 30. And let the parts coming down from the uprights be

 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

 he made these uprights equal, so that their joints might not be near one another, but every joint alternate, being distant from the other, and it migh

 so that both the 60 cubits of the height and the 17 of the length of the base itself will have the same proportion to the feet, and likewise also the

 of a place, they batter the upper parts of the walls with rams for anything standing up and projecting is easily broken and easily demolished, as it

 projecting from the mouths to which it is necessary to be wound with the tensioner by means of shoulder or back sinews of all animals except pigs, pa

 let it admit the construction of the aforementioned ladders. And let the one that is about to be raised be decked with planks over its whole length, a

 from below, in front of the enemy they fall easily and are held fast from behind, but from above they are cut to a fine point, converging at the top a

 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,

 the ships, 270 the machine may be preserved upright and without falling, And against the winds it is necessary to have ready the prepared defenses aga

 places it against the other bank of the river, fitting it along its entire length, with the multitude gathered and ready for the battle line. And thos

from below, in front of the enemy they fall easily and are held fast from behind, but from above they are cut to a fine point, converging at the top and fitted to a sharp angle, 262 forming a triangular shape with the base and receiving iron nails from the sides, so that when the nets are thrown over them they become entangled from there for the reverse pull and gathering, no longer turning back. Those about to mount the wall, throwing these down in the face of the enemy, will be kept unharmed for the assault. And if some of those standing on the gangway and with hand-held rotating fire-throwers shoot with fire against the face of the enemy, they will so terrify those standing before the wall that, unable to endure the attack from the battle and the force of the fire, they will flee the place more quickly. And the diagrams have been drawn. But it is also possible to ascend a wall without ladders, as the 263 Ctesibius of Ascra, the teacher of Hero of Alexandria, showed in his own Commentaries, by means of such a machine, as Athenaeus says: that one must construct a four-wheeled wagon, covered on all sides, or a ram-bearing tortoise, and to one of these in the middle fix two upright standing timbers, and place on top another transverse timber of unequal width, moving against them widthwise, having round cuttings on either side, and receiving a kind of superimposed tube, pipe-like and vaulted, constructed of wood, nailed on the sides and covered with planks nailed on the outside or fenced around with only thick and strong hides as they are lighter, so that an armed man can enter upright and at one time advance, and at another retreat; when this is done, the tube is raised from above and moved to whatever part one wishes. As one end comes down to the ground, the other will be raised to a height, because it is pulled by iron chains on either side of it upon the cuttings of the superimposed timber and 264 rotates. When it is carried aloft, and its opening is against the wall, and the four-wheeled tortoise or wagon is brought up, the man inside is to open the front door and mount the wall armed; and similarly also more men who have their way forward inside through the base of the tube itself. And the tube on the nailed-on planks is undergirded on all sides strongly with stout ropes, and is covered with soaked skins, so that it may be protected from fire-bearers. But Ctesibius did not arrange measurements for the construction of this device, but only a memorandum, entrusting these things to the architects who handle them as mathematicians. For it is possible for them to alter the proportions of the engines and adapt them to the corresponding need of the place. But we, for the sake of practice for beginners, have set out the following proportion for the construction of the device. Let the frame, then, which is placed upon the four-wheeled or six-wheeled wagon or tortoise be ˉιˉε cubits in length, and ˉι in width; let the [uprights] for the wheels be ˉκ; and the transverse beam moving upon them with the superimposed tube be ˉλ cubits in length, having a width at the base of one and a half feet, and a thickness of a span; so that, whatever 265 ratio the length of the frame has to the width, the moving transverse beam has the same to the standing uprights; and again, whatever ratio the same moving beam has to the length of the frame, the standing uprights have the same to the same width; for as ˉιˉε is to ˉι, so is ˉλ to ˉκ; and as ˉλ is to ˉιˉε, so is ˉκ to ˉι; and ˉιˉε is one-and-a-half times ˉι; for it has ˉι and ˉ#ˉ1ˉ7ˉ2 of it; therefore ˉλ is also one-and-a-half times ˉκ; and again ˉλ is double ˉιˉε, therefore ˉκ is also double ˉι. And likewise the width of the base is double its thickness. But also the diameters of the wheels are proportional to the measurement and in harmony

κάτωθεν, κατὰ μὲν πρόσωπον τῶν ἐναντίων ῥᾳδίως καταπίπτοντα καὶ ἀντεχόμενα ὄπισθεν, ἄνωθεν δὲ πρὸς ὄνυχα ἐκκεκομμένα, κατὰ κορυφὴν συννεύοντα καὶ πρὸς ὀξεῖαν ἐφαρμοζόμενα γωνίαν, 262 τρίγωνον σχῆμα σὺν τῇ βάσει τελοῦντα καὶ ἥλους σιδηροῦς ἐκ πλαγίων δεχόμενα, ὅπως ἐπιρριπτόμενα τὰ ἀμφίβληστρα ἐκεῖθεν παρεμπλέκηται πρὸς τὴν ἀνάπαλιν ἕλξιν καὶ ἐπισυναγωγὴν μηκέτι ἀναστρέφοντα. Οἱ δὲ τῷ τείχει ἐπιβαίνειν μέλλοντες κατὰ πρόσωπον ταῦτα τῶν ἐναντίων καταρριπτοῦντες πρὸς τὴν ἐπίβασιν ἀνεπηρέαστοι συντηρηθήσονται. Εἰ δέ τινες τῶν ἐπὶ τῆς διαβάθρας ἑστώτων καὶ μετὰ στρεπτῶν ἐγχειριδίων πυροβόλων κατὰ πρόσωπον τῶν πολεμίων διὰ πυρὸς ἀκοντίζουσι, τοσοῦτον τοὺς τείχει προεστῶτας πτοήσουσιν, ὥστε τὴν ἀπὸ τῆς μάχης προσβολὴν καὶ τὴν τοῦ πυρὸς μὴ ὑποφέροντας ῥύμην τάχιον αὐτοὺς ὑπεκφεύξεσθαι τοῦ τόπου. Καὶ τὰ σχήματα καταγέγραπται. ∆υνατὸν δέ ἐστι καὶ ἄνευ κλιμάκων ἐπὶ τεῖχος ἀνέρχεσθαι, ὡς ὁ 263 Ἀσκρηνὸς Κτησίβιος ὁ τοῦ Ἀλεξανδρέως Ἥρωνος καθηγητὴς ἐντοῖς ἑαυτοῦ ἐδήλωσεν Ὑπομνήμασι, διὰ μηχανήματος τοιούτου, καθ' ἅ φησιν Ἀθηναῖος· ὅτι δεῖ κατασκευάζειν τετράτροχον ἅμαξαν, περισκεπῆ πάντοθεν οὖσαν, ἢ κριοφόρον χελώνην, καὶ πρὸς θατέραν τούτων κατὰ μέσον πηγνύναι δύο ξύλα ὄρθια ἱστάμενα, καὶ ἕτερον πλάγιον ἑτεροπλατὲς ἄνωθεν πρὸς αὐτὰ κινούμενον κατὰ πλάτος ἐπιθεῖναι, ἐκκοπὰς ἔχον στρογγύλας ἀφ' ἑκατέρων τῶν μερῶν, καὶ δεχόμενον ὡς αὐλόν τινα ἐπικείμενον σωληνοειδῆ καμαροειδῆ ξύλοις κατεσκευασμένον, ἐκ πλαγίων δὲ προσηλωμένον καὶ σανίσιν ἔξωθεν καθηλωμέναις ἐπιδεχόμενον ἢ βύρσαις μόναις παχείαις καὶ εὐτόνοις ὡς ἐλαφροτέραις περιπεφραγμένον, ὥστε χωρεῖν ἄνδρα ἔνοπλον εἰσέρχεσθαι ὄρθιον καὶ ὁτὲ μὲν προπορεύεσθαι, ὁτὲ δὲ ἀναχωρεῖν· οὗ γενομένου μετεωρίζεσθαι ἄνωθεν τὸν αὐλὸν καὶ μεταφέρεσθαι πρὸς ὃ ἄν τις ἐθέλῃ μέρος. Τοῦ δ' ἑνὸς μέρους ἐπὶ τοῦ ἐδάφους κατερχομένου, τὸ ἕτερον εἰς ὕψος ἀναχθήσεται, διὰ τὸ ἐπὶ τὰς ἐκκοπὰς τοῦ ἐπικειμένου ξύλου σιδηραῖς ἁλύσεσι πρὸς ἑκατέραν αὐτοῦ πλευρὰν ἐφελκόμενον περι264 στρέφεσθαι. Μετεώρου δὲ φερομένου ὅτε τὸ στόμα αὐτοῦ κατὰ τὸ τεῖχος γένηται, τῆς δὲ τετρατρόχου προσαχθείσης χελώνης εἴτε ἁμάξης, τὸν ἔνδοθεν ὄντα διανοῖξαι τὴν κατέμπροσθεν θύραν καὶ τῷ τείχει ἔνοπλον ἐπιβῆναι· ὁμοίως δὲ καὶ πλείονας διὰ τῆς αὐτοῦ τοῦ αὐλοῦ βάσεως ἔνδον τὴν πρόοδον ἔχοντας. Ὑποζώννυται δὲ ὁ ἐπὶ ταῖς προσηλωθείσαις σανίσιν αὐλὸς πάντοθεν σχοινίοις εὐτόνοις ἐνδυναμουμένως, καὶ βυρσοῦται δέρμασι διαβρόχοις, ἵνα ἀπὸ τῶν πυροφόρων φυλάττηται. Μέτρα δὲ τοῦ προβλήματος τούτου πρὸς τὴν κατασκευὴν μὴ συντεταχέναι τὸν Κτησίβιον, ἀλλ' ὑπόμνημα μόνον ὡς μαθηματικοῖς τοῖς μεταχειριζομένοις ἀρχιτέκτοσι ταῦτα ἀνατιθέμενον. Ἔξεστι γὰρ τούτοις τὴν τῶν ὀργάνων μετασκευάζειν συμμετρίαν καὶ πρὸς τὴν ἀνήκουσαν μεταφέρειν τοῦ τόπου χρείαν. Ἡμεῖς δὲ γυμνασίας χάριν τοῖς εἰσαγομένοις ἐξεθέμεθα εἰς κατασκευὴν τοῦ προβλήματος συμμετρίαν τοιαύτην. Γινέσθω τοίνυν τὸ ἐσχάριον τὸ ἐπικείμενον ἐπὶ τῆς τετρατρόχου ἢ ἑξατρόχου ἁμάξης εἴτε χελώνης κατὰ μὲν μῆκος πηχῶν ˉιˉε, ἐπὶ δὲ πλάτος ˉι· αἱ δὲ τῶν τροχῶν γινέσθωσαν ˉκ· τὸ δ' ἐπ' αὐτὰ κινούμενον πλάγιον σὺν τῷ ἐπικειμένῳ αὐλῷ πηχῶν κατὰ μῆκος ˉλ, πλάτος ἔχον κατὰ τὴν βάσιν ποδὸς ἑνὸς ἡμίσεος, τὸ δὲ πάχος σπιθαμιαῖον· ἵνα, ὃν 265 λόγον ἔχει τὸ μῆκος τοῦ ἐσχαρίου πρὸς τὸ πλάτος, τὸν αὐτὸν καὶ τὸ κινούμενον πλάγιον πρὸς τὰ ἱστάμενα ὄρθια· καὶ ὃν πάλιν ἔχει λόγον τὸ αὐτὸ κινούμενον πρὸς τὸ μῆκος τοῦ ἐσχαρίου, τὸν αὐτὸν καὶ τὰ ἱστάμενα ὄρθια πρὸς τὸ αὐτὸ πλάτος· ὡς γὰρ ˉιˉε πρὸς ˉι, οὕτως ˉλ πρὸς ˉκ· καὶ ὡς ˉλ πρὸς ˉιˉε, οὕτως ˉκ πρὸς ˉι· ἡμιόλιος δὲ ὁ ˉιˉε τοῦ ˉι· ἔχει γὰρ τὸν ˉι καὶ τὸ ˉ#ˉ1ˉ7ˉ2 αὐτοῦ· ἡμιόλιος ἄρα καὶ ὁ ˉλ τοῦ ˉκ· διπλάσιος δὲ πάλιν ὁ ˉλ τοῦ ˉιˉε, διπλάσιος ἄρα καὶ ὁ ˉκ τοῦ ˉι. Ὁμοίως δὲ καὶ τὸ τῆς βάσεως πλάτος πρὸς τὸ αὐτῆς πάχος διπλάσιον. Ἀλλὰ καὶ αἱ τῶν τροχῶν διάμετροι σύμμετροι πρὸς τὴν καταμέτρησιν καὶ σύμφωνοι