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

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 might gain strength by the connection and unity of the adjacent parts. And he placed ladders to the crossbeams for ascent, separating diagonally one side from the other. And he secured the tower also with ropes tied from above at the corners and drawn outwards at the middle, making a wider base in shape for the tower, a kind of seat, bound around pegs having pins or iron nails and rings fixed sideways for tension, providing no small help for the support of the tower through the tension of the ropes. Thus from a few small timbers he constructed a great tower, equal in height to the wall, without indicating the divisions of the storeys or 243 the heights, nor declaring the fifth part of the tapering at the top. But if someone, being at a loss, should seek this out, he will get it from the base below through the number assigned to each side. For since the side was given as 10 feet, and being multiplied by the other of equal length to it makes the whole area or the inner space of the quadrangle 250 feet, and the fifth of these is approximately 51 and one-fifth feet; I seek what number, being multiplied by itself or by one equal to it in length, produces this, and I find approximately seven and a sixth; for seven times seven is 49; and seven times a sixth, that is by ten sixtieths, makes seventy prime sixtieths; and again the 10 by 7 makes 70; and from the collected 140 prime sixtieths, 120 are to be counted as two feet, and the rest to the fraction; so that the beams placed at the tapering of the uppermost storey should be seven and a sixth feet in length. But also the nine storeys placed for height from the base below, for the inset of the length and width according to the limit of the quadrangle, subtracting one foot each from the sixteen, leave approximately seven. And let the same method 244 be for those seeking it always for the tapering of the highest part of the tower and for a third and a fourth and any part. And the divisions of the storeys and the elevations for height, Diades and Charias, counting by cubits, set the first storey from the base below at a height of 7 cubits and 12 fingers. and the five upper ones at 5 cubits only; and the remaining ones at four and a third, and they counted in the height both the total thickness of the flooring of the storeys and the part below the hearth together with the gable above. Likewise also in the case of the smaller tower the division of the storeys received the same ratio for height. But the aforementioned Apollodorus, counting the tower by feet, makes the first uprights from the base 9 feet in height; and if he wants them all to be of equal height, he indicates it is six-storeyed and the inset to be of feet only; and he tapers it at the top by approximately a twenty-third of the area of the base, placing the upper beams at 10 feet each. but if he tapers the top by a fifth of the base on a six-storey tower, he indicates the inset of the storeys to be one and a half feet in four parts; but if also ten-storeyed, the inset is one foot each, as has been said before, and it takes off a fifth of the base at the top, so as to make the upper 245 beams seven and a sixth feet each. and in a ten-storeyed tower, the lower uprights are to be 9 feet each, and those on the upper four storeys of feet only, and those yet higher on the remaining four at 5 and a fraction. Thus therefore not only will the storeys of the towers, differing in number, be found to be of equal height to 60 feet, but also the towers constructed from both by cubits and feet, and differing in size, will be shown to be symmetrical to one another according to proportion. For if the cubit is 24 fingers in length, the foot being 10, and the 24 contains the 10 and its half, it is one and a half times it, and the foot is two-thirds of the cubit;

ἐποίησε τοῖς παραστάταις τούτοις ἴσον, ἵνα μὴ αἱ συμβολαὶ αὐτῶν ἐγγὺς ἀλλήλων ὦσιν, ἀλλ' ἀντιπαραλλάσσῃ πᾶς ἁρμὸς ἀφεστηκὼς πρὸς τὸν ἕτερον, καὶ τῇ τῶν παρακειμένων συνοχῇ καὶ ἑνότητι ἰσχὺν λαμβάνῃ. Καὶ κλίμακας δὲ πρὸς τὰς ἐπιζυγίδας διὰ τὴν ἀνάβασιν παρετίθει τὸ ἕτερον ἐκ τοῦ ἑτέρου πλευροῦ διαγωνίως χωριζούσας. Ἠσφαλίζετο δὲ τὸν πύργον καὶ σχοινίοις ἄνωθεν κατὰ τὰς γωνίας δεδεμένοις καὶ κατὰ μέσον ἔξω ἐπισυρομένοις, πλατυτέραν ἐν σχήματι βάσιν τῷ πύργῳ ἐμποιῶν οἱονεὶ ἕδραν, περιδεδεμένοις πασσάλοις περόνας ἔχουσιν ἢ σιδηροῖς ἥλοις καὶ κρίκοις πλαγίοις πρὸς τὴν ἀπότασιν ἐμπησσομένοις, οὐ μικρὰν βοήθειαν διὰ τῆς τῶν σχοινίων τάσεως πρὸς ὑποστήριξιν τῷ πύργῳ παρεχόμενος. Οὕτως ἐξ ὀλίγων καὶ μικρῶν ξύλων μέγα καὶ ἰσοϋψὲς τῷ τείχει κατεσκεύαζε πύργωμα, μήτε στεγῶν διαιρέσεις ἢ 243 ὕψη σημάνας, μήτε τῆς ἄνωθεν συναγωγῆς τὸ πέμπτον μέρος δηλώσας. Εἰ δέ τις ἀπορῶν ἐπιζητοίη τοῦτο, ἐκ τῆς κάτωθεν βάσεως λήψεται διὰ τοῦ ὑποτεθέντος ἐφ' ἑκάστῃ πλευρᾷ ἀριθμοῦ. Ἐπεὶ γὰρ ἡ πλευρὰ ποδῶν ἐδόθη ι, πολλαπλασιαζομένη δὲ ἐπὶ τὴν ἑτέραν καὶ ἰσομήκη αὐτῆς ποιεῖ τὸ ὅλον ἐμβαδὸν ἤτοι τὸ ἔνδον τοῦ τετραπλεύρου χωρίον ποδῶν ˉσˉνˉ, καὶ ἔστι τούτων τὸ πέμπτον ποδῶν ˉνˉα πέμπτον ἔγγιστα· ζητῶ ποῖος ἀριθμὸς ἐφ' ἑαυτὸν ἢ ἐπὶ τὸν ἰσομήκη αὐτοῦ πολλαπλασιαζόμενος τοῦτον ποιεῖ, καὶ εὑρίσκω τὸν ἑπτὰ ἕκτον ἔγγιστα· ἑπτὰ γὰρ ἐπὶ ἑπτὰ ˉμˉθ· καὶ ἑπτὰ ἐπὶ τὸ ἕκτον, τουτέστιν ἐπὶ τὰ δέκα λεπτὰ, ποιοῦσι λεπτὰ πρῶτα ˉο· πάλιν δὲ τὰ ˉι ἐπὶ ˉζ ποιοῦσιν ˉο· καὶ ἐκ τῶν συναγομένων λεπτῶν πρώτων ˉρˉμ τὰ μὲν ˉρˉκ εἰς πόδας δύο καταλογίζεσθαι, τὰ δὲ λοιπὰ εἰς τὸ μέρος· ὥστε τὰ πρὸς τῇ συναγωγῇ τῆς ἀνωτάτω στέγης τιθέμενα ζυγὰ ἀνὰ ποδῶν ἑπτὰ κατὰ μῆκος καὶ μέρους ἕκτου γινέσθωσαν. Ἀλλὰ καὶ αἱ πρὸς ὕψος ἀπὸ τῆς κάτωθεν βά σεως τιθέμεναι ἐννέα στέγαι ἐπὶ τὴν τοῦ μήκους καὶ πλάτους ἐπέμβασιν κατὰ τὸν τοῦ τετραπλεύρου περιορισμὸν ἀνὰ πόδα ἀφαιροῦσαι ἐκ τῶν δεκαὲξ, ἑπτὰ ἔγγιστα καταλιμπάνουσιν. Ἡ αὐτὴ δὲ ἔφοδος 244 ἐπὶ τῆς ἀνωτάτης τοῦ πύργου συναγωγῆς καὶ ἐπὶ τρίτου καὶ τετάρτου καὶ τοῦ τυχόντος μέρους ἀεὶ τοῖς ἐπιζητοῦσιν ἔστω. Τὰς δὲ τῶν στεγῶν διαιρέσεις καὶ τὰ πρὸς ὕψος ἀναστήματα οἱ μὲν περὶ ∆ιάδην καὶ Χαρίαν πρὸς πήχεις ἀριθμοῦντες τὴν ἐκ τῆς κάτωθεν βάσεως πρώτην στέγην πηχῶν πρὸς ὕψος ἐτίθουν ˉζ καὶ δακτύλων ˉιˉβ. τὰς δ' ἀνωτέρας πέντε ἀνὰ πηχῶν ˉε μόνον· τὰς δ' ὑπολειπομένας ἀνὰ τεσσάρων καὶ τρίτου, τό τε σύμπαχον τοῦ καταστρώματος τῶν στεγῶν καὶ τὸ κάτωθεν τοῦ ἐσχαρίου σὺν τῷ ἄνωθεν ἀετώματι τῷ ὕψει συνηρίθμουν. Ὁμοίως δὲ καὶ ἐπὶ τοῦ ἐλάσσονος πύργου ἡ διαίρεσις τῶν στεγῶν τὸν αὐτὸν λόγον πρὸς ὕψος ἐλάμβανεν. Ὁ δὲ ῥηθεὶς Ἀπολλόδωρος, πρὸς πόδας καταριθμῶν τὸν πύργον, τοὺς ἐκ τῆς βάσεως πρώτους παραστάτας ποδῶν ˉθ πρὸς ὕψος ποιεῖ· καὶ εἰ μὲν ἰσοϋψεῖς πάντας βούλεται, ἑξάστεγον αὐτὸν δηλοῖ καὶ ποδῶν μόνων τὴν παρέμβασιν εἶναι· τρίτον δὲ καὶ εἰκοστὸν ἔγγιστα τοῦ ἐμβαδοῦ τῆς βάσεως ἐπισυνάγειν ἄνωθεν ἀνὰ ˉι ποδῶν καὶ τὰ ἀνώτερα τιθεὶς ζυγά. εἰ δὲ τὸ πέμπτον τῆς βάσεως ἐπὶ ἑξαστέγου πύργου ἐπισυνάγει ἄνωθεν, ἑνὸς καὶ ἡμίσεως ποδὸς τὴν τῶν στεγῶν ἐπέμβασιν τετραμερῶς συμφαίνει· εἰ δὲ καὶ δεκάστεγον, ἀνὰ ποδὸς ἑνὸς τὴν παρέμβασιν, ὡς προείρηται, καὶ πέμπτον τῆς βάσεως ἀπολαμβάνειν ἄνωθεν, ὡς ἂν καὶ τὰ ἀνώ245 τερα ζυγὰ ἀνὰ ποδῶν ˉζ καὶ μέρους ἕκτου ποιεῖν. καὶ ἐπὶ μὲν δεκαστέγου τοὺς κάτωθεν παραστάτας ἀνὰ ποδῶν ˉθ γίνεσθαι, τοὺς δὲ ἐπὶ ταῖς ἀνωτέραις τέτρασι στέγαις ἀνὰ ποδῶν ˉ μόνων, τοὺς δ' ἔτι ἀνωτέρους ἐπὶ ταῖς ὑπολοίποις τέτρασιν ἀνὰ ˉε καὶ μέρους. Οὕτως οὖν οὐ μόνον αἱ κατ' ἀριθμὸν διαφέρουσαι τῶν πύργων στέγαι πρὸς ˉξ ποδῶν ὕψος ἰσοϋψεῖς εὑρεθήσονται, ἀλλὰ καὶ οἱ ἐξ ἀμφοτέρων πρὸς πήχεις καὶ πόδας κατασκευαζόμενοι πύργοι καὶ κατὰ μέγεθος διαφέροντες σύμμετροι πρὸς ἀλλήλους κατὰ ἀναλογίαν δειχθήσονται. Εἰ γὰρ ὁ πῆχυς ˉκˉδ κατὰ μῆκός ἐστι δακτύλων, τοῦ ποδὸς ˉιˉ ὄντος, ἔχει δὲ ὁ ˉκˉδ τὸν ˉιˉ καὶ τὸ ἥμισυ αὐτοῦ, ἡμιόλιος αὐτοῦ ἐστιν, ὑφημιόλιος δὲ πρὸς πῆχυν ὁ πούς·