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List of Illustrations 26. Bridges and rams on ships, tube on universal joint and on a screwshaft, folio 40 27. Raft, folio 41 28. Raft, front view, folio 42 29. Measuring the height of a wall, folio 43 30. Measuring an interval from a distance, method 1, folio 43v 31. Measuring an interval from a distance, method 2, folio 44v 32. Finding the position of a line, folio 46 33. The rhombus as two isosceles triangles; the quadrilateral divided into two triangles, folios 46v, 47 34. Measurement of areas, folio 47 35. Measurement of a circle, method 1, folio 48v 36. Measurement of a circle, method 2, folio 49v 37. Measurement of a cube, folio 50 38. Measurement of a sphere and a cylinder, folio 51v 39. Measurement of a cone, folio 52 40. The pyramid and prism, folio 52v 41. Measurement of the capacity of a cistern, folio 53 42. Measuring the discharge from a spring, folio 54v [ xx ]
Introduction Vaticanus graecus 1605, a richly illustrated manuscript dated on palaeographical grounds to the eleventh century, contains just two treatises — instructional manuals on the fabrication of siege machines and on the use of a dioptra (a kind of surveyor’s theodolite) with applied geometry, ostensibly to estimate the required sizes of the machines — generally referred to as the Parangelmata Poliorcetica and the Geodesia. K. K. Müller first showed that the unedited Vaticanus was the archetype of the tradition of these texts, 1 which had been edited previously from the sixteenth-century Bononiensis Universitatis 1497 or its descendants. 2 In his monograph La tradition du texte d’Héron de Byzance, Alphonse Dain elaborated on Müller’s demonstration and provided an exhaustive study of the tradition. 3 The two treatises represent the work of an anonymous tenth-century Byzantine compiler and commentator, who updated and supplemented for his contemporaries the works of classical poliorcetic authors, 4 particularly Apollodorus of Damascus (1st–2nd cen- 1 Müller’s argument rests on the observations that all manuscripts of the tradition exhibit significant lacunae, noticed by earlier editors, which correspond to the loss of folios in the Vaticanus, and incorrect sequences of text that can be shown to result from a faulty rebinding of the Vaticanus. Müller concludes (“Handschriftliches,” 456): “Klar ist nun, dass alle Hss., welche die eben verzeichneten Lücken und die oben dargestellte Unordnung im Texte zeigen, ohne Ausnahme direkt oder indirekt auf den Vat. 1605 zurückgehen.” Müller also provides a list of the readings in the Vaticanus that differ from the editions of Wescher and Vincent, based in part on his own observations and in greater part those of A. Mau. 2 See the editions and translations by Barocius, Martin, Schneider, and Wescher of the Parangelmata, and Vincent of the Geodesia listed in the bibliography; for the stemma see Dain, Tradition, 155. 3 Dain concludes (Tradition, 42) on the archetype value of the Vaticanus: “On sait aussi que le Vaticanus 1605 présentait dans la Poliorcétique, comme dans la Géodésie, des lacunes dues à la chute de folios; ces mêmes lacunes se retrouvent dans tous nos manuscrits, et comme elles correspondent à des fins ou à des débuts de folios du Vaticanus 1605, il en résulte que la parenté avec ce manuscrit est amplement démontrée.” 4 For the classical and Byzantine poliorcetic works and manuscripts, see Dain “Stratégistes,” passim, and H. Hunger, “Kriegswissenschaft” in Die hochsprachliche profane Literatur der Byzantiner (Munich, 1978), II:321–40. [ 1 ]
Page 1 and 2: Dumbarton Oaks Studies XXXVI SIEGEC
Page 3 and 4: © 2000 Dumbarton Oaks Trustees for
Page 5 and 6: Foreword The texts commonly called
Page 7 and 8: List of Abbreviations and Bibliogra
Page 15 and 16: McGeer, Warfare E. McGeer, Sowing t
Page 17: List of Illustrations A. Vaticanus
Page 21 and 22: Introduction overlooking the shore
Page 23 and 24: Introduction teenth-century Vindobo
Page 25 and 26: Introduction for besiegers to dig a
Page 27 and 28: Introduction concepts (noÆmata) ar
Page 29 and 30: Introduction a “surface sx∞ma
Page 31 and 32: Introduction and evinces a clear pr
Page 33 and 34: Introduction die Irre gehenden) Ver
Page 35 and 36: Introduction to the expedition of 9
Page 37 and 38: Introduction xel«nai (670:11), and
Page 39 and 40: Introduction The Anon. Byz.’s new
Page 41 and 42: Introduction to remain as it appear
Page 43 and 44: Introduction Vaticanus graecus 1605
Page 45 and 46: Introduction overlooking the shore
Page 47 and 48: Introduction teenth-century Vindobo
Page 49 and 50: Introduction for besiegers to dig a
Page 51 and 52: Introduction concepts (noÆmata) ar
Page 53 and 54: Introduction a “surface sx∞ma
Page 55 and 56: Introduction and evinces a clear pr
Page 57 and 58: Introduction die Irre gehenden) Ver
Page 59 and 60: Introduction to the expedition of 9
Page 61 and 62: Introduction xel«nai (670:11), and
Page 63 and 64: Introduction The Anon. Byz.’s new
Page 65 and 66: Introduction to remain as it appear
Page 67 and 68: Texts and Translations Parangelmata
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1. Everything about siege machines
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Parangelmata Poliorcetica itself, o
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Parangelmata Poliorcetica be made q
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Parangelmata Poliorcetica words bot
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Parangelmata Poliorcetica rations,
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Parangelmata Poliorcetica host abov
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Parangelmata Poliorcetica slope it
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Parangelmata Poliorcetica 8. It is
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Parangelmata Poliorcetica and left
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Parangelmata Poliorcetica lest the
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Parangelmata Poliorcetica tortoises
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Parangelmata Poliorcetica such dis
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Parangelmata Poliorcetica or oil, w
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Parangelmata Poliorcetica covered b
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Parangelmata Poliorcetica line, wit
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Parangelmata Poliorcetica together,
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Parangelmata Poliorcetica or slight
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Parangelmata Poliorcetica tortoise
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Parangelmata Poliorcetica ened with
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Parangelmata Poliorcetica thickness
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Parangelmata Poliorcetica one of th
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Parangelmata Poliorcetica follow th
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Parangelmata Poliorcetica thick and
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Parangelmata Poliorcetica on the si
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Parangelmata Poliorcetica projectio
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Parangelmata Poliorcetica 33. And u
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Parangelmata Poliorcetica , which d
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Parangelmata Poliorcetica the first
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Parangelmata Poliorcetica both are
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Parangelmata Poliorcetica tortoises
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Parangelmata Poliorcetica effective
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Chapter 1 Commentary the Introducti
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Chapter 1 Commentary 12 ÉAghsistr
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Chapter 1 Commentary the enthymeme
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Chapter 2 Commentary de devant”;
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Chapter 2 Commentary folio 36r. The
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Chapter 3 Commentary 1 §jonuxistÆ
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Chapter 3 Commentary found in G. Pa
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Chapters 3-4 Commentary ≤dÁ gãr
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Chapter 4 Commentary kÊklƒ …w
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Chapters 6-7 Commentary Chapter 6.
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Chapter 7 Commentary descriptions (
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Chapter 10 Commentary frame of the
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Chapter 11 Commentary Mech.: 99:41-
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Chapter 11 Commentary 20 ÍpodÆmas
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Chapters 12-13 Commentary Mech. ava
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Chapter 13 Commentary skop°lvn gei
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Chapters 13-14 Commentary fortifica
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Chapter 15 Commentary 2 daktÊlvn
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Chapters 15-16 Commentary The liyob
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Chapter 17 Commentary entire device
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Chapters 18-19 Commentary 5 éparxo
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Chapters 19-21 Commentary trated on
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Chapter 22 Commentary 13-14 ka‹ d
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Chapter 22 Commentary 38 ÙjurrÊto
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Chapter 24-25 Commentary 5 ka‹ é
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Chapter 25 Commentary sumably the A
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Chapter 27 Commentary n. 31. It is
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Chapters 27-30 Commentary 65), is a
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Chapters 30-31 Commentary Rhodes, w
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Chapters 33-34 Commentary Bild zeig
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Chapters 35-37 Commentary lates bot
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Chapter 39 Commentary Chapter 39. A
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Chapters 39-40 Commentary ßteroi t
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Chapters 41-43 Commentary 4-5 peris
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