160 ken saito and nathan sidoli
always in fl ux, and probably not nearly as determinate as we would like to
believe – nevertheless, a system of objects with a very specifi c locality and
temporality. A Tokyo subway map is useless for Paris. If it was drawn this
year, it will contain stations and lines that did not exist ten years ago and
ten years from now it will again be out of date. Th e manuscript diagram
in Figure 2.13 , however, has no such specifi city. It can refer to any sphere
and does. Anyone who wants to draw a great circle on a sphere tangent to
a given line and through a given point can use this diagram in conjunction
with its proposition to do so. In the centuries since this proposition was
written, a great many readers must have drawn fi gures of this construction- on the plane, on the sphere, in their mind’s eye – and this diagram, strange
and awkward as it is, somehow referred to all of them. It is in such a way
that the overspecifi ed, graphically inaccurate diagrams that we fi nd in the
manuscript tradition achieve the generality for which they were intended.
Bibliography
Manuscripts
Bodleian 301 : Bodleian Library, D’Orville 301. Ninth century.
Bologna 18–19 : Bologna, Biblioteca comunale, 18–19. Eleventh century.
Florence 28 : Florence Laurenziana 28.3 Tenth century.
Leiden 399 : Bibliotheek van de Universiteit Leiden, Or. 399.1. 1144–1145
(539 ah ).
Paris 2466 : Bibliothèque nationale de France, Gr. 2466. Twelft h century.
R a b ā t. 53 : Rabāt., al-Maktaba al-Malikiyya, al-Khyzāna al-H. assaniyya, 53. 1607–
1608 (1016 ah ).
Uppsala 20 : Uppsala Universitetsbibliotek, O. Vet. 20. 1042–1043 (434 ah ).
Vatican 190 : Bibliotheca Apostolica Vaticana, Gr. 190. Ninth century.
Vatican 206 : Bibliotheca Apostolica Vaticana, Gr. 206. Twelft h–thirteenth century.
Vatican 204 : Bibliotheca Apostolica Vaticana, Gr. 204. Ninth–tenth century.
Vatican Ottob. 1850 : Bibliotheca Apostolica Vaticana, Lat. Ottob. 1850. Th irteenth
century.
Vienna 31 : Vienna Gr. 31. Eleventh–twelft h century.Modern scholarship
Andersen , K. ( 1987 ) ‘ Th e central projection in one of Ptolemy’s map constructions ’,
Centaurus 30 : 106 –13.
August , E. F. ( 1826 –9) ΕΥΚΛΕΙΔΟΥ ΣΤΟΙΧΕΙΑ, Euclidis Elementa. Berlin.