|Diagrams in manuscripts||A tool for reproducing diagrams||Indices of propositions used in principal works||This site and its author|
Last update December 14, 2014
From this page you can download diagrams of several Greek mathematical works reproduced from the manuscripts: Euclid's Elements, Books 2-4, 6, 11-13, Phaenomena, Optics, as well Arabic translation of Menelaus' Spherics.
ExampleIn proposition III.13 of the Elements, Euclid proves (by contradiction) that two circles cannot touch at two points either internally or externally. All the modern editions have a diagram similar to the one in the left, which appears in Heiberg's edition. However, the diagram found in the manuscripts is like the one in the right, which is a faithful reproduction from Vatican manuscript of the ninth century. Here, the second circle ΑΚΓ touching externally at two points to the first circle ΑΒΓΔ is represented by a lunule, which Heiberg (more precisely August, whose diagrams were copied by Heiberg) has changed into a circle.
Reproduced Diagrams from Greek and Arabic manuscripts (February 28, 2013, last update December 14, 2014)
DownloadDOWNLOAD whole PDF File
Corrections in Book XII (pp. 141-161) on December 14, 2014.
Correction in page 71 on April 27, 2013.
Diagrams in Greek Mathematical Texts (March 31, 2008. Latest update April 3, 2011)
Changes in ver. 2.03
Older versionsDiagrams: older versions
The program DRaFT
Most of the diagrams in the report is drawn by the program DRaFT developed in this project, which can be downloaded from this site. Download DRaFT
This research was supported by KAKENHI, or Grants-in-Aid for Scientific
Research by Japan Society for the Promotion of Science (JSPS)