The History of Mathematical Proof in Ancient Traditions

Diagrams and arguments in Greek mathematics 143 any shape. 17 In the modern fi gure, because the pentagons are irregular, we som ...

144 ken saito and nathan sidoli construct, on a given line, a parallelogram that contains a given angle and is equal to a given ...

Diagrams and arguments in Greek mathematics 145 As well as metrical indiff erence, the manuscript diagrams oft en seem to reveal ...

146 ken saito and nathan sidoli Archimedes’ Sphere and Cylinder for a polygon with short sides that might be visually confused w ...

Diagrams and arguments in Greek mathematics 147 and in the erased part of Florence 28.^25 I n Bodleian 301 and Paris 2466 we see ...

148 ken saito and nathan sidoli palimpsested as a prayer book some centuries later. 26 In the section of the treatise that Heibe ...

Diagrams and arguments in Greek mathematics 149 obtaining among the objects, but rather to convey specifi c mathematical relatio ...

150 ken saito and nathan sidoli circular arcs that meet at cusps, as seen in Figure 2.11. 29 Th is confi rms that the diagrams w ...

Diagrams and arguments in Greek mathematics 151 Th e schematic role of diagrams in spherical geometry becomes unmis- takable whe ...

152 ken saito and nathan sidoli One diagram for multiple cases In the foregoing three sections, we have discussed characteristic ...

Diagrams and arguments in Greek mathematics 153 does not. In Heiberg’s edition, and Vienna 31 (which oft en has corrected diagra ...

154 ken saito and nathan sidoli In a number of cases, the tendencies toward overspecifi cation and graphical indiff erence resul ...

Diagrams and arguments in Greek mathematics 155 Th e redrawing, however, might also be done at the time when the text was copied ...

156 ken saito and nathan sidoli constructed triangle is depicted as an irregular, acute triangle and all of its sides are depict ...

Diagrams and arguments in Greek mathematics 157 Although, for the most part, the text and diagrams appear to have been copied as ...

158 ken saito and nathan sidoli the thicket of letter names in the text, they relate the letter names to specifi c objects and t ...

Diagrams and arguments in Greek mathematics 159 In fact, we will probably never know much with certainty about the parabolas tha ...

160 ken saito and nathan sidoli always in fl ux, and probably not nearly as determinate as we would like to believe – neverthele ...

Diagrams and arguments in Greek mathematics 161 Berggren , J. L. , and Jones , A. ( 2000 ) Ptolemy’s Geography : An Annotated Tr ...

162 ken saito and nathan sidoli ( 1989 ) L’Optique de Claude Ptolémée dans la version latine d’apr`ès l’arabe de l’émir Eugène d ...