The role of geometrical construction in Theodosius's Spherics

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

This paper is a contribution to our understanding of the constructive nature of Greek geometry. By studying the role of constructive processes in Theodoius's Spherics, we uncover a difference in the function of constructions and problems in the deductive framework of Greek mathematics. In particular, we show that geometric problems originated in the practical issues involved in actually making diagrams, whereas constructions are abstractions of these processes that are used to introduce objects not given at the outset, so that their properties can be used in the argument. We conclude by discussing, more generally, ancient Greek interests in the practical methods of producing diagrams.

Original languageEnglish
Pages (from-to)581-609
Number of pages29
JournalArchive for History of Exact Sciences
Volume63
Issue number6
DOIs
Publication statusPublished - 2009 Oct

Fingerprint

Diagram
Diagrams
Object
Framework
Abstraction
Greek Mathematics
Ancient Greek
Geometry

ASJC Scopus subject areas

  • History and Philosophy of Science
  • Mathematics (miscellaneous)

Cite this

The role of geometrical construction in Theodosius's Spherics. / Sidoli, Nathan Camillo; Saito, Ken.

In: Archive for History of Exact Sciences, Vol. 63, No. 6, 10.2009, p. 581-609.

Research output: Contribution to journalArticle

@article{2b61e097b13245458a55e27ecd5f5160,
title = "The role of geometrical construction in Theodosius's Spherics",
abstract = "This paper is a contribution to our understanding of the constructive nature of Greek geometry. By studying the role of constructive processes in Theodoius's Spherics, we uncover a difference in the function of constructions and problems in the deductive framework of Greek mathematics. In particular, we show that geometric problems originated in the practical issues involved in actually making diagrams, whereas constructions are abstractions of these processes that are used to introduce objects not given at the outset, so that their properties can be used in the argument. We conclude by discussing, more generally, ancient Greek interests in the practical methods of producing diagrams.",
author = "Sidoli, {Nathan Camillo} and Ken Saito",
year = "2009",
month = "10",
doi = "10.1007/s00407-009-0045-2",
language = "English",
volume = "63",
pages = "581--609",
journal = "Archive for History of Exact Sciences",
issn = "0003-9519",
publisher = "Springer Verlag",
number = "6",

}

TY - JOUR

T1 - The role of geometrical construction in Theodosius's Spherics

AU - Sidoli, Nathan Camillo

AU - Saito, Ken

PY - 2009/10

Y1 - 2009/10

N2 - This paper is a contribution to our understanding of the constructive nature of Greek geometry. By studying the role of constructive processes in Theodoius's Spherics, we uncover a difference in the function of constructions and problems in the deductive framework of Greek mathematics. In particular, we show that geometric problems originated in the practical issues involved in actually making diagrams, whereas constructions are abstractions of these processes that are used to introduce objects not given at the outset, so that their properties can be used in the argument. We conclude by discussing, more generally, ancient Greek interests in the practical methods of producing diagrams.

AB - This paper is a contribution to our understanding of the constructive nature of Greek geometry. By studying the role of constructive processes in Theodoius's Spherics, we uncover a difference in the function of constructions and problems in the deductive framework of Greek mathematics. In particular, we show that geometric problems originated in the practical issues involved in actually making diagrams, whereas constructions are abstractions of these processes that are used to introduce objects not given at the outset, so that their properties can be used in the argument. We conclude by discussing, more generally, ancient Greek interests in the practical methods of producing diagrams.

UR - http://www.scopus.com/inward/record.url?scp=70449532464&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70449532464&partnerID=8YFLogxK

U2 - 10.1007/s00407-009-0045-2

DO - 10.1007/s00407-009-0045-2

M3 - Article

VL - 63

SP - 581

EP - 609

JO - Archive for History of Exact Sciences

JF - Archive for History of Exact Sciences

SN - 0003-9519

IS - 6

ER -