GREEK GEOMETRY - THALES TO EUCLID

the development of practical and theoretical geometry by the ancient Greeks was a significant cultural accomplishment, and it proved critical for the evolution of Greek architecture. Interest in geometry in Greece may be divided into three phases. the earliest phase emphasized philosophical and religious applications, such as the speculations of two pre‐Socratic philosophers who used geometric models to articulate their views of the cosmos, thales of Miletos and anaximander of Miletos, both of them active in the first half of the sixth century bce. the second phase was centered in hellenistic alexandria, where the most important compiler, euclid, was active in the third century bce. Our existing corpus of writing about geometry has been preserved from this period. the third phase of exploration of geometry took place in the late hellenistic period, when archimedes of Syracuse and apollonius of perga were prominent among geometers; this period also was remarkable for practical developments in mechanics and engineering (heath 1921: I.345–348, II. 346–352, thomas 1941). the text of Vitruvius illustrates the wide range of interests of such authors; although he regarded himself as an architect and a designer, Vitruvius was, as we would define the role, an engineer (rowland and howe 1999: 21). he wrote his still‐ preserved treatise, De architectura, about 20 bce and dedicated it to the emperor augustus. the development of early Greek geometry took place concurrently with several significant cultural events in the seventh century bce. the reign of psammetichus I (664–610 bce) marked the beginning of increased contact between Greeks and egyptians (hahn 2001: 66–69). During the reign of amasis (570–526 bce), Cyprus fell first under egyptian rule, then that of the assyrians. the capture of the city of Sardis by persia in 547/6 bce opened a direct link between the Greek world, persia, and India (Burkert 2004: 49–55, 70–74). thales observed the solar eclipse of 585 bce, and his book on the cosmos is datable to 547 bce. although individuals such as thales and, later, pythagoras (circa 550–495 bce) could have traveled to egypt and Babylon to gain specialized knowledge, the geometry that existed in egypt and Babylon was not the philosophical geometry of the pre‐Socratics; instead, it featured pragmatic solutions for calculating areas, needed because of the ever‐changing topography due to the annual flooding of the Nile (heath 1921: 122–126). the egyptian rhind Mathematical papyrus documents the interest in area calculations. But the calculations included inaccuracies and approximations, and the level of accuracy was not what we would accept today. Yet the Greeks did not have to go far to meet egyptians or Babylonians as these people were coming to them. It is no coincidence that the early Greek geometers thales and anaximander were from Ionia and that, in the following generation, pythagoras was originally from Samos, just off the Ionian coast.

2010

Supportive attitudes can bring to a blossoming science, while neglect can quickly make science absent from everyday life and provide a very primitive view of the world. We compare one important Greek achievement, the computation of the Earth meridian by Eratosthenes, to its later interpretation by the Roman historian of science Pliny.

Translated by Gianluca Longa 1 Résumé : Cet article vise à montrer dans quelle mesure l'examen de certains passages de l'oeuvre d'Aristote peut contribuer à la résolution d'importants problèmes liés à l'interprétation de l'analyse géométrique ancienne. Nous nous concentrons notamment sur le célèbre passage des Seconds Analytiques dans lequel Aristote se réfère de manière apparemment cryptique à l'analyse pratiquée par les géomètres (Seconds Analytiques, livre I, chapitre 12) et nous montrons l'importance fondamentale de ce passage pour une compréhension correcte de l'analyse géométrique ancienne.

Interconnectivity, relations, entanglement etc. are notions related to recent globalization studies. Some of these terms are known and used in historiography since long. The present paper has for aim to investigate the idea of an interconnected world present in historiographical research of the late eighteenth and early nineteenth centuries on the topic of Greek sciences. The example of the formation and character of Greek science, as well as the directions it spread to other parts of the Ancient world will provide actual research on global history of knowledge with possibilities to rethink its terminology.

This research analize the proportions and architectural features of Osireion Hypogeum in order to determine the level of knowledge of the geometric rules achieved by Egyptian Priests and Harpedonaptae before the birth of Euclidean Geometry.

The Mathematical Intelligencer, 2016

Thales The Measurer, 2022

'Thales The Measurer' is the title of a book of mine, published by Routledge in 2022. Here is a survey of its contents. This book is devoted to a sustained investigation on the celebrated Milesian and what he is likely to have contributed to the beginnings of Greek science. One of the conclusions reached is that Thales spent his whole life as an investigator. If so, he was the first (first on the world!) to devise the very idea of an investigator (wth investigation as a a profession and a sort of excellence). As a consequence, our present society, with its millions of professional investigators, owes a lot to him.

2005