History of Science Online - Course Info - Time tips - Semester at a glance - Weekly assignments at a glance - Timeline - Week 5: Hellenistic Science

Euclid of Alexandria, fl. 300 BC

Background

Euclid was in Alexandria at the time of Ptolemy Soter (Ptolemy I, 308-285 B.C.), and allegedly informed him that there is “no royal road to geometry.”

Euclid's Elements of Geometry builds on the work of previous mathematicians, especially that of Hippokrates of Chios (late fifth century, in Athens) who introduced geometrical proof and the postulatory-deductive method. The postulatory-deductive system consists of identifying assumed but unproven postulates and deducing theorems from them according to specified logical rules. Once proven (i.e., deduced), a theorem is added to the assumed postulates for possible use in deducing later theorems.

In his Elements, Euclid began with definitions (e.g., of a point, line, acute angle, etc.), then listed postulates (e.g., all right angles are equal to each other; one and only one straight line connects two points, etc.), which were followed by “common notions” or logical rules (e.g., if equals be subtracted from equals, the remainders are equal, etc.), and finally by propositions of theorems to be proved. This process, the establishment of postulatory-deductive systems, characterizes mathematical endeavors in the Hellenistic period, for which Euclid's Elements stands as the paradigm.

Assignments

Review what Lindberg says about Euclid (1992, pp. 86-89; 2007, pp. 83-85).

Explore this online edition of Euclid:

1. Make sure you know how to rotate and move the java animations
2. Read the first ten definitions, and read the Guide to the Definitions.
3. Read the postulates and common notions and read the Guide About the Postulates and Common Notions.
4. Work through the proof of the first proposition.

Optional:

• Table of Contents
• Quick Trip through Euclid's Elements
• Summary of the life and works of Euclid from the MacTutor Archive of the Department of Mathematics at the University of St. Andrews, Scotland.

	HSCI 3013. History of Science to 17th century Kerry Magruder, Instructor, 2004-14 Brent Purkaple, TA Report typos or broken links	Go to this course at Janux spellcheck.net | wordcounter.net Many thanks to the pedagogical model developed in Mythology and Folklore and other online courses by Laura Gibbs, which have been an inspiration for this course.	Academic Calendar
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