source file: mills2.txt Date: Sun, 2 Mar 1997 09:00:31 -0800 Subject: Greek theorists From: John Chalmers Aristoxenos wrote around 320 BCE, Archytas about 375-390. Euclid's geometry dates from about 300 and Ptolemy's Harmonics were written about 160 CE. The heyday of the Pythagoreans was more like early 5th or late 6th century than 3rd or 4th. By the time of Archytas, irrationals were well known. He was the first to describe three the simplest means as important for music, the three being the arithmetic, harmonic and geometric, the latter, of course, creates irrationals in most cases. The geometrical algebra of the later geometers is really impressive. See Heath's 2 volume "A History of Greek Mathematics" for more details than you'll probably want. --John Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 3 Mar 1997 01:08 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA02252; Mon, 3 Mar 1997 01:08:57 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA02255 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id QAA14603; Sun, 2 Mar 1997 16:05:48 -0800 Date: Sun, 2 Mar 1997 16:05:48 -0800 Message-Id: <199703030001.RAA27442@freenet.uchsc.EDU> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu