The Legacy of Greece: Essays By: Gilbert Murray, W. R. Inge, J. Burnet, Sir T. L. Heath, D'arcy W. Thompson, Charles Singer, R. W. Livingston, A. Toynbee, A. E. Zimmern, Percy Gardner, Sir Reginald Blomfield
Philosophy
The Legacy of Greece: Essays By: Gilbert Murray, W. R. Inge, J. Burnet, Sir T. L. Heath, D'arcy W. Thompson, Charles Singer, R. W. Livingston, A. Toynbee, A. E. Zimmern, Percy Gardner, Sir Reginald Blomfield
Greece -- Civilization
Euclid wrote other books on both elementary and higher geometry, and on
the other mathematical subjects known in his day. The elementary
geometrical works include the _Data_ and _On Divisions_ (_of figures_),
the first of which survives in Greek and the second in Arabic only; also
the _Pseudaria_, now lost, which was a sort of guide to fallacies in
geometrical reasoning. The treatises on higher geometry are all lost;
they include (1) the _Conics_ in four Books, which covered almost the
same ground as the first three Books of Apollonius's _Conics_, although
no doubt, for Euclid, the conics were still, as with his predecessors,
sections of a right-angled, an obtuse-angled, and an acute-angled cone
respectively made by a plane perpendiular to a generator in each case;
(2) the _Porisms_ in three Books, the importance and difficulty of which
can be inferred from Pappus's account of it and the lemmas which he
gives for use with it; (3) the _Surface-Loci_, to which again Pappus
furnishes lemmas; one of these implies that Euclid assumed as known the
focus-directrix property of the three conics, which is absent from
Apollonius's _Conics_.
In applied mathematics Euclid wrote (1) the _Phaenomena_, a work on
spherical astronomy in which ὁ ὁριζων {ho horizôn} (without κυκλος
{kyklos} or any qualifying words) appears for the first time in the
sense of _horizon_; (2) the _Optics_, a kind of elementary treatise on
perspective: these two treatises are extant in Greek; (3) a work on the
Elements of Music. The _Sectio Canonis_, which has come down under the
name of Euclid, can, however, hardly be his in its present form.
In the period between Euclid and Archimedes comes Aristarchus of Samos
(about 310-230 B. C.), famous for having anticipated Copernicus.
Accepting Heraclides's view that the earth rotates about its own axis,
Aristarchus went further and put forward the hypothesis that the sun
itself is at rest, and that the earth, as well as Mercury, Venus, and
the other planets, revolve in circles about the sun. We have this on the
unquestionable authority of Archimedes, who was only some twenty-five
years later, and who must have seen the book containing the hypothesis
in question. We are told too that Cleanthes the Stoic thought that
Aristarchus ought to be indicted on the charge of impiety for setting
the Hearth of the Universe in motion.
Public-domain text, read in full here on John Shaqi.
Reviews
Reviews
No reviews yet
Be the first to share your thoughts on this work.
Elsewhere in the archive
Join the Discussion
Join the discussion
Sign in to leave a comment or review.
Sign InorCreate an account