Euclid (his Elements):

mathematical treatise of 13 books by Euclid in Alexandria (300 BC); a collection of definitions, postulates, propositions & their mathematical proofs, covering plane & solid Euclidean geometry, elementary number theory & incommensurable lines.  It is the oldest extant large-scale deductive treatment of mathematics. It is the most successful & influential textbook ever written; being one of the earliest mathematical works printed after the invention of the printing press (1482) & second only to the Bible in the number of editions.

 

Empedocles (his four elements):

494-434 BC, Greek pre-Socratic philosopher, from Sicily; famous for his cosmogonic theory of the 4 classical elements, these elements- fire, air, water, earth- were the "roots" from which all structures of the world were derived, mixed in differing proportions.  He also proposed forces (Love & Strife) which mixed & separated the elements, respectively.  He claimed to have found the process which corresponds to growth, increase or decrease.  Nothing new can come into being; change is only change in the juxtaposition of element with element. His theory became the dogma for the next 2 thousand years.  Influenced by the Pythagoreans, he challenged the practice of animal sacrifice & killing animals for food.  He developed a doctrine of reincarnation.  He was the last Greek philosopher to have recorded his ideas in verse.  More of his work survives than other pre-Socratic philosopher.  He purportedly killed himself by leaping into the active volcano Mount Etna. 

 

isotopes:

variants of a particular chemical element which differ in neutron number & consequently in nucleon number. All isotopes of a given element have the same number of protons but different numbers of neutrons in each atom.

 

Propylrea: * see EndNote<A>

monumental gateway, commissioned by Pericles in the rebuilding of  the Acropolis after the Persian Wars.  He appointed Phidias as the supervisor & lead architect; it was designed by the architect Mnesikles & financed from the treasury of the Delian League.  Construction began 437 & was terminated in 432 BC (the building unfinished); made of white Pentelic marble & grey Eleusinian marble.

 

Wagner (his music too simple): * see EndNote<B>

Wagner was famous for his leitmotifs.  Some critics, Eduard Hanslick in particular, did not like his music & felt the leitmotifs made the music too simple.  Debussy joined in, saying that leitmotifs in opera was like having a world where crazy people used "visiting cards" to introduce themselves & then start singing their names to be sure everyone knew what was going on.  Hanslick's tastes were conservative: he wrote glowing reports about Brahms but was deeply critical of Wagner.  

 

Michelangelo (ordained for the correction of fools):

This is a reference to the flawed judgement of a critic who Michelangelo dealt with in 1504.  While working on the David Michelangelo was visited by Piero Soderini, the Gonfaloniere of Justice.  This was an extremely powerful post in Florence, part of the government, the head of police & mayor, in short Michelangelo’s boss.  Soderini (who was not an artist) told him the statue was good but flawed: the nose on David was too big.  So Michelangelo climbed up the scaffolding, pretended by a ruse to chisel the nose anew.  Soderini then satisfied, said the statue was perfect.  Vasari says Michelangelo “climbed down, feeling sorry for those critics who talk nonsense in the hope of appearing well-informed.”  Later, after Soderini was removed from power, Michelangelo confided the story to Vasari & Condivi, both of whom would write biographies of the great man. 

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Gauss (concealed his discovery of non-Euclidean geometry):

Gauss, in his letters (before 1829) discussed the problem of parallel lines.  Farkas Bolyai, a close friend of Gauss, also tried in vain to prove the parallel postulate from Euclid's other axioms of geometry.  His son, János Bolyai, discovered non-Euclidean geometry in 1829.  His work was published in 1832.  Upon reading it Gauss wrote:

"To praise it would amount to praising myself.  For the entire content of the work ... coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years."  

Biographers of Gauss (notably Waldo Dunnington) claim Gauss was in full possession of non-Euclidean geometry long before Bolyai, but refused to publish because of his fear of controversy.

 

“clamour of the Boeotians.":

In a letter written in 1829, Gauss wrote: 

"It may take very long before I make public my investigations on this issue: in fact, this may not happen in my lifetime for I fear the 'clamour of the Boeotians.' " 

Boeotia was a province of ancient Greece whose inhabitants were known for their dullness and ignorance.

 

Giordano Bruno:

see Chapter II, page 56

 

Leibniz:

see Chapter I page 42, Chapter III, page 109, Chapter VII pages 236, 251, Chapter VIII page 282

 

Kant:

see Chapter I pages 7, 27, Chapter IV page 125, Chapter V page I70, Chapter VII page 243, Chapter VIII pages 285, 288, Chapter IX pages 299, 308, 309, 310, 311

 

Anaximander:

see Chapter II, page 64

 

Heraclitus:

see Chapter III, page 109

 

Protagoras:

see above page 311