Pythagorean school, importance of arithmetic, 153; theory of Descartes, 154; speculations on series of units, 155; specimens of treatment in arithmetic, 156; results of researches, 156; importance of numbers ten and twelve, 156; discoverers and teachers of science, 166, 167 Pythagoreans, discover science of harmony, 143; famous theory, 143 R Racine and his plays, 48 _Rambles and Studies in Greece_, _see_ J. P. Mahaffy Renaissance (Renascence), 4; artists of, 131 Rénan, Ernest, simplicity of style, 75 Renascence, 4 Representation, local, 189 _Republic_, _see_ Plato Research, original, requisite for, 235 Rogers’s translation of Aristophanes, 61 Roman life and culture, 18, 19 Roman Republic, effect of growth, 211 Romanesque architecture, example of tawdriness, 109 Romans, medium through which Greek learning was spread in Western World, 3, 4, 18, 19, 85, 190, 195; compared with the Greeks, 182 Romantic school, 59 Rome, Greek ruins in time of Renaissance, 146 _Romeo and Juliet_, _see_ Shakespeare Royal College of Physicians, Ireland, 173 Ruskin, John, style, 89 S St. Angelo, castle of, 111 St. Mark’s at Venice, architecture of, 18, 109 _Sakia_, invention of, 165 _Samson Agonistes_, _see_ Milton Sappho, 37; Horace’s version of, 53; love for nature, 59 Satyric drama, 48 Science, definition of term as used, 147; relation to philosophy, 168; abstract thinking necessary to experiment and discovery, 235 Sciences of observation, 147 _Scriptores Erotici Graeci_, 95 Sculpture, Greek: reasons for pre-eminence 112, 113; nude and draped figures, 112, 113; Donatello’s problem, 113, 114; use of bronze and marble, 116, 118; development, 117, 118; decay, 117; never dissociated from painting, 118; coloured statues, 118, 119; principles of composition, 120; second favourite form of composition, 122; effect on Europe, 123 Shakespeare, indebted to Plutarch’s _Lives_, 45; indirect knowledge of Greek poets, 46; Milton on, 47, 48; school of, defended 48 _Antony and Cleopatra_: source in Plutarch’s _Lives_, 45 _Hamlet_: Voltaire’s view of, 48 _Macbeth_: Voltaire’s view of, 48 _Romeo and Juliet_: Greek origin, 95 Shakespeare, school of, and Greek masters, 48 Shelley, combines Greek culture with Romantic imagination, 56, and Pantheism, 228 Sicilian troubles, 186 Sidon, tomb of, 112 Silver Age of Greek Literature, 91 Simonides, Gray compared with, 54 Skellig Michael, beehive huts at, 99 Slavery, among Greeks, 188, 190; Aristotle on, 189 Smyly, Prof., _Essay_; on Greek notation in arithmetic, 158 _Social Life in Greece_, _see_ J. P. Mahaffy Socrates, prosecution of, 215; causes revolution in philosophy, 236, 237 Solon, use of verse, 39; modern, 66; reduces debts in Athens, 186 _Sophist_, of Plato, 152 Sophists, attitude toward scientific speculation, 237