The "General Scholium" (Scholium Generale in the original Latin) is an essay written by Isaac Newton, appended to his work of Philosophiæ Naturalis Principia Mathematica, known as the Principia. It was first published with the second (1713) edition of the Principia and reappeared with some additions and modifications on the third (1726) edition.The General Scholium online, trans. Andrew Motte, 1729.
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Ethics, Part I, Prop. 29, > Scholium. Trans: Edwin Curley. London: Penguin, 1996.
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113 Thucydides is said to have gained from him his accuracy in the use of words.Marcell. Vit. Thuc.; comp. Scholium ap. Hemsterhus. Annot. in Lucian.
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Cynaethus or Cinaethus ( or Κίναιθος) of Chios was a rhapsode, a member of the Homeridae, sometimes said to have composed the Homeric Hymn to Apollo. The main source of information on Cynaethus is a Scholium to Pindar's second Nemean ode.This is found, with slightly different readings, in the Scholia Vetera in Pindari Carmina (ed. Drachmann), Nemean 2, scholium 1c, and in Fragmenta Historicorum Graecorum (ed.
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The speech on the choice of HerculesPhilostratus, p. 496; Xenophon, Mem. ii. 1. § 21 was entitled Horai ().Suda, Horai, Prodicus; Scholium ad Aristoph. Nub. 1. 360.
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According to a scholium attributed to Apollinaris of Laodicea, Papias also related a tale on the grotesque fate of Judas Iscariot: Cf. Schmidt's translation , Smith's translation.
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The General Scholium is a concluding essay added to the second edition, 1713 (and amended in the third edition, 1726).See online Principia (1729 translation) vol.2, Books 2 & 3, starting at page 387 of volume 2 (1729). It is not to be confused with the General Scholium at the end of Book 2, Section 6, which discusses his pendulum experiments and resistance due to air, water, and other fluids.
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Scholium to Odyssey 11.547. The accounts of the Odyssey disagree, suggesting that the Greeks themselves hold a secret vote.Odyssey 11.543–47. In any case, Odysseus is the winner.
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A scholium on the Pharsalia equates Dis Pater with Taranis, the Gaulish god of thunder. In southern Germany and the Balkans, Aericura was considered a consort of Dīs Pater.
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Despite the source being unknown, it was used in both the Scholium of Arethas and in a letter by Patriarch Nicholas III to Emperor Alexios I Komnenos (r. 1081–1118).
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However Euripides and Apollodorus were not alone in making Pleisthenes the father of Agamemnon and Menelaus. These included, so we are told, Hesiod,Scholium on Homer's Iliad 1.7, scholium on Tzetzes' commentary on Homer's Iliad, Tzetzes, Exegesis in Iliadem 1.122 (Most, pp. 204-205). Aeschylus,This come to us by way of Tzetzes, Exegesis in Iliadem 1.122 (Most, pp. 204-205). Tzetzes does not say where Aeschylus says this. As noted above, Aeschylus, Agamemnon 1569 and 1602 indicate a Pleisthenes somewhere in the ancestry of Agamemnon, and this may be the basis for Tzetzes' claim, though elsewhere in the same play Aeschylus says that Atreus is Agamemnon's father 60, 1583, 1590. Porphyry,Scholium on Homer's Iliad 2.249 (Gantz, p. 552).
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From Crete, Aerope was taken to Mycenae. And there she became, according to most accounts, the mother of Agamemnon and Menelaus.Sources which explicitly name Aerope as the mother of Agamemnon and Menelaus include: (by Atreus) scholium on Homer's Iliad 1.7 and scholium on Tzetzes' commentary on Homer's Iliad (Most, pp. 204-205), Euripides, Helen 390-392, Orestes 16, Sophocles, Ajax 1290-1297, Apollodorus, E.2.10-12, E.3.12, Hyginus, Fabulae 97, and (by Pleisthenes) Apollodorus, 3.2.2 , Dictys Cretensis, 1.1 .
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Then a final scholium points out how problems 6 and 7 apply to the horizontal and vertical components of the motion of projectiles in the atmosphere (in this case neglecting earth curvature).
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She buried them alive in the Temple of Hera, believing this would make them immortal. The poet Creophylus, however, blamed their murders on the citizens of Corinth.As noted in the scholium to Medea 264.
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In the 17th century, both John LockeLocke, John. An Essay Concerning Human Understanding, XXI. and Baruch Spinoza Spinoza, Baruch. Ethica ordine geometrico demonstrata [Ethics, Demonstrated in Geometrical Order], Pars II, Propositio XXXV, Scholium; Propositio XLVIII.
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A scholium to the Iliad passage, explains that Hades had commanded that Heracles "master Cerberus without shield or Iron".Schol. Homer Iliad 5.395–397 (Ogden 2013b, p. 66); Ogden 2013a, p. 112; Gantz, p. 416.
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A scholium on the passage remarks that Philocrates, an Athenian comic playwright, had described Philaenis as a hetairistria and a tribas ("tribade"). This is the only known reference to a comic playwright by this name.
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Ol. vi. 162 Other examples are listed below. As Zeus Aeneius or Zeus Aenesius, he was worshiped in the island of Cephalonia, where he had a temple on Mount Aenos.Hesiod, according to a scholium on Apollonius of Rhodes.
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"From this scholium it become clear that Diogenianus did not excerpt directly from Pamphilus, but rather from Vestinus. So we have the chain Pamphilus-Vestinus-Diogenianus-Hesychius." This is the only form in which any of Pamphilus's work may have survived.
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600 BC) was that Zeus was buried somewhere in Crete. For this reason, the Cretans were often considered atheists, and Epimenides called them all liars (see Epimenides paradox). Callimachus, an opponent of Euhemerus' views on mythology, argued that Zeus' Cretan tomb was fabricated, and that he was eternal: A later Latin scholium on the Hymns of Callimachus attempted to account for the tomb of Zeus. According to the scholium, the original tomb inscription read: "The tomb of Minos, the son of Jupiter" but over time the words "Minos, the son" wore away leaving only "the tomb of Jupiter".
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Hypotheses non fingo (Latin for "I feign no hypotheses", "I frame no hypotheses", or "I contrive no hypotheses") is a famous phrase used by Isaac Newton in an essay, "General Scholium", which was appended to the second (1713) edition of the Principia.
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In the scholium on Psalm 123 attributed to Origen is the commentary: This has been considered by many commentators, including the translation source Nathaniel Ellsworth Cornwall, as an allusion to verse 7.The Church Review p. 625-641, 1874., The Genuineness of I John v.
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552; Armstrong, p. 12, with n. 39. Although Atreides, the standard Homeric epithet for Agamemnon or Menelaus, normally understood to mean "son of Atreus", can simply mean "descendant of Atreus", in some places Homer specifically refers to Agamemnon or Menelaus as a son of Atreus ("Ἀτρέος υἱέ") e.g. Iliad 11.131, Odyssey 4.462, see also Iliad 2.104 ff., and while Aerope is not mentioned in the Iliad or Odyssey, we hear from Iliad scholia that Homer (presumably somewhere in the Epic Cycle) names Aerope as their mother, see scholium on Homer's Iliad 1.7 and scholium on Tzetzes' commentary on Homer's Iliad (Most, pp. 204-205).
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In 1705 Leibniz, in an anonymous review of Newton's Opticks, implied that Newton's fluxions (Newton's term for differential calculus) were an adaptation of Leibniz's calculus. In 1712 the Royal Society appointed a committee to examine the documents in question; the same year, the Society published a report, written by Newton himself, asserting his priority. Soon after Leibniz died in 1716, Newton denied that his own 1687 Principia scholium "allowed [Leibniz] the invention of the calculus differentialis independently of my own"; and the third edition of Newton's Principia (1726) omitted the tell-tale scholium. It is now accepted that Newton and Leibniz discovered calculus independently of each other.
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From part of the Scholium, reprinted on page 737 of On the Shoulders of Giants:The Great Works of Physics and Astronomy (works by Copernicus, Kepler, Galileo, Newton, and Einstein). Stephen Hawking, ed. 2002 The Galilean transformations assume that time is the same for all reference frames.
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Most of the General Scholium deals with Newton's religious views. However, it is also considered the least understood part of the essay. Newton saw God as an intelligent, powerful, omnipresent Being which governs all. It has been claimed that the text implies that Newton was an anti-Trinitarianist heretic.
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And indeed some have asserted just this,Dictys Cretensis, 1.1; scholium on Homer's Iliad 2.249; see Gantz, p. 552; Tzetzes, Exegesis in Iliadem 1.122 (Most, pp. 204-205). According to Webster, p. 38, Euripides' Cretan Women probably had "Pleisthenes die young and leave his sons (and his wife) to Atreus".
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7, Scholium on pp.634–635 Ellsworth especially noted the Richard Porson comment in response to the evidence of the Psalm commentary: "The critical chemistry which could extract the doctrine of the Trinity from this place must have been exquisitely refining".Richard Porson, Letters to Mr. Archdeacon Travis, p.234, 1790.
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Odysseus was sent to Thrace to return with grain, but came back empty-handed. When scorned by Palamedes, Odysseus challenged him to do better. Palamedes set out and returned with a shipload of grain.Servius, Scholium on Virgil's Aeneid 2.81 Odysseus had never forgiven Palamedes for threatening the life of his son.
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43, Scholium 1. pp. 92. Kordela argues that this ternary concept of truth — truth, itself and the false — reveals Spinoza's break with the binaries of both Platonism and anti- Platonism. Kordela shows that this ternary structure corresponds to Lacan's argument that truth has the structure of a fiction.Lacan, Jacques. 2002.
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Fornnordiskt lexikon. p 372. It is even more sparsely documented than the famous temple by which it stood. In the 1070s, the writer of a scholium in Adam of Bremen's Gesta Hammaburgensis ecclesiae pontificum explained: > Near that temple is a very large tree with widespread branches which are > always green both in winter and summer.
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360 He came frequently to Athens on public business.Plato, Hipp. Maj. 282. His pupils included the orators TheramenesAeschines in Athenenaeus, v. 220b.; Scholium ad Aristophanes, Nub. 360 and Isocrates,Dionys. Hal. Isocr. 1; Photius, cod. 260 and in the year of the death of Socrates (399 BC), Prodicus was still living.Plato, Apology, 19. c.
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Theseus came to the heart of the Labyrinth and also upon the sleeping Minotaur. The beast awoke and a tremendous fight then occurred. Theseus overpowered the Minotaur with his strength and stabbed the beast in the throat with his sword (according to one scholium on Pindar's Fifth Nemean Ode, Theseus strangled it).Kerényi, Karl (1959).
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Scholia (singular scholium or scholion, from , "comment, interpretation") are grammatical, critical, or explanatory comments — original or copied from prior commentaries — which are inserted in the margin of the manuscript of ancient authors, as glosses. One who writes scholia is a scholiast. The earliest attested use of the word dates to the 1st century BC. Cicero Ad Atticum 16.7.
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"Justin, Apology 64.5, quoted in Robert McQueen Grant, Gods and the One God, vol. 1:155, who observes that it is Porphyry "who similarly identifies Athena with 'forethought'. According to a version of the story in a scholium on the Iliad (found nowhere else), when Zeus swallowed Metis, she was pregnant with Athena by the Cyclops Brontes.Gantz, p.
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According to a scholium, he and a pupil, Olympichus, once saw a mysterious flame on a mountain, attended by strange noises. Pindar then beheld Rhea, the Mother of the Gods, advancing in the form of a wooden image. Pausanias (9.25.3) reported that he set up a monument near his home, dedicated conjointly to Pan and the Mother of the Gods ().
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According to a Scholium on Theocritus,Theocritus, Idyll vii.149 this had taken place during the visit of Heracles to the cave of Pholus on Mount Pelion in Thessaly during his fourth labour, defeating the Erymanthian Boar. While they were at supper, Heracles asked for some wine to accompany his meal. Pholus, who ate his food raw, was taken aback.
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After the completion of his education, Nanautavi became the editor of the press at Matbah-e-Ahmadi. During this period, at Ahmad Ali's insistence, he wrote a scholium on the last few portions of Sahihul Bukhari. Before the establishment of Darul Uloom Deoband, he taught Euclid for some time at the Chhatta Masjid. His lectures were delivered at the printing press.
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Archermus was a sculptor of Chios working in the middle of the 6th century BC.chioslife.gr website [Retrieved 2011-09-15] His father, Micciades, and his sons, Bupalus and Athenis, were sculptors of marble. A scholium on Aristophanes' Birds, cites a scholiast on Aristophanes’ Birds, v. 573. credits Archermus with having been the first to represent Nike and Eros with wings.
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Adam of Bremen, book 4, chapters 23 (with scholium 136); chapters 29-30. Among missionaries in the 'English' tradition,English translations of select texts in Talbot 1954. Bede's historical recording ensured preservation of the memory that St Augustine had been dispatched to England because of a papal initiativeBede, Historia Ecclesiastica Gentis Anglorum, book 1, chapters 23-33 & book 2, chapters 1-3.: for Willibord of UtrechtSee, e.g.
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Ironically, this conformity led to the wrong approach. After Newton's time the -body problem historically was not stated correctly because it did not include a reference to those gravitational interactive forces. Newton does not say it directly but implies in his Principia the -body problem is unsolvable because of those gravitational interactive forces.See Principia, Book Three, System of the World, "General Scholium", page 372, last paragraph.
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He also contends that denying free will is likely to diminish anger and the desire to punish, and in this way can benefit human relationships, both personal and societal. In this respect his position is inspired by the view of Baruch Spinoza, who argues in his Ethics that denying free will would enhance the quality of human life.Spinoza, Baruch: Ethics, Part II, Prop. 49, Scholium.
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Müller) 4.433, Hippostratus frag. #4. The scholium was picked up without reference to the Hymn in the 'modern commentaries' of Thomas Magister and Demetrius Triclinius, Scholia Recentiora Thomano-Tricliniana in Pindari Nemea et Isthmia (ed. Mommsen) #2. This tells us that the school of Cynaethus was prominent among the Homeridae and put out many of their own compositions under Homer's name, Cynaethus himself composing the Hymn.
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Medea murders one of her children (Louvre) In Corinth, Jason abandoned Medea for the king's daughter, Glauce. Before the fifth century BC, there seem to have been two variants of the myth's conclusion. According to the poet Eumelus, to whom the fragmentary epic Korinthiaka is usually attributed, Medea killed her children by accident.As noted in a scholium to Pindar's Olympian Ode 13.74; cf. Pausanias 2.3.10-11.
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237x237pxAccording to an archaic myth,A quote from the lost Titanomachia, provided as a scholium on Apollonius Rhodius' Argonautica I.554 (on-line quote); pseudo-Apollodorus Bibliotheke 1. 8 - 9, may have drawn upon the same source. Chiron was sired by the Titan Cronus when he had taken the form of a horseCompare the stallion- Poseidon who sired the steed Arion upon Demeter. and impregnated the nymph Philyra.Pseudo-Apollodorus.
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An elaboration on a scholium on Apollonius of Rhodes' Argonautica i. Kereny remarks of the jealousy of Hera in this case, "a cheap theme, and certainly not an ancient one" (Kerenyi 1951, p.176). The other gods refused to allow him to live on Mount Olympus and threw him down to Earth, leaving him on a hillside. He was eventually found by shepherds and was brought up by them.
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Of other works only fragments and the titles have survived: Messeniakos, advocating the freedom of the Messenians and containing the sentiment that "God has left all men free; nature has made no man a slave";Aristotle, Rhet. 1373b 18–19 with the scholium of the anonymous commentator (CAG XXI:2, p. 74.31f.)J.D. Bury and Russell Meiggs, A History of Greece to the Death of Alexander the Great, fourth ed.
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80 Other sources talk of Achilles taking Pedasus, Monenia,Demetrius (2nd century BC) Scholium on Iliad Z,35 Mythemna (in Lesbos), and Peisidice.Parthenius Ερωτικά Παθήματα 21 Among the loot from these cities was Briseis, from Lyrnessus, who was awarded to him, and Chryseis, from Hypoplacian Thebes, who was awarded to Agamemnon. Achilles captured Lycaon, son of Priam,Apollodorus, Library 3.12.5. while he was cutting branches in his father's orchards.
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Angels crown Cnut as he and Emma of Normandy (Ælfgifu) present a large gold cross to Hyde Abbey in Winchester. From the Liber Vitae in the British Library. Cnut's actions as a conqueror and his ruthless treatment of the overthrown dynasty had made him uneasy with the Church. He was already a Christian before he was king—being named Lambert at his baptismAdam of Bremen, Gesta Daenorum, scholium 37, p. 112.
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These arguments, and a discussion of the distinctions between absolute and relative time, space, place and motion, appear in a scholium at the end of Definitions sections in Book I of Newton's work, The Mathematical Principles of Natural Philosophy (1687) (not to be confused with General Scholium at the end of Book III), which established the foundations of classical mechanics and introduced his law of universal gravitation, which yielded the first quantitatively adequate dynamical explanation of planetary motion.See the Principia on line at Andrew Motte translation, pp. 77–82. Despite their embrace of the principle of rectilinear inertia and the recognition of the kinematical relativity of apparent motion (which underlies whether the Ptolemaic or the Copernican system is correct), natural philosophers of the seventeenth century continued to consider true motion and rest as physically separate descriptors of an individual body. The dominant view Newton opposed was devised by René Descartes, and was supported (in part) by Gottfried Leibniz.
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He thought that there is an appropriate level of moisture in all living things, and disease is caused when the moisture is out of balance. He also viewed the soul as arising from both mind and water. A medieval scholium on Aristophanes' The Clouds attributes to Hippo the view that the heavens were like the dome () of an oven covering the Earth.Douglas M. MacDowell, (1995), Aristophanes and Athens: An Introduction to the Plays, page 120.
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This leaves open the possibility that the scholium erroneously referred to Antiope but meant Antigone, or originally named Antigone but this became corrupted over time. If so, that would indicate that Antigone was produced between 411 and 406 BCE. Zimmerman has suggested that the likely theme of the play involving Polynices as a traitor who was denied burial mirrored events of the Peloponnesian War in 411 BCE, which may be a further clue to the date of Antigone.
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Spinoza's "eternal" perspective is reflected in his Ethics (Part V, Prop. XXIII, Scholium), where he treats ethics through a geometric investigation that begins with God and nature and then analyzes human emotions and the human intellect. By proceeding with sub specie aeternitatis, Spinoza seeks to arrive at an ethical theory that is as precise as Euclid's Elements. In the history of philosophy, this way of proceeding may be most clearly contrasted with Aristotle's manner of proceeding.
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Diodorus Siculus ( 1st century BC), for instance, describes Lamia of Libya as having nothing more than a beastly appearance. Diodorus, Duris of Samos and other sources which comprise the sources for building an "archetypal" picture of Lamia do not designate her as a dragoness, or give her explicit serpentine descriptions.: "Nothing here explicitly declares.. a serpentine element" (Duris and Scholium), p. 98; "nothing here, again, speaks directly of a serpentin nature" (Diodorus and Heraclitus Paradoxographus), p. 98.
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The 1728 The Last Volume of Swift and Pope's Miscellanies including Pope's Peri Bathous provoked many pamphlets to be produced against the books. Motte's edition of Isaac Newton's Principia (1729) was translated by Andrew Motte (1696–1734), his brother a mathematician and very briefly the lecturer on geometry at Gresham College.Smet and Verelst p. 1Peter Harrington Books, recent acquisitions This was the first English edition and the first translated edition that included the Scholium Generale found in the second Latin edition (1726).
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In formulating his physical theories, Newton developed and used mathematical methods now included in the field of calculus. But the language of calculus as we know it was largely absent from the Principia; Newton gave many of his proofs in a geometric form of infinitesimal calculus, based on limits of ratios of vanishing small geometric quantities. In a revised conclusion to the Principia (see General Scholium), Newton used his expression that became famous, Hypotheses non fingo ("I feign no hypotheses").
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The background described above shows there was basis for Newton to deny deriving the inverse square law from Hooke. On the other hand, Newton did accept and acknowledge, in all editions of the Principia, that Hooke (but not exclusively Hooke) had separately appreciated the inverse square law in the Solar System. Newton acknowledged Wren, Hooke and Halley in this connection in the Scholium to Proposition 4 in Book 1.See for example the 1729 English translation of the 'Principia', at page 66.
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Turms is known more from decoration on everyday objects, such as mirrors, than from cult images, although one dedication has been taken to indicate the existence of a temple of Turms at Cortona. Bernard Combet-Farnoux interprets comments by Servius and Macrobius as indicating that “Hermes-Turms” had the epithet Camillus, meaning ‘servant’ (i.e. of the other deities). A scholium on Callimachus adds that “Cadmilos is Hermes in Tyrrhenia”; Combet-Farnoux considers Camillus and Cadmilos to be variants of the same name.
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In the first paragraph of the General Scholium, Newton attacks René Descartes' model of the solar system. Descartes and his supporters were followers of mechanical philosophy, a form of natural philosophy popular in the 17th century which maintained that nature and natural beings act similar to machines. In his book The World, Descartes suggests that the creation of the solar system and the circular motion of the planets around the Sun can be explained with the phenomena of "swirling vortices".Descartes, René.
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Aedon accidentally killed Itylus "in her madness" and was stricken with grief and guilt. In pity, the gods turned her into a nightingale, which cries with sadness every night. In an explanatory scholium on this passage, an anonymous scholiast, echoed by Eustathius, explains that Aedon attempted to kill the son of her sister-in-law and rival, Niobe, but accidentally killed her own son instead: thus, the gods changed her into a nightingale to weep for eternity. The setting of the episode is Thebes.
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Seleucia Samulias - Seleucia () also transliterated as Seleukeia or Seleukheia; in the Talmud, Selik, Selika, and Selikos; in the Aramaic Targum, Salwaḳia or Salwaḳya - was a Hellenistic colony founded about the end of the 3rd century BC on Lake Merom. According to the inference of Grätz, based on the scholium to Meg. Ta'an., the remnant of the Pharisees spared by Alexander Jannæus found a refuge there. Seleucia and Sogane were the first cities, after Gamala, to revolt from Agrippa in the Jewish Revolt of 66.
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Aegyptus ruled Arabia and conquered nearby country ruled by people called Melampodes and called it by his name, Egypt. Aegyptus fathered fifty sons, who were all but one murdered by forty nine of the fifty daughters of Aegyptus' twin brother, Danaus, eponym of the Danaïdes. A scholium on a line in Euripides, Hecuba 886, reverses these origins, placing the twin brothers at first in Argolis, whence Aegyptus was expelled and fled to the land that was named after him. In the more common version,Apollodorus, 2.1.4-5.
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Either Gregory did not understand Newton's argument, or Newton's explanation was very brief. However, it is possible, with a high degree of confidence, to construct Newton's proof from Gregory's notes, by analogy with his method to determine the solid of minimum resistance (Principia, Book 2, Proposition 34, Scholium 2). A detailed description of his solution of this latter problem is included in the draft of a letter in 1694, also to David Gregory. In addition to the minimum time curve problem there was a second problem which Newton also solved at the same time.
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Phoenix, red-figure kylix, 490 BCE, Louvre (G 152)Beazley Archive 203900. Achilles' surrender of Briseis to Agamemnon, from the House of the Tragic Poet in Pompeii, fresco, 1st century CE, now in the National Archaeological Museum, Naples Brisēís (; , ) ("daughter of Briseus"), also known as Hippodámeia (, ),From the A scholium at Iliad 1.392 we learn that "[Homer] forms the names [of Briseïs and Chryseis] patronymically. For as other ancient [poets] relate, Chryseis was called Astynome, and Briseis was called Hippodameia." Dictys Cretensis calls Briseis by the latter name in his account of the Trojan War.
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It is certain that Hesychius was the author of consecutive commentaries on Leviticus, the Psalms, the Canticle of Canticles, the Twelve Minor Prophets, Isaiah, and Luke (Chapter i?). His name occurs in catenae in connection with an occasional scholium to texts from other books (Genesis, 1 and 2 Samuel, Ezekiel, Daniel, Matthew, John, Acts, the Catholic Epistles), which, however, apart from the question of their authenticity, are not necessarily taken from complete commentaries on the respective books. Likewise the citations from Hesychius in ascetic florilegiaAs in Bodl. Barocc. 143, saec. 12.
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There were two competing mythsBibliotheke 3.1.1. relating how Europa came into the Hellenic world, but they agreed that she came to Crete (Kríti), where the sacred bull was paramount. In the more familiar telling she was seduced by the god Zeus in the form of a bull, who breathed from his mouth a saffron crocus and carried her away to Crete on his back—to be welcomed by Asterion,According to the scholium on Iliad XII.292, noted in Karl Kerenyi, Dionysus: Archetypal Image of Indestructible Life p105.
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Eubulus (, Euboulos) was an Athenian "Middle Comic" poet, victorious six times at the Lenaia, first probably in the late 370s or 360s BC (IG II2 2325.144; just before Ephippus) According to the Suda (test. 1), which dates him to the 101st Olympiad (i.e. 376/2) and identifies him as "on the border between the Middle and the Old Comedy", he produced 104 comedies and won six victories at the Lenaia. An obscure notice in a scholium on Plato (test. 4) appears to suggest that some of his plays were staged by Aristophanes’ son Philippus.
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Newton did not offer any reasons or causes for his law of gravity, and was therefore publicly criticised for introducing "occult agencies" into science.Westfall, Richard S. Never at Rest: A biography of Isaac Newton. Cambridge University Press, 1980. Newton objected to Descartes' and Leibniz's Scientific method of deriving conclusions by applying reason to a priori definitions rather than to empirical evidence, and famously stated "hypotheses non fingo", Latin for "I do not frame hypotheses": The General Scholium then goes on to present Newton's own approach to scientific methodology.
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Isaac Newton: "In [experimental] philosophy particular propositions are inferred from the phenomena and afterwards rendered general by induction": "Principia", Book 3, General Scholium, at p.392 in Volume 2 of Andrew Motte's English translation published 1729. It is a part of classical mechanics and was formulated in Newton's work Philosophiæ Naturalis Principia Mathematica ("the Principia"), first published on 5 July 1687. When Newton presented Book 1 of the unpublished text in April 1686 to the Royal Society, Robert Hooke made a claim that Newton had obtained the inverse square law from him.
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Hooke's letter to Newton of 6 January 1680 (Koyré 1952:332). Hooke remained bitter about Newton claiming the invention of this principle, even though Newton's 1686 Principia acknowledged that Hooke, along with Wren and Halley, had separately appreciated the inverse square law in the solar system,Newton acknowledged Wren, Hooke and Halley in this connection in the Scholium to Proposition 4 in Book 1 (in all editions): See for example the 1729 English translation of the Principia, at page 66. as well as giving some credit to Bullialdus.
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Discoverers understandably take pleasure in their accomplishments and generally seek to claim primacy to their discoveries. When it transpires that a discovery has multiple originators, they may either agree to share the credit or insist on their own exclusive primacy. After Isaac Newton and Gottfried Wilhelm Leibniz had exchanged information on their respective systems of calculus in the 1670s, Newton in the first edition of his Principia (1687), in a scholium, apparently accepted Leibniz's independent discovery of calculus. In 1699, however, a Swiss mathematician suggested to Britain's Royal Society that Leibniz had borrowed his calculus from Newton.
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Adam 2.56; 4.23 Not until the 1060s was there to be another attempt by an archbishop of Hamburg-Bremen to found a bishopric in Sweden, this time at Sigtuna in Svealand, and the attempt failed.Adam 4.23 with Scholium 136. The reason for this failure was, according to Adam, pagan opposition, and we need not doubt that this was one factor. But another reason could have been the favour with which 'English' missionaries, as distinct from those dispatched from Bremen, had come to be regarded by those in the population of Svealand who had by that date embraced Christianity.
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Horrocks was the first to demonstrate that the Moon moved in an elliptical path around the Earth, and he posited that comets followed elliptical orbits. He supported his theories by analogy to the motions of a conical pendulum, noting that after a plumb bob was drawn back and released it followed an elliptical path, and that its major axis rotated in the direction of revolution as did the apsides of the Moon's orbit. He anticipated Isaac Newton in suggesting the influence of the Sun as well as the Earth on the Moon's orbit. In the PrincipiaIsaac Newton, 'Principia', Book 3, Proposition 35, Scholium.
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In what he called a scholium, Bayes extended his algorithm to any unknown prior cause. Independently of Bayes, Pierre-Simon Laplace in 1774, and later in his 1812 Théorie analytique des probabilités, used conditional probability to formulate the relation of an updated posterior probability from a prior probability, given evidence. He reproduced and extended Bayes's results in 1774, apparently unaware of Bayes's work. The Bayesian interpretation of probability was developed mainly by Laplace. Sir Harold Jeffreys put Bayes's algorithm and Laplace’s formulation on an axiomatic basis, writing that Bayes's theorem "is to the theory of probability what the Pythagorean theorem is to geometry".
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For him, even human behaviour is fully determined, with freedom being our capacity to know that we are determined and to understand why we act as we do. By forming more "adequate" ideas about what we do and our emotions or affections, we become the adequate cause of our effects (internal or external), which entails an increase in activity (versus passivity). This process allows us to become both more free and more like God, as Spinoza argues in the Scholium to Prop. 49, Part II. However, Spinoza also held that everything must necessarily happen the way that it does.
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The Roman nurses' lullaby, "Lalla, Lalla, Lalla, aut dormi, aut lacta", is recorded in a scholium on Persius and may be the oldest to survive. Many medieval English verses associated with the birth of Jesus take the form of a lullaby, including "Lullay, my liking, my dere son, my sweting" and may be versions of contemporary lullabies. However, most of those used today date from the 17th century. For example, a well known lullaby such as "Rock-a-bye, baby on a tree top", cannot be found in records until the late-18th century when it was printed by John Newbery (c. 1765).
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In the concluding General Scholium to the Philosophiae Naturalis Principia Mathematica, he wrote: "This most beautiful System of the Sun, Planets and Comets, could only proceed from the counsel and dominion of an intelligent and powerful being." Other famous founders of science who adhered to Christian beliefs include Galileo, Johannes Kepler, and Blaise Pascal. According to 100 Years of Nobel Prizes a review of Nobel prizes award between 1901 and 2000 reveals that (65.4%) of Nobel Prizes Laureates, have identified Christianity in its various forms as their religious preference. Overall, Christians are considered a total of 72.5% in Chemistry between 1901 and 2000,Shalev, Baruch (2005).
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The secret of these mysteries has largely been kept; but we know that of three things about the ritual, the aspirants were asked the worst action they had ever committed. The mysteries of Samothrace did not publish the names of their gods; and the offerings at the shrine are all inscribed to the gods or to the great gods rather than with their names. But ancient sourcesKerenyi 1951:87 note 210 credits a scholium on Apollonius of Rhodes' Argonautica i.916, for the connection of the four names of divinities recorded at Samothrace— Axieros, Axiokersa, Axiokersos and Kadmilos — with Demeter, Persephone, Hades and Hermes respectively.
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In the concluding General Scholium to the Philosophiae Naturalis Principia Mathematica, he wrote: "This most beautiful System of the Sun, Planets and Comets, could only proceed from the counsel and dominion of an intelligent and powerful being." Other famous founders of science who adhered to Christian beliefs include Galileo, Johannes Kepler, and Blaise Pascal. According to 100 Years of Nobel Prizes a review of Nobel prizes award between 1901 and 2000 reveals that (65.4%) of Nobel Prizes Laureates, have identified Christianity in its various forms as their religious preference. Overall, Christians have won a total of 72.5% in Chemistry between 1901 and 2000,Shalev, Baruch (2005).
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In ancient Greek religion Artemis CaryatisDiana Caryatis, noted in Servius scholium on Virgil's Eclogue viii.30. was an epithet of Artemis that was derived from the small polis of Karyai in Laconia;References to Karyai are collected in Graham Shipley, "'The other Lakedaimonians': the dependent Perioikic poleis of Laconia and Messenia" in M.H. Hanson, ed. The Polis as an Urban Centre and as a Political Community, (symposium) Copenhagen 1997:189-281. there an archaic open-air temenos was dedicated to Carya, the Lady of the Nut-Tree, whose priestesses were called the caryatidai, represented on the Athenian Acropolis as the marble caryatids supporting the porch of the Erechtheum.
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Newton also underlined his criticism of the vortex theory of planetary motions, of Descartes, pointing to its incompatibility with the highly eccentric orbits of comets, which carry them "through all parts of the heavens indifferently". Newton also gave theological argument. From the system of the world, he inferred the existence of a Lord God, along lines similar to what is sometimes called the argument from intelligent or purposive design. It has been suggested that Newton gave "an oblique argument for a unitarian conception of God and an implicit attack on the doctrine of the Trinity", but the General Scholium appears to say nothing specifically about these matters.
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In Exposition du système du monde, Laplace quotes Newton's assertion that "the wondrous disposition of the Sun, the planets and the comets, can only be the work of an all-powerful and intelligent Being".General Scholium, from the end of Book III of the Principia; first appeared in the second edition, 1713. This, says Laplace, is a "thought in which he [Newton] would be even more confirmed, if he had known what we have shown, namely that the conditions of the arrangement of the planets and their satellites are precisely those which ensure its stability".Laplace, Exposition du système du monde, 6th edition. Brussels, 1827, pp. 522–523.
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Problem 1 then explores the case of a circular orbit, assuming the center of attraction is on the circumference of the circle. A scholium points out that if the orbiting body were to reach such a center, it would then depart along the tangent. (Proposition 7 in the Principia.) Problem 2 explores the case of an ellipse, where the center of attraction is at its center, and finds that the centripetal force to produce motion in that configuration would be directly proportional to the radius vector. (This material becomes Proposition 10, Problem 5 in the Principia.) Problem 3 again explores the ellipse, but now treats the further case where the center of attraction is at one of its foci.
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The later Icelandic source Hervarar saga contains a description of how the tree was used in the pagan rites, concerning an event taking place only a few years after the scholium was written. It is in reference to the ancient Indo- European ritual of horse sacrifice: > Svein, the King's brother-in-law, remained behind in the assembly, and > offered the Swedes to do sacrifices on their behalf if they would give him > the Kingdom. They all agreed to accept Svein's offer, and he was then > recognized as King over all Sweden. A horse was then brought to the assembly > and hewn in pieces and cut up for eating, and the sacred tree was smeared > with blood.
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A scholium of Servius on Aeneid iii. 72 accounts for the island's archaic name OrtygiaOr as a separate island birthplace of Artemis— "Rejoice, blessed Leto, for you bare glorious children, the lord Apollon and Artemis who delights in arrows; her in Ortygia, and him in rocky Delos," says the Homeric Hymn; the etymology Ortygia, "Isle of Quail", is not supported by modern scholars. by asserting that Zeus transformed Leto into a quail (ortux) in order to prevent Hera from finding out about his infidelity, and Kenneth McLeish suggested further that in quail form Leto would have given birth with as few birth-pains as a mother quail suffers when it lays an egg.McLeish, Kenneth.
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') This becomes Proposition 11 in the Principia. A scholium then points out that this Problem 3 proves that the planetary orbits are ellipses with the Sun at one focus. (Translation: 'The major planets orbit, therefore, in ellipses having a focus at the centre of the Sun, and with their radii (vectores) drawn to the Sun describe areas proportional to the times, altogether (Latin: 'omnino') as Kepler supposed.') (This conclusion is reached after taking as initial fact the observed proportionality between square of orbital period and cube of orbital size, considered in corollary 5 to Theorem 1.) (A controversy over the cogency of the conclusion is described below.) The subject of Problem 3 becomes Proposition 11, Problem 6, in the Principia.
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He also identifies a geometrical criterion for distinguishing between the elliptical case and the others, based on the calculated size of the latus rectum, as a proportion to the distance the orbiting body at closest approach to the center. (Proposition 17 in the Principia.) A scholium then remarks that a bonus of this demonstration is that it allows definition of the orbits of comets, and enables an estimation of their periods and returns where the orbits are elliptical. Some practical difficulties of implementing this are also discussed. Finally in the series of propositions based on zero resistance from any medium, Problem 5 discusses the case of a degenerate elliptical orbit, amounting to a straight-line fall towards or ejection from the attracting center.
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It is debated, based on a scholium from a line in Euripides' Medea whether Medea's poisoning of Creon may have been another feature,Medea 264. which Franz Stoessl suggested will have been a comparative aside in the telling of Deianira,Stoessel, Der Tod des Heracles (Zurich, 1945:16ff), noted in Malcolm Davies, "Deianeira and Medea: A foot- note to the pre-history of two myths", Mnemosyne, Fourth Series, 42.3/4 (1989:469-472) p. 469 note 6. in her original guise as the "man-destroyer" of her etymology: "the innocent Deianeira, whose murder of Heracles is tragically inadvertent, will be a later invention," Malcolm Davies asserts,Davies 1989:469; Davies raises doubts about the use of Medea as a parallel in .
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In Proposition 34 of Book 2 of the Principia, Newton wrote, If in a rare medium, consisting of equal particles freely disposed at equal distances from each other, a globe and a cylinder described on equal diameter move with equal velocities in the direction of the axis of the cylinder, the resistance of the globe will be but half as great as that of the cylinder. Following this proposition is a scholium containing the famous condition that the curve which, when rotated about its axis, generates the solid that experiences less resistance than any other solid having a fixed length, and width. In modern form, Newton's problem is to minimize the following integral:Chandrasekhar, Subrahmanyan. Newton's Principia for the common reader.
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Robert Boyle was the first person to hail an experiment as experimentum crucis when he referred to the famous mercury barometer experiment on Puy-de-Dome in 1648. This experiment settled the question: Was there some natural resistance to the creation of an apparently empty space at the top of the tube, or was the height of the mercury determined solely by the weight of the air? In his Philosophiæ Naturalis Principia Mathematica, Isaac Newton (1687) presents a disproof of Descartes' vortex theory of the motion of the planets.Isaac Newton (1687), Principia Mathematica Book iii, Proposition 43, General Scholium and Book ii, Section ix, Proposition 53, as referenced by William Stanley Jevons (1874), The Principles of Science: A Treatise on Logic and Scientific Method p. 517.
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One of the epigrams attributed to him on the authority of Maximus Planudes is a eulogy on the celebrated Hypatia, daughter of Theon of Alexandria, whose death took place in 415. Another was, according to a scholium in the Palatine Manuscript (the most important source for our knowledge of Greek epigram), written in the reign of the joint emperors Valentinian and Valens (364–375). A third epigram on the destruction of Beirut (Anth. Gr. 9.27) suggests an alternative chronology dating Palladas' activity to the age of Constantine the Great."Palladas and the Age of Constantine'", Journal of Roman Studies, 99 (2009), pp. 36–60. It is based on his edition of a papyrus codex that arrived from a private collection to the Beinecke Library at Yale University in 1996.
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The trial of those who had broken down the statues of Hermes, the profanation of the mysteries, and the accusation of Alcibiades, are symptoms which show that the unbelief, nourished by the speculations of philosophers and the sophists, began to appear very dangerous to the conservative party at Athens. There is no doubt that Diagoras paid no regard to the established religion of the people, and he may occasionally have ridiculed it; but he also ventured on direct attacks upon public institutions of the Athenian worship, such as the Eleusinian mysteries, which he endeavoured to lower in public estimation, and he is said to have prevented many persons from becoming initiated in them. These at least are the points of which the ancients accuse him,Craterus, ap. Scholium Aristophapnes; Tarrhaeus, ap.
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Theorem 4 shows that with a centripetal force inversely proportional to the square of the radius vector, the time of revolution of a body in an elliptical orbit with a given major axis is the same as it would be for the body in a circular orbit with the same diameter as that major axis. (Proposition 15 in the Principia.) A scholium points out how this enables determining the planetary ellipses and the locations of their foci by indirect measurements. Problem 4 then explores, for the case of an inverse-square law of centripetal force, how to determine the orbital ellipse for a given starting position, speed, and direction of the orbiting body. Newton points out here, that if the speed is high enough, the orbit is no longer an ellipse, but is instead a parabola or hyperbola.
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Lagus (Greek Λάγος; lived 4th century BC) from Eordaea was the father, or reputed father, of Ptolemy, the founder of the Ptolemaic dynasty. He married Arsinoe, a concubine of Philip II, king of Macedon, who was said to have been pregnant at the time of their marriage, on which account it is told that the Macedonians generally looked upon Ptolemy as in reality the son of Philip; but it is possible that this is a later myth fabricated to glorify the Ptolemaic dynasty. From an anecdote recorded by Plutarch, it is clear that Lagus was a man of obscure birth; hence, when Theocritus calls Ptolemy a descendant of Heracles, he probably means to represent him as the son of Philip. Lagus is believed by some to have subsequently married Antigone, niece of Antipater, by whom he became the father of Berenice, afterwards the wife of Ptolemy, but this is based on a misreading of a corrupt scholium; her father's name was almost certainly Magas.
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Of Roman-Carthaginian diplomacy leading up to the final confrontation, A. E. Astin, F. W. Walbank, M. W. Frederiksen (Rome and the Mediterranean to 133 B.C., Cambridge Ancient History VIII, "Rome and Carthage" 1989:149) note that the sources, "principally Appian and the Epitome of Livy are contaminated by more or less obvious falsehoods, especially the Epitome. The reason for this was of course the desire of contemporary and, even more, of later Romans to justify Rome's conduct". Cleitarchus' paraphrase of a scholium to Plato's Republic has a description of the practice which predates the fall of Carthage in 146 BC: > There stands in their midst a bronze statue of Kronos, its hands extended > over a bronze brazier, the flames of which engulf the child. When the flames > fall upon the body, the limbs contract and the open mouth seems almost to be > laughing until the contracted body slips quietly into the brazier.
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"Its attitude towards women is decidedly more illiberal than that of epic; a good wife is indeed the best prize a man can win (702), but a bad one is the greatest curse; generally speaking women are a snare and a temptation (373–5) and Pandora was the origin of all our woes". The Hesiodic myth did not, however, completely obliterate the memory of the all-giving goddess Pandora. A scholium to line 971 of Aristophanes' The Birds mentions a cult "to Pandora, the earth, because she bestows all things necessary for life".Jeffrey M. Hurwit, "Beautiful Evil: Pandora and the Athena Parthenos" American Journal of Archaeology 99.2 (April 1995: 171–186) And in fifth-century Athens, Pandora made a prominent appearance in what, at first, appears an unexpected context, in a marble relief or bronze appliqués as a frieze along the base of the Athena Parthenos, the culminating experience on the Acropolis.
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In the sixteenth century, the Italian philosopher Giordano Bruno, an early supporter of the Copernican theory that Earth and other planets orbit the Sun (heliocentrism), put forward the view that the fixed stars are similar to the Sun and are likewise accompanied by planets. In the eighteenth century, the same possibility was mentioned by Isaac Newton in the "General Scholium" that concludes his Principia. Making a comparison to the Sun's planets, he wrote "And if the fixed stars are the centres of similar systems, they will all be constructed according to a similar design and subject to the dominion of One." In 1952, more than 40 years before the first hot Jupiter was discovered, Otto Struve wrote that there is no compelling reason why planets could not be much closer to their parent star than is the case in the Solar System, and proposed that Doppler spectroscopy and the transit method could detect super-Jupiters in short orbits.
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In his astronomical works, Liceti attempted to defend Aristotelian cosmology and geocentrism against the new ideas of heliocentrism proposed by Galileo and his followers. With the appearance of the famous comets of 1618 (which later gave rise to Galileo's work The Assayer), Liceti published a series of works arguing the Aristotelian view that comets occurred in the sphere of the upper heaves. These works included De novis astris, et cometis libri sex (1623), Controversiae de cometarum quiete, loco boreali sine occasu, parallaxi Aristotelea, sede caelesti, et exacta theoria peripatetica (1625), Ad ingenuum lectorem scholium Camelo Bulla (published as an appendix to his 1627 work De intellectu agente), De regulari motu minimaque parallaxi cometarum coelestium disputationes (1640), and De Terra unico centro motus singularum caeli particularum disputationes (also 1640). Liceti used these studies primarily to attack the views of G. C. Gloriosi (who had succeeded Galileo as chair of mathematics at the University of Padua) and Scipione Chiaramonti, both of whom published their own scathing counter-attacks on Liceti's views.
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