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On the distances and sizes of the sun and the moon
Although this book contains much historical background, the highlight, in my opinion, is the complete translation of Aristarchus' only extant work, On the distances and sizes of the sun and moon (c. -270). I am going to summarise this work here. My summary will contain all the main results of the treatise, and indicate what is essentially Aristarchus' derivations. However, my summary will be a simplification in that I will assume that the sun lights up exactly half the moon, whereas Aristarchus knows that this is not quite true and so has a small correction factor in the calculations to account for this.

I will use this notation: E, M, S are the centers of the earth, moon and sun respectively, and E', M', S' are points on their apparent perimeters.

The ratio of the distances from the earth to the moon and from the earth to the sun can be determined by measuring the angle MES at half moon. For at half moon the angle EMS=90° and the angle MES is measurable, so we know all angles of this triangle and thus the ratios of its sides.

The ratio of the sizes of the moon and the sun can then be inferred at a solar eclipse. For at a solar eclipse, the moon precisely covers the sun. Thus EMM' is similar to ESS', with the scaling factor discovered above, i.e. SS':MM'::ES:EM.

The ratio of the distance of the moon to its size can be inferred from its angular size. For the angle EMM'=90° and the angle MEM' is measurable, so we know all angles of this triangle and thus the ratios of its sides.

These distances can be related to the radius of the earth at a lunar eclipse. For the shadow that the earth casts on the moon is about two moon-diameters wide. To incorporate this information into a similar triangles setup, let O be the point beyond the moon from which the earth has the same angular size as the sun (i.e. precisely blocks out the sun). Then SS':EE'::OS:OE. Now the algebra gets a little bit involved. We want to know the LHS so we have to reduce the RHS to a number, which we will do by expressing both OS and OE in terms of OM. From above we know SS':MM', and now we have OS:OM::SS':2MM', which enables us to express OS in terms of OM. To express OE in terms of OM we first note that OE=OM+EM. From above we know how to express EM in terms of ES, or, if we prefer, MS. But again from OS:OM::SS':2MM' we know OS=OM+MS in terms of OM, so we know MS in terms of OM, so we are done. OS:OE is now some multiple of OM over some multiple of OM, i.e. a number, so we have found SS':EE', i.e. we have expressed the size of the sun (and thereby the size of the moon, of course) in terms of the size of the earth.

The title doesn't do it justice
Thomas Heath published this book in 1913. As he explains, he was first motivated by a request from a friend to produce a translation of Aristarchus's treatise "On the sizes and distances of the sun and the moon." In that book Aristarchus does not say anything about heliocentrism or the motion of the earth, but we know from ancient reports that he was an early heliocentrist, probably the first. However, at the time Heath wrote this, the definitive studies of ancient heliocentrism and the earth's motion had been written by Schiaparelli, who insisted that Aristarchus had been anticipated by Heraclides Ponticus. (Yes, Schiaparelli was the astronomer who found "canali" on Mars!) Heath took the opportunity to set the record straight, and ended up writing a fantastic study of Greek astronomy up to Aristarchus in the 3rd century BC. The book is nearly a hundred years old, so don't rely on it as your only source if you want a detailed up-to-date picture of early astronomy. (If that's what you want, start with James Evans's "History and Practice of Ancient Astronomy" and work from the footnotes.) But this is a real classic, constantly cited by later authors, and more readable than a lot of what you will find written on Greek astronomy. Heath's translation of Aristarchus's work, at the back of the book, became the definitive English translation.

If you want to know more about what the Greeks did after Aristarchus, I recommend, in addition to Evans's book mentioned above, JLE Dreyer's "A History of Astronomy from Thales to Kepler," another classic survey from about the same time.

best history of Greek astronomy
This old (early twentieth century) book is not just about Aristarchus, the "Greek Copernicus" -- that comes in the final chapters.Rather, it is the best survey I know of ancient Greek astronomy, starting from the very beginning.I kept coming across references to this book by Sir Thomas Heath in books on the Copernican revolution, e.g. those by Angus Armitage and Thomas Kuhn, and finally decided to read it -- after having bought his smaller volume on Greek astronomy, also reprinted by Dover.

Heath really goes into detail on each of the ancient schools of astronomy in Greece.There were in fact a good many points of view -- the earth-centered view, the view that the earth rotates daily about its axis, the view of everything going around a fiery center, the "concentric spheres" variant of Eudoxus of the earth centered view, the Aristotelian variant of that, the eventual Ptolemaic view of epicycles and all that ... and finally the view of Aristarchus, which was essentially the Copernican sun-centered view (but without Copernicus' marvelous insights into how such a view simplified everything).

Heath not only goes into detail about each of these schools of thought -- it can be pretty rough going trying to follow all of this, especially because of the esoteric modes of speaking they often employed -- he also gives pithy summaries of what each school was saying, and a critical evaluation of their worth and influence.

If you really want to gain an appreciation of the variety of the ancient Greek schools of thought, of their struggle and progress over seven centuries in describing the motions in the heavens, of the reasonableness of much of their thinking, of the magnificence of their achievement -- I heartily recommend this book, then I recommend, either before or after, exploring the Copernican revolution and the rest of the scientific revolution, in the books by Armitage, Kuhn, Hall, and others. ... Read more

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This is a reproduction of the original edition including imperfections. Included with the purchase of this book is free trial access to Million-Books.com where you can read more than a million books for free, including many of the greatest books of all time like: * The complete works of Shakespeare, Charles Dickens, Mark Twain * Swift's Gulliver's Travels * Defoe's Robinson Crusoe * Thackeray's Vanity Fair * Jane Austen's Sense and Sensibility and Pride and Prejudice * Sigmund Freud's Interpretation of Dreams * Albert Einstein's Relativity * F. Scott Fitzgerald's Great Gatsby * George Orwell's 1984 * Milton's Paradise Lost * Smith's Wealth of Nations * Darwin's Origin of Species * Aristotle's Ethics * Plato's Dialogues * Thos. à Kempis' Imitation of Christ * Hume's History of England * Carlyle's French Revolution * Gibbon's Decline and Fall of the Roman Empire * . . .and more than a million more books These books have been a source of inspiration, joy and enlightenment to millions through the ages. Now they can all be yours. ... Read more

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Sir Thomas Heath's classic work examines the path that led to the Greek Copernicus, and includes a critical Greek text and translation of Aristarchus' work, On the Sizes and Distances of the Sun and Moon.This book reviews Aristarchus' claim to immortality, and disperses the mist obscuring his neglected by certain genius.Heath's history of Greek astronomy from Homer and Hesiod to Aristarchus serves to increase the wonder at Aristarchus' simple, radical reversal of perspective and the meager, almost casual references to it. ... Read more

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Title: Aristarchus of Samos, the Ancient Copernicus ; a History of Greek Astronomy to Aristarchus, Together With Aristarchus's Treatise on the Sizes and Distances of the Sun and Moon : a New Greek Text With Translation and NotesPublisher: Oxford : Clarendon PressPublication date: 1913Subjects: Astronomy, Greek -- HistoryNotes: This is an OCR reprint. There may be typos or missing text. There are no illustrations or indexes.When you buy the General Books edition of this book you get free trial access to Million-Books.com where you can select from more than a million books for free. You can also preview the book there. ... Read more

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This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

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Chapters: Ancient Samians, Pythagoras, Epicurus, Aristarchus of Samos, Conon of Samos, Aesop, Melissus of Samos, Aris Poulianos, Duris of Samos, Nikos Stavridis, Themistoklis Sophoulis, Telesarchus of Samos, Polycrates, Agatharchus, Agathocles, Kostas Roukounas, Patriarch Cyril Ii of Jerusalem, Choerilus of Samos, Syloson, Semonides of Amorgos, Philaenis, Lynceus of Samos, Theodorus of Samos, Hedylus, Aeaces, Asclepiades of Samos, Creophylus of Samos, Theon of Samos, Rhoecus, Nicaenetus of Samos, Colaeus, Mandrocles. Source: Wikipedia. Pages: 135. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Pythagoras of Samos (Greek: , O Pythagoras o Samios, "Pythagoras the Samian", or simply ; c. 570-c. 495 BC) was an Ionian Greek philosopher and founder of the religious movement called Pythagoreanism. Most of our information about Pythagoras was written down centuries after he lived, thus very little reliable information is known about him. He was born on the island of Samos, and may have travelled widely in his youth, visiting Egypt and other places seeking knowledge. Around 530 BC, he moved to Croton, a Greek colony in southern Italy, and there set up a religious sect. His followers pursued the religious rites and practices developed by Pythagoras, and studied his philosophical theories. The society took an active role in the politics of Croton, but this eventually led to their downfall. The Pythagorean meeting-places were burned, and Pythagoras was forced to flee the city. He is said to have ended his days in Metapontum. Pythagoras made influential contributions to philosophy and religious teaching in the late 6th century BC. He is often revered as a great mathematician, mystic and scientist, and he is best known for the Pythagorean theorem which bears his name. However, because legend and obfusca...More: http://booksllc.net/?id=23275 ... Read more

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Aristarchus of Samos was the first man to suggest that the sun, and not the earth, is the real centre of our system, and thus for the first time to assign to the earth a subordinate rank. In this volume, Heath gives us a translation of that work, plus a detailed history of Greek astronomy. ... Read more

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Chapters: Archimedes, Eratosthenes, Epicurus, Zeno of Citium, Aristarchus of Samos, Dicaearchus, Alexis, Theophrastus, Alexander Ii of Epirus, Chrysippus, Alexander Aetolus, Aratus, Pyrrho, Conon of Samos, Nicomedes I of Bithynia, Theocritus, Philochorus, Menander, Hiero Ii of Syracuse, Cleanthes, Arcesilaus, Menedemus, Attalus I, Antigonus Ii Gonatas, Philitas of Cos, Aratus of Sicyon, Demetrius of Pharos, Amerias, Aristo of Chios, Philopoemen, Cleomenes Iii, Erasistratus, Strato of Lampsacus, Nabis, Lysimachus, Agis Iv, Timon of Phlius, Phylarchus, Herodas, Demetrius of Phalerum, Lycophron, Philo of Byzantium, Metrodorus of Lampsacus, Autolycus of Pitane, Hermarchus, Scopas of Aetolia, Eumenes I, Mithridates I of Pontus, Cercidas, Aristophanes of Byzantium, Hieronymus of Syracuse, Idomeneus of Lampsacus, Polemon, Timocharis, Mithridates Ii of Pontus, Sphaerus, Chares of Lindos, Deidamia Ii of Epirus, Agathocles, Theodotus of Aetolia, Persaeus, Dinarchus, Polyaenus of Lampsacus, Zenodotus, Epigonus, Herillus, Alexarchus of Macedon, Demochares, Machanidas, Alcaeus of Messene, Theodoridas of Syracuse, Hieronymus of Cardia, Leonidas Ii, Lacydes of Cyrene, Lyco of Troas, Areus I, Sotades, Aristo of Ceos, Ziaelas of Bithynia, Nicolaus of Aetolia, Acrotatus Ii, Colotes, Olympias Ii of Epirus, Lysandra, Stratonice of Macedon, Hermippus of Smyrna, Philotimus, Pyrrhias of Aetolia, Leonidas of Tarentum, Crates of Athens, Anaxandra, Ariobarzanes of Pontus, Chamaeleon, Hicetas, Ptolemy of Epirus, Anyte of Tegea, Xanthippus of Carthage, Abantidas, Asclepiades of Phlius, Philemon, Amynomachus, Etazeta of Bithynia, Agetas, Sositheus, Zeuxis of Tarentum, Rhianus, Nicocles, Timocrates of Lampsacus, Laodice of Pontus, Cleomenes the Cynic, Lagoras, Alcimus, Alexon, Rhinthon, Antisthenes of Rhodes, Brachyllas, Batis of Lampsacus, Antigonus of Carystus, Philinus of Cos, Xenoetas, Oxyathres of Heraclea, Alexander of Trichonium, Pyrrhus Ii of Epirus, Nea...http://booksllc.net/?id=1844 ... Read more

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This digital document is an article from Science and Its Times, brought to you by Gale®, a part of Cengage Learning, a world leader in e-research and educational publishing for libraries, schools and businesses.The length of the article is 110 words.The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase.You can view it with any web browser.The histories of science, technology, and mathematics merge with the study of humanities and social science in this interdisciplinary reference work. Essays on people, theories, discoveries, and concepts are combined with overviews, bibliographies of primary documents, and chronological elements to offer students a fascinating way to understand the impact of science on the course of human history and how science affects everyday life. Entries represent people and developments throughout the world, from about 2000 B.C. through the end of the twentieth century. ... Read more

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High Quality Content by WIKIPEDIA articles! Greek astronomy is the astronomy of those who wrote in the Greek language in classical antiquity; for example, Aristarchus of Samos Greek astronomer/mathematician and his heliocentric model of the solar system. Greek astronomy is understood to include the ancient Greek, Hellenistic, Greco-Roman, and Late Antiquity eras. It is not limited geographically to Greece or to ethnic Greeks, as the Greek language had become the language of scholarship throughout the Hellenistic world following the conquests of Alexander. This phase of Greek astronomy is also known as Hellenistic astronomy, while the pre-Hellenistic phase is known as Classical Greek astronomy. During the Hellenistic and Roman periods, much of the Greek and non-Greek astronomers working in the Greek tradition studied at the Musaeum and the Library of Alexandria in Ptolemaic Egypt. The development of astronomy by the Greek and Hellenistic astronomers is considered by historians to be a major phase in the history of astronomy in Western culture. It was influenced by Babylonian astronomy; in turn, it influenced Islamic, Indian, and Western European astronomy. ... Read more

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Chapters: Ancient Greek Astronomers, Hipparchus, Ptolemy, Eratosthenes, Anaximander, Pytheas, Aristarchus of Samos, Menelaus of Alexandria, Andronicus of Cyrrhus, Posidonius, Sporus of Nicaea, Aratus, Conon of Samos, Heraclides Ponticus, Apollonius of Perga, Seleucus of Seleucia, Autolycus of Pitane, Oenopides, Geminus, Timocharis, Philip of Opus, Hypsicles, Cleomedes, E. M. Antoniadi, Theon of Alexandria, Emilios T. Harlaftis, Callippus, Sosigenes of Alexandria, Meton of Athens, Sosigenes the Peripatetic, Stamatios Krimigis, Cleostratus, John S. Paraskevopoulos, Aglaonike, Theodosius of Bithynia, Carpus of Antioch, Agrippa, Hicetas, Euctemon, Ecphantus the Pythagorean, Bion of Abdera, Harpalus, Aristillus, Attalus of Rhodes, Jean Focas. Source: Wikipedia. Pages: 201. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Pytheas of Massilia (Ancient Greek ), 4th century BC, was a Greek geographer and explorer from the Greek colony, Massilia (modern day Marseille). He made a voyage of exploration to northwestern Europe at about 325 BC. He travelled around and visited a considerable part of Great Britain. Some of his observations may refer to Stonehenge, the earliest report (if true). Pytheas is the first person on record to describe the Midnight Sun, polar ice, and Germanic tribes and the one who introduced the idea of distant "Thule" to the geographic imagination. His account is the earliest to state that the moon is the cause of the tides. Pliny says that Timaeus (born about 350 BC) believed Pytheas' story of the discovery of amber. Strabo says that Dicaearchus (died about 285 BC) did not trust the stories of Pytheas. That is all the information that survives concerning the date of Pytheas' voyage. Presuming that Timaeus would not have written until after he was 20 years old at about 330 BC and ...More: http://booksllc.net/?id=23348 ... Read more

Product Description
This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

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Chapters: Ancient Samians, Samian Colonies, Pythagoras, Epicurus, Aristarchus of Samos, Samothrace, Conon of Samos, Perinthus, Aesop, Melissus of Samos, Duris of Samos, Tunnel of Eupalinos, Aeschines, Telesarchus of Samos, Polycrates, Agatharchus, Agathocles, Choerilus of Samos, Syloson, Semonides of Amorgos, Philaenis, Lynceus of Samos, Theodorus of Samos, Hedylus, Aeaces, Asclepiades of Samos, Creophylus of Samos, Theon of Samos, Rhoecus, Nicaenetus of Samos, Colaeus, Mandrocles, Bisanthe. Source: Wikipedia. Pages: 148. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Pythagoras of Samos (Greek: , O Pythagoras o Samios, "Pythagoras the Samian", or simply ; c. 570-c. 495 BC) was an Ionian Greek philosopher and founder of the religious movement called Pythagoreanism. Most of our information about Pythagoras was written down centuries after he lived, thus very little reliable information is known about him. He was born on the island of Samos, and may have travelled widely in his youth, visiting Egypt and other places seeking knowledge. Around 530 BC, he moved to Croton, a Greek colony in southern Italy, and there set up a religious sect. His followers pursued the religious rites and practices developed by Pythagoras, and studied his philosophical theories. The society took an active role in the politics of Croton, but this eventually led to their downfall. The Pythagorean meeting-places were burned, and Pythagoras was forced to flee the city. He is said to have ended his days in Metapontum. Pythagoras made influential contributions to philosophy and religious teaching in the late 6th century BC. He is often revered as a great mathematician, mystic and scientist, and he is best known for the Pythagorean theorem which bears his name. However, because legend and obfuscation cloud his work even m...More: http://booksllc.net/?id=23275 ... Read more