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LibraryThing: Science in Ancient Mesopotamia Week 5: Hellenistic Science

Topic 1: Hellenistic mathematical sciences

# Due Date Pts Activity Time
2 Wednesday
11:59 p.m.

Topic 1 + Quiz
Background: Without a sense of context, history is anachronistic.
Primary sources: Without documentary evidence, history is speculation
The first of two topic assignments per week involving both background and primary sources.

90 min.

Aristotle, teacher of Alexander the Great, died in 322 B.C., one year after his renowned pupil. The passing of these two scientific and political giants represents a profound transition between the Classical (or Hellenic) and the later Hellenistic periods. Hellenistic natural philosophy was characterized more by the mathematical sciences than by physics or natural philosophy of the sort practiced by the presocratics. Mathematical approaches to knowing nature diversified into fields such as geometry, trigonometry, astronomy, optics, statics, and music, among others.

The intellectual centers, like the political ones, moved from Greece and Athens. Other cities achieved prominence in natural philosophy, including Alexandria in Egypt, Syrakusa in Sicily, and Pergamos in Asia Minor. In Alexandria the Ptolemaic dynasty provided lavish support for natural philosophy, among other intellectual studies, with the establishment of the unsurpassed library and the Temple to the Muses (museum).

Note on names: Don’t let the various forms of ancient names fool you: ancient Greek names are often translated in different ways. For example, Greek names often end in "-os," and Latin names often end in "-us." Where Greek names often include a "k," Latin names would substitute a hard-sounding "c." Because it was once common practice to use Latinized names, Greek names would be given in their Latin spelling. For example, "Eudoxos of Knidos" would be Latinized as "Eudoxus of Cnidus.” You will find both Latin and Greek forms of many names; I myself prefer the name that was used at the time and place under consideration; i.e., Eudoxos would refer to Eudoxos as known in his own place and time; Eudoxus would refer to later understanding of him in western, Latin-speaking Europe.

The study questions will help you assess your knowledge; print them out and complete them as you read.


  1. Watch the “From the vault: Hellenistic Mathematical sciences” video prompt for this assignment.
  2. Share your thoughts in the Discussion.
  3. Read the following pages about Hellenistic mathematical sciences:
    1. Mathematics
      1. Euclid of Alexandria, fl. 300 BC
      2. Ktesibios of Alexandria, fl. 250 BC
      3. Archimedes of Syrakusa, d. 212 BC
    2. Astronomy
      1. Eudoxos of Knidos, fl. 375 BC
      2. Aristarchos of Samos, fl. 250 BC
      3. Apollonios of Perge, fl. 220 BC
      4. Hipparchos of Nikaia, fl. 150 BC
      5. The Antikythera Mechanism, ca. 150 BC
    3. Geography
      1. Eratosthenes of Kyrene, fl. 200 BC

  4. Background readings for this week come from one of your textbooks: David Lindberg, Beginnings of Western Science.
    1. If you have the 2007 edition, read the following pages: Chapter 5 (pp. 82-99 & 105-110; excluding the section on Ptolemy).
    2. Or, if you have the 1992 edition, read the following pages: Chapter 5 (pp. 85-99 & 105-110; excluding the section on Ptolemy).

  5. Quiz: Afterwards, take a Topic 1 quiz over the Hellenistic mathematical sciences in the assignments area of Janux. The quiz will be composed of 12 of the true/false questions listed in the Study Guide. Topic 1 quizzes must be completed before Wednesday night at 11:59 p.m.


TOPIC QUIZ: The statements are either True or False. When you take the quiz at Janux, you will see 12 of these statements, chosen at random, worth 2 points each.


  1. T or F ? Aristarchus of Samos (3rd century) argued that the Sun is in the center and the Earth circles the Sun as a planet.
  2. T or F? Heraclides of Pontus (4th century) invented a method for calculating the sizes and distances of the Sun and Moon.
  3. T or F? Aristarchus of Samos (3rd century) argued that the Earth rotates on its axis.
  4. T or F? Archimedes (3rd century) used geometry to advance the study of statics, the science of weights and levers.
  5. T or F? Apollonios of Perga (late 3rd century) wrote a geometrical treatise on the conic sections (ellipse, parabola, hyperbola).
  6. T or F? Apollonius discovered precession (the 26,000 year cycle in which the equinox points travel around the celestial equator).
  7. T or F? Hipparchos radically transformed Greek astronomy by introducing Babylonian methods, aims, and numbers (parameters).
  8. T or F? Hipparchos calculated the average length of the lunar month to within one second of the modern value.
  9. T or F? Alexander the Great established an empire that reached from Spain in its westernmost extent all the way to Jerusalem on its eastern border.
  10. T or F? Zeno of Citium founded the Stoic school of philosophy in Athens.
  11. T or F? After the death of Alexander the Great, one of his generals named Ptolemy ruled Egypt.
  12. T or F? The Museum of Alexandria was both a religious shrine and a place of learning, founded by a former member of Aristotle’s Lyceum.
  13. T or F? At its peak, the Library of Alexandria was said to contain nearly half a million scrolls.
  14. T or F? The second head of the Lyceum, Theophrastus, rejected Aristotle’s empirical approach and renounced the pursuit of natural sciences such as botany and mineralogy, favoring the study of pure logic instead.
  15. T or F? The third head of the Lyceum, Strato, demonstrated from a stream of falling water that heavy bodies accelerate as they descend.
  16. T or F? Epicurus, founder of the Epicurean school, taught that bodies are made of particles (corpuscles or atoms) with intervening void spaces.
  17. T or F? The philosophy of Epicurus was deterministic, in the sense that it postulated that all events have a mechanistic cause.
  18. T or F? Both Stoics and Epicureans advocated the study of science (natural philosophy) as an aid to ethics.
  19. T or F? Stoics argued that the cosmos is like a piece of mechanical clockwork, passive and inert.
  20. T or F? According to the Stoics, there is a dichotomy (radical distinction) between the sub-lunar (terrestrial) and supra-lunar (celestial) regions.
  21. T or F? According to the Stoics, there is an eternal cycle of worlds, constantly generating and dissolving, in a purposeful and determined sequence.
  22. T or F? The Epicureans defended teleology and viewed the universe as an organism.
  23. T or F? According to Aristotle, every field of natural science should be expressed in the language of mathematics.
  24. T or F? Greek mathematics emphasized geometry.
  25. T or F? The length of the diagonal of a square, whose sides are each 1 unit long, cannot be expressed as a ratio of two whole numbers.
  26. T or F? Euclid’s Elements of Geometry consists of a catalog of reported discoveries in mathematics, arranged in alphabetical order.
  27. T or F? A conclusion of a geometrical proof follows inevitably and necessarily from its premises, according to Euclid.
  28. T or F? Around 425 BC, Meton proposed a cycle of 19 years for synchronizing the lunar and solar calendars.
  29. T or F? Plato and Eudoxus explained the motions of the heavens with what is called a “Two sphere” kind of model.
  30. T or F? The celestial equator lies directly above the Earth’s equator.
  31. T or F? Fixed stars were believed to lie on a giant sphere that rotated around the Earth once a day.
  32. T or F? The ecliptic is the path taken by the Sun as it travels around the sky each year.
  33. T or F? Zodiac constellations contain the ecliptic.
  34. T or F? The Sun crosses the celestial equator at the equinoxes.
  35. T or F? The Sun lies directly overhead the equator on a solstice.
  36. T or F? The Moon travels around the zodiac about once each month.
  37. T or F? The planets all travel roughly eastward against the background of fixed stars on a path very near to the ecliptic.
  38. T or F? Retrograde motion occurs when a planet’s usual eastward motion through the zodiac is temporarily reversed.
  39. T or F? Mercury and Venus always appear near the Sun, while the other planets sometimes appear opposite the Sun in the sky.
  40. T or F? Plato, according to later reports, challenged astronomers to explain all the motions of the planets as combinations of uniform and circular motions.
  41. T or F? The astronomical models of Eudoxus of Knidos (4th century) generated quantitative predictions of planetary positions.
  42. T or F? Aristotle combined the concentric spheres of the planets, according to Eudoxus, into a single cosmological system of over 50 spheres (including unrolling spheres to cancel effects as needed).
  43. T or F? A temple of healing at Epidaurus was a center of hundreds of Greek temples devoted to Asclepius, whom Homer regarded as a great physician.
  44. T or F? The Hippocratic corpus is a collection of about 70 treatises all of which were written by Hippocrates of Cos.
  45. T or F? Most Hippocratic writings, such as On the Sacred Disease, de-emphasize divine intervention as a direct cause of specific cases of illness, attributing the course of nature itself to the divine.
  46. T or F? Hippocratic medicine often attributed disease to imbalances of the four humors, where treatments of diet, exercise and purgings were designed to restore a proper balance.
  47. T or F? Instead of using medicines derived from plants, most Hippocratic medicines were chemical in origin, such as mercury or arsenic.
  48. T or F? Hippocratic writers all agreed that a theoretical understanding of the causes of disease is essential to effective treatment.
  49. T or F? According to Roman authors, anatomists in Alexandria conducted human vivisections (dissections of living prisoners).
  50. T or F? In Alexandria, Herophilus of Chalcedon advanced anatomy by drawing clear distinctions between sensory and motor nerves, and between arteries and veins.
  51. T or F? In Alexandria, Erasistratus of Ceos, described the valves of the heart and argued that they function by ensuring that blood flows only one direction through the heart.
  52. T or F? “Empiricists” opposed Herophilus and Erasistratus by arguing that human dissection should be forbidden, because past experience provides a more reliable foundation for medicine than the study of human anatomy and physiology.


Do you have a great quote for this page? Let me know! (If used, a new quote is worth 1 point extra credit)

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HSCI 3013. History of Science to 17th centuryCreative Commons license
Kerry Magruder, Instructor, 2004
Brent Purkaple, TA

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Many thanks to the pedagogical model developed in Mythology and Folklore and other online courses by Laura Gibbs, which have been an inspiration for this course.

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