21. Poster Of Hipparchus hipparchus of rhodes. lived from 180 BC to 125 BC. Hipparchus an early exampleof trigonometric tables and gave methods for solving spherical triangles. http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/PstrfHpp.htm

Hipparchus of Rhodes lived from 180 BC to 125 BC Hipparchus an early example of trigonometric tables and gave methods for solving spherical triangles. Find out more at http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Hipparchus.html

22. Astro-Fact Carmen Rush, The First Star Catalogue. hipparchus of rhodes was aGreek astronomer and geographer, born in 170 BC. Inspired by the http://ottawa.rasc.ca/astronomy/astro_facts/hipparcus.html

Astro-Fact: Hipparcus of Rhodes by Carmen Rush The First Star Catalogue Hipparchus of Rhodes was a Greek astronomer and geographer, born in 170 BC. Inspired by the observation of a new star in 134 BC, Hipparchus constructed a catalogue of about 850 stars and was the first to assign a scale of magnitude to indicate their apparent brightness. His scale, numbered from 1 to 6,from brightest to faintest, is still used today although it has since been refined. He then studied the equinoxes and discovered they grew progressively earlier in relation to the sideral year. He determined the length of the sideral and tropical years accurate to within 6 minutes. Then came improved methods for determining latitude and longitude on the Earth's surface and the beginning of trigonometry with a construction of a table of chords the precursor of the sine ratio. All of Hipparchus writing have been lost. Thankfully, his work was recorded by Ptolemy and passed down through the ages. This page last modified: May 3, 2001

23. Alexandria Alexandria. Yet it was Claudius Ptolemy (believed to be Egyptian) thatprovided us with our best knowledge of hipparchus of rhodes. And http://www.math.wichita.edu/history/topics/alexandria.html

The City of Alexandria Topic Tree Home Great Alexandria 700 Years Of Excellence Before the arrival of the Greeks there was agriculture, tremendous yields because of favorable climate, rich silty soils, and abundant fresh water. Wherever there is an agricultural surplus, trade is essential. With trade an area gains renown. Stronger (or hungrier) nations want the area as their own. With the establishment of the city by Alexander, fertile ideas became the greatest crop of the Nile delta. A storehouse for surplus knowledge was soon needed. Many things may have contributed to the success of Alexander's plan. Centrality? Athens was a great seaport with access to the Mediterranean. By contrast, Alexandria had land bridges to three continents and access to the Mediterranean as well as access to the Indian Ocean. Hence, a diverse nature was grounded in more than just theory. The geography allowed for the arrival of many new peoples and ideas while at the same time promoting export of goods and services. Central to the city itself was the compilation of the world's knowledge - a kind of internet for the ancient world. Even if learning was not a person's primary interest, there was trade and favorable climate. Alexandria must have been an exciting place just to visit with all of the things that were being brought in from around the world. Collegiality? Sequels and examples of one-upmanship either did not survive the centuries or did not greatly exist. For example, Eratosthenes provided the world with a calculation for the earth's circumference. Hipparchus criticized Eratosthenes' geography and refined it. Yet he and Claudius Ptolemy were able to use the earth circumference calculations along with Pythagorean and Euclidian principles to determine the earth's diameter, distance to the moon and the moon's diameter. Possibly Rhodes would be seen as an area in competition to the knowledge that was taking place in Alexandria. Yet it was Claudius Ptolemy (believed to be Egyptian) that provided us with our best knowledge of Hipparchus of Rhodes. And the ancient world was also provided with the Colossus of Rhodes and the Lighthouse of Pharos rather than Colossus I and Colossus II.

24. Flat Earths And Moving Suns Apollonius of Perga in the third century BC and hipparchus of rhodesin the second century BC both further developed this theory. http://www.geocities.com/anatheist2001/subflatearths.htm

Back Flat Earths and Moving Suns In ancient Greek, the word cosmos literally meant "a beautiful thing". Even today, who could deny that the cosmos are truly a wondrous sight to behold? We have learned more about the Universe in the past 400 years, from the original publication of Copernicus's On the Revolutions of the Celestial Spheres in 1543 to the discovery of experimental evidence for so-called dark matter in 1997, than we have in all of prior human history. Why such a recent explosion of knowledge in so short a time? For this, I point to three factors: 1) The loss of the Church's power and with it the view that the Church has absolute authority on all worldly manners. 2) The invention of the scientific method as a means for objectively analyzing data by exposing it to rigorous amounts of testing and re-testing. 3) A rapid surge in technological advances, especially within the past century. Flat Earths and Moving Suns The ancient Greeks believed that the Earth was flat or disc-shaped. Indeed, the Bible does support this view in many places. Job 37:3 makes reference to the ends or edges of the Earth. "He directeth it under the whole heaven, and his lightning unto the ends of the earth." Isaiah 11:12 and Revelation 7:1 tells us that the Earth has four corners. In Matthew 4:8, "the devil taketh him up into an exceeding high mountain, and sheweth him all the kingdoms of the world", and Luke 4:5 Jesus is said to be capable of seeing all the Kingodms of Earth from the top of a really tall mountain. Of course, this would be impossible if the Earth was spherical. Christopher Columbus almost suffered a mutiny in the 15th century because his crew feared falling over the edge of the Earth.

25. JCA: Education: Parallax & Parsec hipparchus of rhodes estimated the distance to the Moon from measurements takenduring a solar eclipsein 189BCE. The eclipse was full in Hellespont (NW. http://www.jca.umbc.edu/~george/html/courses/glossary/parallax.html

Glossary Index Definition , Historical: Solar-system Stellar Parallax is the apparent change of position of a (closer) object as measured against the positions of more distant object(s) due to the movement of the observer. (see Bothun , Fig.1.3; also Silk A Parsec is defined as the distance of an object that exhibits parallax of 1 arcsec (Easy to remember since the word parsec is a construction from par allax and arc sec Image EnchantedLeaning.com 1 parsec = 3.085678 x 10 m = 3.261633 lyr (light years) Note: Make sure you understand that Larger parallax means smaller distance Historical Attempts to Detect Astronomical Parallax Historically - Solar Sytem Objects We how know that the measurement of the parallax of objects in the Solar System is hampered by the vast distances (hence small parallax angles) invloved. Furthermore, of course before the first telescopes were invented (c.1600), all observations were performed using the naked-eye. Moon Hipparchus of Rhodes estimated the distance to the Moon from measurements taken during a solar eclipsein . The eclipse was "full" in Hellespont (NW. Turkey), but only partial in Alexandria (Egypt) where 20% of the Sun's disk remained visible. Since 20% of the Sun's disk corresponds to 6~arcmins, then by estimating the distance between Hellespont and Alexandria (derived from their latitude [using say Polaris], and knowing the circumference of the Earth), one can derive the distance of the Moon.

26. JCA: Education: Physics 316 (generally ignored). hipparchus of rhodes, c.125BCE, Distance to the Moon Start of Scaling the Cosmos. Claudius Ptolemy, c.150, Geocentric - Epicylces. http://www.jca.umbc.edu/~george/html/courses/2002_phys316/lect3/lect3.html

[4097] Physics 316: Extragalactic Astronomy and Cosmology (Summary of Lectures) Lecture 3 [Early Cosmo] Other Early Cosmologies (?) It should be remembered that our knowledge of history is solely dependent on us having written records Few (if any) of the original works survive. Thus we must rely on later works making reference to those from earlier periods. This adds concerns as to whether these later works indeed provide a true and complete reporting/representation of the earlier ideas. Indeed, the cosmological ideas of some cultures are almost completely absent from the historical record. Who knows what other cosmological ideas might have been lost... [Early Cosmo] Timeline/Summary of Early Developments Adapted from Silk, "The Big Bang" Table 2.1: Who... When... What... Thales of Miletus c.585BCE universe run by nature processes Pythagoras of Samos c.530BCE spherical rotating Earth orbiting a central Fire Anaxagoras of Clazomenae c.430BCE "heaven" is knowable Plato c.420BCE Geocentric planets in circular orbits , stationary Earth Democritus of Abdera c.400BCE

27. OBSERVATORY hipparchus of rhodes, the founder of modern astronomy, by repeating observationsmade at Alexandria, discovered the precession of the equinoxes, and http://12.1911encyclopedia.org/O/OB/OBSERVATORY.htm

OBSERVATORY OBSERVATORY. Up to a comparatively recent date an " observatory " was a place exclusively devoted to the taking of astronomical observations, although frequently a rough account of the weather was kept. When the progress of terrestrial magnetism and meteorology began to make regular observations necessary, the duty of taking these was often thrown on astronomical observatories, although in some cases separate institutions were created for the purpose. In this article the astronomical observatories will be chiefly considered. Up to about 300 B.C. it can scarcely be said that an observatory existed anywhere, as the crude observations of the heavens then taken were only made by individuals and at intervals, employing the simplest possible apparatus. Thus, according to Strabe. While the necessity of following the sun, moon and planets as regularly as possible increased the daily work of observatories, other branches of astronomy were opened and demanded other observations. Hitherto observations of the fixed stars had been supposed to be of little importance beyond fixing points of comparison for observations of the movable bodies. But when many of the fixed stars were found to be endowed with proper motion, it became necessary to include them among the objects of constant attention, and in their turn the hitherto totally neglected telescopic stars had to be observed with precision, when they were required as comparison stars for comets or minor planets. Thus the field of work for meridian instruments became very considerably enlarged.

28. History Of Constellation And Star Names This article and Part II of such, published 1988/1989, comprise a study of theCommentary on the Phainomena of Aratus and Eudoxus by hipparchus of rhodes. http://members.optusnet.com.au/~gtosiris/page6.html

An Annotated Bibliography Of Studies of Occidental Constellations and Star Names to the Classical Period Compiled by Gary D. Thompson Go to: Star Maps References With Extensive Bibliographies Return To Site Contents Page Star Maps Books/Pamphlets: Grasshoff, Gerd. (1990). The History of Ptolemy's Star Catalogue. [Note: Based on the author's doctoral thesis. See the (English-language) book review by James Evans in Journal for History of Exact Sciences, Volume 43, Pages 133-144.] Knoel, E[?]. (1877). "The Chronology of Star Catalogues." (Memoirs of the Royal Astronomical Society, Volume 43, Pages 1-74). [Note: Comprehensive.] Stott, Carole. (1991). Celestial Charts: Antique Maps of the Heavens. [Note: Well illustrated but poorly organised. See the (English-language) book review by Elly Dekker in Annals of Science, Volume 49, Number 6, 1992, Pages 598-599.] Warner, Deborah. (1979). The Sky Explored: Celestial Cartography 1500-1800. [Note: Excellent.] Whitfield, Peter. (1995). The Mapping of the Heavens. [Note: At times uncritical and unreliable.] Articles/Entries: Berggren, J[?]. [Len]. (1991/1992). "Ptolemy's Maps of Earth and the Heavens: A New Interpretation." (Archive for History of Exact Sciences, Volume 43, Pages 133-144).

29. Trigonometry hipparchus of rhodes Born 190 BC in Nicaea (now Iznik), Bithynia (now Turkey)Died 120 BC in probably Rhodes, Greece The founder of trigonometry. http://www.vittayasart.net/articles/trigone.html

Home Hipparchus of Rhodes Born: 190 BC in Nicaea (now Iznik), Bithynia (now Turkey) Died: 120 BC in probably Rhodes, Greece The founder of trigonometry ¤ÇÒÁ¨Ô§Ç§¡ÅÁ¡çà»ç¹àËÅÕèÂÁàËÁ×͹¡Ñ¹ ¤×ÍÁըӹǹàËÅÕèÂÁà»ç¹Í¹Ñ¹µì Ë×Í Infinity àÇÅÒ¤Ô´ÊÙµ¤Ó¹Ç³¾×é¹·Õèǧ¡ÅÁ àÒàÍÒ¾×é¹·ÕèÊÒÁàËÅÕèÂÁ·Õèà»ç¹àËÁ×͹ٻ ¾Ô««èÒ ã¹Ç§¡ÅÁ¹Ñé¹ ¨Ó¹Ç¹ Infinity ÁÒÇÁ¡Ñ¹ ·ÕèàÕ¡ Integration ä´é¾×é¹·Õè à·èҡѺ Pi ¤Ù³´éÇÂÑÈÁÕ¡ÓÅѧÊͧ ¤èÒ Pi ¹Õè¨Ô§æäÁèãªè 22/7 ÍÂèÒ§·Õ褹ÊèǹÁÒ¡à¢éÒ㨠áµèà»ç¹¤èÒ¤§·Õè ·ÕèÁըش·È¹ÔÂÁäÁèÙ騺 ¤×Í »ÐÁÒ³ 3.141592653589793 㹡Ҥӹdz·Ò§ÇÔ·ÂÒÈÒʵìÊÁÑ¡è͹àÒãªéà¾Õ§·È¹ÔÂÁÊÕèËÅÑ¡¤×Í 3.1416 ¡ç¾Í áµè»Ñ¨¨ØºÑ¹à¢Òº¨Ø¤èÒ Pi äÇéà»ç¹ Constant ã¹à¤×èͧ¤Ô´àÅ¢áÅéÇ Êдǡ´Õ ¾Ç¡ªèÒ§¡Å⧧ҹãªéÊÙµ¤Ó¹Ç³¾×é¹·Õèǧ¡ÅÁ = Pi/4 x d2 Ë×Í = 0.785 x d2 ¤×ÍãªéàÊé¹¼èÒÈÙ¹Âì¡Åҧ㹡Ҥӹdz äÁèãªéÑÈÁÕ à˵ؼÅà¾ÒÐ ¡Ò¡Ó˹´¨Ø´ÈÙ¹Âì¡ÅÒ§¢Í§à¾ÅÒÇèÒÍÂÙè·Õèä˹ÂÒ¡ÁÒ¡¡ÇèÒ¡ÒÇÑ´àÊé¹¼èÒÈÙ¹Âì¡ÅÒ§ ¡ÒÇÑ´àÊé¹¼èÒÈÙ¹Âì¡ÅÒ§§èÒÂÁÒ¡ ·Óä´é´éÇ¡Òãªé Vernier Caliper Çѵ¶Ø·ÕèÁ¹ØÉÂì·Ó¢Öé¹ÁÒ ·Õèà»ç¹Ç§¡ÅÁ Ë×Í·§¡ÅÁ ÁÕÁÒ¡¨Ô§æ à¾ÒзӧèÒ´éÇ¡ÁÇÔ¸Õ¡ÅÁ¡Å×¹¡Ñº¸ÁªÒµÔÁÒ¡¡ÇèÒÙ»·§Í×è¹ àªè¹ã¹¡Ò»Ñé¹ËÁéÍ ¶éÒ»Ñé¹à»ç¹·§ÊÕèàËÅÕèÂÁ¨ÐÂÒ¡ÁÒ¡¡ÇèÒ¡Ò»Ñé¹ËÁéÍ·§¡ÅÁ áÅжéÒ»Ñé¹ä´é¡çãªé§Ò¹ä´éäÁè´Õà·èÒ·§¡ÅÁ ¨Ðᵡ§èÒÂà¾ÒÐÁըشÍè͹·Õ赧ÁØÁ ·Õèà»ç¹¨Ø´ÇÁ¢Í§¤ÇÒÁà¤Õ´ ¤×ÍÁÕ Stress ÁÒ¡·ÕèÁØÁ áµèËÁéÍ·§¡ÅÁÁÕ¡Òà©ÅÕè¤ÇÒÁà¤é¹ä»ÍºæµÑÇ µÒÁ·ÄÉ®ÕáÅéÇ à·èҡѹ·Ø¡¨Ø´Íº´éÒ¹ áÅÐà»ç¹¤ÇÒÁà¤é¹á§´Ö§ (Tensile Strength)à·èÒ¹Ñé¹ äÁèÁÕá§ËÑ¡ (Bending Moment) ËÅÑ¡¡Ò¹Õéà»ç¹¨Ô§¡Ñº¶Ñ§á¡êÊ ¡ÐºÍ¡ÊÙº ¢Ç´«ÕÍÔéÇ áÅÐäË»ÅÒéÒ

30. OML: Neptune's Realm: Ocean Divided hipparchus of rhodes (c. 167127 BC), one of the greatest of Greek astronomers,had marked off the earth s surface at the equator into 360 partsthe degrees http://www.usm.maine.edu/maps/exhibit8/nrlong.html

Charting Neptune's Realm An Ocean Divided As voyaging increased into the uncharted regions of the open ocean, mariners brought back their findings to be retained in written records and represented on maps. To create accurate maps cartographers needed more than recounted tales and estimated distances. It became apparent that a grid system dividing the earth into coordinates of latitude and longitude was necessary. Thus, a grid was constructed whereupon any point on the earth's surface could be located. 19. Charles Pierre Claret de Fleurieu French, 1738-1810 A New General Chart of the Atlantic or Western Ocean and Adjacent Seas Copper engraving, 49.1cm x 69.9cm London: Sayer and Bennet, 1777 In his "New General Chart of the Atlantic or Western Ocean and Adjacent Seas," de Fleurieu placed great emphasis on geographic accuracy as determined by astronomical observations for latitude and longitude. On this English edition of one of his charts, two prime meridiansthe starting line of zero degrees longitudeare indicated by longitude scales at the top of the chart: one, located at the Greenwich Observatory in England; the other, positioned in Paris. A third scale at the bottom of the chart shows Time in hours and minutes, in effect another way of indicating longitude. Even latitude, with its fixed reference points of the equator and poles, is marked off in two different scales. Latitude on the left-hand margin of the chart is measured in degrees, while latitude on the right-hand margin is expressed in marine leagues.

31. A History Of Science Volume I - Chapter X While hipparchus of rhodes was in his prime, Corinth, the last stronghold of themainland of Greece, had fallen before the prowess of the Roman, and the http://www.worldwideschool.org/library/books/sci/history/AHistoryofScienceVolume

A History of Science Volume I by Henry Smith Williams Terms Contents BOOK I Chapter I ... Chapter XI Chapter X Science of the Roman Period All in all, then, this epoch of Roman domination is one that need detain the historian of science but a brief moment. With the culmination of Greek effort in the so-called Hellenistic period we have seen ancient science at its climax. The Roman period is but a time of transition, marking, as it were, a plateau on the slope between those earlier heights and the deep, dark valleys of the Middle Ages. Yet we cannot quite disregard the efforts of such workers as those we have just named. Let us take a more specific glance at their accomplishments. Please read the terms under which this book is provided to you

32. Title hipparchus of rhodes Ca. 190 BCE to 120 BCE Although little is knownof the life and times of Hipparchus, and very little of his http://www.math.uvic.ca/courses/math415/Math415Web/greece/gmen/hippartext.html

HIPPARCHUS OF RHODES Ca. 190 BCE to 120 BCE Although little is known of the life and times of Hipparchus, and very little of his original work has survived, his contributions to mathematics were very important. Hipparchus' major contributions come through his love of astronomy. Described by many as being the greatest Astronomer of antiquity, Claudius Ptolemy based much of his Almagest on Hipparchus' work. Hipparchus is credited with bringing the 360 degree circle from Mesopotamia to Greece. This is undoubtedly the reason why we use 360 degrees to divide a circle today. He is also considered by many to be the father of trigonometry, and discovered many trigonometric methods and formulas.

33. Astronomy And Space Timeline - Ancient History Through The Renaissance 120 BC, hipparchus of rhodes (161 BC122 BC, ) Defines the cosmos by latitudeand longitude; and makes triangular measurement of celestial navigation. http://space.about.com/library/weekly/bltimea.htm

zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') About Homework Help Space / Astronomy Home ... Featured Astronomy Image of the Week zau(256,152,145,'gob','http://z.about.com/5/ad/go.htm?gs='+gs,''); Multimedia Resources News - Current Events Stars Planets Galaxies Education - Astronomy/Space ... Help zau(256,138,125,'el','http://z.about.com/0/ip/417/0.htm','');w(xb+xb); Stay Current Subscribe to the About Space / Astronomy newsletter. Search Space / Astronomy Astronomy and Space Timeline Ancient History Through The Renaissance (This timeline is a work in progress.) 2680 BC The Great Pyramid at Giza completed. Chinese astronomers start to observe the sky A comet is observed for the first time by the Chinese 1860 BC The Construction of Stonehenge. Babylonians begin to keep observational records Chaldean astronomers identify the zodiac Solar eclipse observed and recorded by Babylonians Pythagoras suggests that the Earth is a sphere and not flat, as had been previously assumed 440 BC Greek philosopher Leucippus and Democritus, his student present the concept that all matter consists of fundamental particles called atoms. (Atom comes from the Greek word meaning"indivisible.") Chinese spot first moons of Jupiter with the naked eye 350 BC Aristotle writes Meteorologica, the first book on weather.

34. GSD6322 Fundamentals Of GIS Theory And Applications Around 50 years later, a greek, hipparchus of rhodes invented a worldwide referencingsystem of meridians and paralells that we use to describe earth locations http://www.gsd.harvard.edu/pbcote/courses/gsd6322/projections/

Homepage Lectures/Labs Announcements People GSD6322 Fundamentals of GIS: Theory and Applications Geographic and Projected Earth Referencing Systems The magic of geographic information systems is that these tools can bring together and associate representations from diverse sources. This ability depends on our data sources using well defined (coordinate) referencing systems. This is not to say that the coordinate systems need to be the same, only that they are well defined. The notion of spatial refernicing systems is one of the most fundamental and interesting ideas that all users of GIS should understand. THis document provides an overview of the basic ideas. Topics Covered: A brief History and Theory of Latitude and Logitude The Graphical Problem of Latitude and Longitude Projections: Transforming Geographic Coordinates to Orthogonal Systems Metadata Issues with Map Projections ... Additional References Related Documents ESRI's Handbook on Map Projections From The Geographer's Craft University of Colorado at Boulder Handy Map of UTM Zones Aligning Layers in ArcGIS Technical Issues of Map Projections in ArcGIS Using ArcMap pages 107-112 Instructions for dealing with forward projection of datasets having well-defined projection information.

35. History Of Geometry hipparchus of rhodes (190120 BC) is the first to systematically use anddocument the foundations of trigonometry, and may have invented it. http://geometryalgorithms.com/history.htm

History Home Overview [History] Algorithms Books Gifts Web Sites A Short History of Geometry Ancient This is a short outline of geometry's history, exemplified by major geometers responsible for it's evolution. Click on a person's picture or name for an expanded biography at the excellent: History of Mathematics Archive (Univ of St Andrews, Scotland) Also, Click these links for recommended: Greek Medieval Modern History Books ... History Web Sites Ancient Geometry (2000 BC - 500 BC) Babylon Egypt The geometry of Babylon (in Mesopotamia) and Egypt was mostly experimentally derived rules used by the engineers of those civilizations. They knew how to compute areas, and even knew the "Pythagorian Theorem" 1000 years before the Greeks (see: Pythagoras's theorem in Babylonian mathematics ). But there is no evidence that they logically deduced geometric facts from basic principles. Nevertheless, they established the framework that inspired Greek geometry. A detailed analysis of Egyptian mathematics is given in the book: Mathematics in the Time of the Pharaohs India (1500 BC - 200 BC) The Sulbasutras Baudhayana (800-740 BC) Apastamba (600-540 BC) Greek Geometry (600 BC - 400 AD) Time Line of Greek Mathematicians Major Greek Geometers (listed cronologically) [click on a name or picture for an expanded biography].

36. Round Earth Society - Atheos: How Jesus Got A Life In 128 BCE the Greek astronomer hipparchus of rhodes discovered the precessionof the equinoxes see Figure 2. Because the earth s axis is tilted http://www.str.com.br/English/Atheos/jesus.htm

Published: 03/27/2001 Updated: 05/04/2001 Click on the sponsor's banner above and help the Round Earth Society to grow! Welcome What's New Authors Acknowledgements ... Draw! Areas of the RES Main R.E.S. Atheos Scientia ... Links Support Us: Donate! Donate Any Ammount! Need Help? Got Questions? Member Registration Click and register now! Debate Survey D o you believe that the predictions and the claims of astrology are valid? Y es N o O ther Opinion See The Current Results Spread The RES! S end this text to a friend! Hosted By HOW JESUS GOT A LIFE by Frank R. Zindler NAPOLEON: Monsieur Laplace! I have read with great interest your Traité de mécanique céleste - all five volumes - but nowhere have I found any mention of the Good Lord. LAPLACE: Sire, I have had no need of that hypothesis. O ur world is an unstable place. Nations rise, and governments topple. Unbalanced people the world around torture and kill each other for the sake of religion or other groundless causes. Earthquakes, volcanoes, and wars periodically scourge our globe. Continents drift about and collide with each other, and oceans form and disappear. Even planet Earth itself has the wobblies. As it spins on its axis, the earth is not stable. Like the center peg of a toy top, the axis of the spinning earth slowly wobbles in a circle, tracing out the surface of a double cone in space [ see Figure 1 Figure 1.

37. A Potted History Of Computers - The Birth It is worth noting, however, that the man who invented trigonometry and firstscientifically catalogued the stars positions was hipparchus of rhodes. http://www.hodgy.net/computer_history/page_1/page_1a.htm

T he birth of computers - life Jim but not as we know it! Abacus Egyptians and Romans 1st Century BC 2nd Century ... Marconi Abacus An Abacus is a simple device for performing arithmetic calculations and therefore is the ancestor of the modern calculating machine and computer. It is basically a calculating device, probably of Babylonian origin, sometime between 1,000 BC and 500 BC, (although some pundits are of the opinion that it was actually invented by the Chinese) that was long important in commerce. The word abacus comes to us by way of Latin as a mutation of the Greek word abax . In turn, the Greeks may have adopted the Phoenician word abak , meaning "sand", although some authorities lean toward the Hebrew word abhaq , meaning "dust." Irrespective of the source, the original concept referred to a flat stone covered with sand (or dust) into which numeric symbols were drawn. The first abacus was almost certainly based on such a stone, with pebbles being placed on lines drawn in the sand. Over time the stone was replaced by a wooden frame supporting thin sticks, braided hair, or leather thongs, onto which clay beads or pebbles with holes were threaded. A variety of different types of abacus were developed, but the most popular became those based on the bi-quinary system, which utilizes a combination of two bases (base-2 and base-5) to represent decimal numbers. Although the abacus does not qualify as a mechanical calculator, it certainly stands proud as one of first mechanical aids to calculation.

38. Important Astronomers, Their Instruments And Discoveries 1 hipparchus of rhodes (c. 150 125 BC) used the equatorially mountedArmillary Sphere for a variety of measurements. He determined http://nineplanets.org/psc/hist1.html

Important Astronomers, their Instruments and Discoveries by Paul M. Rybski Part 1 Pre-telescopic Instruments, their Inventors and Users Merkets and Waterclocks Babylonian observations (1500 BC?) recorded solar and lunar eclipses as well as planetary observations using merkets and waterclocks. Macedonian philosopher Thales of Miletus (575-532 BC?) predicted a solar eclipse using Babylonian observations and mapped out constellations to aid navigation. Alexandrian astronomer Eratosthenes (260-201 BC?) measured the circumference of the Earth using comparative shadow rod measurements in two places and knowledge of the distance between them. The Cross-Staff Alexandrian astronomers Aristillus and Timocharis charted the positions of the brighter stars (284 BC), producing the first star catalog using a Cross-staff. Aristarchus of Samos (250 BC?) calculated the distance of the Sun from the Earth and the Moon and Sun's sizes relative to Earth by observations during solar and lunar eclipses and at first quarter Moon using a Cross-staff. Armillary Spheres Eratosthenes (204 BC) catalogued more than seven hundred stars using one, and possibly two, armillary spheres.

39. Appendix 1 A generation later, Greek astronomer hipparchus of rhodes (c190125)compiled the first star catalog of about 850 stars. His follower http://www.visualstatistics.net/Visual Statistics Multimedia/mathmatical_foundat

40. A Chronology Of Interpolation 150 BC hipparchus of rhodes uses linear interpolation in the construction of tablesof the socalled chord-function (related to the sine function) for the http://imagescience.bigr.nl/meijering/research/chronology/

A Chronology of Interpolation From Ancient Astronomy to Modern Signal and Image Processing Erik Meijering Proceedings of the IEEE , vol. 90, no. 3, March 2002, pp. 319-342 It is an extremely useful thing to have knowledge of the true origins of memorable discoveries, especially those that have been found not by accident but by dint of meditation. It is not so much that thereby history may attribute to each man his own discoveries and others should be encouraged to earn like commendation, as that the art of making discoveries should be extended by considering noteworthy examples of it. G. W. Leibniz, Historia et Origo Calculi Differentialis ca. 1714). Translation as in J. M. Child, "Newton and the Art of Discovery", in Isaac Newton 16421727: A Memorial Volume , W. J. Greenstreet (ed.), G. Bell and Sons, London, 1927, pp. 117-129. Ancient Times and the Middle Ages ca. 300 BC and earlier: Babylonian astronomers use linear and higher-order interpolation to fill gaps in ephemerides of the sun, moon, and the then-known planets, written down in cuneiform tablets as shown here. For explanations and more details, see O. Neugebauer

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