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Zenodorus: more detail

140 Bc: 140 Bc Births, 140 Bc Deaths, Tigranes the Great, Su Wu, Huo Qubing, Gaius Julius Caesar, Lucius Licinius Crassus, Zenodorus

Two new charaxinae from Panama and the Canal Zone (Nymphalidae) (Bulletin of the Allyn Museum) by Lee D Miller, 1971

Eugene Le Moult's Prepona types (Lepidoptera: Nymphalidae, Charaxinae) (Bulletin of the Allyn Museum) by Richard Irwin Vane-Wright, 1974

lists with details

Guy Clark Ancient Coins And Antiquities- Roman Provincial Coins
legends weak and partial, dark brown patina, Fine+/Fine ..$50 Photo. RP111.Syria, Chalkis, zenodorus, dated 32/31BC, time of Octavian, AE19.
http://www.ancient-art.com/romprov.htm

Extractions: Guy Clark's Ancient Coins and Antiquities Roman Provincial Coins Last update: 27 February 2003 By popular demand Roman Provincial coins (also called Greek Imperial) have now received their own page. This page is still under construction and I will be adding a number of new coins over time. These coins will retain the Roman page numbers, etc. for the moment but will soon be getting their own identities. Coins that fit more precisely into another scheme, such as the coins issued for Biblical cities during Roman times, will still be found under the other heading. Macedonia, Gaius Publilius, Quaestor, after 146BC, AE21. Athena head rt./Bull feeding rt., BMC76var (has legend of BMC75). Near centered, nice portrait and bull, most legend clear, black patina, about Very Fine........$95 Photo Melita, Triumviral Period, AE19. Veiled female head left/Curule chair, RPC672. Centered, rev. weak as usual, decent portrait, brown patina, SCARCE locality, Very Fine/Good Fine......$150 Photo Crete, Knossos(?), L. Lollius, ca 1st Century BC, AE28. Artemis Diktynna head rt./Stag stands rt., L LOL I VS, RPC909. Near centered on large flan, overstruck on unidentified bronze so there are some areas of slight flatness and garbling but not bad, clear portrait, stag and most of rev. legends, brown patina, the exact location of the mint for these is unknown but supposed to be Knossos, RARE, Very Fine......$475 Photo Phoenicia, Aradus, Marc Antony, ca 38/37 BC, AE18. Antony head rt./Bull gallops left, CWM in exergue, RPC I, 4466sim. Centered on slightly small thick flan, nice clear portrait and rev., olive green patina, RARE, about Very Fine.....$150
Guy Clark Ancient Coins And Antiquities- Greek Coins
$850 Photo. GB333. Syria, Chalkis, zenodorus, 3020 BC, AE22x19. Octavianhead rt./zenodorus head left, Lindgren 2136. Near centered
http://www.ancient-art.com/greekAE.htm

Extractions: Guy Clark's Ancient Coins and Antiquities GREEK BRONZE COINS Last update: 28 January 2003 (I have attempted to scan many of the bronzes to convey a better idea of what they look like. Please note that some have come out with the color off somewhat. I hope to improve this as I learn more about scanning techniques. Few Greek bronzes are of known denomination and so most are designated by a number following AE which indicates the diameter of the coin in millimeters. Thus a coin listed as AE15 is 15mm in diameter. For those who are metrically challenged, there are approximately 24mm per inch.) SPECIAL Miscellaneous Greek Bronze Coins. If, after looking at the selection of bronzes below, you still can't decide where to start, I have a number of miscellaneous Greek bronzes from many areas. These coins will average Fine or better condition with minimal problems such as centering, pitting, etc., so, while not choice specimens, they are not ugly either. These coins can be a good starting point or, if you are only planning to have one representative example, will suffice for an inexpensive type coin. Most are from Syria, Phoenicia, Thrace, Macedonia, and various mints in Asia Minor and date from the 4th to the 1st Century BC. If you order more than one, I will provide variety. Each only ...$14.95 Armenia Armenia, Tigranes II, 95-56 BC, AE12 (Chalcus). King's bust rt./Ear of grain, Nercessian 102ff. Centered on slightly small flan, top of crown and tip of grain ear slightly off, black patina with light earthen cover, portrait and rev. clear, decent example of the smaller bronzes of his reign, Very Fine.....$75
MR: 2003c:53013
About 2300 years ago, zenodorus made the first known attempt to show thatthe circle is the shortest curve in the plane enclosing a given area.
http://www.ams.org/msnhtml/featured-reviews/2003c53013_rev.html

Extractions: FEATURED REVIEW. The study of bubbles and surfaces that minimize area while enclosing given volumes fits into a general class of problems regarding optimal geometric configurations. These problems bring together techniques from geometry, analysis and computation. The existence and regularity results related to the double bubble problem are due to F. J. Almgren, Jr. [Mem. Amer. Math. Soc. 4 (1976), no. 165, viii+199 pp.; MR #8420] and J. E. Taylor [Ann. of Math. (2) 103 (1976), no. 3, 489539; MR Conglomerations of constant mean curvature surfaces in 3-space are much too general to classify completely. However, work of White, Foisy and Hutchings using symmetry techniques showed that an optimal double bubble must be a surface of revolution [see M. Hutchings, J. Geom. Anal. 7 (1997), no. 2, 285304; MR 99j:53010]. In other words the solution to our problem must be symmetric under rotation around an axis. This implies that the pieces of a minimizing surface are subsurfaces of a well-studied class of constant mean curvature surfaces, the Delaunay surfaces. A puzzling aspect of the double-bubble story is that a chief difficulty in its solution is the problem of establishing connectedness of the regions. It is conceivable that the most efficient surface enclosing two volumes actually encloses three (or more) connected regions in space. If this really occurred, then the best shape for a canteen holding a certain amount of milk and a certain amount of lemonade (without mixing of course) would enclose two separate regions containing milk, as well as one or more containing lemonade. Such intuitively unlikely possibilities are difficult to eliminate. Hutchings studied the possible configurations and, while not establishing connectedness in all cases, was able to show that there are a limited number of possible configurations for a minimizer. So, for example, one of the enclosing volumes is always connected.
Recent Articles In St Andrews Archive: How Do We Know About Greekmathematicians?
And when zenodorus the astronomer came down to Arcadia and was introduced to us,he asked us how to find a mirror surface such that when it is placed facing
http://mathforum.org/epigone/math-history-list/whuclangkhix
Hist7
pillaging the Damascenes. zenodorus, whose eparchy Auranitis was givento Herod goes to Rome to protest, but returns unsatisfied. Then M
http://www.abu.nb.ca/Courses/NTIntro/InTest/Hist7.htm

Extractions: 1. Brief Account of Events Said to Have Occurred From 37 until 4 BCE, Herod reigned in Jerusalem and gradually, with the approval of the Romans, expanded his kingdom; his kingdom included both Jews and Gentiles, but he did not follow the Hasmonean policy of forcibly converting gentiles to Judaism. Early in his reign, Antonius and Octavian had a falling out, which led to another civil war. In 31 BCE, Octavius, with the support of the Roman senate, fought and defeated Antonius at the battle of Actium in Greece; both Antonius and Cleopatra managed to escape and arrived in Alexandria; but, when they realized that there was no way of escaping Octavius, they committed suicide. Herod convinced the victorious Octavius to confirm him in his former position as King of the Jews. Herod had serious trouble with his family and his court in general; he was not greatly appreciated by the Jews generally, which bothered him. In a desire to aggrandize himself and perpetuate his memory, he undertook many expensive building projects in parts of his kingdom and beyond. In 19 BCE, Herod undertook to rebuild and enlarge the Temple in Jerusalem (See Testament of Moses [6] for an unflattering description of Herod's reign presented as a prophecy.)
Bible Study Aids On ChristiansUnite.com
to two hundred talents, (21) while Batanea, with Trachonitis, as well as Auranitis,with a certain part of what was called the House of zenodorus, (22) paid
http://bible.christiansunite.com/jos.cgi?b=ant17&c=11
Hmk_greek.htm
. Give a proof of the zenodorus theorem that if a circle and regular polygonhave the same perimeter, the circle has the greater area. (Hint.
http://www.math.tamu.edu/~dallen/masters/Greek/problems/hmk_greek.htm

Extractions: Problems about Greek mathematics will illustrate that the Greeks achieve a full intellectual development comparable to any modern state. Their mathematics was more limited by what they would not accept that what they could not comprehend. You will see an assortment of problems ranging from essay type to actual geometric constructions, from number theory to modern Diophantine equations. Find the analytic formula for the trisectrix. (You will need trigonometry.) Show that in a Pythagorean triple, if one of the terms is odd, then two of them must be odd and one even. Show that in a Pythagorean triple, if the largest term is divisible by 4, then so are the other two terms. Show that is incommensurable. Use your argument to show that every non-square number is incommensurable. Given that an equilateral pentagon and triangle can be inscribed in a circle, show how to inscribe a 15-gon in a circle. (Note. This must be extablished strictly by Euclidean construction.) Show the other part of the double reductio ad absurdem argument for proving the Eudoxus theorem that the ratio of the areas of two circles are as the squares of their diameters. That is, you need to obtain the contradiction using circumscribed
Modele
Translate this page A- Price on Request Agrias amydon tryphon aristoxenes SA Peru m 25 Agrias amydontryphon aristoxenes SA Peru m A- 15 Agrias amydon zenodorus flavicellus (yellow
http://www.insect-trade.com/Selection/rhopalocera.html
LacusCurtius Pliny The Elder's Natural History Book 34
Translate this page 45, verum omnem amplitudinem statuarum eius generis vicit aetate nostra zenodorusMercurio facto in civitate Galliae Arvernis per annos decem, HS manipretii
http://www.ku.edu/history/index/europe/ancient_rome/L/Roman/Texts/Pliny_the_Elde

Extractions: Proxime dicuntur aeris metalla, cui et in usu proximum est pretium, immo vero ante argentum ac paene etiam ante aurum Corinthio, stipis quoque auctoritas, ut diximus. hinc aera militum, tribuni aerarii et aerarium, obaerati, aere diruti. docuimus quamdiu populus Romanus aere tantum signato usus esset: et alia re vetustas aequalem urbi auctoritatem eius declarat, a rege Numa collegio tertio aerarium fabrum instituto. Vena quo dictum est modo foditur ignique perficitur. fit et e lapide aeroso, quem vocant cadmean, celebri trans maria et quondam in Campania, nunc et in Bergomatium agro extrema parte Italiae; ferunt nuper etiam in Germania provincia repertum. fit et ex alio lapide, quem chalcitim appellant in Cypro, ubi prima aeris inventio, mox vilitas praecipua reperto in aliis terris praestantiore maximeque aurichalco, quod praecipuam bonitatem admirationemque diu optinuit nec reperitur longo iam tempore effeta tellure. proximum bonitate fuit Sallustianum in Ceutronum Alpino tractu, non longi et ipsum aevi, successitque ei Livianum in Gallia. utrumque a metallorum dominis appellatum, illud ab amico divi Augusti, hoc a coniuge.
LacusCurtius Rome The Colossus Of Nero (Platner & Ashby, 1929)
COLOSSUS NERONIS a colossal bronze statue of Nero, 120 feet high, the work of zenodorus,a Greek, erected by Nero himself in the vestibule of the DOMUS AUREA
http://www.ku.edu/history/index/europe/ancient_rome/E/Gazetteer/Places/Europe/It

Extractions: London Oxford University Press C OLOSSUS N ERONIS a colossal bronze statue of Nero, 120 feet high, the work of Zenodorus, a Greek, erected by Nero himself in the vestibule of the D OMUS A UREA ... (q.v.) on the summit of the Velia ( Suet. Nero 31 Plin. NH xxxiv.45 ), but after the death of that emperor changed by Vespasian into a statue of the Sun (Plin. loc. cit; Suet. Vesp. 18 ; Mart. de spect. 2.1 (see D OMUS A UREA ... Cass. Dio lxv.15 oJ . . . kolosso`V wjnomasmevnoV ejn th'/ iJera/ oJdw'/ iJdruvqh HJ 321) considers iJdruvqh to be a loose translation of refectus est , so that we need not suppose that the statue was actually moved. Dio states that some said it was like Nero and others like Titus. Hadrian, perhaps early in 128
Greek Mathematics
rotating about axis of revolution). zenodorus (200140 BC) workedon various geometric optimization problems. He showed that the
http://members.fortunecity.com/kokhuitan/greek.html

Extractions: The Greeks are responsible for initial explosion of Mathematical ideas. For several centuries, Greek mathematics reign the mathematical world, with great advances in Number Theory, the Theory of Equation, and in particular Geometry. The first great Greek mathematician is Thales of Miletus (624-547 BC). He brought the knowledge of Egyptian Geometry to the Greeks and discovered several theorems in elementary Geometry. He predicted a Solar Eclipse in 585 BC and could calculate the height of a pyramid, as well as how far a ship is from land. One of his pupils, the Greek philosopher, Anaximander of Miletus (610-546 BC), is considered the founder of Astronomy. Perhaps the most prominent Greek mathematicians is Pythagoras of Samos (569-475 BC). His ideas were greatly influenced by Thales and Anaximander. His school of thought practiced great secrecy and he (and his followers, called Pythagoreans) believe everything in the world can be reduced to numbers. This idea stemmed from Pythagoras' observations in Music, Mathematics and Astronomy. E.g. Pythagoras noticed that vibrating strings produce harmonics in which the lengths of the strings are in ratios of whole numbers. In fact, he contributed greatly to the mathematical theory of music. He had the notion of Odd and Even Numbers, Triangular Numbers, Perfect Numbers, etc. In particular, he is well known today for his Pythagoras Theorem. Although this theorem is known to the Babylonians and Chinese long before Pythagoras, he seemed to be the first person to provide a proof of it.
Feb 16, 2001, The Benson Collection Part 1 - Chapter 142
Chalcis. zenodorus, c. 3225 BC. Bare head of Octavian right, date around.Reverse Head of zenodorus left, Greek inscription around. RPC 4774.
http://www.goldbergcoins.net/catalogarchive/20010216/chap142.shtml

Extractions: Aegina. Aegina, 457-431 BC. AR Stater (12.1 g). Top view of land tortoise with segmented shell. Reverse: Refined skew punch. SNG Delepierre 1535ff. Countermark at middle of shell; sunburst countermark in lower field. An especially refined, handsome depiction of this animal. Attractive toning. A pleasing Extremely Fine.
Optimoinnin Historiaa
todistus); 200 eaa zenodorus tutkii (Pappuksen Theonin mukaan) Didonongelmaa, jota on kuvattu myös Virgilin aeneidissa 19 eaa;
http://www.sal.tkk.fi/Opinnot/Mat-2.139/historia.html

Extractions: 300 eaa Eukleides tarkastelee pisteen etäisyyttä suoraan ja osoittaa, että neliö on suurin niistä suorakulmioista, joiden yhteenlaskettu särmien pituus on kiinnitetty (kts. todistus 200 eaa Zenodorus Didon ongelmaa , jota on kuvattu myös Virgilin aeneidissa 19 eaa 100 eaa Heron osoittaa Catopricassa , että valo kulkee lyhintä polkua kahden pisteen välillä heijastuessaan peilistä Kepler pohtii optimaalista viinitynnyriä Galileo Galilei yrittää ratkaista miten riippuva ketju asettuu mutta epäonnistuu Fermat esittää, että funktion ääriarvoa tulee etsiä gradientin nollakohdasta. Vuonna 1657 Fermat osoittaa, että valo kulkee matkan kahden pisteen välillä minimiajassa
Les Dieux, Hommes Et Peuples
Translate this page ZAGREUS ZALMOXIS ZAMOLXIS ZEGRENSES ZENOBIA zenodorus ZENON (FLAVIUS ZENO) ZEUSZEUS BRONTON ZEUS CASIOS ZEUS DOLICHAIOS ZEUS ELEUTHERIOS ZEUS HELIOPOLITANUS
http://argentoratum.u-strasbg.fr/cgi-bin/aurweb/BAHR/PdhpBAHR?aur_file=dhpb.Z
The Words Tessellate And Tessellation Come From A Latin Word Which Means small
plane with no holes. A Greek mathematician named zenodorus (200 BC) discoveredthat regular. Around 300 AD,. Pappus expanded the discovery of zenodorus.
http://www2.gvsu.edu/~oxfordj/geom.html

Extractions: What is a Tessellation? The words tessellate and tessellation come from a Latin word which means "small stones" and "to pave with small stones". A tessellation or tiling is a group of polygons or tiles that have non-overlapping congruent sides and these tiles completely cover the plane with no holes. A Greek mathematician named Zenodorus (200 B.C.) discovered that regular polygons (polygons with congruent sides) enclosed the greatest area. Around 300 A.D., Pappus expanded the discovery of Zenodorus. Pappus gave an example of honeybees. Pappus believed that bees made their honey exclusively for human consumption. For this reason, bees needed to store their honey in a way in which none would be wasted. A proposition came from Pappus belief about the bees. It states "There are only three ways to arrange identical regular polygons about a common vertex without interstices". (Dunham, pg. 108 with proof) In proving this proposition, the conclusion was n n being the number of sides in the regular polygon. Let us look at each case for n 6. Since a polygon is a closed figure, we can start
CATHOLIC ENCYCLOPEDIA: Gospel Of Saint Luke
(Catholic Encyclopedia)Category Society Religion and Spirituality L A certain zenodorus took on lease the possessions of Lysanias, 23BC, but Trachonitis was soon taken from him and given to Herod.
http://www.newadvent.org/cathen/09420a.htm

Extractions: X. Saint Luke and Josephus I. BIOGRAPHY OF SAINT LUKE The name Lucas (Luke) is probably an abbreviation from Lucanus, like Annas from Ananus, Apollos from Apollonius, Artemas from Artemidorus, Demas from Demetrius, etc. (Schanz, "Evang. des heiligen Lucas", 1, 2; Lightfoot on "Col.", iv, 14; Plummer, "St. Luke", introd.) The word Lucas seems to have been unknown before the Christian Era; but Lucanus is common in inscriptions, and is found at the beginning and end of the Gospel in some Old Latin manuscripts (ibid.). It is generally held that St. Luke was a native of Antioch. Eusebius (Hist. Eccl. III, iv, 6) has: Loukas de to men genos on ton ap Antiocheias, ten episteuen iatros, ta pleista suggegonos to Paulo, kai rots laipois de ou parergos ton apostolon homilnkos ho de Loukas to men genos apo tes Boomenes Antiocheias en St. Luke was not a Jew. He is separated by St. Paul from those of the circumcision (Col. iv, 14), and his style proves that he was a Greek. Hence he cannot be identified with Lucius the prophet of Acts, xiii, 1, nor with Lucius of Rom., xvi, 21, who was
Pot-pourri.fltr.ucl.ac.be/files/AClassFTP/Textes/Pline_Ancien/hist_nat_34.txt
Translate this page 45 uerum omnem amplitudinem statuarum eius generis uicit aetate nostra zenodorusMercurio facto in ciuitate Galliae Aruernis per annos decem, HS manipretii
http://pot-pourri.fltr.ucl.ac.be/files/AClassFTP/Textes/Pline_Ancien/hist_nat_34
History Of Astronomy: Roughly Sorted Links - Biographies (2)
Translate this page zenodorus Al-Maghribi Jabir_ibn_Aflah Al-Khalili Al-Nayrizi Al-Farisi Al-Quhi DioclesAl-Haytham al-Haytham Al-Kashi Al-Samarqandi Ahmed Al-Jayyani Al-Khazin Al
http://www.astro.uni-bonn.de/~pbrosche/unsorted/rough_bio_02.html

Extractions: Please note that the links were found some time ago and may be outdated meanwhile. This list is not a permanent one. Any link may be moved or deleted without special announcement, and also this file may be deleted. Johann Hieronymus Schroeter - Wie der Name Silberschlag auf den Mond kam W. Barthel und H.-J. Vollrath: Otto Volk 1892-1989 Jahresbericht der Deutschen Mathematiker Vereinigung 94 (1992), 118-129. Kleinplanet soll Boelsche heissen Alexander von Humboldt in America Artikel aus den Mitteilungen - Alexander von Humboldts Amerikareise Artikel aus den Mitteilungen - Alexander von Humboldt his past and his present ... Joseph von Hammer-Purgstall "Zeitschrift "Fundgruben des Orients", in der alles erdenkliche Orientalische in reichen und üppigen Folgen vorgelegt wurde: ... die kommentierte Übersetzung mittelalterlicher islamischer astronomischer Werke ..." Placidus Fixlmillner Johann Georg Palitzsch 275. Geburtstag von Johann Georg Palitzsch Felix Donat Kyd ... White, Frederick William George- Biographical entry Cf. http://www.science.org.au/academy/memoirs/casey.htm :
Euophryinae
Saitis Semnolius Servaea Sidusa Siloca Spilargis Stoides Talavera Tariona ThianiaThorelliola Thyenula Tylogonus Udvardya zenodorus Unidentified Euophryinae.
http://tolweb.org/tree?group=Euophryinae&contgroup=Salticidae
La Domus Aurea
Translate this page Verum omnem amplitudinem statuarum eius generis uicit aetate nostra zenodorus Mercuriofacto in ciuitate Galliae Aruernis per annos decem, Hs quater centies
http://members.xoom.virgilio.it/AndreaZoia/approfondimenti/domus.aurea2.htm

Extractions: XXXIV Verum omnem amplitudinem statuarum eius generis uicit aetate nostra Zenodorus Mercurio facto in ciuitate Galliae Aruernis per annos decem, Hs quater centies centena milia manupretii; postquam satis artem ibi adprobauerat, Romam accitus a Nerone, ubi destinatum illius principis simulacro colossum fecit CXIX pedum longitudine, qui dicatus Soli uenerationi est, damnatis sceleribus inius principis. Mirabamur in officina non modo ex argilla similitudinem insignem, uerum et de paruis admodum surculis quod primum operis instaurati fuit. Ea statua indicauit interisse fundendi aeris scientiam, cum et Nero largiri aurum argentumque paratus esset et Zenodorus scientia fingendi caelandique nulli ueterum postponeretur. La statua bronzea, alta più di 35 metri, raffigurava Nerone con attributi solari e si ispirava, con ogni probabilità, al colosso di Rodi. L'imperatore era rappresentato nudo e con il braccio sinistro piegato per sorreggere una sfera, il destro proteso in avanti. Sul capo portava una corona composta da sette raggi, lunghi ben sei metri ciascuno. Le uniche raffigurazioni che ci rimangano dell'immane colosso sono state ritrovate su alcune monete degli imperatori Gordiano III ed Alessandro Severo.

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