21. Zenodoro Zenodorus Translate this page Zenodoro/us (200 - 140 a. C) Astrônomo e matemático grego nascidoem Atenas, que trabalhou em Arcadia e é mais conhecido por http://www.sobiografias.hpg.ig.com.br/Zenodoro.html

Zenodor o us (200 - 140 a. C) Diocles Philonides e Pappus . Pappus fez uso do de Alexandria . Em seguiu o estilo de Euclides e de Arquimedes Nova B U S C A :

22. Caterpillar Food Plants GO TO FOOD PLANT SUMMARY Costa Rican Hesperiidae checklist Pyrrhopygezenodorus Displaying records 1 to 20 of 687 records VOUCHER http://janzen.sas.upenn.edu/caterpillars/dblinks/cklistfd.lasso?herbsp=Pyrrhopyg

23. Caterpillar Food Plants SUBFAMILY, CATERPILLAR SPECIES. 92SRNP-278, Clusiaceae, Vismia baccifera,Hesperiidae, Pyrrhopyginae, Pyrrhopyge zenodorus. 93-SRNP-5284.1, http://janzen.sas.upenn.edu/caterpillars/dblinks/cklistfd.lasso?herbsp=Pyrrhopyg

24. Pythagoras : Wiskundetijdschrift Voor Jongeren WISKUNDETIJDSCHRIFT VOOR JONGEREN. Gevonden zenodorus. Gevonden artikelenin archief Het spiegelingsprincipe Welke driehoek heeft http://www.pythagoras.nu/mmmcms/public/zoek1096.html

voorpagina rekenwerk veelvlakken wis-spellen ... English WISKUNDETIJDSCHRIFT VOOR JONGEREN Gevonden : Zenodorus Gevonden artikelen in archief: Het spiegelingsprincipe Welke driehoek heeft van alle driehoeken met een gegeven omtrek de grootste oppervlakte? Dat is natuurlijk een gelijkzijdige driehoek. Deze bewering kun je bewijzen met het spiegelingsprincipe. Zie archief: jaargang 37, nummer 1, oktober 1997 (totaal gevonden: 1) pythagoras op papier laatste nummer vorig nummer archief over pythagoras ... oude jaargangen

25. A_a_zenodorus Agrias amydon zenodorus. Rio Huallaga Valley, Peru form flavicellus male, Jepalico, Peru form zenodorus male. Toantins, Brasil http://home.att.net/~agrias/A_a_zenodorus.htm

Agrias amydon zenodorus Rio Huallaga Valley, Peru form "flavicellus" male Jepalico, Peru form "zenodorus" male Toantins, Brasil form "flavicellus" female Toantins, Brasil form "flavicellus" female verso Pano Teno, Ecuador red form "zenodorus" Pano Teno, Ecuador form "zenodorus" male verso Banos, Ecuador form "inca" TYPE French Museum Moyabamba, Ecuador form "inca" male

26. Pythagoras' Database: Zoeken U zocht op Trefwoorden, zenodorus. Er zijn is 1 artikel dat aan dezecriteria voldoet. 100% oktober 1997, Het spiegelingsprincipe, door http://pythwww.math.leidenuniv.nl/mmmcms/admin/intern/zoeken.php?trefwoord=Zenod

27. Salticidae Jumping Spiders The spider was hidden beneath a sheet of silk. Genus Zenodores. zenodorus ZZ048,zenodorus ZZ048. zenodorus ZZ063, zenodorus ZZ063. Zenodores ZZ044, Zenodores ZZ052. http://www.xs4all.nl/~ednieuw/australian/salticidae/Salticidae.html

Salticidae Jumping Spiders Home Most salticids, 4000 or more species, live in the tropics. In Australia 76 genera and 252 described species are present. The spiders are daylight hunters and can be easily spotted. Their size is relatively small (3-20 mm) but most of them are smaller than 10 mm. A lot of them are colored beautifully. The salticids live for the most part on vegetation. The rectangular thorax, stout body, the rather short legs, their distinctive eye arrangement and their jumping capabilities make them one of the most easily recognizable families. Some species exhibit an amazing resemblance with ants and are called "ant like " spiders. They belong to the genus Myrmarachne. This one was found in Australia. Because of its resemblance to ants, it can walk between them without being attacked. The eyesight is enhanced like a zoom lens and it is capable to adjust its looking angle from 10 to 60 degrees. In experiments it was shown that the spider is capable to distinct dangerous insects and prey. The eyes are also capable to see color. After the object is recognized as eatable the spider carefully moves towards it victim As you can see the on the picture they also catch prey, much bigger than themselves. It was spectacular to see the little Salticus scenicus catching the big fly.

28. Crosswalk.com INTRODUCTION HOW HEROD SENT HIS SONS TO ROME; HOW ALSO HE WAS ACCUSED BY zenodorusAND THE GADARENS, BUT WAS CLEARED OF WHAT THEY ACCUSED HIM OF AND WITHAL http://www.biblestudytools.net/History/BC/FlaviusJosephus/?book=Ant_15&chapter=1

29. History : Josephus' Writings - Book 15, Ch. 10 HOW HEROD SENT HIS SONS TO ROME; HOW ALSO HE WAS ACCUSED BY zenodorus AND THEGADARENS, BUT WAS CLEARED OF WHAT THEY ACCUSED HIM OF AND WITHAL GAINED TO http://www.godrules.net/library/flavius/flaviusb15c10.htm

JOSEPHUS' WRITINGS - BOOK 15, CH. 10 PREVIOUS CHAPTER NEXT CHAPTER HELP HOW HEROD SENT HIS SONS TO ROME; HOW ALSO HE WAS ACCUSED BY ZENODORUS AND THE GADARENS, BUT WAS CLEARED OF WHAT THEY ACCUSED HIM OF AND WITHAL GAINED TO HIMSELF THE GOOD-WILL OF CAESAR. CONCERNING THE PHARISEES, THE ESSENS AND MANAHEM. 1. WHEN Herod was engaged in such matters, and when he had already re-edified Sebaste, [ Samaria ,] he resolved to send his sons Alexander and Aristobulus to Rome , to enjoy the company of Caesar; who, when they came thither, lodged at the house of Pollio, (19) who was very fond of Herod 's friendship ; and they had leave to lodge in Caesar's own palace , for he received these sons of Herod with all humanity , and gave Herod leave to give his, kingdom to which of his sons he pleased; and besides all this, he bestowed on him Trachon, and Batanea, and Auranitis, which he gave him on the occasion following: One Zenodorus (20) had hired what was called the house of Lysanias, who, as he was not satisfied with its revenues, became a partner with the robbers that inhabited the Trachonites, and so procured himself a larger income; for the inhabitants of those places lived in a mad way, and pillaged the

30. Ancient Greek Optimization Problems hyperbola. Some remarkable theorems on maximum areas are attributedto zenodorus, and preserved by Pappus and Theon of Alexandria http://www.mlahanas.de/Greeks/Optimization.htm

Optimization Geometric Optimization As Geometry plays a important role in Greek Ancient Science it is not very surprising that optimization problems have been considered and solved. Euclid, book III of the Elements finds the greatest and least straight lines that can be drawn from a point to the circumference of a circle, and in book VI. (in a proposition generally omitted from editions of his works) finds the parallelogram of greatest area with a given perimeter. Apollonius investigated the greatest and least distances of a point from the perimeter of a conic section, and discovered them to be the normals, and that their feet were the intersections of the conic with a rectangular hyperbola. Some remarkable theorems on maximum areas are attributed to Zenodorus, and preserved by Pappus and Theon of Alexandria: Of polygons of N sides with a given perimeter the regular polygon encloses the greatest area. Of two regular polygons of the same perimeter, that with the greater number of sides encloses the greater area. The circle encloses a greater area than any polygon of the same perimeter.

31. Pappus quadratrix. Book V reviewed the plane tessellation problem; the 13semiregular solids of Archimedes; and the results of zenodorus. http://www.mlahanas.de/Greeks/Pappus.htm

Pappus Synagoge th October 320 AD. Commandinus provided the first translation into Latin 1589. Others like Wallis followed until 1878 when Friedrich Hultsch provided a complete translation. The Mathematical Collections of Pappus in a translation of Federico Commandino (1589). An Image from a Vatican Exhibition Although there is little originality, Pappus showed great understanding in all topics. Book I and II covered Arithmetics. Book III contained a range of topics: mean proportional; arithmetic, geometric and harmonic means; some geometrical paradoxes; inscription of the 5 Regular Polyhedra in a Sphere. Book IV treated curves such as spirals and the quadratrix. Book V reviewed the plane tessellation problem; the 13 semi-regular solids of Archimedes; and the results of Zenodorus. Book VI is on Astronomy and Book VIII is on Mechanics. Pappus's Hexagonal Theorem Book VII contained 'Pappus Problem' (now known as Pappus' Hexagon Theorem). If ABC and DEF are straight lines; and X, Y, Z are the intersections of AE with BD, AF with CD, BF with CE respectively. Then XYZ is a straight line. Pappus's Centroid Theorem Volume of revolution = (area bounded by the curve) * (distance traveled by the center of gravity) Eric W. Weisstein. "Pappus's Centroid Theorem." From

32. Octavian, Roman Imperatorial Coins Of, At WildWinds.com Text, Image. RPC 4775, F Quintillius Varus, Æ21 of Octavian zenodorus fromChalkis. Head of zenodorus left / Head right, with countermark VAR monogram. http://www.wildwinds.com/coins/imp/octavian/i.html

Browsing Roman Imperatorial Coins of Octavian RIC 254b / Sear 1552 Click here for the Octavian page with thumbnail images. RIC 90 *SAMUS* Octavian AR denarius Temple/Caesar Text Image RIC 94 Text Image RIC 250a Octavian Denarius. Italian mint, 32 - 31 BC. Diademed head of Venus right / CAESAR DIVI F, Octavian in military attire advancing left, his right hand extended and holding transverse spear in left. (One example) RIC 251 Octavian AR Denarius. Diademed head of Venus right / CAESAR-DIVI F across field, Octavian standing left, holding spear. RSC 70. ... Reverse RIC 270 Octavian denarius. Laureate head right, thunderbolt behind / Octavian on curile chair with Victoriola. BMC 637, RSC 116. (One example) RIC 271 Octavian Denarius. 29-27 BC. Laureate bust right / IMP - CAESAR, statue of Octavian on rostral column. RSC 124. ... Reverse RPC 518 Octavian Æ 30mm of Narbo, Gaul. c 40 BC. Bare head right / Prow of galley right. Text Image RPC 620 Octavian sestertius(?). Bare head of Octavian right / laureate head of Julius Ceasar. Cohen 3, Syd 1335. (5 examples) RPC 621 Octavian Æ Sestertius. Italian mint, ca 38 BC. DIVI F, bare head right, star before / DIVOS IVLIVS in laurel wreath. Cr535/2. ... Image RPC 4774.1 Text Image RPC 4774 Octavian AE19 of Chalcis. 32/31 BC. Bare head of Octavian right / Bare head of Zenodoros left. RPC 4774, SG 5899.

33. His Prosperity the territories of Trachonitis, Batanea, and Auranitis which had been occupiedby nomad robber tribes with whom the neighboring tetrarch zenodorus had made http://www.bible-history.com/herod_the_great/HERODHis_Prosperity.htm

Herod the King 25-14 B.C. This period is marked with splendor and enjoyment but there were also moments of great disturbance. The first thing mentioned about this period by Josephus is when Herod violated the Jewish law by introducing the quinquennial games in honor of Caesar and in so doing he built great theaters, amphitheaters, and race courses for both men and horses. Some time later, around 24 B.C., Herod built for himself a royal palace and also built or rebuilt many fortresses and Gentile temples, including the rebuilding of Straton's Tower which was renamed Caesarea (Jos. Antiq. xv. 8. 5-9. 6; 292-341). Of course, his greatest building was the Temple in Jerusalem which was begun in 20 or 19 B.C. Josephus considers it the most noble of all his achievements (Jos. Antiq. xv. 11. 1 ; 3 80). Rabbinic literature states: "He_who has not ,seen the Temple of Herod clever seen a beautiful building" -T BT: Baba Bathraa`-Tlso, It is suggested that it was his "atonement for having slain so many sages of Israel" -Midrash : Num 14:8 Also, during this period, he took great interest in culture and surrounded himself with a circle of men accomplished in Greek literature and art. The highest offices of state were entrusted to Greek rhetoricians, one of whom, Nicolas of Damascus, was Herod's instructor. He was Herod's advisor and was always included in Herod's dealings both before and after his death. Herod received instructions from him in philosophy, rhetoric, and history.

34. A Commentary On The NT--Chorographical Notes It is hard to say whether this house of Zenon, have any relation withzenodorus the robber. Josephus, in the place above quoted, mentions http://philologos.org/__eb-jl/notes.htm

From the Talmud and Hebraica by John Lightfoot Philologos Religious Online Books Philologos.org Back Table of Contents A Commentary on the New Testament from the Talmud and Hebraica John Lightfoot Chorographical Notes Chapter 1: Of the places mentioned in Luke 3. Whether Perea may not also be called Galilee. Some things in general concerning the country beyond Jordan. Trachonitis Auranitis ... 2 Samuel 20:18 discussed. Chapter 2: Sarepta. Zarephath, Obadiah verse 20, where. Sepharad, where. The situation of Sarepta. Chapter 3: Nain, Luke 7:11. Concerning Nain near Tabor, shewn to strangers. Concerning the Nain in Josephus and the Rabbins. Engannim Chapter 4: Emmaus, Luke 24. Several things about its name and place. Its situation. Some story of it. Also of Timnath and mount Gilead, Judges 7:3. Chapter 1 Before we make any particular inquiries into the countries mentioned Luke 3:1, it will not be amiss to dip into history a little more generally. "Augustus Caesar received Herod's sons, Alexander and Aristobulus, upon their arrival at Rome, with all the kindness imaginable, granting a power to Herod to establish the kingdom in which of his sons he pleased: yea, and moreover, gave him the region of Trachonitis, Batanea, and Abranitis

35. Luke According to Josephus, Philip had received Batanea, Trachonitis, Auranitis, andsome parts of zenodorus’s domain around Panias (War 2.95; Ant. 17.319). http://www.biblicalheritage.org/People/luke.htm

BIBLICAL HERITAGE CENTER M aking our world a better, happier and safer place by providing our generation accurate information about the past HOME l BHC PLEDGE l ... MAKE AN ONLINE DONATION Tell a friend about our site click here "Science without religion is lame, religion without science is blind." (Albert Einstein) Was Luke Familiar With The Land? I turaeans Ituraea Herod Philip Ituraea Herod Philip Ituraea Herod Philip " T etrarch of the region of Ituraea and Trachonitis" (Luke 3:1). A ccording to Josephus, Philip had received Batanea Trachonitis Auranitis Panias War Ant. 17.319). Both Luke and Josephus appear to be referring to the same area. B Ituraea Herod Philip Ituraea Herod Philip Ituraea Herod Philip " T etrarch of the region of Ituraea and Trachonitis" (Luke 3:1). A ccording to Josephus, Philip had received Batanea Trachonitis Auranitis Panias War Ant. 17.319). Both Luke and Josephus appear to be referring to the same area. B Ituraea Herod Philip Ituraea Herod Philip Ituraea Herod Philip "

36. Wars Of The Jews Ib the region called Trachonitis, and what lay in its neighborhood, Batanea, and thecountry of Auranitis; and that on the following occasion zenodorus, who had http://www.meta-religion.com/World_Religions/Christianity/History/Flavius_Joseph

to promote a multidisciplinary view of the religious, spiritual and esoteric phenomena. About Us Links Search Contact ... Back to Christian History Religion sections World Religions New R. Groups Ancient Religions Spirituality ... Extremism Science sections Archaeology Astronomy Linguistics Mathematics ... Contact The Web Metareligion More sections: Subscribe to the Metareligion Newsletter Submit your site Banners Index ... Polls Please, help us sustain this free site online. Make a donation using Paypal: The Wars of the Jews Preface Ia Ib IIa ... VII Book Ib CHAPTER 20. HEROD IS CONFIRMED IN HIS KINGDOM BY CAESAR, AND CULTIVATES A FRIENDSHIP WITH THE EMPEROR BY MAGNIFICENT PRESENTS; WHILE CAESAR RETURNS HIS KINDNESS BY BESTOWING ON HIM THAT PART OF HIS KINGDOM WHICH HAD BEEN TAKEN AWAY FROM IT BY CLEOPATRA WITH THE ADDITION OF ZENODORUSS COUNTRY ALSO. CHAPTER 21.

37. BeeSource.com | ViewPoint | Lusby | Part 4 structures. The first known research on the structure on honeycomb dealtwith the hexagonal form of the cells by zenodorus, of Sicily. http://www.beesource.com/pov/lusby/part4.htm

Honeybee Comb: Brief History, Size and Ramifications Part 4 From very early times, the comb built by honeybees has been studied and admired as a solution, to the problem of combining light weight and great strength, to be duplicated in the building of structures. The first known research on the structure on honeycomb dealt with the hexagonal form of the cells by Zenodorus, of Sicily. This was done in the 2nd century B.C., right after the time of Archimedes. Zenodorus proved back then that, of the three regular figures that will completely fill a plane surface (namely, the equilateral triangle, the square, and the regular hexagon), the hexagon has the greatest content for a given circumference. Pappus later, around A.D. 500 copying from Zenodorus, also found that bees wisely choose the hexagon form for the cell-mouth which they suspect will contain and hold the most honey for the same expenditure of wax in its construction. He was the first one to put forth the suggestion that honeybees economize wax, a notion believed for many years, though in today's world now known to be far removed from the realities of the matter. After Pappus there was no known study of honeycomb construction until a person by the name of Kepler, an astronomer in 1611, published a very good cell description. He was credited with being the first to notice the rhombs at the base of individual cell construction.

38. BeeSource.com | ViewPoint | Lusby | The Bee World Its author was zenodorus, of Sicily, in the second century BC, shortlyafter the time of Archimedes. zenodorus proved that, of the http://www.beesource.com/pov/lusby/bwjul1921.htm

The Bee World July, 1921 - Pages 37-38 The Structure of Comb. - 1. By MISS ANNIE D. BETTS, B.Sc. From references by the classical writers it is clear that the comb of the honey-bee 500) copied from Zenodorus, and remarked that the bees wisely choose that one of the three forms for the cell-mouth which they suspect will contain most honey for the same expenditure of wax in its construction. This suggestion, that the bees economise wax, grew later into a wonderful myth, far removed from the realities of the matter. The ideal form of the bee's cell - seldom completely realised in actuality - is that of a regular six-sided prism, the base of which is formed of three rhombs of lozenges meeting in a point at the bottom of the cell (see Fig. 13). A'B'C'D'E'F' is the cell-mouth; A'A, B'B, etc., are the edges of the cell; ABOF, CDOB, EFOD are the three rhombs; O being the bottom of the cell. Let us now consider the other side of the comb. From O there starts a cell-edge similar to those at A'A, C'C, or E'E; so that the three rhombs each form part of the base of a different cell on the other side of the comb; A, C, and E being the bottom points of these three cells, and correspending to O in the first cell. The edges B'B, D'D, and F'F are continuous right through the comb from one side to the other; a point that is probably of importance in counecton with the well-known and hitherto unexplained ''pitch'' of the cells.

39. Who Was Who In Roman Times: Data On Persons: Zenodorus austrian literature online Kataloge - zenodorus. zenodorus - 1989. zenodorus - 1987. ZENTRALBAU. ZENTRALBAU - 1989. http://www.romansonline.com/Persns.asp?IntID=2581&Ename=Zenodorus

40. 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

Recent Articles in St Andrews Archive: How do we know about Greekmathematicians? by Antreas P. Hatzipolakis reply to this message post a message on a new topic Back to math-history-list Subject: Recent Articles in St Andrews Archive: How do we know about Greekmathematicians? Author: xpolakis@otenet.gr Date: http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/Greek_sources_2.html APH The Math Forum

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