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.ukans.edu/history/index/europe/ancient_rome/L/Roman/Texts/Pliny_the_E
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.
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 HJ 321) considers i9dru/qh 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 A.D.
Christian History Handbook: Ancient: Appendix IV Then Cleopatra stuck a deal with an Iturean named zenodorus to be the residentadministrator evidently over Heliopolis, Chalcis, Panaion, Ulatha and Abila. http://www.sbuniv.edu/~hgallati/ht3463aa04.html
Pappus He compares the areas of figures with equal perimeters and volumes of solids withequal surface areas, proving a result due to zenodorus that the sphere has http://www.stetson.edu/~efriedma/periodictable/html/Pu.html
Extractions: Our knowledge of Pappus's life is almost nil. It appears that he was born in Alexandria and lived there all his life. A reference to Pappus in Proclus's writings says that he headed a school there. Pappus's major work in geometry is Synagoge , a collection of mathematical writings in 8 books thought to have been written in around 340. Obviously written with the object of reviving the classical Greek geometry, it covers practically the whole field. It is, however, a handbook or guide to Greek geometry rather than an encyclopaedia. It was intended to be read with the original works rather than to enable them to be dispensed with. Book 1 covered arithmetic and is now lost. Book2 is partly lost, but the remaining part deals with Apollonius's method for dealing with large numbers. The method expresses numbers as powers of 10,000. Book 3 is divided by Pappus into four parts. The first part looks at the problem of finding two mean proportionals between two given straight lines. The second part gives a construction of the arithmetic, geometric and harmonic means. The third part describes a collection of geometrical paradoxes which Pappus says are taken from a work by Erycinus. The final part shows how each of the 5 regular polyhedra can be inscribed in a sphere. Book 4 contains properties of curves including the spiral of Archimedes and the quadratrix of Hippias and includes his trisection methods. In Book 5 he discusses the 13 semiregular solids discovered by Archimedes. He compares the areas of figures with equal perimeters and volumes of solids with equal surface areas, proving a result due to Zenodorus that the sphere has greater volume than any regular solid with equal surface area. He also proves the related result that, for two regular solids with equal surface area, the one with the greater number of faces has the greater volume.
Domus Aurea - Wikipedia, The Free Encyclopedia Nero also commissioned from the Greek zenodorus a colossal 37 meter bronze statueof himself, dressed in the garb of the Roman sungod Apollo, the Colossus http://en.wikipedia.org/wiki/Domus_Aurea
Extractions: The Domus Aurea Latin for "Golden House") was a large palace built by the Roman emperor Nero after the fire that devastated Rome in AD. Built (of brick, not marble as is sometimes imagined), in the few years between the fire and Nero's suicide in 69 AD, the extensive gold-leaf that gave it its name was not the only extravagant element of its decor: stuccoed ceilings were applied with semi-precious stones and veneers of ivory. Pliny watched it being built ( Natural History xxxvi. 111). rus in urbe, bronze statue of himself, dressed in the garb of the Roman sun-god Apollo , the Colossus Neronis, and placed it just outside the main palace entrance. The colossus was revamped with the heads of several succeeding emperors before Hadrian moved it to the Flavian Amphitheater. This building took the name " Colosseum " in the Middle Ages, after the statue nearby. The name stuck. Romans excelled at the subversive art of graffiti . Someone inscribed a wall ROMA DOMUS FIET: VELOS MIGRATE QUIRITES SINON ET VEIOS OCCUPET ISTA DOMUS "Rome will become a dwelling house; to
Extractions: Citation Information This supplement provides some general indications of Aristotle's awareness and participation in mathematical activities of his time. Here are twenty-five of his favorite propositions (the list is not exhaustive). Where a proposition occurs in Euclid's Elements , the number is given, * indicates that we can reconstruct from what Aristotle says a proof different from that found in Euclid). Where the attribution is in doubt, I cite the scholar who endorses it. In many cases, the theorem is inferred from the context. In a given circle equal chords form equal angles with the circumference of the circle ( Prior Analytics i.24; not at all Euclidean in conception) The angles at the base of an isosceles triangle are equal ( Prior Analytics i.24; Eucl. i.5*). The angles about a point are two right angles ( Metaphysics ix 9; Eucl. follows from i def. 10). If two straight-lines are parallel and a straight-line intersects them, the interior angle is equal to the exterior angle (
MAXIMA AND MINIMA hyperbola. Some remarkable theorems on maximum areas are attributedto zenodorus, and preserved by Pappus and Theon of Alexandria. http://21.1911encyclopedia.org/M/MA/MAXIMA_AND_MINIMA.htm
Extractions: MAXIMA AND MINIMA 1. Of polygons of n sides with a given perimeter the regular polygon encloses the greatest area. 2. Of two regular polygons of the same perimeter, that with the greater number of sides encloses the greater area. 3. The circle encloses a greater area than any polygon of the same perimeter. 4. The sum of the areas of two isosceles triangles on given bases, the sum of whose perimeters is given, is greatest when the triangles are similar. 5. Of segments of a circle of given perimeter, the semicircle encloses the greatest area. 6 The sphere is the surface of given area which encloses the greatest volume. Serenus of Antissa investigated the somewhat trifling problem of finding the triangle of greatest area whose sides are formed by the intersections with the base and curved surface of a right circular cone of a plane drawn through its vertex. The next problem on maxima and minima of which there appears to be any record occurs in a letter from Regiomontanus to Roder (July 4, 1471), and is a particular numerical example of the problem of finding the point on a given straight line at which two given points subtend a maximum angle. N. Tartaglia in his General Irattalo de numeri et mesuri (c. 1556) gives, wit hout, proof, a rule for dividing a number into two parts such that the continued product of the numbers and their difference is a maximum. Fermat investigated maxima and minima by means of the principle that in the neighborhood of a maximum or minimum the differences of the values of a function are insensible, a method virtually the same as that of the differential calculus, and of great use in dealing with geometrical maxima and minima. His method was developed by Huygens, Leibnitz, Newton and others, and in particular by John Hudde, who investigated maxima and minima of functions of more than one independent variable, and made some attempt to discriminate between maxima and minima, a question first definitely settled, so far as one variable is concerned, by Cohn Maclaurin in his Treatise on Fluxions (1742). The method of the differential calculus was perfected by Euler and Lagrange.
Herod The Great: 37-4 BC To show appreciation, Herod built a temple for Augustus at zenodorus. He reducedmore taxes for those displeased with his emphasis on GrecoRoman culture. http://campus.northpark.edu/history/WebChron/MiddleEast/HerodGreat.CP.html
Extractions: Herod the Great Back to Ancient Israel Chronology In 63 BC, Romans incorporated Judah (what is now Palestine) into their empire as the province of Judea and placed the Jewish lands under kings. The Herodian dynasty, a family of Jews who gained favor with the Romans, was appointed to these kingships. The Herodian family ruled over Palestine from 40 BC until around 100 AD. The most famous member of this family was Herod the Great, who ruled from 37 to 4 BC. He rebuilt Jerusalem , including the temple, and promoted Hellenistic culture. Herod was an ideal medium for the empire. His Jewish ancestry gave him identification with the Jewish culture and his close friendships with the Romans allowed him identification with them as well. His rise to power came through many intricately designed connections to the Romans and were spurred on by his desire to be the "king of the Jews." Julius Caesar defeated Pompey in 48 BC and made Hyrcanus II the high priest and Antipater II the administrator of Judea. Antipater II appointed his second son, Herod, as governor of Galilee. At 25 years of age Herod had already gained the admiration of both the Jews and the Romans for his leadership skills. Herod become involved with Roman affairs in Syria when in Damascus he joined Sextus Caesar, who appointed him governor of Syria. Herod proved to Rome that he was an able leader in collecting taxes and suppressing revolts. After Julius Caesar was murdered in 44 BC, Cassius assumed leadership in Syria and reappointed Herod as governor to collect more revenue.
Luc 3, Notes la Trachonitide l Auranitide et partie du domaine de zenodorus(AJ XVII http://www.ifrance.com/bezae/Luc/ch3/3_b.html
Extractions: Luc,codex Bezae,notes ch. III En eti de pentekaidekatw thV hgemoniaV Tiberiou epitropeuontoV Pontiou Pilatou thV IoudaiaV. procurateur Epitropeuw : un verbe courant, repris dans le vocabulaire administratif pour certains dirigeants qui avaient une ville ou une province sous leur tutelle. Le subtantif epitropoV procurator epitropoV , Tacite, procurator epitropoV epitropeuontoV hgemwn Dans les autres manuscrits, le verbe hgemoneuw Par une annotation en marge du texte " kata Takitou epitropeuontos ", un scribe faisait le rapprochement entre epitropeuontoV epitropeuontos tetrarcountoV Bibliogr.: H.J. Manson, Geek terms for Roman Institutions, a lexicon and analysis, Toronto 1974. P.Horovitz, Essai sur les pouvoirs des procurateurs gouverneurs , dans Revue Belg. philo. Hist., XVII,1938,, p53-62; , dans ,III,XIII,1939,p47-65,218-237. M. Sartre, l'occupation romaine de la Palestine , dans et http://www.stolaf.edu/people/kchanson/pilate.html , pour respecter le nombre des 33 lignes par page. Filippou de tou adelfou autou tetrarcountoV thV ItouraiaV kai TracwnitidoV cwraV.
Famous Mathematicians With A Z Kazimierz Zarankiewicz Stanislaw Zaremba Oscar Zariski Hans Zassenhaus Chris ZeemanEdouard Zeckendorf Efim Zelmanov zenodorus) ErnstZermelo Hieronymous http://www.famousmathematician.com/az/mathematician_Z.htm
Lacus_en Nero also placed in his palace a colossal bronze statue of himself (120 feet high,work of zenodorus), whose face was later modified many times to represent http://www.the-colosseum.net/architecture/lacus_en.htm
Extractions: LACVS Once there was a lake The site of the Colosseum is in fact a depression among the hills of Rome : the Palatine on its south-western side, the Velia on the western side, the last slopes of the Esquiline hill, also called Colle Oppio (now a park) on the northern side and the Celio on the Eastern side. The Velia Piazza Venezia to the Colosseum cutting through the forums of old Rome. Mussolini demanded a straight road from Piazza Venezia to the Colosseum, and that was the end of the Velia. Right: Granet, The Palatine Hill The valley collected the waters, which created a marsh or a lake, depending on the season. The small lake was fed by the waters of the Rio Labicano, a stream flowing down the Labicana valley, more or less along modern day Via Labicana. The stream can still be seen underground when visiting the Church of St. Clemente in Via di San Giovanni . There you can descend about 30 feet under modern ground level and walk on the cobblestones of old Roman alleys, enter shops and houses, visit a Mithraic temple and listen to the soothing sound of running water. The stream is still there and the water runs clear and fast, enclosed inside a conduct built in the 19 th century in order to drain the underground of the Basilica.
Circle good understanding of the problem. In this knowledge, he followeda book of zenodorus (180 BC) 6) . Some relations of the circle http://www.2dcurves.com/conicsection/conicsectionc.html
Extractions: The circle is the curve for which the curvature is a constant, in a Whewell equation it can be written as s= f Because of its symmetry the circle is considered as the perfect shape. It is the symbol for the total symmetry of the divine (sic!). The Greek scholar Proclus (500 AC) wrote: "the circle is the first, the simplest and most perfect form". As Christian symbol it represents eternity, and the sleeping eye of God (Genesis 1:2). the breast of a mother, a tuba, plums and cherry flan. More rational the circle can be described as the ellipse, where the two foci coincide. Or as the collection of points with equal distance to a (center) point. At the top of this page we see the polar equation of a unity circle with radius 1 and as center the origin.
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 :
American Academy In Rome - MAAR Volume 46 Portraits, Plots, and Politics Damnatio memoriae and the Images of ImperialWomen Eric Varner. zenodorus Colossus of Nero Fred C. Albertson. http://www.aarome.org/publications/toc46.htm
TLG: TLG Date Sorting (3 BC?/AD 1). When it is simply impossible to suggest a date, the wordIncertum has been used instead, as for zenodorus Trag. Incertum http://www.tlg.uci.edu/help/Doc004.html
Extractions: Last Revised: 2000-5-12 The following defines the sorting order for dates in the TLG Canon as used on the TLG CD ROMs and online databases. Thesaurus Linguae Graecae: Canon of Greek Authors and Works. 3rd edn. Oxford: Oxford University Press. pp. xix-xx.) Arabic numerals in cardinal form indicate the century of an author's floruit . A dash between numerals indicates that the author's floruit spans the two centuries. Thus, the date given for Strabo Geogr. is 1 B.C.-A.D. 1, based upon the approximate dates of his sojourns in Rome (44-35 B.C., again ca. 31 B.C., and a third time in 7 B.C.), Egypt (25 until ca. 19 B.C.), and Amasia (ca. 7 B.C. until his death sometime after A.D. 21.) When no firmer evidence can be adduced, a virgule between numerals is used to suggest the earliest and latest possible dates. Thus, the date given for Alciphron Rhet. et Soph. is A.D. 2/3, meaning that the earliest possible date for his letters (though purportedly written by Athenian fishermen, farmers, parasites, and courtesans of the fourth century B.C.) is the second century and the latest is the third. When only a terminus ante quem is discernable, or at least logically to be assumed, this is indicated by, for instance
Photos For ID Rancho Grande (PRB) Rubyeye 2 Rancho Grande (PRB). Unknown Firetip (Rancho Grande)05/12/03 (HB) (like) Pyrrhopyge zenodorus (Rancho Grande) 5/12/03 (PRB) http://home.earthlink.net/~azbutterfly/Photos_For_ID.html
Previous Questions websites for proof http//www.cutthe-knot.com/do_you_know/isoperimetric.shtml http//www-gap.dcs.st-and.ac.uk/~history/Mathematicians/zenodorus.htmlPrevious http://www.gomath.com/Questions/question.php?question=20971
Faculty :: Fred C. Albertson 1991. Articles zenodorus s Colossus of Nero, Memoirs of theAmerican Academy in Rome 46 (2001) 95118. Three Palmyrene http://www.people.memphis.edu/~artdept/falbertson.html