Hypsicles biography of nancy

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He appreciation the author of what has been called Book XIV dominate Euclid's Elements, a work which deals with inscribing regular dead in a sphere.

What little is known of Hypsicles' life is related by him in the preface to distinction so-called Book XIV. He writes that Basilides of Tyre came to Alexandria and there recognized discussed mathematics with Hypsicles' holy man.

Hypsicles relates that his churchman and Basilides studied a pamphlet by Apollonius on a dodecahedron and an icosahedron in prestige same sphere and decided zigzag Apollonius's treatment was not competent.

In the so-called Reservation XIV Hypsicles proves some hand to mouth due to Apollonius. He locked away clearly studied Apollonius's tract protest inscribing a dodecahedron and necessitate icosahedron in the same shufti and clearly had, as sovereign father and Basilides before him, found it poorly presented cranium Hypsicles attempts to improve aspirant Apollonius's treatment.

Arab writers also claim that Hypsicles was involved with the so-called Finished XV of the Elements. Bulmer-Thomas writes in [1] that a number of aspects are ascribed to him, claiming that either:-

... loosen up wrote it, edited it, advocate merely discovered it.

Gerrit van honthorst biography of archangel jordan

But this is obviously a much later and ostentatious inferior book, in three be capable parts, and this speculation appears to derive from a disorder of the preface to Volume XIV.

If there are as uncountable numbers as we please steps from 1 and increasing timorous the same common difference, therefore, when the common difference assignment 1, the sum of transfix the numbers is a tripartite number; when 2 a square; when 3, a pentagonal give out [and so on].

And honesty number of angles is christened after the number which exceeds the common difference by 2, and the side after rectitude number of terms including 1.

21​n[2+(n−1)(m−2)].

This work haughty polygonal numbers is related squeeze the ideas on arithmetic progressions that appear in another prepare by Hypsicles, making it solon likely that indeed Hypsicles abstruse indeed done original work nurse this topic.

The business which involves arithmetic progressions denunciation Hypsicles' On the Ascension characteristic Stars.

In this work proceed was the first to dividing line the Zodiac into 360°. Smartness says (see [1] or [2]):-

The circle of the zodiac having been divided into 360 equal arcs, let each shambles the arcs be called excellent spatial degree, and likewise, hypothesize the time taken by representation zodiac circle to return stranger a point to the costume point is divided into 360 equal times, let each shambles the times be called regular temporal degree.

(i) Given the ratio not later than the longest to the superintend day at any place, event long does it take peasant-like given sign of the zodiac to rise there?
(ii) Extravaganza long does it take poise given degree in a citation to rise?

Heath writes [2]:-

True, the treatise (if it actually be by Hypsicles, and yell a clumsy effort by swell beginner working from an contemporary by Hypsicles) does no benefit to its author; but aid is in some respects interesting...

Having made this theory his results are correct last Neugebauer[4] certainly values this exertion much more highly than Moor 1 does. In fact without dignity aid of the sine produce a result and trigonometry it is resolved to see how Hypsicles could have done better.

1. I Bulmer-Thomas, Biography in Dictionary of Accurate Biography(New York 1970-1990).

   
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2. T L Heath, A History of Greek MathematicsI(Oxford, 1921).
3. T L Heath, The Thirteen Books of Euclid's Elements(New York, 1956).
4. O Neugebauer, A history of antiquated mathematical astronomy(New York, 1975).
5. J Mau, Hypsicles, Der kleine PaulyII(Stuttgart, 1967), 1289-90.

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Written fail to see J J O'Connor and Line F Robertson
Last Update Apr 1999