02784nam a22003495a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200160016708400150018310000270019824501400022526000820036530000340044733600260048133700260050733800360053334700240056949000560059350600660064952015200071565000350223565000310227070000340230185600320233585600670236794-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20081201sz fot ||| 0|eng d a978303719559870a10.4171/0592doi ach0018173 7aPBX2bicssc a01-xx2msc1 aBeery, Janet,eauthor.10aThomas Harriot’s Doctrine of Triangular Numbers: the ‘Magisteria Magna’h[electronic resource] /cJanet Beery, Jacqueline Stedall3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (144 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aHeritage of European Mathematics (HEM) ;x2523-52141 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThomas Harriot (c. 1560–1621) was a mathematician and astronomer, known
not only for his work in algebra and geometry, but also for his
wide-ranging interests in ballistics, navigation, and optics (he
discovered the sine law of refraction now known as Snell’s law).
By about 1614, Harriot had developed finite difference interpolation
methods for navigational tables. In 1618 (or slightly later) he composed
a treatise entitled ‘De numeris triangularibus et inde de
progressionibus arithmeticis, Magisteria magna’, in which he derived
symbolic interpolation formulae and showed how to use them. This
treatise was never published and is here reproduced for the first time.
Commentary has been added to help the reader to follow Harriot’s
beautiful but almost completely nonverbal presentation. The introductory
essay preceding the treatise gives an overview of the contents of the
‘Magisteria’ and describes its influence on Harriot’s contemporaries and
successors over the next sixty years. Harriot’s method was not
superseded until Newton, apparently independently, made a similar
discovery in the 1660s. The ideas in the ‘Magisteria’ were spread
primarily through personal communication and unpublished manuscripts,
and so, quite apart from their intrinsic mathematical interest, their
survival in England during the seventeenth century provides an important
case study in the dissemination of mathematics through informal networks
of friends and acquaintances.07aHistory of mathematics2bicssc07aHistory and biography2msc1 aStedall, Jacqueline,eauthor.40uhttps://doi.org/10.4171/059423cover imageuhttps://www.ems-ph.org/img/books/harriot_mini.jpg