The 17th century Spain is very advanced culturally and, in certain respects, very refined. Although Spanish culture in the reached an unprecedented peak, mathematics activity in Spain entered a period of decline and did not share in the burst of mathemathical knowledge occurring in other European countries during this century

Lupiáñez, José Luis

Rico, Luis

English

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Spanish	  Heritage	   	   	  ICME12	  SEOUL	  The work of Spanish mathematicians in this century was	  removed	  from	  contemporary	  advances	  in	  Europe,	  possibly	  due	  to	  the	  policy	  of	  intellectual	  isolaCon	  imposed	  at	  the	  end	  of	  the	  reign	  of	  Philip	  II	  	  (conCnued	  by	  his	  successors),	  and	  to	  the	  control	  of	  Catholic	  hierarchy.	  Spain	  does	  maintain	  traits	  of	  genuine	  mathemaCcal	  knowledge,	  however,	  it	  is	  expressed	  with	  the	  greater	  freedom	  in	  Hispanoamerica.	  On	  the	  peninsula,	  the	  mixing	  of	  science	  and	  religion	  prevents	  acceptance	  of	  the	  advances	  of	  the	  scienCﬁc	  revoluCon,	  the	  Copernican	  model	  of	  the	  universe,	  Kepler’s	  laws,	  and	  the	  advances	  of	  analyCc	  geometry	  and	  algebra	  that	  occur	  during	  this	  century.	  The	  Copernican	  system	  was	  excluded	  from	  the	  orthodox	  scienCﬁc	  model	  for	  ideological	  reasons.	  	  ScienCﬁc	  acCvity	  in	  Hispanoamerica	  enjoyed	  more	  degrees	  of	  freedom	  although	  the	  less	  poliCcal	  power	  of	  the	  church	  and	  a	  lower	  level	  of	  intellectual	  acCvity.	  The	  sun’s	  declinaCons	  were	  calculated	  in	  “De	  RevoluConibus”	  (Dominican	  Republic).	  In	  1663,	  Lázaro	  Flórez	  used	  the	  work	  of	  Copernicus	  and	  Tycho	  Brahe	  to	  adapt	  the	  calculaCon	  tables	  to	  the	  Havana	  Meridian.	  	  José Zaragoza	  was	  the	  main	  Spanish	  astronomer	  of	  this	  century.	  	  He	  was	  very	  knowledgeable	  of	  the	  latest	  foreign	  bibliography.	  As	  a	  	  mathemaCcian,	  Zaragoza	  made	  several	  notable	  contribuCons.	  He	  	  introduced	  the	  concept	  of	  a	  geometric	  point	  with	  the	  properCes	  of	  	  the	  physical	  center	  of	  gravity	  for	  a	  system	  of	  weighted	  parts.	  He	  	  demonstrated	  all	  of	  these	  properCes	  with	  Euclidian	  rigor	  and	  applied	  	  this	  knowledge	  to	  solving	  problems	  involving	  the	  calculaCon	  of	  raCos	  	  among	  geometric	  magnitudes.	  Zaragoza	  anCcipated	  Barycentric	  Calculus	  by	  over	  a	  century.	  Antonio Hugo de Omerique was	  one	  of	  the	  most	  important	  Spanish	  	  mathemaCcians	  of	  the	  17th	  century.	  He	  published	  his	  geometric	  Analysis	  in	  1698,	  a	  work	  praised	  by	  Newton	  and	  that	  anCcipates	  some	  results	  of	  the	  analyses	  published	  later,	  although	  the	  work	  had	  hardly	  any	  inﬂuence	  on	  the	  mathemaCcians	  of	  his	  Cme.	  MATHEMATICS IN THE BAROQUE PERIOD IN SPAIN  Dr. Luis Rico and Dr. José Luis Lupiáñez University of  Granada, Spain The	  17th	  century	  Spain	  is	  very	  advanced	  culturally	  and,	  in	  certain	  respects,	  very	  reﬁned.	  Although	  Spanish	  culture	  in	  the	  reached	  an	  unprecedented	  peak,	  mathemaCcs	  acCvity	  in	  Spain	  entered	  a	  period	  of	  decline	  and	  did	  not	  share	  in	  the	  burst	  of	  mathemaCcs	  knowledge	  occurring	  in	  other	  European	  countries	  during	  this	  century.	  Cervantes	  and	  Velázquez	  are	  unique	  examples	  of	  high	  level	  Spanish	  culture	  of	  the	  Cme.	  Both	  exemplify	  the	  disseminaCon	  of	  the	  culture	  of	  mathemaCcs	  in	  Spain	  during	  their	  lives.	  In	  Don	  Quixote,	  Cervantes	  revealing	  his	  knowledge	  about	  mathemaCcs:	  “…	  they	  must	  bring	  	  tangible,	  easy,	  intelligible,	  demonstrable,	  unques=onable	  examples,	  with	  mathema=cal	  proof	  	  that	  cannot	  be	  denied,	  as	  when	  they	  say:	  ‘If	  we	  take	  equal	  parts	  from	  two	  equal	  parts,	  the	  	  parts	  leE	  are	  also	  equal’	  (Part	  I,	  Chapter	  33).	  Baroque Mathematics: from Viète’s death (1603) to Euler’s birth (1707)  In	  execuCng	  his	  work,	  Velázquez	  shows	  mastery	  	  of	  highly	  advanced	  knowledge	  of	  geometry	  in	  his	  	  treatment	  of	  geometric	  forms	  The	  Universal	  Arithme=c	  that	  includes	  the	  greater	  and	  lesser	  art,Common	  and	  Specious	  Algebra,	  published	  in	  Valencia	  in	  1670,	  introduces	  Spain	  for	  the	  ﬁrst	  Cme	  to	  Viète’s	  algorithm	  for	  calculaCng	  the	  roots	  of	  polynomial	  equaCons.	  

Mathematics in the Baroque Period in Spain

http://funes.uniandes.edu.co/2036/1/Rico2012Baroque.pdf

Mathematics in the Baroque Period in Spain

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