Galileo and the Law of Motion Lecture Slides

GALILEO  AND  THE  LAWS  OF  MOTION   Philosophy  is  wriTen  in  this  grand  book,  the   universe,  which  stands  conXnually  open  to  our  gaze.   But  the  book  cannot  be  understood  unless  one  first   learns  to  comprehend  the  language  and  read  the   leTers  in  which  it  is  composed.  It  is  wriTen  in  the   language  of  mathemaXcs,  and  its  characters  are   triangles,  circles,  and  other  geometric  figures   without  which  it  is  humanly  impossible  to   understand  a  single  word  of  it;  without  these,  one   wanders  about  in  a  dark  labyrinth.  [Galileo,  Il   Saggitore,  EN  VI  232,  Disc.&Op.  237-­‐8]   [Law  1]  Each  and  every  thing,  in  so  far  as  it  can,  always   conXnues  in  the  same  state;  and  thus  what  is  once  in   moXon  always  conXnues  to  move.  [Descartes,  Princ..   II.37]       [Law  2]  All  moXon  is  in  itself  recXlinear;  and  hence  any   body  moving  in  a  circle  always  tends  to  move  away   from  the  center  of  the  circle  which  it  describes.    [Princ.   II.39]       [Law  3]  If  a  body  collides  with  another  body  that  is   stronger  than  itself,  it  loses  none  of  its  moXon;  but  if  it   collides  with  a  weaker  body,  it  loses  a  quanXty  of   moXon  equal  to  that  which  it  imparts  to  the  other   body.    [Princ.  II.40]   In  the  beginning  [God]  created  ma3er,  along  with  its  mo8on  and  rest;   and  now,  merely  by  his  regular  concurrence,  he  preserves  the  same   amount  of  mo8on  and  rest  in  the  material  universe  as  he  put  there  in  the   beginning.  …  For  we  understand  that  God's  perfecXon  involves  not  only  his   being  immutable  in  himself,  but  also  his  operaXng  in  a  manner  that  is   always  uTerly  constant  and  immutable.  Now  there  are  some  changes   whose  occurrence  is  guaranteed  either  by  our  own  plain  experience  or  by   divine  revelaXon,  and  either  our  percepXon  or  our  faith  shows  us  that   these  take  place  without  any  change  in  the  creator;  but  apart  from  these   we  should  not  suppose  that  any  other  changes  occur  in  God's  works,  in   case  this  suggests  some  inconstancy  in  God.  Thus,  God  imparted  various   mo8ons  to  the  parts  of  ma3er  when  he  first  created  them,  and  he  now   preserves  all  this  ma3er  in  the  same  way,  and  by  the  same  process  by   which  he  originally  created  it;    and  it  follows  from  what  we  have  said  that   this  fact  alone  makes  it  most  reasonable  to  think  that  God  likewise   always  preserves  the  same  quan8ty  of  mo8on  in  ma3er.  [Princ.  II.36]     The  reason  for  this  second  rule  is  the  same  as  the   reason  for  the  first  rule,  namely  the  immutability   and  simplicity  of  the  operaXon  by  which  God   preserves  moXon  in  maTer.  For  he  always   preserves  the  moXon  in  the  precise  form  in  which  it   is  occurring  at  the  very  moment  when  he  preserves   it,  without  taking  any  account  of  the  moXon  which   was  occurring  a  liTle  while  earlier.  [Princ.  II.39]   Since  God  preserves  the  world  by  the   selfsame  acXon  and  in  accordance  with   the  selfsame  laws  as  when  he  created  it,   the  moXon  which  he  preserves  is  not   something  permanently  fixed  in  given   pieces  of  maTer,  but  something  which  is   mutually  transferred  when  collisions   occur.    [Princ.  II.42]   Nature  …  is  inexorable  and  immutable;  she   never  transgresses  the  laws  [leggi]  imposed   upon  her,  or  cares  a  whit  whether  her   abstruse  reasons  and  methods  of  operaXon   or  understandable  to  men.  [Galileo,  Le1er  to   the  Grand  Duchess,    EN  V  316,  Disc  &  Op.  182]   We  bring  forward  a  brand  new  science   concerning  a  very  old  subject.  There  is  perhaps   nothing  in  nature  older  than  MOTION,  about   which  volumes  neither  few  nor  small  have  been   wriTen  by  philosophers;  yet  I  find  many  essenXals   of  it  that  are  worth  knowing  which  have  not  even   been  remarked,  let  alone  demonstrated.  [Discorsi,   EN  VIII  190]   ProposiXon  II.  Theorem  II   If  a  moveable  descends  from  rest  in   uniformly  accelerated  moXon,  the  spaces   run  through  in  any  Xmes  whatever  are  to   each  other  as  the  duplicate  raXo  of  their   Xmes;  that  is,  are  as  the  squares  of  those   Xmes.  [Discorsi,    EN  VIII  209]   I  say  that  moXon  is  equably  or  uniformly   accelerated  which,  abandoning  rest,  adds   on  to  itself  equal  momenta  of  swiiness  in   equal  Xmes.  [Discorsi,  EN  198,  205]   And  first,  it  is  appropriate  to  seek  out  and  clarify  the   definiXon  that  best  agrees  with  that  which  nature   employs.  Not  that  there  is  anything  wrong  with   invenXng  at  pleasure  some  kind  of  moXon  and   theorizing  about  its  consequent  properXes  …  But   since  nature  does  employ  a  certain  kind  of   acceleraXon  for  descending  heavy  things,  we  decided   to  look  into  their  properXes  so  that  we  might  be  sure   that  the  definiXon  of  accelerated  moXon  which  we   are  about  to  adduce  agrees  with  the  essence  of   naturally  accelerated  moXon.  [Discorsi,  EN  VIII  197]   It  may  also  be  noted  that  whatever  degree  of  speed   is  found  in  the  moveable,  this  is  by  its  nature   indelibly  impressed  on  it  when  external  causes  of   acceleraXon  or  retardaXon  are  removed,  which   occurs  only  on  the  horizontal  plane:  for  on  declining   planes  there  is  cause  of  more  acceleraXon,  and  on   rising  planes,  of  retardaXon.  From  this  it  likewise   follows  that  moXon  in  the  horizontal  is  also  eternal,   since  if  it  is  indeed  equable  it  is  not  weakened  or   remiTed,  much  less  removed.  [Discorsi,  EN  VIII  243]   When  a  projecXle  is  carried  in   moXon  compounded  from  equable   horizontal  and  from  naturally   accelerated  downward  [moXon],  it   describes  a  semiparabolic  line  in  its   movement.  [Discorsi,  EN  VIII  269]   Every  body  consXtuted  in  a  state  of  rest   but  naturally  capable  of  moXon  will  move   when  set  at  liberty  only  if  it  has  a  natural   tendency  toward  some  parXcular  place;   for  if  it  were  indifferent  to  all  places  it   would  remain  at  rest,  having  no  more   cause  to  move  one  way  than  another.   Having  such  a  tendency,  it  naturally   follows  that  in  its  moXon  it  will  be   conXnually  acceleraXng.  [Two  World   Systems,  EN  VII  56,  Drake  31-­‐32]   …the  parts  of  the  earth  do  not  move  so  as   to  go  toward  the  center  of  the  universe,   but  so  as  to  unite  with  the  whole  earth   (and  that  consequently  they  have  a   natural  tendency  toward  the  center  of  the   terrestrial  globe,  by  which  tendency  they   cooperate  to  form  and  preserve  it)…  [Two   World  Systems,  EN  VII  57-­‐8,  Drake  33]   Let  us  suppose  that  among  the  decrees  of  the  divine   Architect  was  the  thought  of  creaXng  in  the  universe   those  globes  which  we  behold  conXnually  revolving,  and   of  establishing  a  center  of  their  rotaXons  in  which  the   sun  was  located  immovably.  Next,  suppose  all  the  said   globes  to  have  been  created  in  the  same  place,  and   there  assigned  tendencies  of  moXon,  descending   toward  the  center  unXl  they  had  acquired  those  degrees   of  velocity  which  originally  seemed  good  to  the  Divine   mind.  These  velociXes  being  acquired,  we  lastly  suppose   that  the  globes  were  set  in  rotaXon,  each  retaining  in  its   orbit  its  predetermined  velocity….  Two  World  Systems,   EN  VII  53,  Drake,  29   Generally  speaking,  I  find  that  he  philosophizes  much  more   ably  than  is  usual,  in  that,  so  far  as  he  can,  he  abandons  the   errors  of  the  Schools  and  tries  to  use  mathemaXcal   methods  in  the  invesXgaXon  of  physical  quesXons.  On  that   score,  I  am  completely  at  one  with  him,  for  I  hold  that  there   is  no  other  way  to  discover  the  truth.  But  he  conXnually   digresses,  and  he  does  not  take  Xme  to  explain  maTers   fully.  This,  in  my  view,  is  a  mistake:  it  shows  that  he  has  not   invesXgated  maTers  in  an  orderly  way,  and  has  merely   sought  explanaXons  for  some  parXcular  effects,  without   going  into  the  primary  causes  in  nature;  hence  his  building   lacks  a  foundaXon.  [Descartes  to  Mersenne,  11  Oct.  1638,   AT  II  380]   [I  plan]  three  books  on  local  moXon— an  enXrely  new  science  in  which  no   one  else,  ancient  or  modern,  has   discovered  any  of  the  most   remarkable  characterisXcs  [sintomi]   which  I  demonstrate  to  exist  in  both   natural  and  violent  movement….   [  Galileo  to  Vinta,  7  May  1610,  EN  X   351-­‐2]   I’m  interested  in  examining  what  might   be  the  characterisXcs  [sintomi]  which   accompany  the  moXon  of  a  moving   body,  which,  starXng  from  a  state  of  rest,   it  goes  on  moving  with  a  speed  that   constantly  increases  in  the  same  way…   [Galileo  to  Baliani,  7  January  1639,  EN   XVIII  12]