and　a　huge　bridge　of　planks　laid　upon　eight　ships　chained　together；
  upon　which　was　carried　the　engine　to　cast　stones　and　darts；
  assaulted　the　walls；　relying　on　the　abundance　and　magnificence　of
  his　preparations；　and　on　his　own　previous　glory；　all　which；　however；
  were；　it　would　seem；　but　trifles　for　Archimedes　and　his　machines。
  These　machines　he　had　designed　and　contrived；　not　as　matters　of
  any　importance；　but　as　mere　amusements　in　geometry；　in　compliance　with
  King　Hiero's　desire　and　request；　some　little　time　before；　that　he
  should　reduce　to　practice　some　part　of　his　admirable　speculation　in
  science；　and　by　accommodating　the　theoretic　truth　to　sensation　and
  ordinary　use；　bring　it　more　within　the　appreciation　of　the　people　in
  general。　Eudoxus　and　Archytas　had　been　the　first　originators　of　this
  far…famed　and　highly…prized　art　of　mechanics；　which　they　employed　as
  an　elegant　illustration　of　geometrical　truths；　and　as　means　of
  sustaining　experimentally；　to　the　satisfaction　of　the　senses；
  conclusions　too　intricate　for　proof　by　words　and　diagrams。　As；　for
  example；　to　solve　the　problem；　so　often　required　in　constructing
  geometrical　figures；　given　the　two　extremes；　to　find　the　two　mean
  lines　of　a　proportion；　both　these　mathematicians　had　recourse　to　the
  aid　of　instruments；　adapting　to　their　purpose　certain　curves　and
  sections　of　lines。　But　what　with　Plato's　indignation　at　it；　and　his
  invectives　against　it　as　the　mere　corruption　and　annihilation　of　the
  one　good　of　geometry；　which　was　thus　shamefully　turning　its　back
  upon　the　unembodied　objects　of　pure　intelligence　to　recur　to
  sensation；　and　to　ask　help　（not　to　be　obtained　without　base
  supervisions　and　depravation）　from　matter；　so　it　was　that　mechanics
  came　to　be　separated　from　geometry；　and；　repudiated　and　neglected　by
  philosophers；　took　its　place　as　a　military　art。　Archimedes；　however；
  in　writing　to　King　Hiero；　whose　friend　and　near　relation　he　was；　had
  stated　that　given　the　force；　any　given　weight　might　be　moved；　and　even
  boasted；　we　are　told；　relying　on　the　strength　of　demonstration；　that
  if　there　were　another　earth；　by　going　into　it　he　could　remove　this。
  Hiero　being　struck　with　amazement　at　this；　and　entreating　him　to
  make　good　this　problem　by　actual　experiment；　and　show　some　great
  weight　moved　by　a　small　engine；　he　fixed　accordingly　upon　a　ship　of
  burden　out　of　the　king's　arsenal；　which　could　not　be　drawn　out　of
  the　dock　without　great　labour　and　many　men；　and；　loading　her　with　many
  passengers　and　a　full　freight；　sitting　himself　the　while　far　off；　with
  no　great　endeavour；　but　only　holding　the　head　of　the　pulley　in　his
  hand　and　drawing　the　cords　by　degrees；　he　drew　the　ship　in　a
  straight　line；　as　smoothly　and　evenly　as　if　she　had　been　in　the　sea。
  The　king；　astonished　at　this；　and　convinced　of　the　power　of　the　art；
  prevailed　upon　Archimedes　to　make　him　engines　accommodated　to　all
  the　purposes；　offensive　and　defensive；　of　a　siege。　These　the　king
  himself　never　made　use　of；　because　he　spent　almost　all　his　life　in　a
  profound　quiet　and　the　highest　affluence。　But　the　apparatus　was；　in
  most　opportune　time；　ready　at　hand　for　the　Syracusans；　and　with　it
  also　the　engineer　himself。
  When；　therefore；　the　Romans　assaulted　the　walls　in　two　places　at
  once；　fear　and　consternation　stupefied　the　Syracusans；　believing
  that　nothing　was　able　to　resist　that　violence　and　those　forces。　But
  when　Archimedes　began　to　ply　his　engines；　he　at　once　shot　against
  the　land　forces　all　sorts　of　missile　weapons；　and　immense　masses　of
  stone　that　came　down　with　incredible　noise　and　violence；　against　which
  no　man　could　stand；　for　they　knocked　down　those　upon　whom　they　fell　in
  heaps；　breaking　all　their　ranks　and　files。　In　the　meantime　huge
  poles　thrust　out　from　the　walls　over　the　ships　sunk　some　by　the
  great　weights　which　they　let　down　from　on　high　upon　them；　others
  they　lifted　up　into　the　air　by　an　iron　hand　or　beak　like　a　crane's
  beak　and；　when　they　had　drawn　them　up　by　the　prow；　and　set　them　on　end
  upon　the　poop；　they　plunged　them　to　the　bottom　of　the　sea；　or　else　the
  ships；　drawn　by　engines　within；　and　whirled　about；　were　dashed　against
  steep　rocks　that　stood　jutting　out　under　the　walls；　with　great
  destruction　of　the　soldiers　that　were　aboard　them。　A　ship　was
  frequently　lifted　up　to　a　great　height　in　the　air　（a　dreadful　thing　to
  behold）；　and　was　rolled　to　and　fro；　and　kept　swinging；　until　the
  mariners　were　all　thrown　out；　when　at　length　it　was　dashed　against　the
  rocks；　or　let　fall。　At　the　engine　that　Marcellus　brought　upon　the
  bridge　of　ships；　which　was　called　Sambuca；　from　some　resemblance　it
  had　to　an　instrument　of　music；　while　it　was　as　yet　approaching　the
  wall；　there　was　discharged　a　piece　of　rock　of　ten　talents　weight；　then
  a　second　and　a　third；　which；　striking　upon　it　with　immense　force　and　a
  noise　like　thunder；　broke　all　its　foundation　to　pieces；　shook　out
  all　its　fastenings；　and　completely　dislodged　it　from　the　bridge。　So
  Marcellus；　doubtful　what　counsel　to　pursue；　drew　off　his　ships　to　a
  safer　distance；　and　sounded　a　retreat　to　his　forces　on　land。　They　then
  took　a　resolution　of　coming　up　under　the　walls；　if　it　were　possible；
  in　the　night；　thinking　that　as　Archimedes　used　ropes　stretched　at
  length　in　playing　his　engines；　the　soldiers　would　now　be　under　the
  shot；　and　the　darts　would；　for　want　of　sufficient　distance　to　throw
  them；　fly　over　their　heads　without　effect。　But　he；　it　appeared；　had
  long　before　framed　for　such　occasions　engines　accommodated　to　any
  distance；　and　shorter　weapons；　and　had　made　numerous　small　openings　in
  the　walls；　through　which；　with　engines　of　a　shorter　range；
  unexpected　blows　were　inflicted　on　the　assailants。　Thus；　when　they　who
  thought　to　deceive　the　defenders　came　close　up　to　the　walls；　instantly
  a　shower　of　darts　and　other　missile　weapons　was　again　cast　upon
  them。　And　when　stones　came　tumbling　down　perpendicularly　upon　their
  heads；　and；　as　it　were；　the　whole　wall　shot　out　arrows　at　them；　they
  retired。　And　now；　again；　as　they　were　going　off；　arrows　and　darts　of　a
  longer　range　inflicted　a　great　slaughter　among　them；　and　their　ships
  were　driven　one　against　another；　while　they　themselves　were　not　able
  to　retaliate　in　any　way。　For　Archimedes　had　provided　and　fixed　most　of
  his　engines　immediately　under　the　wall；　whence　the　Romans；　seeing　that
  indefinite　mischief　overwhelmed　them　from　no　visible　means；　began　to
  think　they　were　fighting　with　the　gods。
  Yet　Marcellus　escaped　unhurt；　and　deriding　his　own　artificers　and
  engineers；　〃What；〃　said　he；　〃must　we　give　up　fighting　with　this
  geometrical　Briareus；　who　plays　pitch…and…toss　with　our　ships；　and；
  with　the　multitude　of　darts　which　he　showers　at　a　single　moment　upon
  us；　really　outdoes　the　hundred…handed　giants　of　mythology？〃　And；
  doubtless；　the　rest　of　the　Syracusans　were　but　the　body　of
  Archimedes's　designs；　one　soul　moving　and　governing　all；　for；　laying
  aside　all　other　arms；　with　this　alone　they　infested　the　Romans　and
  protected　themselves。　In　fine；　when　such　terror　had　seized　upon　the
  Romans；　that；　if　they　did　but　see　a　little　rope　or　a　piece　of　wood
  from　the　wall；　instantly　crying　out；　that　there　it　was　again；
  Archimedes　was　about　to　let　fly　some　engine　at　them；　they　turned　their
  backs　and　fled；　Marcellus　desisted　from　conflicts　and　assaults；
  putting　all　his　hope　in　a　long　siege。　Yet　Archimedes　possessed　so　high
  a　spirit；　so　profound　a　soul；　and　such　treasures　of　scientific
  knowledge；　that　though　these　inventions　had　now　obtained　him　the
  renown　of　more　than　human　sagacity；　he　yet　would　not　deign　to　leave
  behind　him　any　commentary　or　writing　on　such　subjects；　but；
  repudiating　as　sordid　and　ignoble　the　whole　trade　of　engineering；
  and　every　sort　of　art　that　lends　itself　to　mere　use　and　profit；　he
  placed　his　whole　affection　and　ambition　in　those　purer　speculations
  where　there　can　be　no　reference　to　the　vulgar　needs　of　life；
  studies；　the　superiority　of　which　to　all　others　is　unquestioned；　and
  in　which　the　only　doubt　can　be　whether　the　beauty　and　grandeur　of
  the　subjects　examined；　of　the　precision　and　cogency　of　the　methods　and
  means　of　proof；　most　deserve　our　admiration。　It　is　not　possible　to
  find　in　all　geometry　more　difficult　and　intricate　questions；　or　more
  simple　and　lucid　explanations。　Some　ascribe　this　to　his　natural
  genius；　while　others　think　that　incredible　effort　and　toil　produced
  these；　to　all　appearances；　easy　and　unlaboured　results。　No　amount　of
  investigation　of　yours　would　succeed　in　attaining　the　proof；　and
  yet；　once　seen；　you　immediately　believe　you　would　have　discovered
  it；　by　so　smooth　and　so　rapid　a　path　he　leads　you　to　the　conclusion
  required。　And　thus　it　ceases　to　be　incredible　that　（as　is　commonly
  told　of　him）　the　charm　of　his　familiar　and　domestic　Siren　made　him
  forget　his　food　and　neglect　his　person；　to　that　degree　that　when　he
  was　occasionally　carried　by　absolute　violence　to　bathe　or　have　his
  body　anointed；　he　used　to　trace　geometrical　figures　in　the　ashes　of
  the　fire；　and　diagrams　in　the　oil　on　his　body；　being　in　a　state　of
  entire　preoccupation；　and；　in　the　truest　sense；　divine　possession　with
  his　love　and　delight　in　science。　His　discoveries　were　numerous　and
  admirable；　but　he　is　said　to　have　reque