Draft
7.6PreModernPeriod, Seventeenth Century 147
63 ThePrincipia'sappearancealsoinvolved Newtonin anunpleasant episode withtheEnglish
philosopherandphysicistRobertHooke. In 1687Hooke claimedthatNewtonhadstolenfrom
hima centralideaof thebook:thatbodiesattracteach otherwitha forcethatvariesinversely
asthesquareof theirdistance. However,mosthistorians donotacceptHooke'schargeof
plagiarism.
64 Newtonalsoengaged in a violent disputewith Leibnizover priority in theinventionof
calculus. Newtonusedhispositionas president of theRoyal Society to have a committeeof
thatbodyinvestigatethequestion,andhe secretlywrotethecommittee'sreport,which charged
Leibnizwithdeliberateplagiarism.Newtonalsocompiledthebook of evidencethatthesociety
published.Thee ectsof thequarrellingerednearlyuntil hisdeathin 1727.
65 In additionto science,Newtonalsoshowed aninterestin alchemy, mysticism,andtheology.
Many pagesof hisnotesandwritingsparticularlyfromthelateryearsof hiscareeraredevoted
to thesetopics. However,historianshave foundlittleconnectionbetweentheseinterestsand
Newton'sscienti cwork.
7.6.3 BernoulliFamily1654-1782
66 TheBernouillifamilyoriginallylived in Antwerp,butbecauseof religiouspersecution,they
leftHollandandsettledin Basel.Neartheendof theseventeenth centurythisfamilyproduced
outstandingmathematiciansformorethana hundredyears. JacobandJohnwerebrothers.
Johnwas thefatherof Daniel,andEulerhispupil.
67 WhereasGalileo(andMariotte)investigatedthestrengthof beams(Strength),JacobBernoulli
(1654-1705)madecalculationof theirde
ection(Sti ness)anddidnotcontributeto ourknowl-
edgeof physicalproperties.JacobBernouilliis alsocreditedin beingthe rstto to have assumed
thata bf planesectionof a beamremainsplaneduringbending,butassumedrotationto be
withrespectto thelower ber (asGalileodid)andthisresultedin an erroneoussolution(where
is theexactlocationof theaxisof rotation?). Healsoshowedthatthecurvatureat any point
alonga beamis proportionalto thecurvatureof thede
ectioncurve.
68 Bernoullimadethe rstanalyticalcontributionto theproblemof elastic
exureof a beam.
In 1691he publisheda logogriphQrzumubaptdxqopddbbp...whosesecretwas revealedin 1694.
A letteris replacedby thenextin theLatinalphabet,thesecondby theletterthreeaway, and
thethirdby thelettersixaway, so thataaaaawouldbe encodedasbdgbd. Thelogogriphreads
Portioaxisapplicatem... andthedecodedis thattheradiusof curvatureat any point of an
initiallystraight beamin inverselyproportionalto thevalueof thebendingmoment at that
point.
69 DanielBernoulli(1700-1782) rstpostulatedthata forcecanbe decomposedinto itsequiv-
alent (\Potentiisquibuscunquepossuntsubstituiearundemaequivalentes". Anotherhypothesis
de nedthesumof two \conspiring"forcesappliedto thesamepoint. Accordingto Bernoulli,
this\necessarytruth"followsfromthemetaphysicalprinciplethatthewholeequaltsthesum
of itsparts,(Penvenuto1991).
7.6.4 Euler1707-1783
70 LeonhardEulerwas bornin Baselandearlyoncaught theattentionof JohnBernoulli
whoseteachingwas attractingyoungmathematiciansfrom allover Europe, Fig. 7.15. He