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starting-point？Ashasbeensaid，therightangleisthoughttobe
priortotheacute，andtheacutetotheright，andeachisone。
Accordinglytheymake1thestarting-pointinbothways。Butthisis
impossible。Fortheuniversalisoneasformorsubstance，whilethe
elementisoneasapartorasmatter。Foreachofthetwoisina
senseone-intrutheachofthetwounitsexistspotentially(at
leastifthenumberisaunityandnotlikeaheap，i。e。if
differentnumbersconsistofdifferentiatedunits，astheysay)，but
notincompletereality；andthecauseoftheerrortheyfellinto
isthattheywereconductingtheirinquiryatthesametimefromthe
standpointofmathematicsandfromthatofuniversaldefinitions，so
that(1)fromtheformerstandpointtheytreatedunity，theirfirst
principle，asapoint；fortheunitisapointwithoutposition。
Theyputthingstogetheroutofthesmallestparts，assomeothers
alsohavedone。Thereforetheunitbecomesthematterofnumbersand
atthesametimepriorto2；andagainposterior，2beingtreatedasa
whole，aunity，andaform。But(2)becausetheywereseekingthe
universaltheytreatedtheunitywhichcanbepredicatedofa
number，asinthissensealsoapartofthenumber。Butthese
characteristicscannotbelongatthesametimetothesamething。
Ifthe1-itselfmustbeunitary(foritdiffersinnothingfrom
other1’sexceptthatitisthestarting-point)，andthe2is
divisiblebuttheunitisnot，theunitmustbelikerthe1-itself
thanthe2is。Butiftheunitislikerit，itmustbelikertothe
unitthantothe2；thereforeeachoftheunitsin2mustbeprior
tothe2。Buttheydenythis；atleasttheygeneratethe2first。
Again，ifthe2-itselfisaunityandthe3-itselfisonealso，both
forma2。Fromwhat，then，isthis2produced？
Sincethereisnotcontactinnumbers，butsuccession，viz。
betweentheunitsbetweenwhichthereisnothing，e。g。betweenthose
in2orin3onemightaskwhetherthesesucceedthe1-itselfor
not，andwhether，ofthetermsthatsucceedit，2oreitherofthe
unitsin2isprior。
Similardifficultiesoccurwithregardtotheclassesofthings
posteriortonumber，-theline，theplane，andthesolid。Forsome
constructtheseoutofthespeciesofthe’greatandsmall’；e。g。
linesfromthe’longandshort’，planesfromthe’broadandnarrow’，
massesfromthe’deepandshallow’；whicharespeciesofthe’great
andsmall’。Andtheoriginativeprincipleofsuchthingswhichanswers
tothe1differentthinkersdescribeindifferentways，Andinthese
alsotheimpossibilities，thefictions，andthecontradictionsof
allprobabilityareseentobeinnumerable。For(i)geometrical
classesareseveredfromoneanother，unlesstheprinciplesofthese
areimpliedinoneanotherinsuchawaythatthe’broadandnarrow’
isalso’longandshort’(butifthisisso，theplanewillbeline
andthesolidaplane；again，howwillanglesandfiguresandsuch
thingsbeexplained？)。And(ii)thesamehappensasinregardto
number；for’longandshort’，&c。，areattributesofmagnitude，but
magnitudedoesnotconsistofthese，anymorethanthelineconsists
of’straightandcurved’，orsolidsof’smoothandrough’。
(Alltheseviewsshareadifficultywhichoccurswithregardto
species-of-a-genus，whenonepositstheuniversals，viz。whetheritis
animal-itselforsomethingotherthananimal-itselfthatisinthe
particularanimal。True，iftheuniversalisnotseparablefrom
sensiblethings，thiswillpresentnodifficulty；butifthe1andthe
numbersareseparable，asthosewhoexpresstheseviewssay，itisnot
easytosolvethedifficulty，ifonemayapplythewords’noteasy’to
theimpossible。Forwhenweapprehendtheunityin2，oringeneralin
anumber，doweapprehendathing-itselforsomethingelse？)。
Some，then，generatespatialmagnitudesfrommatterofthis
sort，othersfromthepoint-andthepointisthoughtbythemtobe
not1butsomethinglike1-andfromothermatterlikeplurality，but
notidenticalwithit；aboutwhichprinciplesnonethelessthesame
difficult
