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Forjustastheuniversalpropositionsofmathematicsdealnot
withobjectswhichexistseparately，apartfromextendedmagnitudes
andfromnumbers，butwithmagnitudesandnumbers，nothoweverqua
suchastohavemagnitudeortobedivisible，clearlyitispossible
thatthereshouldalsobebothpropositionsanddemonstrationsabout
sensiblemagnitudes，nothoweverquasensiblebutquapossessedof
certaindefinitequalities。Forastherearemanypropositionsabout
thingsmerelyconsideredasinmotion，apartfromwhateachsuchthing
isandfromtheiraccidents，andasitisnotthereforenecessarythat
thereshouldbeeitheramobileseparatefromsensibles，oradistinct
mobileentityinthesensibles，sotoointhecaseofmobilesthere
willbepropositionsandsciences，whichtreatthemhowevernotqua
mobilebutonlyquabodies，oragainonlyquaplanes，oronlyqua
lines，orquadivisibles，orquaindivisibleshavingposition，oronly
quaindivisibles。Thussinceitistruetosaywithoutqualification
thatnotonlythingswhichareseparablebutalsothingswhichare
inseparableexist(forinstance，thatmobilesexist)，itistrue
alsotosaywithoutqualificationthattheobjectsofmathematics
exist，andwiththecharacterascribedtothembymathematicians。
Andasitistruetosayoftheothersciencestoo，without
qualification，thattheydealwithsuchandsuchasubject-notwith
whatisaccidentaltoit(e。g。notwiththepale，ifthehealthything
ispale，andthesciencehasthehealthyasitssubject)，butwith
thatwhichisthesubjectofeachscience-withthehealthyifit
treatsitsobjectquahealthy，withmanifquaman:-sotooisit
withgeometry；ifitssubjectshappentobesensible，thoughitdoes
nottreatthemquasensible，themathematicalscienceswillnotfor
thatreasonbesciencesofsensibles-nor，ontheotherhand，of
otherthingsseparatefromsensibles。Manypropertiesattachtothings
invirtueoftheirownnatureaspossessedofeachsuchcharacter；
e。g。thereareattributespeculiartotheanimalquafemaleorqua
male(yetthereisno’female’nor’male’separatefromanimals)；so
thattherearealsoattributeswhichbelongtothingsmerelyas
lengthsorasplanes。Andinproportionaswearedealingwith
thingswhicharepriorindefinitionandsimpler，ourknowledgehas
moreaccuracy，i。e。simplicity。Thereforeasciencewhichabstracts
fromspatialmagnitudeismoreprecisethanonewhichtakesitinto
account；andascienceismostpreciseifitabstractsfrom
movement，butifittakesaccountofmovement，itismostpreciseif
itdealswiththeprimarymovement，forthisisthesimplest；andof
thisagainuniformmovementisthesimplestform。
Thesameaccountmaybegivenofharmonicsandoptics；forneither
considersitsobjectsquasightorquavoice，butqualinesand
numbers；butthelatterareattributespropertotheformer。And
mechanicstooproceedsinthesameway。Thereforeifwesuppose
attributesseparatedfromtheirfellowattributesandmakeanyinquiry
concerningthemassuch，weshallnotforthisreasonbeinerror，any
morethanwhenonedrawsalineonthegroundandcallsitafootlong
whenitisnot；fortheerrorisnotincludedinthepremisses。
Eachquestionwillbebestinvestigatedinthisway-bysetting
upbyanactofseparationwhatisnotseparate，asthe
arithmeticianandthegeometerdo。Foramanquamanisone
indivisiblething；andthearithmeticiansupposedoneindivisible
thing，andthenconsideredwhetheranyattributebelongstoaman
quaindivisible。Butthegeometertreatshimneitherquamannorqua
indivisible，butasasolid。Forevidentlythepropertieswhich
wouldhavebelongedtohimevenifperchancehehadnotbeen
indivisible，canbelongtohimevenapartfromtheseattributes。Thus，
then，geometersspeak
