〃great。〃　　　　　What；　we　may　be　asked；　is　the　limit　of　this　progression？　What；　we　retort；　is　the　limit　of　beauty；　or　of　heat？　Whatever　limit　you　impose；　there　is　always　a　〃hotter〃；　yet　〃hotter〃　is　accounted　a　relative；　〃hot〃　a　pure　quality。　　　　　In　sum；　just　as　there　is　a　Reason…Principle　of　Beauty；　so　there　must　be　a　Reason…Principle　of　greatness；　participation　in　which　makes　a　thing　great；　as　the　Principle　of　beauty　makes　it　beautiful。　　　　　To　judge　from　these　instances；　there　is　contrariety　in　Quantity。　Place　we　may　neglect　as　not　strictly　coming　under　the　category　of　Quantity；　if　it　were　admitted；　〃above〃　could　only　be　a　contrary　if　there　were　something　in　the　universe　which　was　〃below〃：　as　referring　to　the　partial；　the　terms　〃above〃　and　〃below〃　are　used　in　a　purely　relative　sense；　and　must　go　with　〃right〃　and　〃left〃　into　the　category　of　Relation。　　　　　Syllable　and　discourse　are　only　indirectly　quantities　or　substrates　of　Quantity；　it　is　voice　that　is　quantitative：　but　voice　is　a　kind　of　Motion；　it　must　accordingly　in　any　case　＇quantity　or　no　quantity＇　be　referred　to　Motion；　as　must　activity　also。　　　　　13。　It　has　been　remarked　that　the　continuous　is　effectually　distinguished　from　the　discrete　by　their　possessing　the　one　a　common；　the　other　a　separate；　limit。　　　　　The　same　principle　gives　rise　to　the　numerical　distinction　between　odd　and　even；　and　it　holds　good　that　if　there　are　differentiae　found　in　both　contraries；　they　are　either　to　be　abandoned　to　the　objects　numbered；　or　else　to　be　considered　as　differentiae　of　the　abstract　numbers；　and　not　of　the　numbers　manifested　in　the　sensible　objects。　If　the　numbers　are　logically　separable　from　the　objects；　that　is　no　reason　why　we　should　not　think　of　them　as　sharing　the　same　differentiae。　　　　　But　how　are　we　to　differentiate　the　continuous；　comprising　as　it　does　line；　surface　and　solid？　The　line　may　be　rated　as　of　one　dimension；　the　surface　as　of　two　dimensions；　the　solid　as　of　three；　if　we　are　only　making　a　calculation　and　do　not　suppose　that　we　are　dividing　the　continuous　into　its　species；　for　it　is　an　invariable　rule　that　numbers；　thus　grouped　as　prior　and　posterior；　cannot　be　brought　into　a　common　genus；　there　is　no　common　basis　in　first；　second　and　third　dimensions。　Yet　there　is　a　sense　in　which　they　would　appear　to　be　equal…　namely；　as　pure　measures　of　Quantity：　of　higher　and　lower　dimensions；　they　are　not　however　more　or　less　quantitative。　　　　　Numbers　have　similarly　a　common　property　in　their　being　numbers　all；　and　the　truth　may　well　be；　not　that　One　creates　two；　and　two　creates　three；　but　that　all　have　a　common　source。　　　　　Suppose；　however；　that　they　are　not　derived　from　any　source　whatever；　but　merely　exist；　we　at　any　rate　conceive　them　as　being　derived；　and　so　may　be　assumed　to　regard　the　smaller　as　taking　priority　over　the　greater：　yet；　even　so；　by　the　mere　fact　of　their　being　numbers　they　are　reducible　to　a　single　type。　　　　　What　applies　to　numbers　is　equally　true　of　magnitudes；　though　here　we　have　to　distinguish　between　line；　surface　and　solid…　the　last　also　referred　to　as　〃body〃…　in　the　ground　that；　while　all　are　magnitudes；　they　differ　specifically。　　　　　It　remains　to　enquire　whether　these　species　are　themselves　to　be　divided：　the　line　into　straight；　circular；　spiral；　the　surface　into　rectilinear　and　circular　figures；　the　solid　into　the　various　solid　figures…　sphere　and　polyhedra：　whether　these　last　should　be　subdivided；　as　by　the　geometers；　into　those　contained　by　triangular　and　quadrilateral　planes：　and　whether　a　further　division　of　the　latter　should　be　performed。　　　　　14。　How　are　we　to　classify　the　straight　line？　Shall　we　deny　that　it　is　a　magnitude？　　　　　The　suggestion　may　be　made　that　it　is　a　qualified　magnitude。　May　we　not；　then；　consider　straightness　as　a　differentia　of　〃line〃？　We　at　any　rate　draw　on　Quality　for　differentiae　of　Substance。　　　　　The　straight　line　is；　thus；　a　quantity　plus　a　differentia；　but　it　is　not　on　that　account　a　composite　made　up　of　straightness　and　line：　if　it　be　a　composite；　the　composite　possesses　a　differentiae　of　its　own。　　　　　But　＇if　the　line　is　a　quantity＇　why　is　not　the　product　of　three　lines　included　in　Quantity？　The　answer　is　that　a　triangle　consists　not　merely　of　three　lines　but　of　three　lines　in　a　particular　disposition；　a　quadrilateral　of　four　lines　in　a　particular　disposition：　even　the　straight　line　involves　disposition　as　well　as　quantity。　　　　　Holding　that　the　straight　line　is　not　mere　quantity；　we　should　naturally　proceed　to　assert　that　the　line　as　limited　is　not　mere　quantity；　but　for　the　fact　that　the　limit　of　a　line　is　a　point；　which　is　in　the　same　category；　Quantity。　Similarly；　the　limited　surface　will　be　a　quantity；　since　lines；　which　have　a　far　better　right　than　itself　to　this　category；　constitute　its　limits。　With　the　introduction　of　the　limited　surface…　rectangle；　hexagon；　polygon…　into　the　category　of　Quantity；　this　category　will　be　brought　to　include　every　figure　whatsoever。　　　　　If　however　by　classing　the　triangle　and　the　rectangle　as　qualia　we　propose　to　bring　figures　under　Quality；　we　are　not　thereby　precluded　from　assigning　the　same　object　to　more　categories　than　one：　in　so　far　as　it　is　a　magnitude…　a　magnitude　of　such　and　such　a　size…　it　will　belong　to　Quantity；　in　so　far　as　it　presents　a　particular　shape；　to　Quality。　　　　　It　may　be　urged　that　the　triangle　is　essentially　a　particular　shape。　Then　what　prevents　our　ranking　the　sphere　also　as　a　quality？　　　　　To　proceed　on　these　lines　would　lead　us　to　the　conclusion　that　geometry　is　concerned　not　with　magnitudes　but　with　Quality。　But　this　conclusion　is　untenable；　geometry　is　the　study　of　magnitudes。　The　differences　of　magnitudes　do　not　eliminate　the　existence　of　magnitudes　as　such；　any　more　than　the　differences　of　substances　annihilate　the　substances　themselves。　　　　　Moreover；　every　surface　is　limited；　it　is　impossible　for　any　surface　to　be　infinite　in　extent。　　　　　Again；　when　I　find　Quality　bound　up　with　Substance；　I　regard　it　as　substantial　quality：　I　am　not　less；　but　far　more；　disposed　to　see　in　figures　or　shapes　＇qualitative＇　varieties　of　Quantity。　Besides；　if　we　are　not　to　regard　them　as　varieties　of　magnitude；　to　what　genus　are　we　to　assign　them？　　　　　Suppose；　then；　that　we　allow　differences　of　magnitude；　we　commit　ourselves　to　a　specific　classification　of　the　magnitudes　so　differentiated。　　　　　15。　How　far　is　it　true　that　equality　and　inequality　are　characteristic　of　Quantity？　　　　　Triangles；　it　is　significant；　are　said　to　be　similar　rather　than　equal。　But　we　also　refer　to　magnitudes　as　similar；　and　the　accepted　connotation　of　similarity　does　not　exclude　similarity　or　dissimilarity　in　Quantity。　It　may；　of　course；　be　the　case　that　the　term　〃similarity〃　has　a　different　sense　here　from　that　understood　in　reference　to　Quality。　　　　　Furthermore；　if　we　are　told　that　equality　and　inequality　are　characteristic　of　Quantity；　that　is　not　to　deny　that　similarity　also　may　be　predicated　of　certain　quantities。　If；　on　the　contrary；　similarity　and　dissimilarity　are　to　be　confined　to　Quality；　the　terms　as　applied　to　Quantity　must；　as　we　have　said；　bear　a　different　meaning。　　　　　But　suppose　similarity　to　be　identical　in　both　genera；　Quantity　and　Quality　must　then　be　expected　to　reveal　other　properties　held　in　common。　　　　　May　the　truth　be　this：　that　similarity　is　predicable　of　Quantity　only　in　so　far　as　Quantity　possesses　＇qualitative＇　differences？　But　as　a　general　rule　differences　are　grouped　with　that　of　which　they　are　differences；　especially　when　the　difference　is　a　difference　of　that　thing　alone。　If　in　one　case　the　difference　completes　the　substance　and　not　in　another；　we　inevitably　class　it　with　that　which　it　completes；　and　only　consider　it　as　independent　when　it　is　not　complementary：　when　we　say　〃completes　the　substance；〃　we　refer　not　to　Subtance　as　such　but　to　the　differentiated　substance；　the　particular　object　is　to　be　thought　of　as　receiving　an　accession　which　is　non…substantial。　　　　　We　must　not　however　fad　to　observe　that　we　predicate　equality　of　triangles；　rectangles；　and　figures　generally；　whether　plane　or　solid：　this　may　be　given　as　a　ground　for　regarding　equality　and　inequality　as　characteristic　of　Quantity。　　　　　It　remains　to　enquire　whether　similarity　and　dissimilarity　are　characteristic　of　Quality。　　　　　We　have　spoken　of　Quality　as　combining　with　other　entities；　Matter　and　Quantity；　to　form　the　complete　Sensible　Substance；　this　Substance；　so　called；　may　be　supposed　to　constitute　the　manifold　world　of　Sense；　which　is　not　so　much　an　essence　as　a　quale。　Thus；　for　the　essence　of　fire　we　must　look　to　the　Reason…Principle；　what　produces　the　visible　aspect　is；　properly　speaking；　a　quale。　　　　　Man's　essence　will　lie　in　his　Reason…Principle；　that　which　is　perfected　in　the　corporeal　nature　is　a　mere　image　of　the　Reason…Principle　a　quale　rather　than　an　essence。　　　　　Consider：　the　visible　Socrates　is　a　man；　yet　we　give　the　name　of　Socrates　to　that　likeness　of　him　in　a　portrait；　which　consists　of　mere　colours；　mere　pigments：　similarly；　it　is　a　Reason…Principle　which　constitutes　Socrates；　but　we　apply　the　name　Socrates　to　the　Socrates　we　see：　in　truth；　however；　the　colours　and　shapes　which　make　up　the　visible　Socrates　are　but　reproductions　of　those　in　the　Reason…Principle；　while　this　Reason…Principle　itself　bear