a history of science-1-第24章

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　may　discern　the　mast　and　sails　rising　gradually　above　the　horizon；　to　be　followed　in　due　course　by　the　hull。　Similarly；　on　approaching　the　shore；　high　objects　become　visible　before　those　that　lie　nearer　the　water。　It　is　at　least　a　plausible　supposition　that　Pythagoras　may　have　made　such　observations　as　these　during　the　voyage　in　question；　and　that　therein　may　lie　the　germ　of　that　wonderful　conception　of　the　world　as　a　sphere。　To　what　extent　further　proof；　based　on　the　fact　that　the　earth's　shadow　when　the　moon　is　eclipsed　is　always　convex；　may　have　been　known　to　Pythagoras　we　cannot　say。　There　is　no　proof　that　any　of　the　Italic　philosophers　made　extensive　records　of　astronomical　observations　as　did　the　Egyptians　and　Babylonians；　but　we　must　constantly　recall　that　the　writings　of　classical　antiquity　have　been　almost　altogether　destroyed。　The　absence　of　astronomical　records　is；　therefore；　no　proof　that　such　records　never　existed。　Pythagoras；　it　should　be　said；　is　reported　to　have　travelled　in　Egypt；　and　he　must　there　have　gained　an　inkling　of　astronomical　methods。　Indeed；　he　speaks　of　himself　specifically；　in　a　letter　quoted　by　Diogenes；　as　one　who　is　accustomed　to　study　astronomy。　Yet　a　later　sentence　of　the　letter；　which　asserts　that　the　philosopher　is　not　always　occupied　about　speculations　of　his　own　fancy；　suggesting；　as　it　does；　the　dreamer　rather　than　the　observer；　gives　us　probably　a　truer　glimpse　into　the　philosopher's　mind。　There　is；　indeed；　reason　to　suppose　that　the　doctrine　of　the　sphericity　of　the　earth　appealed　to　Pythagoras　chiefly　because　it　accorded　with　his　conception　that　the　sphere　is　the　most　perfect　solid；　just　as　the　circle　is　the　most　perfect　plane　surface。　Be　that　as　it　may；　the　fact　remains　that　we　have　here；　as　far　as　we　can　trace　its　origin；　the　first　expression　of　the　scientific　theory　that　the　earth　is　round。　Had　the　Italic　philosophers　accomplished　nothing　more　than　this；　their　accomplishment　would　none　the　less　mark　an　epoch　in　the　progress　of　thought。　That　Pythagoras　was　an　observer　of　the　heavens　is　further　evidenced　by　the　statement　made　by　Diogenes；　on　the　authority　of　Parmenides；　that　Pythagoras　was　the　first　person　who　discovered　or　asserted　the　identity　of　Hesperus　and　Luciferthat　is　to　say；　of　the　morning　and　the　evening　star。　This　was　really　a　remarkable　discovery；　and　one　that　was　no　doubt　instrumental　later　on　in　determining　that　theory　of　the　mechanics　of　the　heavens　which　we　shall　see　elaborated　presently。　To　have　made　such　a　discovery　argues　again　for　the　practicality　of　the　mind　of　Pythagoras。　His；　indeed；　would　seem　to　have　been　a　mind　in　which　practical　common…sense　was　strangely　blended　with　the　capacity　for　wide　and　imaginative　generalization。　As　further　evidence　of　his　practicality；　it　is　asserted　that　he　was　the　first　person　who　introduced　measures　and　weights　among　the　Greeks；　this　assertion　being　made　on　the　authority　of　Aristoxenus。　It　will　be　observed　that　he　is　said　to　have　introduced；　not　to　have　invented；　weights　and　measures；　a　statement　which　suggests　a　knowledge　on　the　part　of　the　Greeks　that　weights　and　measures　were　previously　employed　in　Egypt　and　Babylonia。　The　mind　that　could　conceive　the　world　as　a　sphere　and　that　interested　itself　in　weights　and　measures　was；　obviously；　a　mind　of　the　visualizing　type。　It　is　characteristic　of　this　type　of　mind　to　be　interested　in　the　tangibilities　of　geometry；　hence　it　is　not　surprising　to　be　told　that　Pythagoras　〃carried　that　science　to　perfection。〃　The　most　famous　discovery　of　Pythagoras　in　this　field　was　that　the　square　of　the　hypotenuse　of　a　right…angled　triangle　is　equal　to　the　squares　of　the　other　sides　of　the　triangle。　We　have　already　noted　the　fable　that　his　enthusiasm　over　this　discovery　led　him　to　sacrifice　a　hecatomb。　Doubtless　the　story　is　apocryphal；　but　doubtless；　also；　it　expresses　the　truth　as　to　the　fervid　joy　with　which　the　philosopher　must　have　contemplated　the　results　of　his　creative　imagination。　No　line　alleged　to　have　been　written　by　Pythagoras　has　come　down　to　us。　We　are　told　that　he　refrained　from　publishing　his　doctrines；　except　by　word　of　mouth。　〃The　Lucanians　and　the　Peucetians；　and　the　Messapians　and　the　Romans；〃　we　are　assured；　〃flocked　around　him；　coming　with　eagerness　to　hear　his　discourses；　no　fewer　than　six　hundred　came　to　him　every　night；　and　if　any　one　of　them　had　ever　been　permitted　to　see　the　master；　they　wrote　of　it　to　their　friends　as　if　they　had　gained　some　great　advantage。〃　Nevertheless；　we　are　assured　that　until　the　time　of　Philolaus　no　doctrines　of　Pythagoras　were　ever　published；　to　which　statement　it　is　added　that　〃when　the　three　celebrated　books　were　published；　Plato　wrote　to　have　them　purchased　for　him　for　a　hundred　minas。〃＇2＇　But　if　such　books　existed；　they　are　lost　to　the　modern　world；　and　we　are　obliged　to　accept　the　assertions　of　relatively　late　writers　as　to　the　theories　of　the　great　Crotonian。　Perhaps　we　cannot　do　better　than　quote　at　length　from　an　important　summary　of　the　remaining　doctrines　of　Pythagoras；　which　Diogenes　himself　quoted　from　the　work　of　a　predecessor。＇3＇　Despite　its　somewhat　inchoate　character；　this　summary　is　a　most　remarkable　one；　as　a　brief　analysis　of　its　contents　will　show。　It　should　be　explained　that　Alexander　（whose　work　is　now　lost）　is　said　to　have　found　these　dogmas　set　down　in　the　commentaries　of　Pythagoras。　If　this　assertion　be　accepted；　we　are　brought　one　step　nearer　the　philosopher　himself。　The　summary　is　as　follows：

〃That　the　monad　was　the　beginning　of　everything。　From　the　monad　proceeds　an　indefinite　duad；　which　is　subordinate　to　the　monad　as　to　its　cause。　That　from　the　monad　and　the　indefinite　duad　proceed　numbers。　And　from　numbers　signs。　And　from　these　last；　lines　of　which　plane　figures　consist。　And　from　plane　figures　are　derived　solid　bodies。　And　from　solid　bodies　sensible　bodies；　of　which　last　there　are　four　elementsfire；　water；　earth；　and　air。　And　that　the　world；　which　is　indued　with　life　and　intellect；　and　which　is　of　a　spherical　figure；　having　the　earth；　which　is　also　spherical；　and　inhabited　all　over　in　its　centre；＇4＇　results　from　a　combination　of　these　elements；　and　derives　its　motion　from　them；　and　also　that　there　are　antipodes；　and　that　what　is　below；　as　respects　us；　is　above　in　respect　of　them。　〃He　also　taught　that　light　and　darkness；　and　cold　and　heat；　and　dryness　and　moisture；　were　equally　divided　in　the　world；　and　that　while　heat　was　predominant　it　was　summer；　while　cold　had　the　mastery；　it　was　winter；　when　dryness　prevailed；　it　was　spring；　and　when　moisture　preponderated；　winter。　And　while　all　these　qualities　were　on　a　level；　then　was　the　loveliest　season　of　the　year；　of　which　the　flourishing　spring　was　the　wholesome　period；　and　the　season　of　autumn　the　most　pernicious　one。　Of　the　day；　he　said　that　the　flourishing　period　was　the　morning；　and　the　fading　one　the　evening；　on　which　account　that　also　was　the　least　healthy　time。　〃Another　of　his　theories　was　that　the　air　around　the　earth　was　immovable　and　pregnant　with　disease；　and　that　everything　in　it　was　mortal；　but　that　the　upper　air　was　in　perpetual　motion；　and　pure　and　salubrious；　and　that　everything　in　that　was　immortal；　and　on　that　account　divine。　And　that　the　sun　and　the　moon　and　the　stars　were　all　gods；　for　in　them　the　warm　principle　predominates　which　is　the　cause　of　life。　And　that　the　moon　derives　its　light　from　the　sun。　And　that　there　is　a　relationship　between　men　and　the　gods；　because　men　partake　of　the　divine　principle；　on　which　account；　also；　God　exercises　his　providence　for　our　advantage。　Also；　that　Fate　is　the　cause　of　the　arrangement　of　the　world　both　generally　and　particularly。　Moreover；　that　a　ray　from　the　sun　penetrated　both　the　cold　aether　and　the　dense　aether；　and　they　call　the　air　the　cold　aether；　and　the　sea　and　moisture　they　call　the　dense　aether。　And　this　ray　descends　into　the　depths；　and　in　this　way　vivifies　everything。　And　everything　which　partakes　of　the　principle　of　heat　lives；　on　which　account；　also；　plants　are　animated　beings；　but　that　all　living　things　have　not　necessarily　souls。　And　that　the　soul　is　a　something　tom　off　from　the　aether；　both　warm　and　cold；　from　its　partaking　of　the　cold　aether。　And　that　the　soul　is　something　different　from　life。　Also；　tha