Part IX.

P TT H A G O R A S.
l-.'.v:.''.
I'
I
(h) PtkI. in EkI, lib. 4. Prop. 32. Com. 5.
ro EMclid.
lib. I. Prop.
(d) Vitrur. Archit. p. I.
^w'.y ..
•'U.iC .
■■VMn'.l D ak'basi .lixi
(e) Lmf.
ffj Vitrur. loco cir.
compleat four right Angles, as do alfo three Hex agones and four ^uarps* But of all other Poly¬ genes i^rh^tfoever, joinecl together at the Angles, lome exceed four right Angles, others fall fhort. This calls ihagor^ans. . ■ . ■
tvery.Triangle.h^h, the internal Angles equal to tWQ. right Angles. This Theoren;i; A’»- de,mus, th^ Peripatetick, aferibes to the Vythago- reatis mapner pempnftration fee in
Vroclusis ,
{c) In r^Sangle ,Tri^{ng{es ih^ fguare whioh is made of ^de that fubtt^ndeth the -right: Arg^-, is equal to jfe Squares ^hich. are made .of jhe jides contai^im tj)e/ight A^glc. »: "
(VJ ,This Theorem out 3
andby dt fhewed howto, make agnomen, or Iquare (vyhich the* Carpenters cannot do- ,vy \th9ut much difficulty and Uncertainty) not .Mechani¬ cally, bhf according to Rule ^ for if we talie three Rulers, one of them being, three foot,. long^ the Second four foot, ^the.'fiufd, five foot, .and, put tlrefetriree^,,together thajt they touch; one ano¬ ther at, the epds in a Trian^c, they thake aper- feft'Square : Now if tq e^ich of thefc Rulers be adferihed ^Square, that .which confifted of three fc^.wiy. imve ^ j that , which of 4, wiAhave 16 j that wilhh^ye '25. So that how ma¬
ny feet the area's of the two lefier Mquarfs. of three and fopr make, ip ,m^ny will the/quareof 5 ma^,!,.’; hj,: j
, (ef [Aytyllodprus the'" 'Logijlkk:, and others, re- 1 late, ^that upon the invention of this Tbeprgpi^ Py- Sacrificed a f^eeftomb (f) to. the' Mu- in copfitmation whereof they alledge thisE- pigram,' ' - V ‘
'khat noble Scheme SyA^2i%oi2iS devis'd^ Sorinbichahecatomb hef aerified..
fg)Nonpoffc (i) Plutarch faith,., jit was onlyfl«,0;r^ and fui viv. fee. even that is queftioneo by as incon-
fiftent . with his doStrinc, which forbad bloody fa- t. cor. accurate therefore ( laith '^Pro-
♦V^g. P^y^i^^)S^‘> hefacrificedan Ok made of Timer
Epift* 01, 2is (t) Gregory Nazianzen^ of Clay. . .S Ckj Non pojfe But; .(/&) Plutarch doubts, whether it were for Aaviterynierei. thQ invention of the forementioned Propofitlon, fcc.Epicurum.j]^jp^^-^^^^j^^ facrificed an Ox, or for the Pro¬ blem concerning the Area of aParabole. Indeed,
(l) Prod: va{l)the application offpaces or figures, to lines, is,
£«c/. lib.4. as his followers an invention of
l?fop* 44* (}jg Pyhagorick Mufe, Parabole, Hyperbole, Elleip-
fis. ^romthem the later Writers taking ihefie names ^ transfer/ d them to, Conical lines, calling one Para- bale, another Hyperbole, another Elleipfu where- fignifiedby thofe names the defeription of places, ap-
(m) ^cz^vssgpii^S a determinate right line, (tn) For when oT'ar jS \v- a righHifte'heingpropoSed,thefpace given is wholly
adequate to the right line', then, they fay, the /pace !w T? w9e/qt ‘ l^fig^h of the Jpace greater than that ' of the right ciu-xf^Tii- line, then, they fay, ft exceeds.-, (ysri^^AKKuv) but ^7m when lefs,fo as the /pace being dejeribed, there is part of the right line beyond it, then it falls 'ZSTiMt.- (luKindy y fn this fenje Euclid ufiethPara- Sec. bole, lib. i. prop. 44. and Hyperbole ,and EUeipfis, inthe$thBoot r / ; ’
. \ . . '1 ; - .
CHAP. III.
How he colie fled the Stature of Hercules.
(fl) in his Treatife, entituled, How C^J-Agel, I. u
JL great difference there is in the Ibuls and bodies of men, as to ingenuity and ftrength, re¬ lates, that Pythagoras reafoned curioufly and ' fubtilly, in finding out and'collefling the extraor¬ dinary ftature and length of Hercules his body : for, it being manifeft, that Hercules meafured with his feet the running courfe' of 01yitipian-// (?r at Pifq, and that he made it that the Other running coutfes in Greece, infti- tuted afterwards by other perfons were 600 foot lotigj yet fhorter than this ; ' He^ eafily-un- ; derftp6d the meafure of 'Hercules his foot^ con- fidfcfing that it was proportfenably fd much long- • . er thab- that of other men, as the' ’Olytripick dourfe was longer than all others. " Arxi Having comprehended the fize oflWg/rA/^x'-'hW'fbot, he corifidered what length cf body didfuit wfethat meafure, according to the natural proportion of all the members one to another ; ' and fo coIleQed the donfequent. That 'Hercules was fo much taller in body than others, by how mucli-thc Olympick couffe was longer than the reft, Which were made after the fame number of feet,
.f
-.ii'u'
-■■A -M
■ SE-CT y. _
Afirpnomy.. ■ -v .
■ f
( JL\ /peculation of (ekfiial things^ fin which f44*
Pythagoras wtu exquifife, as appears by thefe few remains. ' ’ .
C -H A P. I.
The Syfienf of the Spheres,
(^^J^'T^HE wbrd Heaven, 4s. taken three W
X -Ways; firA, fpr the fphere of fixed Stars ; fecondly, for all that is betwixt the fphere of'^^'’^' fixed Stars and the Moon ; laftly, fpr the whole world, both Heaven and Earth,. . f , , . . . .
(^) Thetnonymous writer of the life of Py. (b)kpa&.Photi thagoras affirms, that hefiaid, there are twelve or¬ ders in heaven, zchereof the fv'fl and outmofi is the fixed fphere, next to this is the Star of Saturn, and then the other fix Planets, Jupiter,- -^arS, Venus,
Mercury, Sun and Moon next th^cAhe fphere of Tire, then that of Air, then that' of Wgter, lafi of all the Earth.
But they who feem more ftrifily to follow the mind of Pythagoras and his difciples, ayerr, Tl^ey held the celefiial Jpheres to be ten, whereof nine only arevifible to m, ( the fixed Sphere, .thefeven Planets, and our Eanh) the tenth is Antiehthon, an Earth above, or oppofite to ours. This Antich- . thon they (d) added, to make up the .number of the 'simple moving bodies. TQX. \e') confid»ring,thc{tthe aficSi- AkHou ons and proportions of Aiufick confiji in numbers, that all other things appear to be aJfimiUffd to num¬ bers, that numbers are the firj] of all nature, that the elements of numbers are the eUnipnts of all beings 3
They
39'
P T T H^A G OKAS,
P A R DC
fO Am. Cnejo. lib. U/Phyf.
■ They afler ted, that all Heaven is Harmony and Number, and that the afteHions and parts of Hea¬ ven arecorrefpondent to number : and qcfllje^ling thele, they adapted them to the compofition of the whole, wherein if any thing were 'wanting, they fupplied it, that the whole might be -alike compa^led. As, becaufe the Decad, feera^i-tp be perfeft, and to comprehend the whole i^ture of numbers, therefore they aflerted the CelefUal Spheres to be Ten. Now there being- Nine only vifible to us , hereupon they . cpr?:eived the Tenth to be Atnichtljon^ an Earth bppofite to purs.' .
As cofleerning the Order and^ Syftem. of ;the.fe^ ^^Aip^ythqgoreans (f)\^l6.i Tb/it in tke-mjclle of 01 (as (:i)Stoktus)inthe mc/jl ^f^h^TMffWenients iiibe.fiejy Globe, Unity,, r^Ajyhiph:! they term Vejia and Monad. : Thty unw. {fiH^-:S;'^plfamX who. unaexftcnd,, this thing ntore tMimaie^^ay\ that this fire i>sfi)€:j>ro£r^aj'i:oe^,nin- irit 'i\}fy^ild.yx€itatiaiefi(iv)er,;%^^^ is in the midjt ef the fiqttb. BatSimplicii(s, himlelf feems not to have apprehended the right meaning of thCj^- thagoreans^. Who by this fire., or figry Globe of U- mty^ meant nothing elfe but the Sun, leatedrin, the midft of the Upiverfe, immoveable, about which the other .parts of the World are moved.. This Opinion Pythagoras leems to haye deriyetj Item the JEgyptians, who Hieroglyphically leprefen- 9.;’ « ^ Beetle;' becaufe, aS the Beetle
lib.’ 5. ° ' ii^yinglormed a Ball of Cow-dung, and lying up on its back, rouls it about fiom Claw to Claw lb theother parts ofthe World ^re moved and roul- ed by and about the Sun.
'Thar by this immovable fire in the midft ofthe CO Loc: dc. llniverft, they underftood not (as (1) Simplicius conceiveth) the Earth, is manifeft, tbralrauchas (^J Pint, in they further held, that (tn ) the Earth is not immo- d. norfeatedin the rnidft ofthe Globe, but Coelo. lib. 2. ^ulpended, asbeing (n) one pf the Stars carried about the fire which is inthe middle, and that (o) Arm. loc. thereby it makethDay and Night, (o) TheRea- fon why the Earth ought not to have ' the middle place, is, becaufe the moft excellent body ought to have the moll excellent place ; but Fire is more excellent than Earth, and the Center more excel¬ lent than all places without it ^ therefore they r ^ ^ -yr -L-j conceived, that not theEarth, but the Fire, is (]>) Arm. ibid, placed in the tpidft. (p) Moreover, becaufe that which is the molt excellent of the Univerfe, ought principally to be prelerved, and the middle is fuch, therefore they term the Fire, Atls thecu- ftpdy of Jupiter.
U) A-l'l ibid. (^) The fame they held of the Antichthon aUo, Lviz. That like our Earth it is fulpended, as be¬ ing one ofthe Stars carried about the Fire, and thereby maketh Day and Night. ] By this An- tichthon^ Clemens faithj they underftood Sint/>/ict us, the Aloen, as beingakind ofactherial Earth, as well for. that it eclipfeth the light ofthe Sun, which is proper to the Earth, as for that it is the bound ofCoeleftials, as the Earth of Subluna- ries. But the contrary is manifeft, as well from the compleating ofthe number ten, (in refpeft where- ' p’ut imagined) as for that they
/i,c. * ’ .■> not vifible to us, byreafon, that fol¬
lowing the motion of this Earth, it is always oppo- lite to, or beneath us, and the bignels of our Earth hinders us from feeing it : And Ariftotle affirms there were fome who conceived the Antichthon to
.'fii’ii; / C'r.) .1 .y .lii'- lA
luoia.
be the caufe why there are more Eclipfes of the Moon than of the Suh, which may likewifo hap¬ pen, by feifon of mapy other bodies, invifitle t6 ; ’■ ‘ " .. ■’ '
■(f) UaePtius., who faith was the firftC/) in I’Wo-
that conceived .the Earth tq have a Circular ; Mo- tion,'feemsto'mean.Po more, than that' he firft (''>
comnaftted this Opinion oi.Pythagordsiih •’ andfimmade itpublick; for EufebuA^'^t^r^y affirffis'/^j^ar he committed to writing- ‘fhe'difler- tatfons of His Opinion,, as dplivelffeA ,
hy Pllufarch and St obltusfis exaftlytfiefemei for he plated fire in the mjdfft,' which , he caff'oj ffie ‘ Genius ofthe tlniveffe, and the Mahfidttof/iy- /’/Vfr,,and. the Mother -ofGbds, end^taf, and Waid, and Meafufe-df-Nafiire.-: hecdrtd^v^ that the ‘.Ten Celcfrial Bodies ^moVe ab^ut^ 4t.'v * fjfea^ ven, -of.the'fphere of fixediSta^s, fH^'fivfe',Piandt^- the Sun, the Moon, th^Edrth, and la'ftly'th^ An-
tichrhon: ' . . .
From the fame Fountain feefws AcifikhMs 'the Samian to have derived ’this HypbthefiSj fome aferibe the inveptiofi thereof foffii^p •( TOrhii fuppofed, that .///) the Sun and Archtmti.
but that the Earth rhoveth round about the Simi in which is feared in the middle. (x)PIutarcidaMs. P^**^*?* that ‘Plato in his old age repented fof that he hha (|) in pUmi placed theEarth in the midit of the U’niyiffe^ aM qu*A.' aod i« not in‘ its ‘proper place. \ ni
This Opinion was of late revived b^ 7^r Copernicus.^ whocopfideringhow inconvenient and troublefbmeit is to undefftand, and maintain the motions ofthe Heavens, and immobilitir'df'thd Earth, explained it with admirable Ing6riu^, ah ter the mind of the Pythagoreans. Accofdiftg to whofe Hypothefis) the Sun (as we faid ) is fettled iii the midft of the World, immovable : The.fphere of fixed Stars in the extremity or outfide df the World, immovable alfb^ betwixt thefearedif^- fed the Planets, and amongft them the Earth as one of them; the Earth moves both about the Sun, and about his proper Axis. Its diurnal Mo¬ tion by one revolution, makesa night and a day'; its annual motion about the Sun, by one revoluti¬ on makes a year ; fo as by reafon of his diurnal motion to the Eaf the Sun and other Stars feem to move to the IVefi ; and by reafon of its annual motion through the Zodiac^, the Earth it felf is in one Sign, and the Sun feems to be in the 'Sign oppofite to it : Betwixt the Sun and theEarth.they place Mercury and Venus : Betwixt the Earth and the fixed Stars, Mars., Jupiter., and Saturn: The Moon being next the Earth, is continually moved within the great Orb betwixt. Pf/7//x and M.ars.y roundabout theEarth, as its Centre ; Its revolu¬ tion about the Earth is compleated in a Month ; about the Sun (together with the Eanh) in a Year.
C H A P. II. fhe Motions ofthe Planets.
AS concerning the Courfe and Revolution of • i the Planets, (a) they affirm the great year to/^) abod. vit. ; be the Revolution of Sat urn, foi the reft ofthe Pla- pyth. apud nets abfolve their Periods in a fhorter time'; but Sa- ' |
turn innolefs than Thirty Years, Jupiter ini z Years, ytfi/rx in Two ; the Sun ffpeaking accord- ^
ing
r I