Part Vi

Laert.
to be produced^ of which ^ ;// all coherent nhture continued with all its parts^ was efefled the Worldfeyond which there is not any part of Mat¬ ter orBody: Tit parts oj the World are all things therein fept together by a fenftive naturepwhere- in is likewife perfehlReafon : It is alfo fempiter- nal^for there is nothing more firong whereby it
invenrion of t Analytical Method^ zvhich redu- 1 i^en. tmU eeth the thing fought unto its principle^ the beft of Methods. He taught it to heodamai\ and by ’ it found out many things in Geometry : Analyfis^ as defined by the Scholiaft upon Euclid^ is a * Uh 13, fumpt ion of the thing fought.^ by the confequenis.^
{as if it toe re already known J to find out the truth.
the Worlfi God^ a certain Providence over all things fubjelled to hint/egarding in the firji place heavenly things.^ next on the Earth thofe things which appertain to Man. The fame they fometimes call EJecejfity^ becaufe nothing can be otherwife than is by him Ordained : a fatal immutable conti¬ nuation of EternalOrder: fometimes Port une.^ as producing many things not forefeen or expected by by us^ by reafon of the obfeurity and our ignorance of the Caufes.
may be difjelved ; This poioer they call the Soul of Examples thereof we find in the five firit propO'
SefV. 3.
Eialelfick.
litions of the 13 th Book of befides feve- ral others, that occur in Apollonius Pergaus^, and Pappus Alexandrinus.
Amongft his Geometrical Inventions alfomuft be remembred the duplication of a Cube.^ the oc- cafion and manner whereof is related by t Plu- f « delpk. tarch2sA ^ Philoponus. The afHiQed^./"^^*^’-/^*
with the Peftilence confulted the Oracle of A- pollo^ he anfwered, the Plague would ceafe if they doubled their Altar, which was of a Cu- bick figure. Plutarch faith, that hereupon the Overleers of the Altar, made all the four fides double to what they were before, fo inftead of
Of the third part of Philofoph}\ confifling in j doubling the Altar, they made it offuple to
/t’llTovf/tt'in'ti thpv tvp/itpn thuc I ixrliat il- WhilntiirniJc' tciifn f—titfoA
Reafon and differtation.^ they treated thus. Tho Judgment arife from the Senfie., yet the Judgment of Truth Is not in the Senfes. 2 he Mind they af¬ firmed to be Judge of things^ conceiving her only fit to be credited.^ becaufe floe alone feeth that | which is fimple.^ and unijorm.^ and certain : This they called Idea. All Senfe they conceived to be ob- iufe and Jlow.^ and no way able to perceive thofe things which feem fubjetf to Senfe^ which are fo little.^ as that they cannot fall under Senfe ^ fo moveable andvariousfhat nothing is oneponjlant^ nor the fame.^ becaufe all things are in continual alteration and fluxion. All this part of things^ they called Opinative : Science they affirmed to be no where but in the Reafons and Amotions of Mind^ whence they approved definitions of thingsyind ap¬ plied them to all whereon they difeourfed, ' They approved likewife explications of words by Etymo- gies: They ufed Arguments and Marks for things^ to prove and conclude what they meant to explain: In this confificd all the difcipline of DialedliQffiat of Speech concluded by Reafon.
ts.ot
This Account in general Cictro gives of the old Academy .* Plutarch., Imcrtius.^ Apulcius^ and others have made Colleflions more particu¬ lar, we (hall make choice of that of Akinous^ as moft full and perfefl, which by reafon of the length is referred as an Appendix to Plato’s Life.
CHAP. VIII.
His Inventions.
He added mudi to Learning and Language by many Inventions, as well of things as of words. To omit Pdialetiick., of which we treated laft, ^ Phavorinus attributes to his in¬ vention, d'lfcourfng by way of a Quejiion : but A- rifiotle aferibes it to Alexamenus .a SiirianoiTei- an.y and it appears by the Dialogues of P/ Socrates alfo ufed that form of arguing. Laertius informs us, that Zeno Eleates was the firji com- poj'er of Dialogues., yet in my Opinion., faith he, Plato hath fo much refined the form thereof that he deferves to be preferred before all others., as well for invention as P.eformation.
More properly may be attributed to.hinfthe
what it was. Pbiloponus' IMth, they caufed another Cube of the lame bignels with the for¬ mer to be fet upon if, whereby they changed the Figure of the Altar, which was no longer a Cube, but d quadrilateral Pillar. The
firlf way it was Cubical, but not double j the fecond way double, but not Cubical. The Plague not ceafing, they confulted the Oracle again. Apollo anfwered, they had not fulfil¬ led his Command, which was to build a Cubi¬ cal Altar as big again as the former. Hereupon they went to Plato, as moft skilful in Geome¬ try, to learn of him the Oracle’s meaning, and how they Ihould find out the way of doubling a Cube, retaining the Cubick Figure. Plato anfwered, that the God mocked the Grecians for their negled of Philofophy and Learning, infulting over their Ignorance, that he com¬ manded them lerioully to addict themfelves to Geometry, that this could not be done any other way,* than by finding out two mean pro-*^ portionals between two right Lines in a Duple proportion, (Plato's particular Method is livered by Eutochim in his Comment upon the firft Propofition of the fecond Book of Archi¬ medes de Sphara & Cylindro. ) He added that Eudoxus the Gnidian, or Helico the Cyzicene would do it for them. That the God needed not this duplication of his Altar, but commanded all the that avoiding War and the Mife-
ries wherewith it is attended, they Ihould ap¬ ply themfelves to the Mufes j and having fet- ledthe turbulent Commotions of their Minds, converfe harmlefly and beneficially with one another. Philoponus that Plato expounded thk Problem to his Difciples, who writ much upon this Subjell, though nothing thereof be extant. Of the Antients, laboured in this Problem belides Plato, Archytas thsTarenline, Menachmus, Era- tofthenes Philq of Byzantium, Hero, Apollonius, Pergeeus, Alicomedcs , Diodes , and Sporus ; t Valerius Maximus faith, that Plato remitted theOvevfeers of the Sacred Altar to Euclid Geometrician, as fubmilting to his Science and Projejfion-, but this is an Error, becaufe Eu¬ clid the Geometrician was much later than Plato, and the other Euclid, Plato’s Contem¬ porary, nothing eminent in Mathematicks, as
hath
z. 13.
Part. V.
» prel. i.j
fLaerfi.
f Laert.
'fLaert* * Laert.
PLATO.
162
hath been before me obferved by Sir ^ Uemy Sa-
vile.
ThatP/ the Mathematicks, ( more than appears from thofe Writings of his that are extant) and was moft eminent therein, may be. argued from the three Books of Theon\ Smyr/2£us^ the firft A- rhhmetick^ the fecond, ■ the laft,
(not yet publiftied)^ Astronomy, Thofe Books contained many things, Angular and choice, not to be met with elfewhere. The defign is acknow¬ ledged by the Author, to he as an introduction necefiary to the underftanding of Vlato\ Wri¬ tings.
There are alfo divers words of wlii^ch he is efteemed to be the firft Author, Y' 2.% Antipoles^ a word by him firft introduced into Philofophy, to fignifie thofe People whofe feet are diametri cally oppolite.
^ 2to/x«o>'j Element.^ until his time was con¬ founded with Erincipte., by all Philofo- phers ftom Thales. Elato diftinguifti’d them thus, Erinciple., is that which hath no
thing before it whereof it might be generated Elements., are compounded.
t The word Eoem alfo, though fince very trivial, was not ufed by any before hjm.
^ He firft ufed this term, tIv
' oblong number., Sjn Theateto'] thereby figni- fying the produCl of a greater number muliplied by a lefler.
'w'
t He alfo firft introduced the word Superficies, for which before was ufed i-s-fTrAov a Elane. Eh.\xs .Laertius^ though ^ inEucHT
plies, that neither Elato not. Arijiotle vAq word, but for it, Divine Elato faith,
he, calls Geometry, thecontemplatrlxofElanes, oppofing it to Stereometry^ as if Elane an i Su- perjkies were the fame. So likeioife, doth Arifto- tle. But Euclid and thofe who fucceeded. him, make Superficies the Genus, Elane a Species thereof.
t iresvoU, Divine Erovidcnce, a WordfLwf.' fince much ufed by Chriftians, was fiift the ex- prefiion of Elato. ' ’ . ,
^ He firft of Philofophers wrote againft' Ly-, , , fias. Son of Cephalus, in Eh’^edro. *' -
t He firft confidered the force and efficacy of + uert. Grammar. ’
^ ^ He firft wrote againft all that were before wil^uce it is wondred at, that he never menti^s ■ .fir.-,,
C H A P. VIII.
\ I
His Diftinbiions.
J!.hi J.j
OF his Diftinflions Arijiotletmde this Col
_ leftion in'fome pieces not Extant,
by Laertius. c - ^
cited
Good is three- J Iti the Soul, as Juftice, Prudence, Fortitude, Temperance, and the like.
fold.
Eriendfhip is threefold.
Government is of, five kinds.
iln the Body, as Beauty, good Habit.
External, as Friends, Prolperity of our Country : Wealth. ‘ '
I i
rNatural, which Parents bear to their Children, and Kindred to one another 5
{ I which kind allb is arhongft; Beafts.
Sociable, begotten by converfation, without any Relation of Kindred j liich as was that betwixt Eylades and Orefies.
Hof pit able, towards Guefts, or wherewith we affeCl Strangers even upon Let¬ ters of Recommendation. o
Some add a fourth kind, amatory
'^Democratical : a Democracy is that wherein the People Rules and have power to make Magiftrates and Laws.
Arijiocratical ; an is that wherein neither Rich nor poor nor No¬
bles Govern, but the beft Perlbnsof the whole Cityi Olygarchical : An Oligarchy is when Governors areEleCled by the Votes of Ma¬ giftrates, for they are fewer than the Poor.
cEleHive by Law: as that of the Carthaginians: for it is Civil.
Regal : L who confine themfelves to a certain Race.
Tyrannical, Tyranny is that wherein Men are brought to Subjeflion either by . Fraud or Force. i
fold.
Towards the Gods: they who Sacrifice as the Law requires, and perfoim the ^ . , Divine Rites, are juft towards the Gods.
Jfifjtce IS three-. Towards Men: They who reftore what was lent or committed to their Truft, ’ are juft towards Men.
\Towards the Dead : They who take care of Sepulchres are juft toward the dead.
'^^EraBice, as playing on the Flute, Lute, and the like-, which affe£l nothing vifible. _
Mechanick, As Architeflure of Houles, Ships, or the like: which produceth Wf IS three J , ^ vifible eflfca
Theoretick, as Geometry, Harmonick Aftronomy, which a£l not, neither pro¬ duce any thing. The Geometrician confiders the proportion of Lines to one : another , Harmonick founds : Aftronomy, Stars, and the World*
X 2
Medicine
Me^chte is of five kinds.
haw is two¬ fold. ’
^f?harmaceutick^ cureth Difeafes by. application of Medicine.
I Chyrurgick^ by incifion or cauterifing.
'Dmtetick^ by Diet.
I Nofognmonick, dilcerns Difeafes.
^[Boetheticky removeth Difeafes. - • ' ■
■ Written : fuch are thole by which States are Governed.
)Not written^ grounded upon Cuftom ^ as that no Man fhall go naked into the forunty habited like a Woman, is not forbidden by any written Law, but forborn becaufe of the unwritten.
Speech is qf five^ kinds.
.Political^ ufed in Orations by fuch as Govern States.
Rhetoricaly ufed by Lawyers in Pleading either to Confirm, Praife, Difpraife, ( or Accufe.
\Vulgar^ ufed by People in common Difcourfe.
DialeU 'icaly ufed by fuch as difcourfe in fhort queftions and anfwers.] . -Artificial^ ufed by Tradefmen in their feveral rrofelTions.
rOf the Voice only.
Mufick is three- ) Of the Voice and Hands, as linging to the Lute. cOf the Hand only,' ^s the Harp.
I- ' ■ ■
SIf the Predeceffors were upright, juft, and honeft.
If the Predeceflbrs were Rulers of Princes.
If the Predeceffors acquired Honours, as the Command of an Army, or were Crown’d in Publick Games .* thofe who are defeended from fuch as we call Noble.
If a Man be endued with a Generous Mind •, this is the beft kind of Nobility.
fold.
Nobility is of four kinds.
. CCommendahle, as a fait form.
Beauty is three' fold. ^^Beneficial^ as all that belongs to inftitution of Laws.
'The Soul hath three parts.
FerfeU Virtue hath four kinds.
Government is of five kinds.
Of RJbetorick are fix kinds.
eRationaly the Principle whereby we Judge, Difcourfe, and the like.
XiArnJcjble^ whereby we are emboidned, joyed, grieved, enraged.
-Wifdom, the Principle of doing things right.
Tuftice, the Principle of doing things equal in private Converlation and Pub- ^ lickAffeirs. ■
I Fortitude, the Principle of not flying Danger through Fear, but meeting it. Temperance, the Principle of fubduing Defires, and yielding to no Pleafures, but living Moderately.
By Law : Thofe who are chofen Magiftrates in a City Governed by Law By Nature : The Males not only of Mankind, but of moft other Creatures are predominant over the Fe-males by Nature.
By Cufioniy as that which Mafters have, over their Difeiples.
By Dejcenty as the Lacedemonian Kings, who fucceed out of one Family : and in Macedonia they ufe the lame Cuftom.
[By Fc/rcOy as thofe. who Rule a Kingdom againft the will of the People.
JAdhortationy as when we perfwade a War againft any.
Dehortationy as when we diffwade from War.
Accufationy when we declare that we have been injured by one whom wa prove caufe of our Misfortune.
IDefencOy When a Man proves he did not any Injury or Offence.
Fncomiuniy when we Ipeak well of another.
[ yVituperationy when we declare a Man to be wicked.
I
1
Of Right
Speak- 1
’ fWhat is requifite : thofe things which will benefit both the hearer and Ipeaker. As much as is requifite'. if we fpeak neither more nor lefs than concerns the bufinels.
ingzxQ fourkinds:,> thofe to whom it is requifite : as when we Ipeak to old men that have done
when we Ipeak |
amifs in fuch terms as are fit for old Men, or to young as becomes young.
I When it is requifite : neither too foon nor too late ^ for if that be not obfer- LUved, nothing can be fpoken aright.
Beneficencfy
I