I. 2.

ATulejus, who calls Thales the inventer of Geometry amongft the Grecians, is more juif to his memory than Anticlides and others, who alcribe the honour thereof to Alaris, or to Fytha- goras, who by the acknowdedgment of » d^m- lilichus, a Pythagorean, learnt Mathematicks of Thales. The original andprogrefs of this fcience.
In Euclid. 2.^. the perfeftion it received from Fythagoras gles, they JhalUikewiJ'e have the other fides, equal
is it to be wondered at, that as well this, as other fciences,jhould have t heir beginning from Commodi ■ 1
oufnefs and opportunity fince, as A f aid in genera¬ tion, it proceeds from imperfelt to perfeth, there- Supply the fore not without reafon is the tranjition from fence breach in the to confideration, and from confideration to the mind.
As therefore among theFhcenicians, by reafon oj ^ ooriri a#- Alerchandife and traffic k, the certain knowledge oJ ^
numbers had its beginning -,fo Tikewife among tbe &c. Egyptians, Geometry was found out upon t before- F Bamius faid occafion-,andThAQSgoing to Egypt,^);^ brought over this fcience into Greece : And many things he found out himfelf, and taught his fellows the princi¬ ples of many things, dcclaringfome more generally, other things more plainly, diext him Amerift ^
ther to Stelichorus the Foet, is remembred ' as hav- j ing touched Geometry, ofiohom Hippias the Elean makes mention, as eminent is that knowledge .* After }i«pU}eiat thefe Fythsigotss confldering the principles there- fore more highly, advanced it into a liberal fcience. f"''**'*'^***
Sed. I . Fropofitions invented by him.
THat he improved ( as Froclus implies ) the Geometry which he learnt of the^oEgypti- ans with many propoficions of his own, is confirm¬ ed by Laertius, who faith, that he much advanc¬ ed ihofe things the invention whereof Callima¬ chus in the lambicks, aferibes to Euphorbus Hjc Phrygian, as fcalenous triangles, and others. Nor is it to be doubted, but that many of them are of thofe, which Euclid hath reduced into his Ele¬ ments •, whole delign it was to colleft and digelf thole that were invented by others, accurately demonlfrating liich as were more negligently proved, but of them only, thefe are known to be his.
|[ '* Every Diameter divides its circle into two^ Lib. i, Jef. equal parts.} This propofition which Euclid makes part of the definition of a Diameter, ^ _ ...
Froclus affirms to have been firft demonftrated , .
byT/«/«. M.
2. [ In all Ifofceles triangles, the angle at the *. Euclid, bafe are equal the one to the other, and thofe right $•
lines being produced, the angles under the bafe are equal. Froclus faith, Fcaxlorthe invention of this
likewije, as oj many other propojttions, we are be- holding to Tluhs, for he firfl obfervedandfiid, that of every Ifofceles, the angels at the bafe are equal, and according to the antients called equal like. Thele are three paffages in tlie demonftration, which in¬ fer nothing towards the conclufion, of which kind there are many in Euclid, and feem to confirm tlie-'antiquity thereof, and that it was lefs curi- oufty reformed by him.
3. [ If two lihes cut one the other, the verticle angels jhall equal the one the other Eudemus Euclid lib. attefts this Theorem to have been invented by Thales, but firft demonftrated by Euclid.
4. If two triangles have two angles equal to ^emcM lib. i.
two angels the one to the other and one fide equal to pop. 26. one fide, either that which is adjacent to the equal ■ingles, or that which J ubtendeth one of the equal an-
( which gave occahon to that miftake ) is thus delivered by Froclus.
Geometry was invented by the Egyptians, taking Its beginning from meafuring fields-, it being necef f try for them, by reafon of the inundation oj Nilus, which wajhedaway the bounds of theirfeverals. Nor
to the other fides, both to both, and the remaining angle equal to the remaning angle ] ’ Eudemus at¬ tributes ihisTheorutn f faith Pm/.Yx j/i^Thales, ‘ Fn>cl. lib. jorjhowing the di fiance of fliips upon the Sea, in 3** that mannpr as he is f aid to do, it is neceff ary that he perform it by this.
Pamphila
ART
I.
THALES.
f] Geo!ft>
Pamphilia (faith Laerti//s)afjirm,that Eefirfl j the end of the Jhadom of the Fyramid., and by tvoo r...L. /. -r , ii, d triangles 7nade by the Beams of the sinfe imonr
frated.^that what proportion there was between the fhadows.^the fame was betwint the Fyr amid and the Staff: A demonftration fb ratioiTaL,’thac
9
defcribedthe reSagle triangle of a circleff) Ramus attributes to Thales(yrpon this authority of Laer¬ tius'} the fecond, third, fourth, and fifth propo- litions of the fourth Book of Euclid^ which are concerning the adfcription of a> Triangle and a Circle, and confequently takes here
to include both Inlcription, and circumfcripti- on i whereas in all thole propofitions, there is nothing proper to a Reblangle Triangle lb that if the word os^^oycimv be retain’d, it mull; relate to the 3 ift propolition of the third Book, whence may be deduced the delcription of a Reblangle Triangle in a Circle. But becaufe there is no fuch propolition in Euclid.^ and this hath but an oblcure reference to part of that Theorem •, it is to be doubted that the Text of Laert'ius is cor¬ rupt, and the word (or mark) inferred by accident, without which thefe words
to T^iyoyov o^^oyuytov exaftly correlpond ^ Lib. lo. cap. with thofe of i Vetruv'nts.^^ythagoricum tr'igo- J I. ^ num orthogonium defcr 'ibere ; % which he means
k. Lib. / 25 jje 2J- i2j-ge exprelfeth k elfewhere, ) the
20 gffjj Propolition of the firft Book of En
clid.^ that in re Li angle triangles.^ the fquare of the hypothenufe is equal to the fquare oj the Jides con¬ taining the right Angle. That Vitruvius.^ Rroclus.^ and others, attribute this Invention to Fythago- ras\ confirms it to be the fame here meant by La¬ ertius-.^ who adds, xhztThales j or the Invention Sacrificed an Oat, though others -(laith he) among whom is Apollodorus, afcribe it to Pythagoras. And in the Life of Fythagoras., he cites the lame Apollodorus that Fythagoras\ Sacrificed a heca¬ tomb.^ having found out.^ that the hypothenufe of a right Angled Lrianglefis of equal power to the two fide s including the right angle according to the Epigram.
That Noble Scheme Fythagoras devis’d, For which a Hecatomb he Sacrific’d.
I pm!, in Eu- Cicero, tho’ he differ in the Author, agrees in did. lib. 2. def. quantity of the Offering with Laert'ius-., affirm- 4. xihste the Fythagoras upon any new Invention ufed
'areinv^teX Sacr'iffe an Ox : vyhich kind of gratitude begun and fif'Tih': by Thales^ was imitated by others alfo, as by y^ct(a[hi i-ri Ferfeus.
Tof^atf
ivqvu I Finding three Spiral Lines., in SeB'ions five,
Perfeus an Offering to the Gods did give.
Se£l. 2: Of his taking the height of the Fyr amid.
a Polyhift.c.2$. nr HEJPyranaidsof are fuppofed by b Idyl. 2, A c Ub. 12.
it is the ordinary way of taking heights by llia- dows, founded upon this Theorem*. , A g Of equiangle triangles, the fides that are a-i lib: bout equal angles are proport'iQnal^yand the fides that fubtend the equal Angle s\a)te homologous.
Which if Froclus had proceeded as far as the fixth Book of Euclid, we Ihould in all likelihood have found afcribed to Thales-, for the fame ar- guraent wherewith Eudemus proves him inven¬ tor of the fourth Theorem in the f oregoing Sec¬ tion, whereby he took diftances, is of equal force in this, whereby he took altitudes.
The height of the great Pyramid (which Tha¬ les meafured) is by its perpendicular (according to Mr. Greaves) Feet, by its declining afcent, i5P3 Feet.
d Var, form.
7-
15*
c Laert.
g Leb, ^6. cap. 12.
Solinus, b Aufonius, Amm 'ianus c Marcel- lintts, and d Cajfiodorus, to caft no fhadow at all, which (as Mr. Greaves hath obfert^ed in his ex¬ cellent Difcourfe upon this Subjeft) muft be meant either of the Summer time, or, which is nearer the Truth, that for the three quarters of the year, th^ have none at mid-day.
Fot,i\mThales by the fhadow meafured their height, is acknowledged, e Hieronymus faith, he meafured the Fyramids by the Jhadowpbferving when they are of equal bignefs. f FlinyAAtmshe found out a way to take the height of them, and all fuch like, by meafuring the Jhadow, at what time, it is equal to the Body. FutFlutarch hath given a more regular and exa6; account of his manner of opQtSitlon, by ereBing a faff perpendicular upon
CHAP. XVIII.
* «
Of His Afronomy.
OMitting the Fable of Orpheus^s Harp allu* ding to the feven Planets, and the obfer- vationsof Heftod, which were little more than of the Riling and Setting of fome principal Stars, (fo imperfect, that calls ' all thofe who fatisfie themfelves vvith fuch fuperficial knowledge, Afironomers according to Hefiod) we may with and others affirm, tlmtTha- leswasthe firf of the Grecians that was skilful 'in Afronomy. Which Science a allerts to have been brought out of Fhcenicia-, b Ar 'iflotle, i;/ ’ that the Grecians owe much of it to the Egypti- b de C(tio.2.i2 ans, where it hath been a long time praftiled :
Thither indeed c Thales acknowledgeth that he 0 Epifl. ad Travelled to confer with Aftronomers. Pherecyd.
SeQ. I. Of the Celefial Sphere.
T Hales, Fythagoras (fkith. ^ Flutarch repeated by ^ Stobious ) with his followers affirm,that the Ccelefial Sphere Is divided 'into five Circles (which they call Zones) whereof one is called Ar- t'lck, and is always 'in view to us-, one of the Sum¬ mer Trop'icks, one the EquinoB'ial, one the]V'inter Trqp'ick, one the Antartick Circle, never Seen by ' us. The oblique Circle, called the Zodiack, I'leth under the three middle Circles ftoucheth them all three as it paffeth, and each of them is cut in right Angles by the Meridian, which goeth from Foie to Foie. Vnjufly therefore is the 'invention of the Zones afcribed by e Pofidonius to Parmenides 5 and that of the obliquity of the Zodiackby f others i i
Anaximander, Pythagoras, £’/*7$'nipodes.. .. * ^‘?-
g Eudemus f'a\ih,thdLt he firf obferv''dthe>Tro-^ p'icks-,Laertius,thz.x. he firf found out the acceffibn of the Son from Tropick to Tropick. The word fignifies not only theSolfl:ices,but the Equi¬ noxes likewife : h Sextus Empiricus.The Tropick ^ figns are thofe into which the Sun coming,changeth mathem. 5. and maketh converfions of the Air-, fuch qfign is Aries„^zW/^^ oppofite to 'it Libra, fo alfo Capric. andOdiXiZ. for in Aries ts made the vernal conver- fion, in Capr. the winter., in Cm:, the fummerfn C 'Libra the
* De plat, pint. . ,
2/
a F/a/ arch liux'hc teas the pji that v ^e plant,
ohferved the EcHpfe of the Sun^ and faid^ t hat it ' • a. was occajmied by the Moon^ comutg m a da' etl Line underneath hint., which may be fee n rna Ba- fon of Water ^ or Looking-gldfs, b That the Eciiffe , ,
of the Moon is caufedby the Jhadow of the which being placed betwixt thefe tzvo Stars ^ dar¬ kens the lefjer.
The 'I'eftimony of Herodotus., alledged by Laertius IS this: c A five years War was rai fed ^ between the Lydians j/7^/ Medes, in which., fometimes //;£’Medes had the better of the Ly¬ dians, fometimes the Lydians of the Medes, and one battel was fought by night : The War being thus equal on both fide s fin the fxth year., the Ar¬ mies being joyned., it hapned as they were fighting., , the day on a fudden became night-., which alteration of that day., Thales a Milefian had fore¬ told the lonians, defigning the year wherein it Jkould happen. The Lydians and Medes feeing the day turned to night., left off fighting., and la¬ boured to conclude a mutual Peace., which by the Mediation of Syennenfes.Kmg of Cilicia., and Labnitus King of Babylon ( whom Scaliger con¬ ceives to be Nebuchadnezzar) was concluded, with the Marriage of Ary lyattes., with Aflyages., Son of Cyaxaresj Ratifi’d % drinking Blood.
This is the Story of that memorable Ecliple, ^ the time whereof is uncertain : d Pliny placeth it in the fourth year of the forty eighth Olym¬ piad, before the Building of 1 70 years; e Solinus in the 49th Olympiad, the (504th year ^ after the Deftruffion of which falls up-
the autumnal. This Expolicion Laertius con¬ firms, when he faith that Thales compofed only tzwTreatifes, one of the 1 ropteksffe other of the EquindUials., and that he difiinguijhed the feafons of the year.
Sefl. 2i Of the Sun, Moon, and Stars.
He firlfobferved the apparent Diameter of the Sufl, iwhich is the Angle made in the Eye, to be the 720th part of his Orb; This doubtlefs is the iricaning of Laertius, his words thefe, ^ ‘u^uTOf TO Tis uriH i-TTetKoj-ioi-iv eiKOToy fiiesf dimpmetTo' Than which reading, which implies the Sun to be 720 times lefler than the Moon, nothing is more Ridiculous for knowing ( as is granted by all) the caufe of Eclipfes, he mult like- wife know the Sun to be greater than the Moon : nor is it much mended by thofe who
read ^ “^eji to tk iiPm TO T« a-iybjuAis,
the Text feems rather to. require for
or fomething to that efteff, of which, a in Aienar. ^bus, a Archimedes, this we fuppofe when Ari- ■'ftarchus faith, the Sun appear eih, as being the 720th part of the Circle of the Zodiack-, for he confidered how he might by infiruments take the Angie iHadein the eye by the Sun‘’s apparent Dia¬ meter p but to take any fuch thing exaifly is not . • ^ 'eafie-, for neither the. fight, nor the hand, nor the
infiruments wherewith the Obfervation is made, are of Credit fufficieni to demonfirate it exailly.
This Correftion Apuleius thus confirms, in his
declining Age he made an excellent demo nilrationX , , r - r k. ...
of the proportion of the Sun, which I have not on- Olympiad, f Ciemensf
ly learned TTMi Apuleius) but confirmed by pr a- (citing about the fif-
r/;-- 7, . 7„ c . ... L . tieth Olympiad, at what time Father
of Afiy ages Reigned m Media: Alyattes Fsithet of Crafus in Lydia. Eufebius in the fecond year of the forty eighth Olympiad 1430 years after Abraham. Clcomedes faith, it was total in Hel- lefpont m Alexandrina,\)\xto{xcnT\^\is.gjQ-^Lib. 6. Iv
hannesAntiochenus faith,!/' continued many hours-, a xedvto 0 «- but they could not exceed three- Of latter Writers differing Accounts thereof /f *?■' J®”® are delivered by thefe.
Ricciolus placeth it before the Incarnation 585 years. May 28 about 6 a Clock in the af- w ^/xotro- ternoon, the digits Eclipfed 12. ^6.
Calvifius before the Incarnation doy years O- ^ s. 'pre-
13'mpiad 43. 4 differing from P/;/^ 18 years, pitred for the The Learned Bifhop of Armagh, in the Reign oWvaxam, Olympiad 44. 4 the 147 year of Nabonafiar, the fourth day of the Edward Biflit,
Month Pachon, according to the Julian account Hpy September 20 feria i. beginning after SunTife '
I 3m. 25s- digits Eclipfed 9. continuing al- molt two hours.
Petavius Olympiad 45. 4,
' 7 r/i /'/'- uT • N 7 /- 41^7- before the Incarnation
\)\E was the firfi (P^thLaertiu^ that fore- Building of \'^q.July$.
A A told Eclipfes., ..as E\i^tvi\w.s affirms in ^’/J jyiinp- after Midnight 4^. 45™'
2d* '
t.
h Litert. Jchil. Tat. Ifag. in Arut.
Hicefiow may times the Suri s magnitude is compre¬ hended in the Circle which his motion makes. This, as foqn as he found out, Thales fhezoed to Man- dnms 'of Pryene, who being infinitely delighted with this new and unexpeUed knowledge, bad him ask what he iwuld'in recompence for fuch an ex¬ cellent invention : ■ It will be reward enough for me,faidT\\d\QS, if what you have learned of me, .whenfoever you communicate it toothers,you pro- fefs me to be the Inventor.
He fifft found out the Conftellation of the leffer Bear, b Callimachus .
He to Miletus SaiPd, invited ' 'By Thales Glory, who guick.Jjghted Is faid Phave marPd the lejfcr Bear,
The Star by which Phoenicians fieer.
affirms that he firif called it 'AfPl©- the 'Bear. ^
' ’j r. '
Seel. 3. Of Eclipfes.
Herodotus admire him -, attefied alfo by Heracli- ' ^
Julian period 597, after the feria, 3. begin- digits Eclipfed
Hifiory -, for whiejj Xenophanes cind\ 2 am- continuance full two hours.
Kocca confutes Petavius, becaufe that E-
tus and Democritus. Theon, Smyrnms, and Cle¬ mens Alexandrinus cite the lame place of Eude- mus -, the Icope of whofe Book was the Hifiory of Aflrologers, and what every one found out. Thus likevyife Pliny, amongfi the Grecians, the firfi that fe arched into Eclipfes, was Thales the Milefiah.-
clipfe fuits not with the circumflances • of the Story’ as beginning too eajly in the Morning, and being defeflive as to the quantity in Pontus and lefler Afia. ^
Lansbergiut