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# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
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10 Instances oF this ArE in Pappus; and we find; He allo affectins Breviry, (rrhrich indecd he Was
ihc Ffects oF ic plainly in Archimedes, Apollonius, a perteet Malter ot, beins ihorr buc noc obleure)
and some ochers, tho Audioussy corered and dil-invencedmans Compendious Charactersor Lisatures
suised. The sirst Book amons che Crecks, and L
Deliere che only one char crears protessealy ot AI.
to notethesumms, Differences, Rectansles, Squares,
Cubes, and rheir summ, Difference, _c. by Wvtrich
eehra, is char ot Diophantus: Publied ar tirst in means his licrle Book concains more excellent and
Catin by Xylander, afterwards in Oreek and Latin
by Bachet Wich some thines addec oF hisown; and
since him by NIF. Fermat wich lome Addirions ot
his sikevile. Buc ic cercainly vas in use amone
the crabs more ancienely chan amons rhe Cirecks
and rhey are suppoled ro have had ic trom che
Persians, and che Persans trom the indians
Thence, chac is, From che Arabs, the Moors anc
Saracens broughe ir into spain, from whence il
came into Fnsland; and chac belore e hnev
any chine oF Diophantus. The Vse oF the Nu-
mexal Figures, Machemarick Pearning, ard alI
our AKronomy, came ro us likerise che lame vay
uletul Creomerry chan manz ocher large Volumes.
Ouxhered in his Clavis ulually, conceues him selE
wich che Solurion ot Ouadraricks, Parely proceed-
ing co chole of higher Povers, becaule he de-
GBnd it a5 an Introduction t0 Algebra Ouly.
The TaOUS MV. PTarriort WaS Contemporarr
wich Ouchtred, bur died betorehim; hie lese ma-
ny geod chines behind him, ot rhich nochins is
rec publisted, bur his analytice or Alsebra, Whick
AP. Warner princed A. D. 1631. Erom chis
great Man did Des Cartes borro, not 10 lay
Real, al che tamous chinss in his Ceometry, Which
are purely algebraical, 25 any one may sec chac
From ehe Came Original, and abour che Pame ill compare cheir Mechods cogether: FOr ris
Time.
The srA Cipropean Vricer oE Aleebra las pas
hinced above) 15 Lucas Pacciolus Or Lucas de Bure
aMlinorire Friar: Fis Book is in Palian, Prinre
at Venice, 1494. Ile makes mention ol one Leo
nardus Pisanus, and leveral ochers trom whom
he learne it, buc e have none ot cheir Wricinss
Ire Cays, this det came originally to us trom che
Arabs, and mates no mention oE Diophantus;
who cheretore ris probable Was nOE yet LnO
here. Fis Alsebra Poes no Carrher chan Quadra-
rick Clacions.
Nexe came oux scipbelius 2 800d Aurtor, bur
he alto wene nor berond Ouadraricks.
Buc Scipio Ferreus, Cardan, Tartalea, arc
Pome ochers, proceeded ro sire a Solurion of lome
Cubick Equarions
Atrer chis Bombelli vene a liirle Farcher, anet
impossible bur one must be copied atter theorher:
Bur the Geometry oF Des. Carres as noc publisti d
in French eill che YCar 1637; and noc in Latin
eill ehe YCar 1649: Theretore he must havescen
and copied FTarriottS BOOlE.
NIP. Parriore did mondertully improve (in chis
Freacise) chac erhich is purely Alcebra, in the
Follomins Respects, and many ochers which L
mixhemention.
P. Fe brouxhe in sinall Lerrers instead ot the
Capirals uled by Vieta and Ouchered.
2. He maved che CIncourh Terms ot duadra-
+0Cube, Sursolid, ec. explainins che Porver plain-
ly cocheFyC, by onty repeacins The ROOT 25 OF.
ren as che Index of the l’orver.
3. Hle seved etie true Original and Constiru-
cion of all Equations, by purtins all che lqua-
rion over ro one side, and chereby making che
sewed hou ro resolve a Biguadrarick Eguarion Whole equal eo noching; Whereby al(o he deter-
into rvo Ouasrarick ones, by chemeans ot a Cu.
bick.
Then, in ehe last Century, axpeared Nonnius
(NunneZ in Spanisti) Ramus, Schonerus, Saligua
cus, Clavius, ec. Who vrore on chis subjeet in
various wazs. bur generally ene no Furcher char
Ouocrarick legualio
Abour chis rime oue lane Sopsantus, Wotiol
Mechod difters much trom al et ie Arabs.
Wrhich ochers had hirherro all Folloved.
AII this while, che Hnovn Ouanriries in ans
mined ehie Number ot Koors; wtich he Meus are
in Number, Tuch as che Index oF che hishest Po-
et in che liquation.
A. Ele discovers the rrue Construction ot the AB
Solure Number (the Fomogeneum Comparationis)
in a Ouadrarick or Superiour Equarion; Mewino
ic co be che Produet ofche concinual Mulciplica
tion OE allThe ROOES.
5. The same he dorh also by the Co- eHticienes.
6. Ele Mens rhe mas ro mulciply che unkenomr
Roors ot an Equation accordins e0 any PrOPOEtI
siguation rere deligned only by che Numeral on astiened, thereby trecing che Co efficienes
Lecrers, and chere ere no Symbals nor Martes trom Fractions and Surds.
bur for those char vere untnomn or soughe.
7. Ele Meus hon co reduce all adfected Qua-
Bur then cane Vieta, A. D. 1590, and inerodur dearicks ro simple Eguarions, and aIl adfected
ced Wohat he calsed his specious Arithmetick:
Cubicks ro a Form ealily Colrable, by chemeans
wohich is a way of sirins Marks or Symbolsro alI ot destrovins che second Term in luch liqua-
ehe Ouanciries, boch bnoun and untnovn;
Wherebs a rels dte and conspicuous masb
tions.
8. Fe Bews ihe Merhod land 2 verv 500a
Nocation as sained, the whole Operarion ex- one Eis) oF solvins aIl Adfected Ouadraricks by
9. Ie Wphrily also improres he Fxecesis Nu-
 cele rate Impioreenrs, and mans ule
(utich eo avoid Prolixiey Lomit) did Des-lat-
eruc, in his Geometry etiere are abundance ot ex.
The Incomparable MIr. Ouchered followed, and cellene rhines about che accommodarion ot Alre-
bra o Geomerricat Propositions, and many very
nis Clavis Machematiea sic E Publicted 163l. ) Eine Ccometrical Fissections and Constructions; boud
poled alass lo ihe ese M a Mo synopsis, and complearins the square.
fore calen norice Of.
Vieta also introduced che Numerat Exegesis Ot
dlected liquations, Mewins how toextract cheir
mtoa tventea b ieta.
abos in Numbers. And in che Denominarion fres rake trom Parrioc, wichour ever (0 much 25
oF rhe Porers of Numbers he follons Diophantus, (namins him, and publim chem as his own. Fis
add nor chie arabian Manner uled by orhers.
misheily improred che specious Alsebra ot Vietu
nanr Discoveries vere made in Alzebra, nor bc.