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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 85r, page id 00068124:0169
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0 haerou
utcunque offoctat
qtosti duci. noc 
quosnomeus quibusda alyo hancn
Curvaru Thooromata invonisso quorue Duum
ad Curva aliqui quadranda sit Z abj
toro alsussae nor maeitor insistons, uli etorae do.f. d
sou creponontes dignitat quibus assn ; ,  et n’Enducos digu
C + fZ1
dut
Q n
S
f2
ubi ducits in sd tota subsoquents, et A, B, CD vc donotant loros soroi proximd autocedons, n. A-
Uorus erumque 3 B lery Saund, 1 X   et sic domo oyps. Jlaec sorids ubi _= Aracho d, _ nigs nogalioqs. qti
unals  infinit: ubi voro r intogor d  affirmatious qtmnatus ad tot locos H, quot  unctaros 250d o F, et sic
exhibot Geomotruu quadralura Curvae.
nc.
Qeadrandi Curras  hanc soud expla 4 suljungit (quae brovitati gratia pretor melto)  nitoron duos od casus
f + CZ) et hoc casuf scribondq 3 soro X Sooromalo pro e. ot  o f y - n pron,  O + 4 X pro 8. Et
si soucos: noubre easu abrum pils et Pructa radit, concludit Curra d ary nre  quae  posit on quadrari
danc  rogula et aumadvortit dibo m aequationb fuictis ardus oiy gometuu quadratira ad muttont curvary
quarque ordmati applicatae constant ex potostatibus, Eadiibus. V quibus libot dignitatibs binoarii cuju cunque. Et qdo spusmod
Curva d poto Goomolraed quadrari,  ad manu alia shooromata pro comparoot op cy conerit oc  5.  e abi
Bann omaleenna quabus  poto comparari: ad qd sufficor ds Roc ypsys ja doscryple shoordme di dobito quinnetz:
annis alquot post serypla hanc ouistola olaposis, D2 Pavio Grosorius tunc Mathosoos Profosdor Edmburgonsis,
nanc Colloga mous dignisonus invonit palia Mothodus (uti audio) sonem opdo grid et Raced norotonma, quanm
tons complontoubus involnta, damque D Archibatdus Bitcarnu, diobus bribus ercclor V quatuor autoqu nontoncana didorant
in luc Doudit. Nam D Johanas Chacg. qui in Acadomra Cautatrig onsi cum 3 nonotone quorsalus suorat et sduo
o ibi rEdorat postulabat a nortono jede E prstolam ut is oxomplat sordi suae ad ipsus tunc Edri commoranto
nivrot, ut 7 Gregorrana conforri posset
Htans soro D pontons: Mooroma primys vocat: Duit  50 pro Caris quarus Ordmatie  Srmoniis
onbeantz et pro aeio quibusda rogueas aliquas guunasto. Jamque in  ad mo datis aug27, et Sopt 17. 1692
otdri
scubit progrosdionos de hory Thooromaly in infructy pergonles, quae ton ora in sujusmodi Thooromalis gratioribus com
pohondi post.
Si Curvae absusa sit Z et poro toris sup sorioi a + 6Zn +
+d7 3n + d hujuszur e+ f 2n
9721 + R23n + Dc roe pro dors quolibot scubantz  et R rospoctiro; n. 2 pro primis et  pro socundis:
sit (a ordmati appereata 2 = 1 2 R = 1 e ponat  = r, Y + 2 = 5, 5 +2 = E F +  = Y VC: dit ava Currae
ZX in na + Ab sf At a + tc =1fB t91 7 en  d 7f. C = EgB- vRA Lon + v
r+1XC
r+ 2XC
Ubi A, B,. C, e donstant coosficrenles datas lorory soiisz signis suis, nopA prmie lori, coessient B
secundi coossinontom B-sf BC sit donncops.
Y F 1 HC
Dua mothodo in hupmodi sonos imedit minumt dexacat, dando on clouo quibusda coeavit quae rocto ordmd
confitiunt hanc soltiam. Pata aequalione fluontes quoteunque quantitatos mroevonte fluarones invonr: et vud
rorsa. Por fluoures quantitares intolligit Indotoratas 1.0: quae in gondrao Currary p motys Coato sopoluo augonls
diminanat3, et p darus flusecono illiyit cocorctato moromenti  docromonti  Nam quavit fluontos quantitatos et eans
fenocrones ex ima bronto quopolu diffintos rudeantz, (solent  nova diffieitus quspi) eaunds on nonono iico sarilioro
dvasura poutat qui sit nolio momontorys aut ply minimary r difforentiars insuie parvarz; pproptoroa q siqua
de quantitabys gonoruo je moly cotinuy magis naatis d, et facilius qupi3, et Schomata i hac mothodo socont ’inspliioe
qi a phy. Atton d negergit Thoorca taerus phy, A ea e, utilzs quoties iosa Nopus broois roddit. et magas porspreuy; 
ad Eimandas seroronus s portiores condnito abstisum Carvae altamoo alquram quantitatem seroentgaum toimutor
p -
d
X
c+fZ
Huc 0+
S=
EZ
r2
5-
ou
r= 2
5- 2