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# Catalogue record: 5608 — [Wallis: Auszug aus den Briefen von Newton an ihn vom 27. Aug. u. 17. Sept. 1692, veröff. in W' Werken 1693]
# Incipit: [abgerissen] Quadrandi curvas per hanc seriem exempla 4 subjungit (qua
# Date: 1693
# Sender: Newton — Addressee: Wallis
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=5608&katnr=42025
# Work: https://leibnizlegible.com/work/00068124
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folios: Bl. 85–86 (from the shelfmark LH 35, 8, 30 Bl. 85-86): 4 pages, canvases 169–172, page ids 00068124:0169 to 00068124:0172
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=169
# Lines: 215 recognised on 4 of 4 pages, mean confidence 0.81
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
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# After the first blank line, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 85r — 00068124:0169
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 86v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000169.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 67 lines, status machine
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

## Folio 85v — 00068124:0170
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 86r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000170.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 47 lines, status machine
pla
cos et darys socionos
coratae quantitatos,
augontz y duminuanth tangue
. 2 et ppoluy meromontu N docro
de puncus lornis sic nolat V, X ij, Z et hery
Lua 2aV d fluxro quantitatis V et i fluoeco ipsius
denontos practd Y sardae, flusciones dary sue notat.
Eu veronos F y. _ et V aa = 3e X et hary fluaiones st 5 X et
6 = 3
Jere ( doepositis mothodus sua in pepositione ha Problomatita bundat
20b. 1.
Tatâ aequaliond fluontos quotrunque quantitaros mverent invoniro feuacionos.
Solutio.
MultooltoB quilbot aequationit oru soparati q induos singulos dignitatus, quantitatus ocysfluentiu
quae in 1ro 1lo glmontz et m singnes multiplicaorbus mulol3 Calus unys dignitatis in op fluociond, et aggrogali
phodutoru oeu sub propris signis componet aequationo nora, quae rolavom fluscionus involvot.
Explcatio
Sput abE. d. ve quantitates dolratae ot un matabilos; et proponats aequatio quaevis quantitatas
flnontos Z, y, X De involvons puta X - X 44 + a a 2 - 6 =0 Maltiphoent lori prnno por
induos dignitatus ipsis X in iposis contontarus rospoctive, et in qualibot multipliao pro une Caloro d
dignitatis (hoc D ero X unes dimonsconis) soubalz X et summa productorus dut 3 Xex ieua. 
fiat in i et producolh = 2X 41. Gdo fiat in 2, et produrob3 + aa 2 Summa productorys oiu
aequolu nihilo et Rabobiths aequao 3 X X = X 44-X gy + aa 2 =0. 8100 qd haer ont aequa rolacom
fluoeronus invoevens.
Domonstratio.
Sit  e quantitas infincte parva et sint o2, Oi, oX, synchrona momonta sou meromonta
momontanda quantitatus fenontus Z Y B X: et quantitatos prosenno compouis momonto por accosdam
meomontoy momontandon ouadont 2 + 02, y + oi, X + oe quce n aequad grma pro 2 4 et
Xe scrypce, dant lanc aequadoin X =3X x 0X + 3 X 00 s X = 3 X 03 = X 44 - X 0yu = 2X oiu
=2X ooiy + X00y i + x 0 ii + aa Z + aa02 - 6 =0. Subduc aequaoom  pruna et 26suduy divisus p
0 dut 3X 2 = 3X X OX + X 00 - yy - 2∞yi - 2 X oyi + Xoiu + è ooyi + aa 2 =0. Soros
mueliplicalos por e tangue insimo parvos doeo, et manobit aequao 3X  - X un - 2 X 41 + aa Z = 0. g. 3. d
Punali mothodo aequao X = X 4n + aa rax - qu - 6 = 0. oradit 3 X  e nu - 2 Xe qu + aa YaX
1 =0. Ubi si fluxionem rax= un demumaro rotis pone rak - in = =. et p consoquons ax-yu
= 2 et Proposctio dabit a  - 244 = 222, id d a  - 24n = Z sou 21 a X - 4y = rax - yy et
indo aequalio pramo moonta fit 3X X - XyY = 2 Xyy + ad X - 2 avy
a X - 2yy
et dado mothodo pergere lirot ad fluocionos. 2dut ac tortias. P on al3 aequalio 2 1 = 2 + at = 0 et
== 0.
varyu
Propositio undo dabit Z qd + 3Z 147 - 4Z2 = 0, et haes aequa por oporaom roporita dradotZ yd
+ 62i y2 +3299 +62412 4223 -12 22 22-0 et su doncops.
ut appliots haec mothodus ad quad ratura Curvarus. nontones pro flurciono absriso umforim
posita, unitato assuunt, et ordmata ponit pro peuocond arvae; domdorotaom unor alheise a  aequat
ne quavis assumplâ definit, et indo colligondo oavrys fluxciones oennet aequadom nova qua rola inter
abscissam

## Folio 86r — 00068124:0171
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 85v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000171.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 44 lines, status machine
absersoa et ordmata debuitz; et li donus id qua randas Curvad dfficit ut haec aequoo boam qnvis dos.dd
ratei acquorat. et hac mothodo duit s compulo brovisonno et fancimo Thooromata supra posita mve
nisso. d et ado mothodo comparat divoises Curvas inlor d ponondo se Dary ordmatas fluoeronly ab-
socheary rocyroco pportionales.
Sub fino Epistoere anni iby0 scrilit (e Protloma doorandi Curvas p eonditiones tangontius
(Ed Loclitins, ivorsum de tangentibus Proetoma, appoceat) in sua potestato 00. una 7 alys
difficilioribus ad quae solvenda so usyue d dicit duplici mothodo, une concinniore altora gratioro; et
utramque Citoris branspositis colat: quae m ordmom rodactae hanc sottiam drehent. Una imothodus
osistit in extractond fenontis quantitatis  equaod simul involvento fluociond  aevora Hy in
assum plone soudi pro quantitolo qualieot ineognila ex qua caelera commoda douvari posst, et in
coceatione toroiy homologory cequavis resultantis ad emondos dros assump la sondi a mothodon
Eda de veibrs ja racilalis tabsque altorcors xpercao rlugi polo; praoie ab aut hor ja accopi ut sequir
pro oatvahondo
Hec mothodus, ait d d guis 7 da p datrachonde radios  aquadih assocus supores descysta
Pons qu Probeoma rosolvendus durals ad aequadom fluontos quantitatos y et 2 una y dary fluaconbus-
i et 2 invoevento, et qd feuxre ipsius Z unifor mis sit. Ut haec fluono on aequao anestat pro da po
nalz unias et manoet aequad soeas y. 2 et y involvons quam Rosolvonda vocat. Proponl 3=
invonto ypstus y n soud insunte convergoute, que sola Z invoevot. Hoc n alrquibus aequaoi impostilieo
d. maeis praeparaoem aequooqu requin it, ubi voro dordoto consici possit resolatio d hupmodi.
Prob. A.
Ex aequa flunecono raduro imivevonto d osctratloro.
Posolutio.
ou obs ddode equaois Calore osistentes ae quont nitulo et ipsary y et ii Dignitales (si op se
dexramants sit ut dary indues ne aliouli nogation sint, non ubique altioros om ad hunc osson
roquoulz; et sit R= lorys infimae dignitalis vory qui noq pez y noque p oss fon il noq pde
cors digulato qvis multilrantz. Sit P= qu j Jorus alius qualibot et oos ordno vros pourrondo
at su, at lot Rous opmodi nros quot Voii. Hory nory
nacennus vocols vet z out diguitas prumi tou servoi. P2o ojs coossiront ponalh a. et m
aequ’aod quae resolvonda diith Prubo a r proy, et vaz pro y; ac tou oos rosultantos in quilus
2 opdo D dignitatio ac in loro Z suo prosiis signis colloeli, ponantz aequalos nhilo. nam hac
equa dobilo roducta dacit cooffiments a su hos a2 V27 prunque sorvi
Opdrao Sda
ro roliquis orbus hujus soudi vord nonr mvenlis pono P et hotis aequaoom y = are = P. et inde
8)  Prob1, aequaom ij = Ya 2 4 p Jn Rosoluondà pro y et il saulo tros dory valores dt
Robit Rosoluonda nova, ubi  offuns praestat ipsius y: et  hac Rosdlvonda prunque detralos ry sonoi
P eodo modo atque lorus prumus fordi tolius 9 = a2 + p do solvonda prima debr axisti.
Oporao slia et sequentos.
Rosolooda bado a mvomos atque edu moonisti et o ou or hliy sori tolus
daebratos, et similitor Rosolvona quarta mvonies et de d quarty soudi viy, et su in infut
souos (a sit nocula ont ra aequaois qa extraton oportuit.
Ccomplu.
d aequaot  2 = 2 2i - dd 22 +d22 = 0. extrohonda sit radix y. Pono 2 = 1, et
equas oradot yt - 27 i - dd + d 2 =0. quae ont Rosolvona. a voro 1ory infungs in quo nec y noq i
copponto. D 3d. qui phi au esta se L aequats dat 2- B. Sa3 velequus est X 4 pad bs. a uom

## Folio 86v — 00068124:0172
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 85r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000172.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 57 lines, status machine
aequato succossivo, et indo in pimo casu n = 0, a = 2, B = 0, et im 2d0 n = 2, a = 0 et B = 1. C) hunc.
a+ sit in ermno casu 0, in 2 - 1. Undo vd0, et a2 ot var isunt act 0; quam allum duae 80
X- a + B
n Rosoevonda joro y et ii scryplae produrunt aa +02 - dd +d2; et lere aa et modd in quilus indoae digni
tatis ZDX sou e, posili aequalos mihilo dant a = d. Undo pumy souoi lor9 a 2 oradit 
Oporao Da
P20 tous roequas parre p, et hobis aequaoem y = d + p, et jed osse B081) i - p. qui va
Coros. in Rosglvenda pro qot it substituli dant Rosolvanda nova 2d p + pp - 2Z io + d Z = 0. ver
V ot je viros subount ipsam yul y. Tory uny en quo nor p noq i roppduls D d2 que cy toro Se =
collatus dat X = 1. Ssip idlquis 2d p. pp et - ZZ  pond p
casu Robio p = 0, a = 1, et B = 0; in 2d n = 0,  = 2d, B = 0; et in tortio a = 2, a = 0, ∞f = 1. et hunc
X - a + B
 + obedit in erimo rasu 1, in 2d L, n Crtio 0. ando v81. et a2 vra2- sunt a2ot a
Tou duo ullimi ar et a in Rosolvenda pro qu et je resportioo sorpui, producant 2d a 2 + a 2- a 2e
Ad2. et lori 2d a2 ot d = in quibus indox dignitatis 2D2 ou 1, positi aqualos nihieo dant a - - 
undo a 22 brus primus sorvi V sit - = Z s
Oporao lortia.
Pro torio dequis nondus invontit pond 4 et hobis aequaem p = = = Z + 4. et ando (hor Broci)
jo = - =  4: qui valoros puro p et p. in tosolvonda novissima substituri producunt Rosolvonda
nova 2d9 -24 + 44 = 7 2Z = ZZ9 = 9. vli qet a viros supplont ipsory y et i. Tory unreu in
quo noque quo q rporilh D  Z2, que cy LZ collals dat 2 = 2. Cons roliquis 2d4, -24. + 42.
pone l2 a’ il aquaton surossid; ot indo in crimo rasu hobjs n = 0, -168 0
200 p = 1, ∞ =1, B=0; in tortio p = 0, a = 2, f = 0; in  A = 2, ∞ = 0, B = 1: o indo q- u t 
a+
ovadit Teruno casu 2 in E 310 et 4 1. Et hunc V D2, V a2 v. va Z sunt a2 et 2a2: qui
quo
valores. in Rhosocvonda q et a gabsiituli dant Ld a= a7 + aa 2  +2Z- 2a2; ot lri
2d a22 + 4Z. Z in quibu judore dignitatis Z  7 son 2 quositi aqualos dant a =-  undo
a 2 129 primus souvi 4 ouadit -
sovidi
Ooporaca sta
Aro aeliquis, tous du mogulis pond r. 3t hobis aquas 
67
2 +Y, ot
, et vis q es indd Rosoevondam nova 2dr + 27 +Zr + 324 - 322Y + YY - 2E1-
1630
et ea se mothodi suporcone hotrs 
p
64dd
8
C iqus radioe actrahonda y = d + p = d = = 2 + a = d = = 2 - 2 2 2 + r = d 17.
c et oporaoem quinnando prodaon ecot raduo ad tores peuros.
-
Et dado mothodo diit nontons raduos aequaoy, Pluacones Edas, vrtras, alas Cii ii i aerasque involvontuu
rovosunt.
antrahi possd GfS uti 3 2odiy ontractionibus ubi aliae mothodi mtrena in epese craeducta anni 1byb
docet, qd, in soluliono problomati de tangontibus invorsory casu aliqui dants in quibus hac mothodus grabs non coquunlz: 
Peticulantor si m vrcangneo redangulo qd ab ordmata tangonte, et intogarents plo alsussae consuturts, adeae duory
quony ebot ealoubus trien e aquaom quivis dofrats; Rrobloma absque mothodo hacee grali solvi pollont.
mothodi (a hae oos lplculares qui grales collocti sumplae, solulione 2da pis prollomalis qd nontons
suae milio grius opistoere. sus vorbis proposint. Pata aequao quotrunque flnontas quantitatae ivolvento flaxionos
invono et vico vorsa. Nam tola bluocionus mothodus in hujus diro et à et invensa solulione osistit.Gun
morhodo assunsD A Mothodus dicali Lorbrutii  utraque antiquor illa qua 2Is Barroro in Lortionibus Goomotum
exposint,  aguitz D Aelis Loipsiris (auno ibysi monso sau) a quoda qui mothodus adhibot Bibncti sunulo. dqu
adtut onulus B suporeod doi 8 formulam Analssont brverum et comnodorum adaptatio ceml tevors
funid.
4d