# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068124:0171
# Permalink to this reading: https://leibnizlegible.com/page/00068124:0171?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 86r, page id 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.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=171
# 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
# Lines: 44 recognised, mean confidence 0.86
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

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