# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068107:0003
# Permalink to this reading: https://leibnizlegible.com/page/00068107:0003?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 12
# Folio 38r, page id 00068107:0003
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 37v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068107&page=3
# Source image: https://digitale-sammlungen.gwlb.de/content/00068107/jpgs/default/00000003.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 59 lines, status machine
# Lines: 59 recognised, mean confidence 0.96
# 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.

saepe lineas infinitas aut infinite parvas
occurrere, ipsam analysin nos eo ducere.
in aliquo problemate
Ut si quaeratur modus coucenda sit recta
a puncto dato ad rectam positione datam,
quaeraturque punctum ubi recta quaesu ducenda
rectae positione datae occurrere debeat. 
certis casibus evenit ut punctum occursus
infinite absit, quod significat seu ut distantia
ejus a puncto dato sit infinita, quod significat
rectam duci debere ipsi per punctum datum rectam
ipsi positione datae; parallelam atque ita solutum iri
problema. Ut proinde ipsae lsis calculus analyticus
nos etiam in communibus communis Geometriae
quemadmodum multis exemplis
problematibus ad imaginarias quantitates non raro utiliter ducat, ostendi posset
non rago utiliter ducat. (um ergo eta mihi clavem inventionis et ipsa
mihi Analysin sublemioris cui Initia artis
analyticae in sublimiore ista Geometriae quae
algebrae minime sub non subjicitur tradere
propositum sit, eo minus imaginariis
quantitatibus uti verebor. Itqe idqe
etiam ee non tantum consultum, sed et
necessarium puto. Cum enim dubitari possit an allaedentur vere curvae
nec nisi difficulter quae non ex portionibus rectilineris fractis
eat
constent; contrarium certe non nisi difficulter
demonstrari queat. manifestum erit demonst
valiocinationes nostras locum habituras
sive curvae hujusmodi dentur, sive loco earum
non nisi polygoua dentur,  laterum adeo
Subtilium ut distingui non possinta gis
Nam quo subtilior erit cuva magis ad curvam
veram accedent, eo minor error erit, quod si
in eam plane desinant error, erit nullus.
itaque  veram inveniendi artem dere
n exponere contentus, a pagogicis
demonstrationibus tempus nunc non teram,
has enim quivis facile ad imitationem
earum quae apud Arthimedem aliosque extant
Concinnabit
vero
Tum domnia problemata circa
dimensiores curvilineorum reduci possint
ad figurarum planarum quadraturas
ut suo logo ostendetur, id ideo
assumamus in plano lineam quamcunque curvam CC
directicem siveaem
 C3C C ec; junctisque rectis rC.C,
et VC3C, et 3C4G e et rectam aliquam BB
aliquam +B B3B 4 B, jungamusque
et a punctis in curva assumtis atase
ad directricem ducamus recta onei rectas
inter se parallelas + ( B. et 2C2B, et 3B3C et 4BaC
quedvadia apslicata
qu vel quaeratur angulus rectae
datae ad rectato ducendae ad
datam: tunc 
in natira darive possint