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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 240v, page id 00068200:0482
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saeterum magnum hinc orraejudicium sumitur, eodem modo
non posse intersectione durvae transcendentis + analyticet
contactu
inveniri facile punctum transcendentis. Nam non succedit
modus educendi  aequationem tanscecdentem in
serpsam; et post in duas divellendo, quae quidem se tangent.
sed puto X non invenietur, sit veri gratia
xabx in seipsum dabit e a  ibx a ec a
u
quo divulsa in duas: A: a  - 2bXX
dy eq y ay
seu a = 2bX a + y = y + bbXX. aequ. 0 quo divulsa induas
gabit.  y aqu 2bx a = a et y aequ. bb XX
quod si se langual fiet: dus aequ 2b a x + 2bX d = 2a xe ex natura
sangentium tum universum tum logarithinicae cujus numerum primarium posuimus
esse n. pursus ex 5. fiet ius aequ. 2b6XdX quos duos valores
aequando habemus vatorem ipsius tolletur ax. et praeteren habevimus
valorem ipsius a sed supposita e
aequales, seu si aequationem, acubavissemus haberis, tunc aqua
tionem differentialem licuisset iberum multiplicare per di expordentes
et habuissemus nova differentialem, ut
a - bX aequ. 0 unde a - _3 bX a + 3bbxx a - bX aequ. 0
 multiplicemus
addatur ea pyt yago d et divellatia, had
per exponentes, fiet :  3a d C = 3b a x) - 6bX a d e +  bb a X (X)
btr
_ + 3 bb ∞ x (dX) C = 3b3XX () aequ. 0. seu fiet
fea - Yb Xx a - 2b ex a + ibb x a + fblexx - fb X aqu.
quam iterum evocabimus ad differentiales, fiet:
ago 2a  - ba  - 2b a C - 2bel - -bee + 2bb a 4, + 1b60 + 2bbeX- 3b xX
seu  2C a - b x a - 2be a - 2b ex a - 2 be ex + 2bb X a f 2bbeX +rbler 3 (63
houmitrium
unde ope aequationum 2. 4. 6. tolli poterunt xceu a. et X. et e.
0aequ
quod vix andeo credere successurum.
inveniri valores.
potest autem tentari pluribus modis: ut appareat an idem semper
valor ipsius e.
iidendum in curva nalgebraica, inveniri pessit trans
cendentem tangens; per viam rotationo, ec notavi si mdo
evoluta parabolae supra titlo parabol oides semicubora super cycloide
rotetur) licet curvae extendibiles in rectas, tamen, rotatione descripta
non fore algebraicam, quia ipsum punctum cycloidis ex quo caetera
sumenda, non datur algebraice. Opus ergo alia arte an scilicet
duae inverviri curvae transcendente inveniri possint, quam
una super alia rotetur et curva descripta fiat atgebraica,
ut s ordinatam ejus per calcumtum quaerendo adinata curva lipusiem
kentis destinatur, nondum video impossibilitatem Nota
cum curva super curva rolatur, ibi alte punctum illud unius
illi alterius insistit, quo arcus unius aequalis arcui alterius.
alia voluta circuli ac
sumatur verbi gratiane voluta circuli et votetur super carculo simili, ut cylide
adhibeaturue talis motus compositio ut descripatur inde curva analylica
algobiarca defcriptis quantitati contactus ylbiaiceu tanscendentis haber
poterit.
il a aequsa
 aqusX