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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 26 (shelfmark Lh 35, 5, 26)
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sro Circulis ergo osculantibus ad hibeamus Elligises osculantes et
supponamus Ellipsim tangere curvam propositam eC in tribus
punctis inter se coincidentibus, sive obculari secundo oscali genere;
et quaeramus cuma Eltis loca focorum harum Ellipsium ita
osculantium; e seu duas curvas coepolatione generantes
Sed de lies ut dictum mongi in scheda peculiari
sutaii. 1683. ubi deprehensum non posse curvas coevolation
datas dari  Algebraice, quin etiam sentrala Algebraice
pro setemniae generatione autem curvania transcendentium tale
detur
qud fertandum puto
Curvae CC data est proprietas tangentium
cu sedatio seu posita ABX, BC, y cD dx
DE, dy.
luva
rEK
2+
AS7. A RS, v. quaeritur
iuents ex ea langentes RC
ti
producantur ad curvam CC, sin ut R2C
3C et ex punctis 1C in A2C demittatur
aperpendicularis 1CCE, et ex 12 C in RBC perpendicalerus
(2E. Sint ipsae 1E2C, et 2E3C vel differen,
summabiles. itia enim evolvendo curvam R R
et movendo punctum aliquod in fito evoluendo
Mita ut velocitates sint ut AE2C, describetur curva CC.
ebet ergo inveniri relatio inter 1C2C et dx quae sit summabilis
et praecerea debet posse inveniri punctum R, idque ex data AP
ssumamus relationem
subtatis differentialibus, comnuuni Geometria
b summabilem quamtibet inter 1E2C et 1BAB seu 1C +D. seu dx.
et sit 1E2C aequ d mav. xB. posito e dari per X sumum abiliter
sic utaqe  e sit summabilis, quod semper fiet, si componatur e vel
ex mens integuis respectu incognitae, vel si nominatores habet, nisi sim
plionasit
plices habeat. eritque CrE aequi jam 1C1E +  e aequ dx+ dus
ergo habetur , C,E per compend. Cor porro: rege CC d
1erd B ICrdE. sim. 2CDEF. seu iCid: IdF: ICF : : 2C. E: EF. ECF. et
1DF + F, C aequ d dy et 1CF + F,E aequ co. Addatur ex. tum laterum
1
proportionalitate idF: ICF:: _F. E: F2C. Ergo fiet.
IDF. F2C aequ. ICF. F1E seu 2 ~DF dy = 1DF aequ ICFCO- 1CF2
e
Habemus
seu (1CF - 1DF C) dx aequ. ICF co = 1oF du
ergo cDF aequ iCF co - dx: dy Ergo erit
1DF aequ 10F c - 2. CF co dx + dxt,: dy aequ 1CF- de
Ergo habemus 1CF co - 2 iCF co dx + dx aequ dy elt- dydx
habetur ergo 1CF vele si malimus. 1dF faciems:
at CF aequ dx + ad F. ergo fit  idF ds ardys dx idF id  aq sodo raidEV
Substituendo in aequave pro 1dF paulorante inventa et pro cd porendo
palorem per . e. et  dx. dy. et prae dy valorem per dx habebitur
geminatis, Z et B sunt una eaedem, quaeratur ejus aequatio differen- _k. de supponicentanquam in da Gabilas per dm. du. M. H. itaque
aequatro in qua solae extabunt X. y. Z. V.  Et quia X et y. C
tialis habebitur nova aequatio secundum X. y. C. Ax. dy. de. Z. v. restabunt solum Amiran. qua in aequ B. quas sollendo per aequ. 1. datam
et quia de den telet per de Ay sritendo e ascibandi pro eo
1CF aequ dy 1dF + ax,: co. et 1CF ego dy rdF dyde idtidu: 
Habetur ergo idF. Est autem Triangulum dC idF simile Triangulote
RMrC et R M est v+y.et =CM est y-X. ergo fit:
v+y: Z-X :: dx: idF et pro hunc valorem novum ipsius idF