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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 7v, page id 00068197:0014
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EE, FF
invenire duas curvas coevolutione generantes curvan
EE et FF CC. Manifestum est Ellipsia centro
fo umbilicis E. F. descriptam ibi langere curvam
Fingamus dari cur punctum C, et punctum F
quaerique punctum E. Hoc ita invenietur, datur
ex puncto C educatur ep  ad curvam normalis
axi occurrens in p. datur CB aequ y. B Raequ p
jungatur FC Ex Ex F ducatur FG hormalis ad Cp.
et centro C radio CF arcus secabit FG in G. jungatur
CG patet angu ex natura tangentr Ellipsin, angulos
Gep, et FCp fore aequales. Eodem modo inveniatur
2G intersectio rectarm 1C 1G et 2C2G dabit punctum E.
quod jam calculo quaeratuo
Idem brevius: si tangens e curvae Fx incidens in curvan
CC reflectatur inde ad curvam EE debet eam etiam
tangere, unde angulas quem recta PC ad curvam
perpendicularis angulum FCE ca bisecabit. Data
curva CC quaeruntur curvae FF, EE, et ex
his duabus alterutra sumi potest pro arbitrio. Sed
curvam Cc intelligo dari, dif proprietate tan
gentium, seu ratione CB ad Bp expressa per
AB et BC sit AB, X. BC, y. 4
AGZ, FG, v. AH, h. HE, C +G+.
ex F et E in CP perpendi culares FK. Et. producantur
et in eas ex punctis , N _K dem Hantur
normales, TM, NZ. Habetur FF aequo t+ v
ob triangata similia FKC et per F ducatur axi
parallela FW, ipsi cp occurrens in W erit.
FW: TP:: CF: C7 Et rursus habetur FW.
et Fursus FK: FW:: CB: CP  Habetur FK.
en FK T aeqo TP. CF. CB. Et eodem modo
cT. CP
aequ Np. CE. CB
b angulum FCK
CN. Cp
et ECL eundem erunt triangula
CLH CKF, etX et E similia, eritque
Fh: Et: CF: CE. Ergo fiet:
P. CF. NP. CE:: CF: CE
CN
TP. CHA CT  Ergo TP: CT:: NP: CN vel PT: PN:: CT: CN
quod sine calculo praescire poluissem ex noto thcoremate
constat quod bisecto angulo segmenta lateris angulo oppositi, sint
lateribus adjacentibus proportionalia. Est autem angulus
TCN, bisectus recta CP ergo erit pY: pN:: CT: eN. Est autem
PF Denaequ. AP- AF seu X+ p - Z + +, et PN ego A A seu  h+A- X -p
quaeratur BP, p. FG + N A n. Ar . FIatM. . . ...
+F TG: GF :: TB: BC, seu t: v:: x- Z+ t: y.
NH : HE:: NB: BC, seu n: C:: n + h - x: y
opus doneoccurrant alei in R et S
est EL
C7
seu et est detap, et EN ost 9. p pepto esse a t apo f. A Epu eps ad id quad jam cum constat tempe dh. dv.. Z. L. v. 
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