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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 5r, page id 00068197:0009
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 6v); this page is its right half.
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sit curva
CC Quaeritur ejus naturae, ut si
ex puncto curvae proposito quolibet C
ad axem seu rectam infinitam positione datam
AE Arminatur perpendiculares ad axem
CB; et alia a puncto curvae eodem
educatur ad curvam perpendicularis C
quae axi occurrat in P, sit relatio inter
perpendicula CB et BP data. verbi
gratia si sit BC ad Bp respondentem
ut a recta data est ad ipsam BC recta
data B auctam (vel minutam)
quoniam autem curva CC non est determinata, nisi unicum
aliquod ejus punctum sit determinatum, sumamus punctum aliquod in
axe, ut A, per quod curva nostra transire debeat.
aequalio vocemus, AB, X
aequatio
(2
AP, p. BC, y.
Cum
erit
y: p - x:: a: y + b. seu differentiali expressione
1
dx: dy:: a: y +b. Ergo quando curva incidit in axemn A, seu
quando BC evanescit, seu y aequ. 0 tunc fit dx: dy 2: a: b.. sive
quod idem est, si in axe producto ad partes convexas curvae sumatur AE
aequalis ipsi A, et ad eam normalis EF aequalis ipsi b juncta FA
erit hujus curvae tangens in A.
puncto habebitur recta eam tangens.
Et semper quidem dato curvae
aliam curvam
Sed hoc amplius quaeramur curvae hujus curvedinem, sive gene
ratricem id est cujus loc qcurvam quae sit locus centrorum omnium
quaesita
circulorum curvedinem curvae metientium
Id est quaeramus circulum
positione dandum, qui curvam propositam secet in tribus punctis inter
se coincidentibus, ita scilicet, ut quaerendo punctum intersectionis, problem
haberet fres radices aequales. sit ergo circulus GG secans turmem cC
in tribus punctis. sit cantrum ejus R. et ex centro, Rin axem perpendicularis RS
sit AS, it
fipt
rantan
RS, v. erit  Rs + BC quad (+ B5 quad seu + AS = AB quad aequ quadr. RC
qu +Evyty7
RCAt
 f 2Z. 2ZX + pex aegu.
2
cujus differentalis
6
analogia