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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 19
# Folio 2v, page id 00068037:0004
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Opus tamen cuntela esse video, nam sequeretur si haberetur
arcus spatius proportionales, haberi posse et ordinatas spatls pro
portionales seu figniae quadraturat
Hac methodo morifice contrahi potest caleulus.
qidianum an hac utile esse possit, ad efficie inveninm
sincidins 
Curvas dioptricas: sit curva AC  Radius CR C B incidens Refractus SB.
eA
Sinus ronguli imcdentiaeam perpendicularis ad carvum sit PC 9. et
et 
sit cq aequ. C Psex puncto Z demittatur perpendicularis QR
in radium _ incidentem RS. et ex puncto p perpendicularispe
in radiuum refractum CB. erit QR sinus anguli incidentiae
et qes sinus anguli refractionis, quorum ratio erit
in nonenutu debet esse data ut a ad b. licet sem per
eadem  quicunque demum sumatur radius ipsi
RC parallelus,  radio semper refracto
in B. quaeritur quae sit curra quae hoc
praestet. Sit Axis recta AB
parilleta radio transiens per B.
in quem ex ex demi C. demittatur
aps perpendicularis seu ordinata CD aquo y.
C CD. DP: CB.
CD: DB: CB:: PSi SB: BP
ex 13Xoqu Z  A 2
au
Adaequ. X. De aeque
Cvel Pergol y
ZR: 5: : a. b. seu dequa P
AD + DP + PB aqu ABaequ. C.
Ergo cD: PS:: : u c- X: SB: a. b. Ergo SB aequ 2. C. X
l
it PS aequ D CD aequ  y. BP ro sit Ds aequ p. et APegu xtpaequ
Ergo fiet P B aego C- v. et pB aego C-2eV +  aequ. (p3 + 5B
s
S+ 65 HC- ∞
b
compendiosioris calati jam CB aequ 5 +Z. et erego setq aequi
B+ TtSt
rum aelumy+p+b
Unde ex collatione aequatignum 1. et2. poterit tsli v. relicta;
folummodo X. et y. Unde video non esse orpus methodo tangentium
v- 2VX+X
Sed inventa hoc modoa
inversa ad problema hoc sopticum solvendum.
relatione inter X. et V. necesse est inde iterum investigare  vel p.
et palorem ipsius  hocmodo inventum methodo tangentium
directa, et valorem hunc cemparare priori, qui si coincidit, problematate
habetur, t hoc solutum et expicanda si opus, c. et a ut coincidant
valores. Si vero non possint coincidere galores problema tale fii
empossibile. In aequ. 2. pro, v. substituendo valorem ex aequit
fiei: Ssi +CaX  aiqu c+ Sy by cium et uxtex
a
id est eB ago sit DEaequ. q. FHaego b. erit B Hequ SB.
q
c
H aego P. et BG aequ PBBC- g. Ergo vrgo - BG. De C- Bj Xp p
et fier CB aego BH L Constructio ergo haec. Ex puncto figo B educatur BD in
exe sumatur BD. inde erigatur DErequ. a. junctaque EF applicetur FH parabela
qua
Ed, et aqual. B.. Inde ducatur BGetalis qua rtalis,  rectas ED. FK
se in C et G, ita ut sicentro B radio S describus arcumCP_ et jungas
axe Montem si p. et jungas BC. sit sinus esticugli epto _ pnm agili 268, a db.
ta
estinationemi sumendi
simm ea
t
en
pro
rada
diculare
num depehem
sut referre.
culculo
_ nin: