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# Title: Leibniz-Handschriften zur Optik und Dioptrik LH 37, 2
# Folio 111r, page id 00068531:0221
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Regula Refractionis
Quod angulgum Regulam eflexionis
Hero ptolemau et alii veteres
tentemuse, calculus hic prooit.
sint duo media: Ad resistens resistentia
ut ADF. et BEC resistens res stentra
ut  difficultas trajectus. AB, aestimatur
ducta itineris AB in resistentiam medii , seu
ex rectangulo SAD pos Aosito SA ego AB
et difficultas trajectus BC aestimatur ductu itineris BC in resisten
tiam medii quaeritur ubinam sumendum sit punctum B, ut
totus trajectus ABC sit omnium possibilium ab A in C. facillimus
seu ut aggregatum rectangulorum, sit omnium possibilium
minimum
 sit AD aequ X. BE aequ.  AH aego b
WE vet DB aequ Z et EC aequ v. WV C aequ. _c
derique sit equs. et  aequ. co ABqBrguo
AB aequ. e) BC aequ. h.
Habebimus aequationes: X + y aqu b 9+B aequ. c.
 1 +Z aqu e. y yaqu. H.
denique et  he equ. minimo m.
compondii ansa (ab aequ. 3. auferatur aequ. 4, fiet:
X - y a. + Z. v aequ c  h. seu Xty, X- y, + Z+ v9 Z-v, aequ e h
seu per aequ. 1. et2. b X - by + cz- cv aequ. se = b (
additur
tiet x Dyago   bu 1 c causa faciamus e equih.
si contrahendi cllculi q
Ex aequ  in equa sit XZ +  XV + yZ + y V, aequ. bc.
addantur aequ. B et 4. et his addatur duplum aequ. 9.  mulliplicatae per 
X +ZC +Y + V 4Xrvr tg ese extiq ribc
fiet X + Z +y + V aequ retti F ebc
si contrahendi calculi causa faciamus e aequ. S
(10) v. Z
fiet bx - by + 4Z = CV aequ. 0. seu b aequ
(11)
X-y
trpursus per aequ. 1. est X- y  aequ b - 2y et v- Z aequ c - 23
ergo b (2)
c
aequ
X aequ b- y
c=27
b- 28
B aequ c-Z
n. adeoque y aequ b C + 2cZ
et X aequ b + BC, d- 1Z 1 4 c,
FZ2
quam saequationem adinando fir:
ubi mulliplicando per 2. 1. 0
fieret Z aequ E2t 2c
 aequ
4b
et  b- 2by aeque - 2cZ. per
et X aeqo b + C- 2cZ
c. 4021∞42  aequ m 1
3e
 lccum 
+ 5231
+1.
C7 rcb
V
=c
2c
o
+ et aequ. 0
4b2
4 c2
+1 c2+ ubi morum evanescere t. et co
itaque vereor ut hic savendi modus procedat quia quod in problemate
potissimum est non inmeditur in calculum
ex eo demonstravere, quod posito, angut
incidentiae et reflexionis aequali fit.
via radii a puncto a quo venit, ac
punctum ad quo reflexione pervenit, omnui
 rel
possibilium facillima idem si in refractione