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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 82r, page id 00068200:0165
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1) Radi Aeodem puncto lucido L, in planum N, cadentes radii duo
driunt divergentes tanquam a puncto intra Medium a quo
q Lebaa _ Ad hoc probandum assuminus temma notum
Geometria crescentibus angulis neli rect u crescripe
ratio laterum respondentiur vel contra. Seu qui aagulus et
e
sinas ad radiur
ita quia angulo RLP, major angulus pLP etiam major
est ratio B ratione pR: RL major est ratio PC: CL quod si opus esset sc,
facile osfendi posset; ponamus pon triangula duo haebere altitudinem aequalem, ut hic
L patet angulo uncto aucto u augeri et latus ut latera reliqua seu quia ef
majorquum R P, etiam esse sP majorem quam p (P_: PC) = (PR: AL
(PL: R) - (PL: 8L2) sed
(S BH) ) -((R8- PL): RL2
sed PEE major quam P 1: 5 L, quia eL major quam RL ex hypothesi
ergo et ente eadem hypothesi etiam est PC: EL major quam pR: RL
ias mopente enim radio crescunt sinus crescente angulo, ergo
 crescit ratio sinus ad radium, ergos etiam non manente radio, ratio sinus
ad ratio crescet, cum eadem set ratio laterum triangulorum similium, quorum in uno
est  radius pro hypotenusa, in alio alia recta major minorve.
(2) porro in angulis refractionis rationes sinuum ad radios sinum totum
crescunt, in eo ratione, qua proportionaliter  rationibus in angulis
incidentiae, seu sF: FB _ 60   ad V ∞:  ut PR: RL ad PC: et
nam posito esse FR = RL et sp = pL erit SF: (AR = VG: pCP
sit = c ergo g. GP =  SF = c. PR et N 9 = c. P. Hinc fiet
CF SF: FR, ad  P: _e = C. PR: RL ad c. P . s L = PR: RL ad sp: gL
itaque quoniam t (per artic. R1.) ratio Pe. L major quam ratio ratio
ut proponebatur
PR: 5L erit (per artic. 2.) etiam ratio sg: gx majot quam ratio sF: F
itaque raus (per artic 1) angulus  Nmajor angulo FRS. Et proende
rectae FR, Pe concurrunt inmedio a quo. Is concursus sit in C, unde in pR
 sit P R vet PC X agatur normalis C B
PR sit vel po sit X, et Fs erit cx: a et AL est pL sit b, fiet
fiet RL = L(XX + bb) et sF: FR = (CX : a): S(XX + bb) = R B: BC sit
B = Z+X,: V, posito BC esse v, et PB esse Z. Et differentiando
exundum X, quia Hinc vex. a  (Z + X) Y(XX+ bb) seuet: a et
differentando secundum Z, fiet vcia = e (_H at 1)  (ZX: f(a 1bb)) +
(2+X (Z+X, : V(XX +bb)) 1 spex +bb) seu vex: (a, Z+X) = H(XX + bb)
et differentia secundum X fiet VC: (a, Z1X) A NCX(: (a, EFX, Z1X) = X: Y(x + bb)
Z+X, a,: cv. Et habebimus cevv, Z+X ~X = aaZ +X3, s
fiet CcDY(Z+X) = aa (Z+X: cevo = X seu Z+X appellando W, fieti
CC vVWO = aa W3: CCDD = X, quem valorem substituere oportet in
aequatione X: HN+ bb) = Wa: cv _ 1 + (XR: bb) = cc vV: aa W
adeoque fiet
ac denique
et fiet _ seu Xib = N(CC vV = aaWiW): au.
WW (CCVV=aa 1bW) ?: et v =bbCCVV= aaou: aau.
aa W (CC vV - gazoW) = bbct v G seu  Quod si malimus habere Z.
loco W id hhabebitur, aequatro pro carva ex concursu rediorum ejusdem
sedCaeterum quaecunque sit Lex Refractionis necesse est lineam tatem
puncti refractorum facta
onsei nisi radi fiant paralleli refringendo paralleli. Consiterandum etiam
est Si pL fiat major oportere lineam pieri priori similem. Hini si
radius Luminis fnga transeat per duo puncta L et A, oportet radiu
rent lexium t refractum si producatur retro, ambas tangere lineas, 
mo et generaliter omnes lineae quae fiunt a punctis omnibus Z, in eodem
radio incidente sumtis et ficte trabitis pro lucidis, concursu suo formant
restam illamo, quoe est sadius refractus si retio producatur