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# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 14
# Folio 21v, page id 00068187:0044
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lade veterum demonstratio 
officient reflexionis vera depreheu
Nam exempli causa quod radius AG
reflectitur ina radius incidens AB. reflexus
BC faciunt angulos incidentiae ABD et CBE
aequales, dupliciter demonstrari potest,
per causam efficientem quidem considerando r
ax
incidentu  flecti in DFE seq seque restituentem
reperentere in pergo dculari Ae incidens
in perpendiculari BH, Cumque inciddens
mtum in perpendiculari BH (ejus pralleta) A
Hinc jam ratio habetur c cur motus incidentiae
a
eoque et reflexionis compositus intelligatur hic dividendus sit in composi
directione
aneraoce
destennitur lectit, et restitutione ejus in contrarium ertitur , in tantum pum pronfrectitur in
et  horizontala GB, quil eadem ad perpendiculatem
eod ideq quo tempore
quac
summidens descendit
Fnihil passus eadem
proportione, residuus manet X, cujus endem et quo ille pervenit ex B_ in H, hoc iste
coleritatis_A.
ex B in L. si BL ad BH
ratio ad aequadi K _G si HB aequal. AG aequ. CL
motus autem compositus ex directionibus BH et BF est in FC
ed idem veteres demonstravere argumento
petito a causa finali, hoc modo: Sit punctum
et aliud B C posito jam quod illi assumunt,
a quolibet punctoA ad quodlibet ab easdem
ut BG ad AG  vel
superficiei reflectentis partes positu DE partes
positum C. Siliquem radimm reflecti quaerunt jam pervenire
quis sit ille radius,  sivesi sive sitne AMC an ABC
Hoc ut inveniant utuntur smlo principio sumto a
Cauta finali, quod scilicet natura aliquem sibi
finem proponens optima media llgit. Itaque
cum hic ob mud diaphanum uniforme sola
BL aequ BG et
lonsi vel brevis itineris ratio haberi debeat,
sequitur eam a puncto A tendetem  per reflexionem lendentem ad
junctum C ituram per punctum B, si ABC ABC sit via omnium brevissima
seu si aggregatum rectarum AB +BC, sit minus quam aliarum quarum cunue
ut AM + MC. constat autem ex Geometria si anguli ABd et CB
sint aequales nggregatum ABC fore omnium hujusmodi angregatorum possibilium
in receatiores quidam objicere solent
radium ex A eq egredienten nc quaerere an ad C iturus sit, et quaram optima via
minimum. Huic argumentat
cog
eC
iptinavi sed colco impetu incurrere in superficiei refringentis punctum.
u  ad quod concepta jam directione feretur; atque inde serundum Mectanicus
eo sit pervencupus
leges repeut egor reminni. Sed hi non coritant argumentum veterum esse simitum a causa
fenali, et non radium quidem, sed naturam tamen legum opticalum autrem funda
tricem
cognitione praeditam esse, quidque optimum fatorum sit, praevidem
et commodissimum
descensu
incidente
+ ejus quod alias sine
sine
ratione assumitur