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# Title: Leibniz-Handschriften zur Optik und Dioptrik LH 37, 2
# Folio 116r, page id 00068531:0231
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 115v); this page is its right half.
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# Lines: 37 recognised, mean confidence 0.96
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viam omnimm facillimam, ostendit autem ille posito punctum
medium ramus CEd minus resistere quam densius GHC in ratione
EB ad GH vel DA. (positis GH et DA aequalibus item HC. CE. BD
equalibus) ostendit inquam radium a lucido G ad punctum A
facillime pervenire, si transeat per puncta C. B. Ratiocinati
un
ejus elegantissima est, et plane geometrica, ponit enim difficul
tate esse inter se in composita ratione itinerum et
resistentiae
mediorum, exemplicausa difficultas itineris per c B est ad
difficultatem itineris per AB in ratione composita ex
recta
rationeb CB ad AB quae repraesentant longitudinem itineris; et ex
ratione EB ad AD quae rectae repraesentant resistentiam media
en difficultas per CB ad difficultatem per BA, erit ut rectangum
sub CB et BF, ad rectangulum sub BA et Ad. unde Fermatius
per Geometriam de maximis et minimis elegantissime astendit
viam GCBA esse omnium possibilium facillimam, adeoque radium
tendentem en bad A. esse omnium possibilium scillium ex G lucido
ad punctum A. transiturum per C. B.
Huic Fermatianae ratiocinationi sane ingeniosae simul ac felici–
occasionem dedisse videntur Ptolemaequ et alii veteres, qui
simili fere  dct modo, licet in exemplo faciliori
probant aequalitatem angulorum incidentia et reflexion
reflexus
sit punctum lucidum seu radians M, a quo radius transmittendo
est ad punctum N. (nam a quolibet puncto ad quodlibet
punctum radius pervenit si nihil obstet) quaeritur per quam
viam, utrum per punctum P. utrum an per punctum .
aliud ve, et respondetur, per viam omnium facillimam,
ea
autem hoc loco, id in eodem nempe medio, est
omnium brevissima. Itaque eligendum est punctum P tale
ut aggregatum rectarum MP. pN sit omnium hujusmodi possibilium
aggregatorum minimum, id est minus quam aliud quodllibet, verbi
gratia aggregatum rectarum Mo. yN. Geometria autem ostendit
minimum esse si anguli MPA et NPS. sint aequales.