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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 181r, page id 00068200:0363
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Glagnus demont
nempe ut AD + DC.
Angulum incidentiae AB F et reflexionis
CBD esse aequales ostendit Ptolemaeus, quia
 aggregatum rectarum ABC AB + BC est
omnium possibilium minimum, seu minus
aliis quibuscunque inter eadem puncta AB. BC
consentaneum enim naturam ex A in C egis
per brevissimam viam nemje per B. Demonstrandum est ergo AB + BC esse
minores quam AD + DC.
jungatur AB + BC in unam rectam AE, ita ut BE
aequetur ipsi BC. Ieo autem jungi utile est, quia ductu linearum aliquid de toto
hoc demonstrare volumus. Exhibendum est ergo hoc totum. Rursus quia volumus ostende
duas quasdum ut. AD + DC, esse tertia AE majores, idem est ac si diceremus
fieri posse Triangulum cujus basis sit AE, crura AD et DCF DC posito
e
agu ipsi BC. neque enim alia commodiore ratione in lineis exprimere possum
duas quasdam rectas simul esse tertia majore
AE+ ADS+
Tantum ergo quaeritur an
recta focis A. E. filo cujus longitudo AED ellipsis describi possit. Sed
hic feliciter evenire apparet ut tam longe iri necesse non sit, nam feliciter
venit ut ipso sita ipsarum AD AD retento juncta DE, sit aequalis ipsi DC,
quia nam triangulem hrurgulo DBE, triongulo et DBC latus b habent commune
BD, aequalia BE, BC, et angulos aequales DBC, et DBE, ergo et reliquum
latus DE reliquo DC aequale erit. Est autem semper in Triangulo
minus quam A +DC, ergo et
uod eint
dem.
s
3
BC minus quam
AD +
C