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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 28, page id 1041163592:0062
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n 2d
PFITLOSOPETLAE NALDRALIS
evanelcent, ec rationem ultimam habebune aesualitatis. G
Corol. T. Onde ( per B ducatur tangenti parallela B L) tcclat
quamvis AF per Atranse.
untem perpetuo lecans in f,
haec BF ultimo ad arcum c.
vanescentem AB rationem
habebit xequalitatis, co quod
completo parallelosrammo FB D rationem semper habet aequa-
licatis ad AD.
Corol. 2. EF A per B e A ducantur plures rectae BF, BD, AF.
AC. Iccantes tangentem AD ex ipsius parallelam B F; ratio ulti-
ma abscictarum omnium AD, AL, BF, BG, chordaeque e ar-
euS B ad invicem erit ratio aequalitatis.
Corob. 3. FF propterea hae omnes linex, in omni de rationibus ul-
rimis argumencacione, pro se invicem uluxpari DONUNE.
E E MNT A VIIT.
Si rectae datae AR, BR cum arcu AB, chorda AB es tangente
AD, triangula iria ARB, ARB, ARD constirmunt; dein
puncta A, B accedunt ad invicem: dico quod ultima forma
trianculorum evanescentium est similitudinis, e ultima ratio
aequalitatis.
Nam dum punctum B ad punctum 
accedie intellisatur semper AB, AD.
At
ad puncta longinqua b, d ec r producis
ipsique RD parallela agi rb d, ec arcus
B limilis Temper sIE arcuS Ab. EE COC
uncibus punctis A, B, angulus b Ad cra-
nelcet, ec propterea criangula tria lemper
Finica r Ab, r Ab, r Ad coincident, sune-
que eo nomine similia ex aequalia. Vnde
ee hisce semper similia se proxorcionalia
R AB, R AB, R AD hent ultimo sibi Y
invicem similia ec aequalia. 8. F. D.
Corol. E.C hinc criansula illa, in omni de rationibus uleimis argu
mencatione, pro le invicem usurpari BoNUnE.
F. D.
ID E MOZV
LORPORVH
e L to