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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 147r, page id 00068195:0293
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Methodus de Maximis et un mimis diversa x ab ea
quae usitata es
Data basi, et summa laterum dataque altitudine
satur Tiangulm. sist altitudo ed sit n. trianguli
mee AC AB sit a, BC + CAs ut b. AB = BD sit V
fiete B erit AD + DB = a  et ergo, AD = a - DB = v + Bd. et
 DB = a a - v,: 2 et AD = a + v, : 2
E
AC=: Ma + vD + 2avGpum et BC = La + B 2 (aa + Wy 2av +amm et fiet
a Saa + vv + raVL+ Saaa no -  av  2b
seu
fictaa + 2vve +8um + 2 Sac +ov +amm - + aavo = + bl
aa+ un per couendium dicatur 22, et fiet
et Z2+ 4mm - 2b6 = 3aa 1 vV + amin - 4aa bv
seu BB = (22+ a mm) + 4( - f2 Z+ amm) = ( + 4um, - f aa vn
ad eo mn=  si ergo nm sit maximum, pote
se c etiam Hbommerit maxim = Ab + _ faa vv- AbbZZ
Retia erit etiam marium Gaa e bb ZZ bbZZ = aa vV, nam Ab mat sum
minimum
aav bb aa  nam fit b + aa vv = bba - bb vv. sed bb
sed b est majus quam a et sit bb = aa = cc et siet b ccvv - aab1
quod cum debeat esse omnium  possimilum maximum debet  esse
smndum possibilium aa bb + cc e esse omnium possibilium
minimum ergo debet esse ∞ = 1o quod et verum est.
Methodum de maximis et
exemplum dedi
minimis diversa ab ea qu ipsis Magni et
fic lexplicur
parvi visceribus sumtae non trans latae ex coincidentia
geminorum, aut ex evis evanescentia
diferentiae aut ex aequalitate radicum ut bulgo
quid si haec methodus prodesse posset
ad transcendentia.
sane per maxicmum aut minimum
C supposito maximo et minimo difinir osse calculo
EX,9
talytice definiuntur quadraturae peciates admuli
curva
Cogarlhhmicae, p adaxem qui angulum ad Asymplotam
deccral semerectar, quae ratur Z ordinata maxima
maxium non semper procedit, ut si debent
Z maximum an ergo. t q- 1. maxium