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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 25
# Folio 8r, page id 00068043:0015
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datis punctis C et D. et recta indefinita AB
Ducere CED ita, ut sit CE. C + ED. M omniam
possibilium minimum, seu minus quam foret sumto
E alio quocunque
sit  ntu Ex punctis datis C. D. dicantur
ad rectam perpendiculares CF et DG
Dabitur FG aequ. f. et  CF, c. et Gdd
sit FE, X eut GC aequ f -x. et CE aequ XX + CC. Et DErq. H xF
dsebet C CC+xX +M ff. 15X +Xx + dd aequ y esse omnumm
possibilium minimum
sit Lunitates, et utde nosit
sit  nitas L. sit m. seu eat
erit CH aequ. l LCCFAY
sit CH ad eE ut L (sumta in CE si
opus producta) ad CE ut l ad uutatem
et ruisus DK (sumta in DE si opus producta)
ad DE ut M ad unitatem. patet rectom
et per H et K ducantur KN, K P ipsi
AB parallelae, patet quamvis rectam CH ex
dato puncto C. ad Hd rectam HN ductam fore
sccta et quamvis Dk for + m rf. 2fX + X+Yd
CE sit e. quaeritur R eAqu CH erit CH: CE:: (Q: CF seu C
debet autem esse CH aequ. l. CE: +g
Ergo fiet: l. CE: f: CE :: C9; c seu
l: f:: C2: c. sit ergo C9 c: f similiter DR erit Md: f ergo
erunt CH. DK ipsis rectangulis L in CE et M in DE proportionales
quaeritur ergo quomodo assumendam punctum ut fiant rectae CH+ DK
omnium minimae
sec +XX + m Vf - 2fX +XX + dd aequ. y.
Ergo pro manima 2Ix e-a2mf +2mX aequ. c. Ergo m
Scc+X
et faciendo DE aequ. CE. erit
 -
l. X aequ m. f-X
Ergo l. X. DE aequ n. f - X. CE
idem vicissim demonstratur s
e xx sit aqu qque fiet: Xxaeqo 2Z. CC et X aequ( ZZ cc. et fier 1Z +. moss- 2f s cc +4 cc +d ∞q
s
demonstratio linearis non adeo facilis