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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 16v, page id 00068195:0032
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0
X. X ~YC a aequ. 0. fiat:
a nqu. ff. et erit: X3 X- a qu. 0
pone Xaqu. g. fiet: B- X ap.
15939
sive fiet: y- kg y aequ. h3gf. et
omnes numeri y. h. 9. f. erunt integri
Ante omnia certum est aequationem non posse
dividi per divisorem ipsius f. nisi is sit etiam
divisor ipsius h9. Ergo suprest tantum quaeramus
an aequatio dividi possit per divisorem ipsius h9.
Poun si divisio procedit necesse est f nullos alios hm
tinere numeros primitivos quam qui jam latent in
h et g. itaque pro hg scuibamus mf. et
fiet aequatio: y- ms y aequ. hf notundo
tantum nif diridi posse per h. itaque omnis divisor
termini ultimi est etiam, divisor termini penultimi
Melius sic ne quidsubintalligere sit necesse, quia
omnis primus ipsius. F debet esse in hg. ideo scribamus
faequ. H p a etc. et haqua
et h aequ. spla Y etc. et 9 aqu. x qr et
fiet:
 ut in in
P4 F erc, tp 9r Vam.
etterdea, prgrec
p cum aliqua litera abest tantum exponens
ejus porendus aequ. 0. quod autem
ejus modi aequatio dividi non possit
er
y + p (nam perinde est quod cli
pos te eis psnenes
yy aequ’aa+x
Invenire lineam, in ita ut sumtis derbus pun
transeuntem per punctum datum, ita ut si a quolibet
ejus linea puncto ducatur recta ad aliud punctum
(extra lineam) datum, sit relatio inter AY et B)
sive inter X et y. expressa
aequatione hujusmodi yy-xx aequ aa
Haec linea ita invenietur
jungantur duo puncta A. B.
et inde educatur recta ex A
indefinita,
recta perpendicularis Ad AB
ea erit locus quae situs.