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# Title: LBr. 705 · Overbeck
# Folio 35v, page id DE-611-HS-861255:0070
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Vir doctissime
dexterrime qudem nnccleassi calculum, usque ad aeg. 5 et 6 sed ex illis combinatis non seruitur
b: e = p: in = h: f Re paulo attenbius considerata deprehendi posse fieni (inter alias hypotheses
p=0 et e =0 salva generalitate, quia loco Y et Z, potuissent assumi literae velut  et 4 et deinde
fieri 8 =.. v + I et f =.. Z+K et explicare i et X, sic ut evanescerent termini absoluti tam in nominator
commun quam in numeratore ipsius  valoris ipsius y. Itaque venio jam ad Tuas ogg. 4, 5, 6. Nonendo
p = 0 = e. Et quia non curo utram constantes mihi incidant is irrationales, imo etiam in imaginarias, nc
modo ne Rvanescant indeterminatae; Hinc ob aeq. 5 prodit 3hgg +hCC = 0, seu C = + 9 f-3. quo valore
ipsius C substituto in aequ. A, fiet 4 nn -3 = 99- 3g9, et ambiguum signum = explicando per - fiet
nn f-3 = 299. Seu 9 = n 8 -3 : 2 et C= =n 1- 3. 1 - 3: 2 super est ag. 6 ubi abjici-
endo 3599 + fec, qua =0, superest bun + 2cmn = 3f992 Cgb, ubi pro C et o substi-
tuendo vatores inventos per n, fiet bnn 2 mnn  - 3-3: V22b an  - 3 V. 3. 1L3: F Z
seu quia 2) - 3 in  - 3 est Y - 3 et S-3 in Y- 3 est = 3 fiet b - m (2 -3 F- 3 =  1 3b seu 4b = m (2 Y 3.-3
Si faciamus R et e esso c, ex aeg. 5 fiet 2cpn =0 Ergo faciumus et p = 0 ex aeq. 4 fint 99 +cC =0
sed ita fit b: m = c: n
seu g - c =1 eo in aeg. 6 fint 3g9g +fcc quod - 3fec + f cc + 2C96, seu R9b = fC seu b. f = C. 9
Dendu si faciamus h = 0 = p C efficitur u X ut y habeant ratio
ne constantem inter se, ergo nulla hypothesium succedit. Et jiffiit unam ex
quod non licet
hypothesibus generalibus, seu quarum assumtione nulla fit restriciin. non succedere
Perillustri atque Excellen
simo Domino, Domino G. G.
LeiBxisio Regiae Britan
nicae Majestati a Consiliis In
fimis S. S. Rom: Imperii Consi
liario fribunalis Aatia Z0
mino meo Gratiosissimo
Hannoverae
uese crissime