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# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folio 192r, page id DE-611-HS-958803:0385
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AIL LVOA MIAMI A. MIDC ZLC VII
nihivderim, quod amea me sententia dimorerit, quamvispragnan
ces ob causas adhuc ab corum publicatione abstinuerim.
EXCERDTA BA LRAAISACTIOMTBUS PETILOS ANGLIES
ML. TAI. 1695.
EPISTOLA MISSA AD PRNOBTLEM rIEUM D. CAROTuI
Mountaeue armiserum. Scaccarii Regii apud Anglos Cancellarium
s Societatis Regiae Praesidem: in qua solvuntur duo problemata
Mathematica a Johanne Bernoullo Mathematico
celeberrimo proposica.
Problema L.
Arectisanda cA curra linca AD B, in qua grave a dato quoris pun LAb. IV
Ato A ad datum quodris punctum Bri graritatis Cuae cicissime de-
Ccondet.
Soluuo.
A dato puncto A ducatur recta infinita AP CZ hocironui
parallela, et super eadem recta de scribaturtum C reloisquae cunque.
AOP recta AB (ductae ex Si opus sit productae) occurrens in pun-
eto O. cum Crclois alia AB C cujus balis et altitudo sit ad prioris
balem ex alcitudinem respectire ut AB ad A9. Et hac Crcloisno-
villima cranlibicperpunctum B ∞ erit curra illa linca, in qua grave
a puncto A ad punctum B ri graricatis Cuae citissime perveniet. DF. lo
Problema II.
Problema alterum, si recte intellexi (nam quae in Actis LipL.
ab Auctore citantur ad id spectancia nondum ridi) sic proponi po-
rest. Ouaritur curra KII ca lege, ut si recta PRL a dato quodam
puncto P, ceu Polo urcunque ducatur, ec eidem currae in punctis
duobusK_ L Occurrat, potestates duorum ejus seomeneorum PK
ec PE a dato illo puncto P ad occursus illos ductorum, si sint aeque
alta (id es vel quadrata vel cubi vel quadrato-quadrata, ecc:
dacam Cummam PRg f. PCgrel PIcub. + PEcub. eC. (in omni rectae
illius positione) conticiane.
Solutio.
Per datum quodris punctum A ducatur recta quaeris infinica
politione data AD B, recte mobili P RL. occurrens in D, d nominentur
AD, X; CC PR vel PL, Y; Cintque _R quantitates ex quanticatibus qui-
buscunqus datis ec quantitate x quom odocunque constantss e rela-
223
ts
F18. XIo
Fig. ZIII.