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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 21
# Folio 2v, page id 00068066:0004
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acile Llocoom
ctum describens A transeat per alterum punctum inferius datum B.
Dicoportionem AB Crcloidis sic descriptae propolito latistacere.
Si supponatur, quod celeritates acquilita sint in rarione alcitu-
dinum ementarum; dico curram quaesitam AB Fore portionem circu-
li centrum habentis inhorizontali AC, et cranscuntis per data puncta
AdCB. Unde liquet, conjecturam Galilar reram eradere in hachypo-
cheliab ipsius multum diverta.
Tandem sirocentur abscista AC, x; applicaca CB, y; dc gene-
calicer supponatur, quod celeritas acquisita ex descensu per alcitudi-
It
nem CB exprimatur per y.: diconaturam currae quasitae exprimiper
aequationem differentialem dx
My dy
VI mm
DOMTMT MARCLIOMS HOSAITALI SOLUTIO PRO.
blematis publice proposici a DM. IOEL. BERHOULLIO.
ICic ad menuper clarissimus (Joh.) Bernoullus Macheleos Cronin-
ex Proteslor, Programma quoddam ipsis Cal. Tan. anni hujus
2697 ibidem edicum, in quo Machematicis problemata duo Colrenda
Proxonit, quorum alterum phylico geometricum legitur in Aactis
Lipsiensibus mense Funio anni proxime elapsi, paz. 269; quod Aurhori
jam Tolucum misi. Alcerum rero pure geometricum, quod pariter
Solri, hisverbis exprimitur:
Problema alterum pure Ceometricum, quod priori
subnectimus e Arenae loco Frudiris proponimus.
Ab Fuclidis tempore vel Trronibus nocum est, ductam nccun
que a puncto dato rectam lineam, a circuli peripheria ita secari, uc re-
etangulum duorum seomentorum inter punctum datum e utramque
peripherix partem interceptorum su eidem constanciperpetuo aequa
dc. Primus cgo octendi in eod. Actor. Tun. pac. 265, hanc proprietatem
intinicis aliis curris conrenire, illamque adeo circulonon else essen
tialem: arrepta hinc occasione, proposui Geometris determinan-
dam curram vel curras, in quibus non rectangulum sed Tolidum sub
uno e quadrato alterius segmentorum aequetur semper cidem, led a
nemins hactenus solrendi modusprodiit; exhibebimus cum quando-
cus