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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 208v, page id 00067993:0418
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Deoportiones curvitineorum ad Rectilinea investipare GeOmetra
L semper tunt conati, ee tamen nunc quogre, otiam post Algebram
adtribiram, nondum ea res sacis in porestate est, secundum methodos
quidem hactenus publicatas; neqre enim haec problemata ad aequa-
tiones Algebraicasrerocari postunt: _ ulum tamen pulcherrimum
habene, inprimis in Mcchanica ad purae Geometrix terminos reducen-
da, quod norune, qui calia protundius inspexère, pauci quidem, sed
maxime eximii Machemaricorum. Primmus Archimedes, quancum
constac, invenic, quae sic racio incer conum, Ephaeram e cxlindrum
ejusdem alcicudinis de basis, nempe gralis est HUIM CFORUM L,Z, Z, ita DE
exlinder sic criplus coni, d selgrialcer sphaera; unde sphaeram de cylin-
drum etiam sepulero suo insculpi jussit: Idem invenie gradracuram
Parabola. Nostro seculo repertus eAt modus meriendi ApUTAS CUE-
vilineas inmunerabiles, inprimis qrando ordinacae BC, in Schemater,
tunc in ratione nccungre mulciplicaca aut lubmulcipticaca, directa aue
reciproca, abseictarum AB vel DC; eric enim figura ABC A ad rectan
sulum circumseripeum ABCD, ucunitas ad numerum rationis mul.
riplicacionem exprimencem, unitare auctum. Eexempli gracia, quia in
Parabola absciltis AB sive DC, existentibus uc numeris nacuralibus,
22, 3, _c. Ordinacae BC, Tunc uc eorum quadrata 1, 4, 9, _C. Ceu in du-
plicaca ratione numerorum, cunc numerus rationis mulciplicationem
exprimens eris 2: ergo eric sigura ABC A ad rectangulum circum feri-
Deum ABCD, uc1 2d 2.F. 1, Seu uc 1 ad 3: Sire, figura eric tertia pars rectan-
suli. Si AB vel CD mancane numeri naturales, e BC hant cubi, 1,8,
27, _c. (nempe in Paraboloide cubica) Foret ratio ordinaeorum eripli-
cara rationis abscictarum: Ergo figura ad rectangulum, uE + ad Z FL
sre 4: PeU PArS graTTA. Sin DC sint gradrata, BC cubi, sive racioipso
rum BC, racionis iplarum DC criplicata sub duplicata, erie Egura (para-
boloides cubico subquachratica) ABC A ad rectangutum ABCD, uE 1 2d
AEs scu duas quintas rectanguli constituet. In reciprocis, numero
rationis mulciplicacionem exprimenti praetisitur signum =, sive
minus.
Sed circulus nondum hactenus eosipotuit sub hujusmodileres,
qramvis ab omnirecro memoria à Geometris exercitus. Nondum
enim inveniri poruie Numerus exprimens rationem Circuli A, ad qua-
deatum circum (eripium BC Fieur. 2, qrod est qradratum diamerri
DE. Necinreniri pornit ratio circumterensix ad diametrum, qua
et