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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRINCIDLA MAEHEMAETCA.
Onde etiam interfectiones Sectionum Conicarum e Currarum ter-
ciae poreltatis, co quod sex ese ponune, simul prodeunt per _qua. abt.
ciones sex dimentionum, ex incersectiones duarum Curvarum tertice
Poteltatis, quia norem ese portune, simul prodeunt per aequa-
ciones dimentionum novem. Id nisi necellario herec, reducere lice-
ret Problemata omnia Solida 2d Plana, ec plusquam Solida ad Soli-
da. Loquor hic de Curris potestate irreducibilibus. Nam Si Xqua-
tio per quam Curra desinitur, ad inferiorem pocellatem reduci
Pollic: Curra non erie unica, sed ex duabus rel pluribus compoli.
ta, quarum intersectiones per calculos diversos scorsim inveniri
Postune. Ad eundem modum interlectiones bina rectarum de lecti-
onum Conicarum prodeune semper per aequationes duarum dimen-
sionum; cerna rectarum et Currarum irreducibilium certix porestaris
per aequationes erium, quaternae rectarum ex C urvarum irreducibi.
lium quartae potestatis per aequariones dimensionum quatuor, et SIC
in ininicum. Eroo rectx ex Spiralis incerfectiones numero inAinitr, cum
Curra haec sit simplex ex in Curras plures irreducibilis, requirunt x-
quationes numero dimensionum ec radicum infinitas, quibus omnes
portune limul exhiberi. F.K enim eadem omnium lex ec idem calculus.
Nlam s a polo in rectam illam secancem demittatur perpendiculum,
e perpendiculum illud una cum secante revolratur circa polum, in-
cerlectiones Spiralis transibunt in se mutuo, quaeque prima crac seu
proxima, post unam revolutionem lecunda crit, post duas tertias
ec sic deinceps: nec interea mutabitur xquatio nisi Dro mutata mag-
nitudine quantitatum per quas posirio secantis decerminatur. Onde
cum quancitares illo. post singulas rerolutiones redeune ad magni-
cudines primas, aequatio redibit ad Formam primam, adeoque una
cademque exhribebie incersectiones omnes, et propterea radtices ha-
hebit numero infinitas, quibus omnes extriberi portune. Neguie
ergo interlectio rectae ec Spiralis per aequationem tinitam generali-
ter inveniris et idcirco nulla extat Oralis cujus arca, rectis impe-
ratis abscissa, possic per talem aequationem generaliter exhiberi.
Eodem aroumento, si interrallum poli sc puncti, quo Spiralis de-
lcribitur, capiatur Oralis perimetro abscillae proportionale, pro.
bari porest quod longitudo perimetri nequit per tinitam aequario-
nem generaliter exhiberi. De Oralibus autem hic loquor qux non
canguntur a figuris conjusaris in intinitum pergentibus.
LaEBEX
Cd10l.