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# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 146, page id 797435492:0400
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E B C F: ZIII.
verx radices propolicae talsas exhibent. Hlic insuper modus aequatio.
nis propolicae, quatenus illa ex aliarum in se duetu provenie, constiturio.
nem ostendit.
4. Radices maximx Ee minimxe deprehenduntur in quacunque se.
rie ponendo (quoris in gradu seriei) Fore n=o; ut in octara serie sIt
ba- aa  c0 = 0; adeoque 50 = 44- ba, exic a (L . . V --
cc) maxima radix; item in Serie duodeci a CiE Aa ba -66 = 0;
unde c0 -ba- aa; exit et (=
- - 66) redix MBaXMa;
d a (= = = V =cc) radix minima.
5. Curvaram nodi, vel intersectiones innocelcune, cujulris in Seriei
quoris gracu, ponendo fore a =n; ut in octara Serie, ubi b3 -a
. 6C= n, HE a = n; er∞d ba aa ) c0 = aa; vel c0 = 2Ba ba;
vel = aa - =; quare a = ) V--
6
rie duodecimia, ubi aa - ba 60 = nn = a4; erit ide060 = ba; ac inde
2=
6. Ordinaca maximae, minimeque variis nodis, methodisque pas-
Cim nocis investigantur; e80 simul illas atque curvarum tangentes
una opera sic determino. Sit curra A V HI, ad Seriem unelecimam
pertinens, ejusque sradum, cujus aequario eAt cCA- baa - a3 = n3:
Polito T curram tansere, ∞, P ad AHI ordinari, reperio (de su-
pra monstratis) fore P I-
3n3
3aa  2ba- ec tum contidero, si Or-
dinata P sit maxima, fore tansenrem ips HI A Parallelam, seu rectam
P T esse infinitam; quare cum (IE n3 =PPX : 3a4 ). 2b4 - C6; BEn
Sit Enica, Pacet esse 3a4 ] - 2b4 - 66 = 0; vel as  7ba =; adeo-
que a:=-
6
dL0
7. Adnoro demum e maximis de minimis ordinatis radicum li.
mites derirari; nempe si reperiatur ad maximam ordinaram pertinen-
eis radicis (veluc ipsus A P in exemplo proxime luperiori) ralor, e
is ubique in xquatione proipsâ a substienatur, si quod provenit, de
ticiat ab homzoseneo (quod vocan) comparationis, problema construi
requiF
E18. 220.