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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)
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c ued 
ZV TI. Finic suppar modus dictas rectas AP, TP comparandi
cali Theoremate concinetur: Si ad rectam aliquam lincam (hoc cst
ad ejus sinsula gux que puncta) applicentur rectae linex parallela, ad
rectam AD conlimiliter dirilam applicatarum differentiis proxorrio-
nales, resultantis hinc plani ad parallelogrammum xeque altum, ad
eandemque balin politum, rectarum AP, T. P proportionem extri-
bebit. Ucli rectae AD, as similicer (in parres scilicet aquales in-
detinite mulcas) diridanturs _E reCtX C s 7 i, S p rectis BM, N M,
OM (quae difterentix sunt rectarum ad AD applicatarum, incipi-
endo a puncto A) proporrionales line, erit ut figura ast p ad paral-
lelogrammum est icp; ita AP ad TP. Cum enim recta quapiam
ex applicatis ad AD; Puta V. 8. PM aequetur omnibus seipsa mi-
norum difterenciis (iplis nempe BHI, NNM, OM) e crilineum
ad se constituatur e rectis 6u, V u S u eadem proportione crescen-
ribus; ut _ recta CMI aequatur ipsIS B M, NMI; _ ei respondens
exilineum az  quali contatur c parallelis 6 pes 2 pe pari rarione
crescentibus; ex hoc semper eveniat; omnino patet trilinca a st per
a V U a6 i rectis DM, C M, BM proportionari; proindéque
modum hunc in priorem recidere; nec ab eorcipsi difterre. Notetur
autem hic rectas 6 p y p, s pe relocitares repraleneare, quas pun-
ctum mobile curram delineans obriner in respectiris ejus punctis M;
ut e trilinca a 6 per a 7 u a s p velocirates aggregatas exhribent ab
inicio ad detinita respectira cemporis instantia; quibus (ur jam olim
praemonicum) respondentia spatia BM, C M, D Mt proportionantur.
ZVIII. F. supradictis porro consectatur, quod Si C irculus
Ellipsis, ejulmodique curra recurrenres hoc progenitxe concipiantur
modo, punctum eas describens infinitam in recursiis punsto veloci-
carem habebit. Nempe B quadrans A FM ita generetur; quoniam
tangens TM diamerro AZ est parallela, nec illa proinde cum hac
nili ad infinitam distantiam convenit; ergo relocitas in M ad veloci
tatem uniformis motus per A Y se habebit, ut infinita recta ad ipsam
P M; unde relocitas ilta ad M prortus intinita sic oporter. lea quidem
quoad hujusmodi curras; at quoad alias ad infinicum sensim continu
atas (quales parabola _ hyporbola) descendentis puncti velocitas in
quoris delienaro currae puncto finita est. Verum his omissis ad alias
PEOPOCTX CurrX propriecates exponendas progrediamUE.
18. 23, 24.
Fi8. 25.
TI. preced.