ET REFLUxUSs Maries. 203 
LEmMmMA !I. | 
Sit 4B a b Ellipfis, Ccentrum, HI diameter quævis , 
M m ordinata ad diametrum HI in punéto #, ex H & M du- 
cantur retæ H P & m x parallelæ , duabus quibufvis diame- 
tris conjugatis ; & fibi mutud occurrentes in 7; jungantur 
qgu& P M, atque hæ reétæ erunt fibi mutud parallelæ. 
Occurrat reëta HP, ordinatæ Mmin z, & rez Ma 
(quæ parallela fit ipf #1 q )in ©. Sinr Ca , CA & CB femi- 
diametri refpedtivè parallelæ rectis Mm, m x & H P. Du- 
catur GE parallela ipfi € B & producatur donec occurratfe- 
midiametro C Ling. Ex natura Ellipfeos erit Reétangulum 
Mzxzm:HzxzP::CG:CB;& ob parallelas CG & 
Mm,eritgz:è2m::GE:CG.UndeMzxgqz:HzxzP:: 
CGxGE:CB:. VermHzxzP:zuxzP::Hz:zu:: 
Gg:CG. Quare ex xquo Mzxzq:zuxzP::GgxGE: 
CB:. Eft autem Reétangulum fub G g & G E æquale qua- 
drato ex femidiametro CB per notam proprietatem elli- 
pfeos , cùm CI fit conjugata femidiametro CG, & CBipf 
CA.Proinde Mzxzq—zuxzP,&zqzu::2P:2M, 
adeoque g # parallela re&tæ P M. q. e. d. 
… Con. 1. Reëta P O dividitur harmonicè in g & z vel P 4: 
Pgq::42:4q 2. Quippe ducatur se parallela ipfi # x, occur- 
ratque reûtæ H Pin e, tum erit P z:42:: P M:q uv ( ob pa- 
rallelas P M, qu)::Pa:ge. Unde Pg:qz::Pe:qe:: 
ge:ez:: Pexge::qgexez::(quoniam@e, eq funtæqua- 
lks)P 0:07. 
Cor.2.Occurrat reéta m x Ellipf in x , jungatur H x quæ 
occurrat rectæ PM inr, junéta #r erit parallela ipfi #7 x. 
Quippe fit 14 parallela retæ HP & occurrat ipli m xino; 
tum ox erit æqualis reétz g9m&lo:0ox::P4:qm::P 0: 
DM ; adeoque I x erit parallela ipfi P M. Verüm cam 1H 
. fit diameter Éllipfeos & ad x punétum in Ellipfi fitum du- 
&z fint reæ I x, H x ab extremitatibus diametri 1H , erunt 
hæ parallelz duabus diametris conjugatis, ex natura Ellip- 
cos. Quare cm ex punétis H & M eduétæ fint duæ reétæ 
Ccy 
Fi. 11, 
