478 Opusccla 



X'=1_cos.M4,!ifiIi(G-/q:sin.w)J \/(g2 — R2 c'^')4;sln. w j . 



Signura superius pertinehit ad sistema conico-circulare aeque 

 divcrgcns coavergens, inferius ad sistema aeque convergens 

 divergens. 



21. Aeqnationes 



Yz=l±VpX 



Z = A. — Vp'X 



sisiema ofTernnt spondaruni omnlno parabolicum, in quo spon- 

 dae super basi parabolica assurgurit paramelro =p, axe ad li- 

 neaui abscissarom X parallclo, ab eacjue intervallo / dissilo, 

 concavae pro signo su[)eiiori primae acqnationis, convcxae pro 

 inferiori, superne horizonlali semicylindro item parabolico pa- 

 rametro =p', axe parlter ad abscissas X parallelo resectae. Fu- 

 sus vero sit conicus , nempe aequalionis 



r = A ( G - Y ) zzz ^CC - ^qi V/.X)=R' q:i V';. X 



Parametri insuper servent proportionem p:p' ::R'^:C^. Linea 

 spiralis contacluura fnsi, et ceniri ejus Irajectoria has sor- 

 tiuntur aequationes admodum simplices 



( c \ ^ — y ) 



X_ 2CM^£X71^1 R^ 



pW^^4C'-X V C '^ J 



Z' = A 



^/pX^-iSl^^+Z:^,R'q.V; 



^ PAH ■-! /R'qz-VpX^ 



quae postremae, si spondae parabolicae invicetn fuerinl coa- 

 vexae, banc singularem subeuut formam 



X =:X 



Z' =: A + R' 



nimirum fusus hujusmodi spoudis innixus eandern centre per- 

 currit trajectoriam, quani seqiierclur, si super spondas planas 

 parallclas ora reclilinea, atque horizontali terminalas protrude- 

 retur , proinpta spondaruni convergeniia plane compensante 

 declivitaieni . 



Finem facio hisce applicationibus, quaruin praeinissae for- 



