tum e&longs;t Hexagonum minus &longs;ubquadruplum majoris, latera &longs;ci<lb/>
licet minotis &longs;ubdupla &longs;unt laterum majoris) cum interim <lb/>
punctum C retroce&longs;&longs;erit in L, & demum latus CF congruat <lb/>
lineæ LM. </s> <s id="s.001642">Igitur majus polygonum &longs;olùm de&longs;ignat in motu, <lb/>
quo progreditur, lineam CM æqualem lateri minoris polygoni <lb/>
EI; & factâ integrâ conver&longs;ione, de&longs;ignata erit linea &longs;extuplex <lb/>
ip&longs;ius CM & ip&longs;ius EI; atque adeò utrumque polygonum <lb/>
æqualem lineam progrediendo de&longs;ignat. </s> </p>

<p type="main"> <s id="s.001643">Hæc quæ de Hexagonis concentricis exempli gratiâ dicta <lb/>
&longs;unt, de omnibus &longs;imilibus atque concentricis polygonis dicta <lb/>
intelliguntur, quotcumque &longs;int laterum. </s> <s id="s.001644">Jam verò Authores <lb/>
illi concipiunt circulos tanquam polygona infinitorum late<lb/>
rum: & quemadmodum minus polygonum totidem &longs;patia &longs;ub<lb/>
jectæ lineæ intacta relinquit, totidemque tangit, quot habet <lb/>
latera; ita pariter in circuli minoris conver&longs;ione, infinita &longs;pa<lb/>
tia vacua non-quanta (ne &longs;cilicet &longs;i quanta e&longs;&longs;ent, opus e&longs;&longs;et <lb/>
lineâ infinitâ) intermi&longs;ta &longs;patiis, quæ tanguntur, ad&longs;truunt, <lb/>
adeò ut demùm ex omnibus &longs;patiis tactis &longs;imul & intactis coa<lb/>
le&longs;cat linea æqualis ei, quæ tangitur à majore peripheriâ ma<lb/>
joris circuli. </s> </p>

<p type="main"> <s id="s.001645">Mihi tamen arridere non pote&longs;t illa loquendi formula, quæ <lb/>
circulum polygonum infinitorum (& quidem infinitorum &longs;im<lb/>
pliciter) laterum dicit. </s> <s id="s.001646">Polygonum enim utique regulare cir<lb/>
culus e&longs;&longs;et; polygonum autem e&longs;&longs;e non pote&longs;t illud, quod angu<lb/>
lis caret; neque anguli e&longs;&longs;e po&longs;&longs;unt, ubi non e&longs;t lineæ ad li<lb/>
neam inclinatio; in peripheriâ verò circuli linea nulla e&longs;&longs;e po<lb/>
te&longs;t, e&longs;&longs;ent &longs;iquidem infinitæ lineæ æquales invicem, quæ uti<lb/>
que con&longs;tituerent exten&longs;ionem &longs;impliciter infinitam. </s> <s id="s.001647">Quod &longs;i <lb/>
infinita dixeris puncta; non e&longs;t puncti ad punctum inclinatio, <lb/>
quæ po&longs;&longs;it angulum con&longs;tituere, ac proinde circulus non e&longs;t po<lb/>
lygonum infinitorum laterum, ni&longs;i vocabulis ad opinandi li<lb/>
centiam immoderatè abutamur. </s> <s id="s.001648">Adde quod omnia diametri <lb/>
puncta ad omnia puncta peripheriæ e&longs;&longs;ent in Ratione, quam <lb/>
Archimedes <emph type="italics"/>lib.de dimen&longs;ione circuli<emph.end type="italics"/> definivit contineri inter Ra<lb/>
tionem 7 ad 22, & Rationem 71 ad 223: non igitur infinita e&longs;&longs;e <lb/>
po&longs;&longs;unt aut diametri, aut peripheriæ, aut utriu&longs;que puncta; ab <lb/>
infinitis enim Rationem omnem ablegant iidem Authores. </s> <s id="s.001649">Si