diametri prædicti circuli, & produci intelligatur ver&longs;us oculum A, per ip<lb/>
&longs;um tran&longs;ilit; quo in &longs;itu, &longs;i circulus oculo &longs;ubijciatur, non planam ip&longs;ius <lb/>
&longs;uperficiem, &longs;ed circunferentiam <expan abbr="tant&utilde;">tantum</expan> a&longs;picit, <expan abbr="fit&qacute;">fitque</expan>; vt non lineam curuam, <lb/>
&longs;ed rectam videre videatur, vt in præcedenti problemate diximus, & Per<lb/>
&longs;pectiui demon&longs;trant, & Vitellio lib. 4. propo&longs;it. </s> <s id="s.004057">5. & propo&longs;it. </s> <s id="s.004058">50.</s> </p>

<p type="main"> <s id="s.004059">Quidquid porrò &longs;phæram a&longs;pexerit, nece&longs;&longs;ariò ita illam a&longs;picit, vt quod <lb/>
de ip&longs;a videt, &longs;it orbiculare, cum ergò Sol Lunam a&longs;piciat, &longs;iue illuminet, <lb/>
debet illuminatio illa e&longs;&longs;e orbicularis, hoc e&longs;t habere orbicularem ba&longs;im, vt <lb/>
in figura patet, in qua Sol a&longs;piciens Lunam, quamuis in diuer&longs;is locis po&longs;i<lb/>
tam, eius tamen &longs;emper dimidium illu&longs;trat, cuius dimidij ba&longs;is e&longs;t circula<lb/>
ris, <expan abbr="repre&longs;entatur&qacute;">repre&longs;entaturque</expan>; in lineis K B L, K C L, K D L, & c&etail;teris &longs;imilibus, quan<lb/>
do igitur Luna e&longs;t in tali po&longs;itione, vt totus ille orbis illuminationis oculis <lb/>
no&longs;tris in A, po&longs;itis obijciatur, totus vna cum tota illuminatione con&longs;pici<lb/>
tur, vt accidit, quando Luna e&longs;t in F. <expan abbr="tunc&qacute;">tuncque</expan>; e&longs;t oppo&longs;ita diametraliter So<lb/>
li, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; Plenilunium. </s> <s id="s.004060">Cùm autem Luna vetus mutatur in nouam, receden<lb/>
do à Sole, vt quando tran&longs;it à B, in C, tunc <expan abbr="circ&utilde;ferentia">circunferentia</expan> K B L, prædicti or<lb/>
bis, quæ Luna in B, exi&longs;tente, videri non poterat, incipit videri quando fue<lb/>
rit in C. <expan abbr="cernitur&qacute;">cerniturque</expan>; pars illius illuminationis circa punctum L, quæ videtur <lb/>
falcata; quæ pars recedente adhuc magis Luna à Sole, &longs;emper augetur, ide&longs;t <lb/>
&longs;emper maior illuminationis pars cernitur: ita vt cùm fuerit in D, &longs;emiple<lb/>
na appareat, & linea K D L, quæ ibi orbicularis e&longs;t, oculo in A, videtur re<lb/>
ctà, ob cau&longs;am &longs;uperius dictam; tunc igitur lumen Lunæ ex vna parte vide<lb/>
tur terminari linea recta, ex altera circulari, ita vt figura luminis &longs;it &longs;emi<lb/>
circulus. </s> <s id="s.004061">Porrò Luna &longs;emper ex &longs;e oculis no&longs;tris opponitur, quamuis non <lb/>
&longs;emper cernatur, vt accidit in Nouilunio, quando &longs;cilicet Luna e&longs;t infra <lb/>
Solem in B, quia cum Sol &longs;it &longs;upra ip&longs;am, illuminat hemi&longs;phærium eius &longs;u<lb/>
perius, quod oculo in A, e&longs;t auer&longs;um; & ideò videri nequit; po&longs;tea paula<lb/>
tim recidendo à Sole, incipit hemi&longs;phærium illu&longs;tratum ad oculum A, ver<lb/>
gere, & ideo con&longs;pici, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; primo apparet lunularis, &longs;eu falcata, deinde mi<lb/>
nus, ac minus falcata, quia linea interior falcis minus curuatur, & &longs;ectio<lb/>
nem conicam, quam oualem dicunt, refert: deinde magis ad rectitudinem <lb/>
accedit, ita vt circa octauum diem, &longs;eu circa primum Lunæ quadrantem, <lb/>
linea illa videatur recta, Luna autem dixotomos, &longs;eu dimidiata; vbi enim <lb/>
circunferentia illuminationis Solis, ad puncta deuenit vltima, per quæ Lu<lb/>
na bifariam diuiditur, apparet tantum oculo circunferentia illius, & nullo <lb/>
modo ip&longs;um circuli planum, qui ba&longs;is e&longs;t: &longs;ed, vt &longs;upra etiam dictum e&longs;t, <lb/>
planum eius productum &longs;ecaret oculum in A, exi&longs;tentem, & &longs;tatim ab hoc <lb/>
&longs;itu mutatur, & præterit, quod cùm fit, nece&longs;&longs;e e&longs;t, vt prædictus circulus per <lb/>
&longs;umma puncta K L, de&longs;ignatus, non amplius recta linea, &longs;ed curua, & lunu<lb/>
laris appareat, quia aliquo modo planum prædicti circuli ad oculos incli<lb/>
natur, priori tamen circunferentia ex aduersò oculorum, vt dictum e&longs;t, exi<lb/>
&longs;tente, <expan abbr="atq;">atque</expan> hoc modo ex inclinatione ba&longs;is ad oculum aliquid lucis amplius <lb/>
re&longs;ecatur, ide&longs;t ab oculo cernitur. </s> <s id="s.004062">tum etiam extrema huius circunferentiæ <lb/>
in codem per&longs;i&longs;tunt, ide&longs;t in ei&longs;dem punctis, & propterea linea illa magis, <lb/>
& minus incuruatur pro Solis remotione; ita vt tandem reuertatur ad ea<lb/>
dem puncta. </s> <s id="s.004063">fieri enim pote&longs;t, vt infinitas inclinationes &longs;u&longs;cipiat, &longs;i quidem