<emph type="italics"/>initium e&longs;t motus. </s> <s id="id.001603">Plurimum itaque confert ad motus facilitatem, <lb/>
vt tum axis, tum rota intus &longs;int læuißima, vnde aurigæ axungia <lb/>
( quæ inde nomen traxit ) ip&longs;a inungunt. <emph.end type="italics"/></s> 

 <s id="id.001604">Quod parua &longs;ui.] <emph type="italics"/>Prima cau&longs;a e&longs;t facilitatis motus &longs;uper plano <lb/>
in rotundis de modico contactu in omni &longs;ui po&longs;itione. </s> <s id="id.001605">Contactus <lb/>
enim multa parte &longs;ui facit hærere, & &longs;imul e&longs;&longs;e ea, quæ &longs;e&longs;e &longs;ic con<lb/>
tingunt, & quidem tantò magis, quantò maior e&longs;t hic contactus. <lb/>
</s> <s id="id.001606">quò igitur erit minor, eò minus hærere, citiu&longs;que diuelli faciet. </s> <s id="id.001607">Mul<lb/>
ta autem præter rotunda vt triangulum æquilaterum, & tetraë<lb/>
dron planum in puncto contingere po&longs;&longs;unt, &longs;ed non in omni &longs;ui po&longs;i<lb/>
tione, vt cum &longs;ecundum vnam &longs;ui aream &longs;uperiacent: at rotunda <lb/>
&longs;iue &longs;phæra &longs;it, &longs;iue circulus planum in vno puncto quouis modo &longs;e<lb/>
cundum curuaturam po&longs;ita attingunt. </s> <s id="id.001608">quod demon&longs;tratum e&longs;t de <lb/>
illo quidem à Theodo&longs;. prop. 2. lib. 1. de Sphær. de hoc vero ab Eucli<lb/>
de prop. 16. lib. 3. <emph.end type="italics"/></s> 

 <s id="id.001610">Et quia non off.] <emph type="italics"/>Secunda cau&longs;a e&longs;t de occur&longs;antibus, quæ <lb/>
rur&longs;us cum minimam partem rotundorum attingant, & atterant, <lb/>
minus impediunt, quam quæ plus attingunt, pluribu&longs;que occur&longs;ant. <emph.end type="italics"/></s> 

 <s id="id.001611">Di&longs;tat enim angulus.] <emph type="italics"/>Cum rotundum incumbit plano ad <lb/>
omnes rectas à quibus tangitur in ip&longs;o plano angulos facit contin<lb/>
gentiæ, quorum &longs;inguli quia &longs;unt minores quouis acuto angulo re<lb/>
ctilineo, vt e&longs;t demon&longs;tratum prop. 16. lib. 3. </s> <s>procliues &longs;unt maxime <lb/>
ad motum. </s> <s id="id.001612">Latus enim curuum anguli vnius contactus &longs;emotum <lb/>
quidem e&longs;t à plano: &longs;ed parum propter anguli angu&longs;tiam. </s> <s id="id.001613">Et &longs;ic non <lb/>
offen&longs;at, & proximum e&longs;t ca&longs;ui. </s> <s id="id.001614">Hinc etiam vna cau&longs;a colligi po<lb/>
te&longs;t, cur rotunda maiora facilius moueantur minoribus, quod <lb/>
angulos &longs;ui contactus tantò acutiores faciunt: quantò &longs;unt maiora, <lb/>
vt in libello no&longs;tro de angulo contactus demon&longs;trauimus. <emph.end type="italics"/></s> 

 <s id="id.001615">At &longs;i rectilineum e&longs;&longs;et.] <emph type="italics"/>Difficultas motus in mobili pendet <lb/>
ab eius internis aut externis. </s> <s id="id.001616">Interna e&longs;t naturalis cuiu&longs;que <expan abbr="prop&etilde;&longs;io">propen&longs;io</expan>, <lb/>
qua extra locum exi&longs;tens, &longs;i liberum &longs;inatur mobile, ad <expan abbr="e&utilde;">eum</expan> per &longs;e fe<lb/>
ratur. </s> <s id="id.001617">Atque vt ibi vi retineatur, eò tamen quodam motu occulto <lb/>
tendit, vt graue deor&longs;um, leue &longs;ur&longs;um, & &longs;emper &longs;ecundum rectam <lb/>
perpendicularem in qua e&longs;t centrum grauitatis mobilis: aliò nun<lb/>
quam, ni&longs;i vi contraria nixus ille vincatur, vt cum graue &longs;ur&longs;um: <lb/>
aut leue deor&longs;um: aut vtrumque ad latera propellitur. </s> <s id="id.001618">Itaque prima <emph.end type="italics"/>