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<s>TABVLA PRO<lb/>POSITIONVM DE <lb/>PROPORTIONIBVS.<lb/><arrow.to.target n="table1"/></s></p><table><table.target id="table1"/><row><cell>I.</cell><cell>Proportionem <emph type="italics"/>in proportionem duci, e&longs;t &longs;uperiores numeros atque inferiores inuicem ducere.<emph.end type="italics"/></cell><cell><emph type="italics"/>pagina<emph.end type="italics"/> 6</cell></row><row><cell>II.</cell><cell>P<emph type="italics"/>roportio extremorum producitur ex intermedijs.<emph.end type="italics"/></cell><cell>7</cell></row><row><cell>III.</cell><cell>S<emph type="italics"/>i proportio ex duabus proportionibus in quatuor terminis producatur, ip&longs;a uerò proportio inter duas alias quantitates fuerit con&longs;tituta: con&longs;urgent trecen-ti &longs;exaginta modi productionis proportionis.<emph.end type="italics"/></cell><cell>7</cell></row><row><cell>IIII.</cell><cell>S<emph type="italics"/>i fuerit proportio primi ad &longs;ecundum, producta ex proportionibus tertij ad quartum, & quinti ad &longs;extum, producetur etiam ex proportione tertij ad &longs;extum, & quinti ad quartum.<emph.end type="italics"/></cell><cell>8</cell></row><row><cell>V.</cell><cell>S<emph type="italics"/>i fuerit proportio primi ad &longs;ecundum, producta ex proportione tertij ad quartum, & quinti ad &longs;extum: erit proportio tertij ad &longs;extum, producta ex proportionibus primi ad &longs;ecur dum, & quarti ad quintum.<emph.end type="italics"/></cell><cell>8</cell></row><row><cell>VI.</cell><cell>E<emph type="italics"/>x trecentis &longs;exaginta modis producendarum proportionum triginta &longs;ex tantum e&longs;&longs;e nece&longs;&longs;arios.<emph.end type="italics"/></cell><cell>9</cell></row><row><cell>VII.</cell><cell>I<emph type="italics"/>n modis qui nece&longs;&longs;ariò producuntur ex duabus proportionibus, cum duæ quantitates ex illis quæ modos conficiunt, æquales fuerint: proportio producta ad quatuor quanti-tates omiologas reducetur.<emph.end type="italics"/></cell><cell>10</cell></row><row><cell>VIII.</cell><cell>S<emph type="italics"/>i duarum proportionum &longs;uperiores numeri alternatim cum inferioribus multiplicen-tur atque coniungantur, erit proportio aggregati ad productum ex inferioribus in-uicem proportio, ex primis proportionibus compo&longs;ita.<emph.end type="italics"/></cell><cell>11</cell></row><row><cell>IX.</cell><cell>S<emph type="italics"/>i duarum proportionum &longs;uperiores numeri alternatim cum inferioribus multiplicen-tur, minusque productum ex maiore detrahatur, erit re&longs;idui ad productum ex in&longs;e-rioribus proportio uelut illa, quæ relinquitur detracta minore proportione ex ma-iore.<emph.end type="italics"/></cell><cell>11</cell></row><row><cell>X.</cell><cell>S<emph type="italics"/>i fuerit alicuius quantitatis ad unam partem proportio, uelut alterius partis ad &longs;ecun-dam quantitatem, erit proportio cuiu&longs;uis quantitatis eiu&longs;dem generis ad &longs;ecundam compo&longs;ita proportio, ex proportionibus eiu&longs;dem quantitatis, a&longs;&longs;umptæ ad utranque partem primæ quantitatis &longs;eor&longs;um.<emph.end type="italics"/></cell><cell>11</cell></row><row><cell>XI.</cell><cell>P<emph type="italics"/>roportio aggregati quarumlibet duarum quantitatum ad aggregatum duarum æqua-lium <expan abbr="quantitat&utilde;">quantitatum</expan> e&longs;t, compo&longs;ita ex proportionibus primis, & diui&longs;a per duplam.<emph.end type="italics"/></cell><cell>12</cell></row><row><cell>XII.</cell><cell>P<emph type="italics"/>ropo&longs;itis duabus proportionibus unam alteri iungere ab&longs;que multiplicatione.<emph.end type="italics"/></cell><cell>12</cell></row><row><cell>XIII.</cell><cell>P<emph type="italics"/>roportio confu&longs;a aggregata primæ & tertiæ quatuor quantitatum omiologarum ad aggregatum &longs;ecundæ & quartæ, e&longs;t uelut compo&longs;ita ex ei&longs;dem diui&longs;a per du-plam.<emph.end type="italics"/></cell><cell>13</cell></row><row><cell>XIIII.</cell><cell>P<emph type="italics"/>roportiones confu&longs;æ & coniunctæ in tribus quantitatibus inuicem commutantur.<emph.end type="italics"/></cell><cell>13</cell></row><row><cell>XV.</cell><cell>S<emph type="italics"/>i fuerint quatuor quantitates proportio confu&longs;a, aggregati primæ & tertiæ, ad aggre-gatum &longs;ecundæ & quartæ, erit ut monadis addito prouentu, qui fit diui&longs;a differentia, differentiarum primæ & &longs;ecundæ, atque quartæ & tertiæ, per aggregatum tertiæ & quartæ ad ip&longs;am monadem.<emph.end type="italics"/></cell><cell>14</cell></row><row><cell>XVI.</cell><cell>O<emph type="italics"/>mnium quatuor quantitatum propo&longs;ita prima, quæ non minorem habet proportio-nem ad &longs;uam corre&longs;pondentem quàm alia ad aliam, erit proportio confu&longs;a illarum,<emph.end type="italics"/></cell><cell/></row><pb/><row><cell/><cell><emph type="italics"/>ut producti ex aggregato primæ & tertiæ, in tertiam ad productum ex iggre gato tertiæ & omiotatæ ad &longs;ecundam in ip&longs;am quartam.<emph.end type="italics"/></cell><cell>14</cell></row><row><cell>XVII.</cell><cell>O<emph type="italics"/>mnes duæ proportiones conuer&longs;æ producunt æqualem proportionem.<emph.end type="italics"/></cell><cell>15</cell></row><row><cell>XVIII.</cell><cell>S<emph type="italics"/>i fuerint quotlibet quantitates in continua proportione multiplici præter, <expan abbr="ultimã">ultimam</expan> proportio uerò penultimæ ad ultimam, qualis re&longs;idui primæ ad &longs;ecundam, erit primæ ad aggregatum reliquarum, uelut penultimæ ad ultimam.<emph.end type="italics"/></cell><cell>15</cell></row><row><cell>XIX.</cell><cell>S<emph type="italics"/>i fuerint aliquot quantitates arithmeticæ omiologæ, quarum exce&longs;&longs;us &longs;it æqualis minimè, omnibus autem deficientibus &longs;upplementa ad æqualitatem maximè adiungantur, erunt quadrata omnium quantitatum æqualium, adiecto rur&longs;us quadrato primæ cum eo quod fit ex minima primi ordinis in aggregatum o-mnium quantitatum eiu&longs;dem, tripla aggregato quadratorum omnium quanti tatum primi ordinis pariter acceptis.<emph.end type="italics"/></cell><cell>17</cell></row><row><cell>XX.</cell><cell>C<emph type="italics"/>um fuerint quatuor quantitates, fueritque <expan abbr="&longs;ec&utilde;da">&longs;ecunda</expan> æqualis tertiæ, aut prima æqualis quartæ, erit proportio primæ ad quartam, aut tertiæ ad &longs;ecundam, producta ex proportionibus primæ ad &longs;ecundam & tertiæ ad quartam.<emph.end type="italics"/></cell><cell>21</cell></row><row><cell>XXI.</cell><cell>C<emph type="italics"/>um decu&longs;&longs;atim ducta fuerit prima in quartam, & &longs;ecunda in tertiam, produ-ctumque primæ in quartam, diui&longs;um fuerit per productum &longs;ecundæ in tertiam, erit proportio primæ ad &longs;ecundam, diui&longs;a per proportíonem tertiæ ad quar-tam.<emph.end type="italics"/> E<emph type="italics"/>t &longs;imiliter interpo&longs;ita omiologa.<emph.end type="italics"/></cell><cell>22</cell></row><row><cell>XXII.</cell><cell>C<emph type="italics"/>um fuerit proportio primæ ad &longs;ecundam maior quàm tertiæ ad quartam, erit confu&longs;a ex his maior quàm tertiæ ad quartam, minor autem quàm primæ ad &longs;ecundam.<emph.end type="italics"/></cell><cell>23</cell></row><row><cell>XXIII.</cell><cell>O<emph type="italics"/>mnis motus naturalis ad locum &longs;uum e&longs;t: ideò per rectam lineam fit.<emph.end type="italics"/></cell><cell>23</cell></row><row><cell>XXIIII.</cell><cell>O<emph type="italics"/>mnis motus circularis uoluntarius e&longs;t.<emph.end type="italics"/></cell><cell>23</cell></row><row><cell>XXV.</cell><cell>T<emph type="italics"/>res &longs;unt motus omnino &longs;implices naturalis, uoluntarius, & uiolentus.<emph.end type="italics"/></cell><cell>24</cell></row><row><cell>XXVI.</cell><cell>M<emph type="italics"/>otus ergo compo&longs;iti quatuor nece&longs;&longs;ariò &longs;unt &longs;pecies.<emph.end type="italics"/></cell><cell>24</cell></row><row><cell>XXVII.</cell><cell>M<emph type="italics"/>otus uoluntarius e&longs;t in loco: naturalis ad locum: uiolentus ex loco.<emph.end type="italics"/></cell><cell>25</cell></row><row><cell>XXVIII.</cell><cell>M<emph type="italics"/>otus quilibet uoluntarius aut uiolentus in aliquo medio fit.<emph.end type="italics"/></cell><cell>25</cell></row><row><cell>XXIX.</cell><cell>O<emph type="italics"/>mnis motus uoluntarius æqualis e&longs;t &longs;emper: &longs;impliciter etiam quilibet alius mo-tus.<emph.end type="italics"/></cell><cell>25</cell></row><row><cell>XXX.</cell><cell>I<emph type="italics"/>n omni corpore mobili in medio partes medij re&longs;i&longs;tunt obuiæ, aliæ impel-lunt.<emph.end type="italics"/></cell><cell>26</cell></row><row><cell>XXXI.</cell><cell>O<emph type="italics"/>mnis motus naturalis in æquali medio ualidior e&longs;t in fine quàm in principio.<emph.end type="italics"/>V<emph type="italics"/>iolentus contrà.<emph.end type="italics"/></cell><cell>26</cell></row><row><cell>XXXII.</cell><cell>O<emph type="italics"/>mne mobile naturaliter motum &longs;eu uiolenter uelocius mouetur in medio rariore quàm den&longs;iore.<emph.end type="italics"/> M<emph type="italics"/>aior quoque e&longs;t proportio finis motus in corpore rariore ad finem motus in corpore den&longs;iore quàm principij.<emph.end type="italics"/> I<emph type="italics"/>n uiolento autem celerius perueniret ad finem motus in corpore den&longs;iore.<emph.end type="italics"/></cell><cell>27</cell></row><row><cell>XXXIII.</cell><cell>O<emph type="italics"/>mnia duo mobilia æqualis undique magnitudinis quæ æquali in tempore æqualia &longs;pacia pertran&longs;eunt in diuer&longs;is &longs;ub&longs;tantia medijs nece&longs;&longs;e e&longs;t, ut &longs;it ponderis ad pondus, quem ad modum medij ad medium proportio duplicata.<emph.end type="italics"/></cell><cell>27</cell></row><row><cell>XXXIIII.</cell><cell>P<emph type="italics"/>roportio corporis cubi ad &longs;uam &longs;uperficiem quadratam, e&longs;t uelut eiu&longs;dem &longs;uperfi ciei, ad latus eiu&longs;dem uerò ad monadem.<emph.end type="italics"/></cell><cell>28</cell></row><row><cell>XXXV.</cell><cell>V<emph type="italics"/>ocum magnitudines excre&longs;cunt in acumine, non in grauitate, finis autem e&longs;t in utroque extremo.<emph.end type="italics"/> P<emph type="italics"/>ropter hoc minima facta uariatione in hypate acutæ uix ferunt.<emph.end type="italics"/></cell><cell>29</cell></row><row><cell>XXXVI.</cell><cell>S<emph type="italics"/>i proportio per proportionem minorem æquali ducatur, proportio minor pro-<emph.end type="italics"/></cell><cell/></row><pb/><row><cell/><cell><emph type="italics"/>ducetur.<emph.end type="italics"/> V<emph type="italics"/>nde manife&longs;tum e&longs;t duas proportiones minores æqualitate <expan abbr="inuic&etilde;">inuicem</expan> du ctas proportionem minorem unaquaque illarum producere.<emph.end type="italics"/></cell><cell>30</cell></row><row><cell>XXXVII.</cell><cell>S<emph type="italics"/>i plures homines, quorum per &longs;e nauim mouere poßint, aut pondus ferre &longs;imul iuncti eam moueant, aut pondus ferant, erunt illæ proportiones coniunctæ non productæ.<emph.end type="italics"/></cell><cell>30</cell></row><row><cell>XXXVIII.</cell><cell>O<emph type="italics"/>mne corpus tantum re&longs;i&longs;tit motui contrario &longs;uo natúrali, quantum mouetur oc-culto motu quie&longs;cendo.<emph.end type="italics"/></cell><cell>31</cell></row><row><cell>XXXIX.</cell><cell>A<emph type="italics"/>b æquali aut minore ui quàm &longs;it impedimentum non fit motus.<emph.end type="italics"/></cell><cell>31</cell></row><row><cell>XL.</cell><cell>O<emph type="italics"/>mne corpus &longs;pb æricum tangens planum in puncto mouetur ad latus per quam-cunque uim, quæ medium diuidere pote&longs;t.<emph.end type="italics"/></cell><cell>31</cell></row><row><cell>XLI.</cell><cell>S<emph type="italics"/>i fuerint duæ quantitates &longs;umaturque toties <expan abbr="aggregat&utilde;">aggregatum</expan> maioris & minoris, quo-ties aggregatum minoris & maioris, erit proportio confu&longs;a maioris aggregati ad minus, minor quam multiplicis maioris ad multiplex minoris.<emph.end type="italics"/></cell><cell>32</cell></row><row><cell>XLII.</cell><cell>T<emph type="italics"/>rahentium nauim, aut ferentium pondera proportiones in &longs;e inuicem, quomodo ducere oporteat con&longs;iderare.<emph.end type="italics"/></cell><cell>32</cell></row><row><cell>XLIII.</cell><cell>P<emph type="italics"/>roductionem ad additionem retrabere.<emph.end type="italics"/></cell><cell>33</cell></row><row><cell>XLIIII.</cell><cell>S<emph type="italics"/>i fuerit proportio motoris ad id quod e&longs;t maximum non mouens, & &longs;pacium & tempus, nota erit etiam reliquorum nota.<emph.end type="italics"/></cell><cell>33</cell></row><row><cell>XLV.</cell><cell>R<emph type="italics"/>ationem &longs;tateræ o&longs;tendere.<emph.end type="italics"/></cell><cell>34</cell></row><row><cell>XLVI.</cell><cell>A<emph type="italics"/>n &longs;it aliqua proportio & qualis inter animam & uitas, & &longs;ua corpora con&longs;ide-rare.<emph.end type="italics"/></cell><cell>35</cell></row><row><cell>XLVII.</cell><cell>S<emph type="italics"/>i duo mobilia æqualister in eodem circulo iuxta proprios motus moueantur, pro-ductum temporis circuituum inuicem, erit æquale producto differentiæ tempo rum circuitus ductæ in tempus coniunctionis primæ.<emph.end type="italics"/></cell><cell>36</cell></row><row><cell>XLVIII.</cell><cell>S<emph type="italics"/>i tria mobilia ex eodem puncto di&longs;cedant, fuerintque duorum ac duorum coniun-ctiones in temporibus commen&longs;is, illa tria mobilia denuo coniungentur in tem pore producto ex denominatore diui&longs;ionis temporis maioris per minus in mi-nus aut numeratore in maius.<emph.end type="italics"/></cell><cell>37</cell></row><row><cell>XLIX.</cell><cell>P<emph type="italics"/>ropofitio mobilis in circulo circuitus tempore dataque ratione di&longs;tantiæ ab illo mo bilis circuitum inuenire, quod ex <expan abbr="eod&etilde;">eodem</expan> puncto di&longs;cedens <expan abbr="c&utilde;alio">cunalio</expan> mobili in dato puncto <expan abbr="cõueniat">conueniat</expan> &longs;ub <expan abbr="quoc&utilde;que">quocunque</expan> numero <expan abbr="circuitu&utilde;">circuituum</expan> <expan abbr="t&etilde;pus">tempus</expan> quoque <expan abbr="cõiunctionis">coniunctionis</expan>.<emph.end type="italics"/></cell><cell>39</cell></row><row><cell>L.</cell><cell>O<emph type="italics"/>mnes circuituum portiones in ei&longs;dem temporibus repetuntur.<emph.end type="italics"/></cell><cell>40</cell></row><row><cell>LI.</cell><cell>O<emph type="italics"/>perationes dictas exemplo declarare.<emph.end type="italics"/></cell><cell>41</cell></row><row><cell>LII.</cell><cell>T<emph type="italics"/>ria mobilia coniuncta in <expan abbr="eod&etilde;">eodem</expan> puncto, quorum duo & duo conueniant in partib. incommen&longs;is inter &longs;e, in perpetuum in nullo unquam puncto conuenient.<emph.end type="italics"/></cell><cell>42</cell></row><row><cell>LIII.</cell><cell>C<emph type="italics"/>irculorum &longs;e in aduer&longs;um mouentium proportionem declarare.<emph.end type="italics"/></cell><cell>43</cell></row><row><cell>LIIII.</cell><cell>P<emph type="italics"/>roportio circuli ad &longs;uum diametrum per &longs;imilitudinem e&longs;t quarta pars periphe-riæ.<emph.end type="italics"/> R<emph type="italics"/>ur&longs;usque eiu&longs;dem circuli ad peripheriam diametri quarta pars.<emph.end type="italics"/></cell><cell>44</cell></row><row><cell>LV.</cell><cell>P<emph type="italics"/>roportionem medicamentorum per ordines &longs;up po&longs;ita æquali proportione in or-dinibus per quantitates & proportiones demon&longs;trare.<emph.end type="italics"/></cell><cell>44</cell></row><row><cell>LVI.</cell><cell>P<emph type="italics"/>roportio cuiu&longs;uis binomij ad &longs;uum reci&longs;um, uel ei commen&longs;um e&longs;t duplicata ei quæ ad numeri latus.<emph.end type="italics"/></cell><cell>49</cell></row><row><cell>LVII.</cell><cell>M<emph type="italics"/>otus rationem ad pondus inuenire.<emph.end type="italics"/></cell><cell>49</cell></row><row><cell>LVIII.</cell><cell>Q<emph type="italics"/>uæ ex alto de&longs;cendunt, cur non eandem pro di&longs;tantia motus rationem in libero aëre &longs;eruent con&longs;iderare.<emph.end type="italics"/></cell><cell>49</cell></row><row><cell>LIX.</cell><cell>O<emph type="italics"/>mne mobile motum duobus motibus non ad idem tendentibus utroque &longs;eor&longs;um tar dius mouetur &longs;imili motu.<emph.end type="italics"/></cell><cell>50</cell></row><row><cell>LX.</cell><cell>O<emph type="italics"/>mne mobile motu naturali de&longs;cendentis parte, de&longs;cendit grauiore &longs;ecundum gra-<emph.end type="italics"/></cell><cell/></row><pb/><row><cell/><cell><emph type="italics"/>uitatis centrum.<emph.end type="italics"/></cell><cell>51</cell></row><row><cell>LXI.</cell><cell>P<emph type="italics"/>roportionum ictus ad pondus rei & di&longs;tantiam generaliter con&longs;iderare.<emph.end type="italics"/></cell><cell>52</cell></row><row><cell>LXII.</cell><cell>P<emph type="italics"/>roportionem motoris in plano ad motorem, qui eleuat pondus iuxta id quod mouet, inuenire.<emph.end type="italics"/></cell><cell>53</cell></row><row><cell>LXIII.</cell><cell>O<emph type="italics"/>mne graue quanto proximius alligatum plano, tantò facilius trabitur.<emph.end type="italics"/></cell><cell>53</cell></row><row><cell>LXIIII.</cell><cell>O<emph type="italics"/>mne mobile quantò latius tanto tardius moustur in plano.<emph.end type="italics"/></cell><cell>54</cell></row><row><cell>LXV.</cell><cell>P<emph type="italics"/>roportionem duorum mobilium inter &longs;e cum auxilio medij inuenire.<emph.end type="italics"/></cell><cell>54</cell></row><row><cell>LXVI.</cell><cell>P<emph type="italics"/>roportionem laterum eptagoni, & &longs;ubten&longs;arum con&longs;iderare, & quæ à reflexa proportione pendent.<emph.end type="italics"/></cell><cell>55</cell></row><row><cell>LXVII.</cell><cell>S<emph type="italics"/>i fuerint aliquot quantitates ab una quantitate aliæque totidem ab eadem analo-gæ, erit proportio tertiæ unius ordinis ad tertiam alterius, ut &longs;ecundæ ad &longs;e-cundum duplicata, & quartæ ad quartam triplicata, quintæ ad quintam quadruplicata, atque &longs;ic de alijs.<emph.end type="italics"/></cell><cell>57</cell></row><row><cell>LXVIII.</cell><cell>P<emph type="italics"/>ropo&longs;itio collectorum ab<emph.end type="italics"/> E<emph type="italics"/>uclide &<emph.end type="italics"/> A<emph type="italics"/>rchimede.<emph.end type="italics"/></cell><cell>57</cell></row><row><cell>LXIX.</cell><cell>P<emph type="italics"/>ropo&longs;itio collectorum ex quatuor libris<emph.end type="italics"/> A<emph type="italics"/>pollonij<emph.end type="italics"/> P<emph type="italics"/>ergei &<emph.end type="italics"/> <expan abbr="q.">que</expan> S<emph type="italics"/>ereni.<emph.end type="italics"/></cell><cell>59</cell></row><row><cell>LXX.</cell><cell>S<emph type="italics"/>Si fuerint tres quantitates in continua proportione, aliæque totidem in continua proportione poterunt con&longs;tituere tres quantitates in æquali differentia per-uer&longs;im copulatæ.<emph.end type="italics"/></cell><cell>62</cell></row><row><cell>LXXI.</cell><cell>P<emph type="italics"/>roportionem leuitatis ponderis per uirgam torcularem attracti ad rectam &longs;u-&longs;pen&longs;ionem inuenire.<emph.end type="italics"/></cell><cell>63</cell></row><row><cell>LXXII.</cell><cell>P<emph type="italics"/>roportionem ponderis &longs;phæræ pendentis ad a&longs;cendentem per accliue planum inuenire.<emph.end type="italics"/></cell><cell>63</cell></row><row><cell>LXXIII.</cell><cell>P<emph type="italics"/>roportionem ponderum attractorum penes figuram in plano inuenire.<emph.end type="italics"/></cell><cell>64</cell></row><row><cell>LXXIIII.</cell><cell>P<emph type="italics"/>roportionem concutientis ad concu&longs;&longs;um in&longs;tabili inuenire.<emph.end type="italics"/></cell><cell>64</cell></row><row><cell>LXXV.</cell><cell>P<emph type="italics"/><expan abbr="roportion&etilde;">roportionem</expan> immoti in aqua, ad <expan abbr="immot&utilde;">immotum</expan> in terra in excipiendo <expan abbr="ict&utilde;">ictum</expan> inuenire.<emph.end type="italics"/></cell><cell>65</cell></row><row><cell>LXXVI.</cell><cell>P<emph type="italics"/>roportionem <expan abbr="duor&utilde;">duorum</expan> mobilium &longs;ibi <expan abbr="inuic&etilde;">inuicem</expan> <expan abbr="concurrenti&utilde;">concurrentium</expan> per <expan abbr="rectã">rectam</expan> inuenire.<emph.end type="italics"/></cell><cell>66</cell></row><row><cell>LXXVII.</cell><cell>P<emph type="italics"/>roportionem motus obliqui ad motum rectum in nauibus inuenire.<emph.end type="italics"/></cell><cell>66</cell></row><row><cell>LXXVIII.</cell><cell>P<emph type="italics"/>roportionem nauis ad triremes quotuis concurrentes demon&longs;trare.<emph.end type="italics"/></cell><cell>67</cell></row><row><cell>LXXIX.</cell><cell>P<emph type="italics"/>roportionem medicamentorum purgantium inuicem declarare<emph.end type="italics"/></cell><cell>68</cell></row><row><cell>LXXX.</cell><cell>P<emph type="italics"/>roportionem motus &longs;ecundum obliquum ad rectum in &longs;pacio declarare.<emph.end type="italics"/></cell><cell>69</cell></row><row><cell>LXXXI.</cell><cell>Q<emph type="italics"/>uualis &longs;it angulus, per quem pote&longs;t moueri nauis ad rectum explorare.<emph.end type="italics"/></cell><cell>70</cell></row><row><cell>LXXXII.</cell><cell>P<emph type="italics"/>roportionem uelorum indagare.<emph.end type="italics"/></cell><cell>70</cell></row><row><cell>LXXXIII.</cell><cell>P<emph type="italics"/>roportionem rece&longs;&longs;us à recta uia ad obliquitatem inue&longs;tigare.<emph.end type="italics"/></cell><cell>72</cell></row><row><cell>LXXXIIII.</cell><cell>D<emph type="italics"/><expan abbr="i&longs;tantiã">i&longs;tantiam</expan> centri terræ à centro mundi per motum lapidis<emph.end type="italics"/> H<emph type="italics"/>erculei declarare.<emph.end type="italics"/></cell><cell>73</cell></row><row><cell>LXXXV.</cell><cell>P<emph type="italics"/>roportio ponderis unius grauis ad aliud &longs;ub eadem men&longs;ura e&longs;t ueluti eiu&longs;dem ad differentiam ponderis ua&longs;is repleti ex altero graui, & ex ambobus de-tracto priore.<emph.end type="italics"/></cell><cell>74</cell></row><row><cell>LXXXVI.</cell><cell>S<emph type="italics"/>i circuli in æ quales &longs;eu in &longs;phæra &longs;eu in plano &longs;e &longs;ecuerint, nunquàm oppo&longs;itos angulos æquales habent.<emph.end type="italics"/></cell><cell>77</cell></row><row><cell>LXXXVII.</cell><cell>P<emph type="italics"/>roportiones craßitiei aquæ ad <expan abbr="a&etilde;r&etilde;">aerrem</expan> in <expan abbr="cõparatione">comparatione</expan> ad radios demon&longs;trare.<emph.end type="italics"/></cell><cell>78</cell></row><row><cell>LXXXVIII.</cell><cell>I<emph type="italics"/><expan abbr="n&longs;trument&utilde;">n&longs;trumentum</expan><emph.end type="italics"/> A<emph type="italics"/>colingen, quo momenta temporum <expan abbr="deprehendãtur">deprehendantur</expan> fabricare.<emph.end type="italics"/></cell><cell>79</cell></row><row><cell>LXXXIX.</cell><cell>P<emph type="italics"/>roportionem den&longs;itatis aquæ ad aërem per pondera inuenire.<emph.end type="italics"/></cell><cell>82</cell></row><row><cell>XC.</cell><cell>R<emph type="italics"/>ationem impetus uiolenti extra mißi ponderis ad æqualitatem reducere.<emph.end type="italics"/></cell><cell>82</cell></row><row><cell>XCI.</cell><cell>P<emph type="italics"/>roportionem grauis cubi, & &longs;phærici æqualium in accliui, & de&longs;cen&longs;us eorum demon&longs;trare.<emph.end type="italics"/></cell><cell>83</cell></row><row><cell>XCII.</cell><cell>P<emph type="italics"/><expan abbr="roportion&etilde;">roportionem</expan> ponderis æqualis iuxta longitudinis <expan abbr="cõparation&etilde;">comparationem</expan> demon&longs;trare.<emph.end type="italics"/></cell><cell>85</cell></row><row><cell>XCIII.</cell><cell>P<emph type="italics"/>ropter qd in <expan abbr="cõcußione">concußione</expan> <expan abbr="etiã">etiam</expan> leui nauis loco moueatar <expan abbr="o&longs;t&etilde;dere">o&longs;tendere</expan>.<emph.end type="italics"/> V<emph type="italics"/>nde manifi <expan abbr="&longs;i&utilde;">&longs;ium</expan> e&longs;t duas naues &longs;ibi <expan abbr="inuic&etilde;">inuicem</expan> occur&longs;antes retrocedere, & <expan abbr="quãt&utilde;">quantum</expan> <expan abbr="retrocedãt">retrocedant</expan> ambæ.<emph.end type="italics"/></cell><cell>86</cell></row><pb/><row><cell>XCIIII.</cell><cell>S<emph type="italics"/>i <expan abbr="quãtitas">quantitas</expan> aliqua nota atque proportio erit producta, <expan abbr="quãtitas">quantitas</expan> nota &longs;imiliter.<emph.end type="italics"/> E<emph type="italics"/>t &longs;i duæ proportiones notæ fuerint, erit producta ex his atque diui&longs;a coniunctaque atque detra-cta nota.<emph.end type="italics"/> E<emph type="italics"/>t &longs;i fuerit totius ad partem proportio nota, erit et ad aliam partem nota: & alterius partis ad <expan abbr="alterã">alteram</expan> uno minor.<emph.end type="italics"/> E<emph type="italics"/>t &longs;i fuerit partis ad partem, erit ad totum monade minor atque nota.<emph.end type="italics"/> E<emph type="italics"/>t &longs;i fuerit unius <expan abbr="quãtitatis">quantitatis</expan> ad duas <expan abbr="quãtitates">quantitates</expan> proportio nota, erit & <expan abbr="cõfu&longs;a">confu&longs;a</expan> ex eis nota.<emph.end type="italics"/> E<emph type="italics"/>t &longs;i fuerint trium quantitatum omiologarum, aut quatuor analogarum omnes præter unam cognitæ, erunt | & illa alia cognita.<emph.end type="italics"/></cell><cell>87</cell></row><row><cell>XCV.</cell><cell>C<emph type="italics"/>uiu&longs;uis trigoni rectanguli, aut cuius duo auguli &longs;int in dupla proportione, aut qui circulo in&longs;criptus &longs;it cognita quantitate unius lateris in comparatione ad dimetien <expan abbr="t&etilde;">tem</expan>, &longs;i proportio duorum laterum cognita fuerit, <expan abbr="er&utilde;t">erunt</expan> omnia eius latera cognita.<emph.end type="italics"/></cell><cell>88</cell></row><row><cell>XCVI.</cell><cell>C<emph type="italics"/>um in <expan abbr="per&longs;picu&utilde;">per&longs;picuum</expan> den&longs;um radij lumino&longs;i inciderint, quatuor fiunt luminis genera.<emph.end type="italics"/></cell><cell>89</cell></row><row><cell>XCVII.</cell><cell>M<emph type="italics"/><expan abbr="ot&utilde;">otum</expan> inuer&longs;ionis in figuris in <expan abbr="cõparatione">comparatione</expan> ad <expan abbr="mot&utilde;">motum</expan> &longs;phæræ in plano inue&longs;tigare.<emph.end type="italics"/></cell><cell>91</cell></row><row><cell>XCVIII.</cell><cell>P<emph type="italics"/>roportionem ponderum æqualium per differentiam angulorum inuenire.<emph.end type="italics"/></cell><cell>92</cell></row><row><cell>XCIX.</cell><cell>P<emph type="italics"/>roportionem grauitatum per multitudinem &longs;uppo&longs;itorum orbium o&longs;tendere.<emph.end type="italics"/></cell><cell>93</cell></row><row><cell>C.</cell><cell>P<emph type="italics"/><expan abbr="roportion&etilde;">roportionem</expan> grauitatis <expan abbr="ponder&utilde;">ponderum</expan> attractorum per <expan abbr="trochlear&utilde;">trochlearum</expan> <expan abbr="numer&utilde;">numerum</expan> inue&longs;tigare.<emph.end type="italics"/></cell><cell>93</cell></row><row><cell>CI.</cell><cell>P<emph type="italics"/>roportionem precij gemmarum ex tribus in eodem genere cognitis inuenire.<emph.end type="italics"/></cell><cell>94</cell></row><row><cell>CII.</cell><cell>P<emph type="italics"/>roportionem motuum inuer&longs;ionis, & attractionis in plano inuenire.<emph.end type="italics"/></cell><cell>95</cell></row><row><cell>CIII.</cell><cell>P<emph type="italics"/>roportionem eorundem in accliui demon&longs;trare.<emph.end type="italics"/></cell><cell>95</cell></row><row><cell>CIIII.</cell><cell>P<emph type="italics"/>roportionem motus attractionis in decliui ad motum in plano determinare.<emph.end type="italics"/></cell><cell>95</cell></row><row><cell>CV.</cell><cell>P<emph type="italics"/>roportionem ferentium pondus in pertica inuenire.<emph.end type="italics"/></cell><cell>96</cell></row><row><cell>CVI.</cell><cell>Q<emph type="italics"/>uales proportiones angulorum doceant laterum proportiones.<emph.end type="italics"/> A<emph type="italics"/>tque uicißim deter-minare.<emph.end type="italics"/></cell><cell>97</cell></row><row><cell>CVII.</cell><cell>S<emph type="italics"/>i in circulo duæ diametri ad rectum angulum &longs;e &longs;ecauerint: aliæ uerò ad perpendicu-lum ex diametro exicrint ad circum ferentiam, &longs;ingulæ &longs;upra diametrum erunt ma iores portionibus reliquis diametri &longs;uperioribus, infra autem minores.<emph.end type="italics"/> D<emph type="italics"/>imidium autem portionis &longs;uperioris re&longs;iduum ad centrum maius &longs;agitta habebit.<emph.end type="italics"/> I<emph type="italics"/>n aliqua præterea portionis &longs;uperioris parte, quæ uer&longs;us diametrum tran&longs;uer&longs;um po&longs;ita e&longs;t, maior e&longs;t differentia partis diametri ei <expan abbr="corre&longs;põdentis">corre&longs;pondentis</expan>, <expan abbr="&qtilde;">quae</expan> line æ tran&longs;uer&longs;æ.<emph.end type="italics"/></cell><cell>100</cell></row><row><cell>CVIII.</cell><cell>P<emph type="italics"/>unctum æqualitatis differentiæ de&longs;cen&longs;us & remotionis à centro inuenire.<emph.end type="italics"/></cell><cell>100</cell></row><row><cell>CIX.</cell><cell>R<emph type="italics"/>ationem libræ expendere.<emph.end type="italics"/></cell><cell>101</cell></row><row><cell>CX.</cell><cell>S<emph type="italics"/>i duæ &longs;phæræ ex eadem materia de&longs;cendant in aëre, eodem temporis momento ad planum ueniunt.<emph.end type="italics"/></cell><cell>104</cell></row><row><cell>CXI.</cell><cell>C<emph type="italics"/>ur ex medio tela ualidiorem ictum, & naues in &longs;calmo à remo ac malo recipiant in-de ex puppi explorare.<emph.end type="italics"/></cell><cell>105</cell></row><row><cell>CXII.</cell><cell>C<emph type="italics"/>ur ex imo leuia longiùs ferantur declarare,<emph.end type="italics"/></cell><cell>106</cell></row><row><cell>CXIII.</cell><cell>C<emph type="italics"/>ur uirga longius mittatur à puero quam à uiro inueftigare.<emph.end type="italics"/></cell><cell>107</cell></row><row><cell>CXIIII.</cell><cell>C<emph type="italics"/>ircularis motus differentias quatuor e&longs;&longs;e, earumque rationem contemplari.<emph.end type="italics"/></cell><cell>108</cell></row><row><cell>CXV.</cell><cell>P<emph type="italics"/>roportionem motuum impul&longs;ionis, & attractionis inter &longs;e, ab eadem ui decla-rare.<emph.end type="italics"/></cell><cell>110</cell></row><row><cell>CXVI.</cell><cell>C<emph type="italics"/>ur machinæ oblongæ igneæ longius emittant &longs;phæram explorare.<emph.end type="italics"/></cell><cell>111</cell></row><row><cell>CXVII.</cell><cell>I<emph type="italics"/>n curriculis maior e&longs;t uis pulueris copio&longs;ioris ampliore in &longs;pacio, quàm paucioris in minore iuxta proportionem eandem.<emph.end type="italics"/></cell><cell>112</cell></row><row><cell>CXVIII.</cell><cell>Q<emph type="italics"/>uanta proportione decedat ictus in obliquum parietem ab eo qui e&longs;t ad perpendi-culum declarare.<emph.end type="italics"/></cell><cell>114</cell></row><row><cell>CXIX.</cell><cell>Q<emph type="italics"/>uantum ictus machinæ procliuis ad angulum minuatur explorare.<emph.end type="italics"/></cell><cell>115</cell></row><row><cell>CXX</cell><cell>P<emph type="italics"/>roportionem partium nauis ad eundem obliquum uentum explorare.<emph.end type="italics"/></cell><cell>118</cell></row><row><cell>CXXI.</cell><cell>F<emph type="italics"/>labelli uires atque naturam declarare.<emph.end type="italics"/></cell><cell>219</cell></row><row><cell>CXXII.</cell><cell>C<emph type="italics"/>ontemptus circa<emph.end type="italics"/> S<emph type="italics"/>olis rationem in umbris declarare.<emph.end type="italics"/></cell><cell>120</cell></row><pb/><row><cell>CXXIII.</cell><cell>C<emph type="italics"/>ognita ratione umbræ ad gnomonem &longs;inum, & arcum altitudinis ab horizon-te, quouis tempore digno&longs;cere.<emph.end type="italics"/></cell><cell>121</cell></row><row><cell>CXXIIII.</cell><cell>P<emph type="italics"/>roportionem umbræ uer&longs;æ e&longs;&longs;e ad gnomonem, uelut gnomonis ad umbram uer&longs;am.<emph.end type="italics"/></cell><cell>122</cell></row><row><cell>CXXV.</cell><cell>P<emph type="italics"/>roportionem dimetientis, & peripheriæ cuiuslibet circuli paralleli æquino-ctiali per cognitam partem magni circuli demon&longs;trare.<emph.end type="italics"/></cell><cell>123</cell></row><row><cell>CXXVI.</cell><cell>C<emph type="italics"/>irculi horarij naturam declarare.<emph.end type="italics"/></cell><cell>123</cell></row><row><cell>CXXVII.</cell><cell>D<emph type="italics"/>ata poli altitudine ortus amplitudinem demonftrare.<emph.end type="italics"/></cell><cell>124</cell></row><row><cell>CXXVIII.</cell><cell>N<emph type="italics"/>ota amplitudine ortus, cuiu&longs;que puncti arcum &longs;emidiurnum inuenire.<emph.end type="italics"/></cell><cell>124</cell></row><row><cell>CXXIX.</cell><cell>D<emph type="italics"/>ata altitudine<emph.end type="italics"/> S<emph type="italics"/>olis in quacunque regione, quacunque die di&longs;tantiam<emph.end type="italics"/> S<emph type="italics"/>olis à meri-diano cogno&longs;cere.<emph.end type="italics"/></cell><cell>124</cell></row><row><cell>CXXX.</cell><cell>D<emph type="italics"/>ata regionis altitudine, & loco<emph.end type="italics"/> S<emph type="italics"/>olis proportionem gnomonis, tam ad um-bram rectam quàm uer&longs;am, uel etiam in cylindro determinare.<emph.end type="italics"/></cell><cell>125</cell></row><row><cell>CXXXI.</cell><cell>S<emph type="italics"/>i lineæ alicui duplum alterius adiungatur, erit proportio duarum ad primam maior quàm dupli cum prima ad primam cum una adiecta.<emph.end type="italics"/></cell><cell>126</cell></row><row><cell>CXXXII.</cell><cell>S<emph type="italics"/>i ad duas lineas quarum una alteri dupla &longs;it eadem linea addatur, erit aggrega-ti ex minore, & adiecta ad ip&longs;am minorem, minor proportio quàm aggre-gati ex maiore, & adiecta ad ip&longs;am maiorem duplicata.<emph.end type="italics"/></cell><cell>126</cell></row><row><cell>CXXXIII.</cell><cell>S<emph type="italics"/>i fuerint duæ quantitates, <expan abbr="quar&utilde;">quarum</expan> una alteri dupla &longs;it: minuatur à minore quæ-dam quantitas, <expan abbr="ead&etilde;que">eadenque</expan> maiori addatur, erit minoris ad re&longs;iduum maior pro-portio, quàm aggregati ad maiorem duplicata.<emph.end type="italics"/> S<emph type="italics"/>i uerò minori addatur, & à maiore detrabatur, erit aggregati ad minorem minor proportio quàm maioris ad re&longs;iduum duplicata.<emph.end type="italics"/></cell><cell>127</cell></row><row><cell>CXXXIIII.</cell><cell>S<emph type="italics"/>i rectangula &longs;uperficies &longs;it, cuius pars tertia quadrata &longs;it corpus, quod ex la-tere quadratæ in re&longs;iduum &longs;uperficiei con&longs;tat, maius e&longs;t quouis corpore ex eadem &longs;uperficies, aliter diui&longs;a con&longs;tituto.<emph.end type="italics"/></cell><cell>127</cell></row><row><cell>CXXXV.</cell><cell>S<emph type="italics"/>i linea in duas partes, quarum una fit alteri dupla diuidatur, erit quod fit ex tertia parte in quadratum re&longs;idui parallelipedum maius omni pararalleli-pedo, quod ex diui&longs;ione eiu&longs;dem lineæ creari poßit.<emph.end type="italics"/></cell><cell>128</cell></row><row><cell>CXXXVI.</cell><cell>D<emph type="italics"/>enominationes in infinitum extendere.<emph.end type="italics"/></cell><cell>129</cell></row><row><cell>CXXXVII.</cell><cell>R<emph type="italics"/>ationem numerorum ex progreßione declarare.<emph.end type="italics"/></cell><cell>131</cell></row><row><cell>CXXXVIII.</cell><cell>M<emph type="italics"/>odos u&longs;us horum numerorum declarare.<emph.end type="italics"/></cell><cell>131</cell></row><row><cell>CXXXIX.</cell><cell>R<emph type="italics"/>adices omnes à propo&longs;itis numeris extrahere.<emph.end type="italics"/></cell><cell>132</cell></row><row><cell>CXL.</cell><cell>R<emph type="italics"/>adices per numeros fractos determinare.<emph.end type="italics"/></cell><cell>133</cell></row><row><cell>CXLI.</cell><cell>N<emph type="italics"/>umeros fractos ad minores in ea <expan abbr="i&etilde;">iem</expan> proportione ualde propinqud deducere<emph.end type="italics"/></cell><cell>136</cell></row><row><cell>CXLII.</cell><cell>D<emph type="italics"/><expan abbr="enomination&utilde;">enominationum</expan> in <expan abbr="crem&etilde;ta">crementa</expan> ex extrema cognita inuenire.<emph.end type="italics"/> E<emph type="italics"/>t <expan abbr="cõuer&longs;o">conuer&longs;o</expan> modo.<emph.end type="italics"/></cell><cell>137</cell></row><row><cell>CXLIII.</cell><cell>S<emph type="italics"/>i linea in duas partes diuidatur, corpora quæ fiunt ex una parte in alterius quadratum mutuo æqualia &longs;unt corpori, quod fit ex tota linea in &longs;uperfi-ciem unius partis in alteram.<emph.end type="italics"/></cell><cell>138</cell></row><row><cell>CXLIIII.</cell><cell>D<emph type="italics"/>uplum cubi medietatis maius e&longs;t aggregato corporum mutuorum, cuiuslibet diui&longs;ionis quantum e&longs;t, quod fit ex tota in quadratum differentiæ.<emph.end type="italics"/></cell><cell>139</cell></row><row><cell>CXLV.</cell><cell>S<emph type="italics"/>i linea in duas partes diuidatur quadrata ambarum partium detracto eo, quod fit ex una parte in alteram, æqualia &longs;unt producto unius in alteram cum quadrato differentiæ.<emph.end type="italics"/></cell><cell>139</cell></row><row><cell>CXLVI.</cell><cell>C<emph type="italics"/>orpus quod fit ex linea diui&longs;a in &longs;uperficiem æqualem quadratis ambarum par tium detracta &longs;uperficie unius partis in alteram, e&longs;t æquale aggregato cubo-rum ambarum partium.<emph.end type="italics"/></cell><cell>139</cell></row><row><cell>CXLVII.</cell><cell>P<emph type="italics"/>ropo&longs;ita linea diui&longs;a duas ei line as adijcere, ut proportio <expan abbr="additar&utilde;">additarum</expan> &longs;ingularium<emph.end type="italics"/></cell><cell/></row><pb/><row><cell/><cell><emph type="italics"/>& partium &longs;imul iunctarum ad additas &longs;it mutua.<emph.end type="italics"/></cell><cell>148</cell></row><row><cell>CXLVIII.</cell><cell>P<emph type="italics"/>ropo&longs;itis tribus lineis primam &longs;ic diuidere, ut adiectis duabus alijs lineis, &longs;ecun-dum <expan abbr="ration&etilde;">rationem</expan> mutuam &longs;ingularum &longs;ingulis, <expan abbr="aggregat&utilde;">aggregatum</expan> ex una <expan abbr="adiectar&utilde;">adiectarum</expan>, & par te ad <expan abbr="aggregat&utilde;">aggregatum</expan> ex alia parte, & adiecta &longs;e habeat, ut &longs;ecunda ad <expan abbr="tertiã">tertiam</expan>.<emph.end type="italics"/></cell><cell>140</cell></row><row><cell>CXLIX.</cell><cell>D<emph type="italics"/>atam lineam &longs;ic diuidere, ut proportio quadratorum ad dupium unius partis in alteram &longs;it, ut lineæ datæ ad lineam datam.<emph.end type="italics"/></cell><cell>141</cell></row><row><cell>CL.</cell><cell>P<emph type="italics"/>ropo&longs;itis duabus lineis, lineam communem utrique adiungere, ut &longs;it maioris ad ad-ditam proportio, uelut quadratorum minoris, & adiectæ ad duplum unius in alteram.<emph.end type="italics"/></cell><cell>141</cell></row><row><cell>CLI.</cell><cell>P<emph type="italics"/>roportio differentiæ quadratorum partium cuiu&longs;uis lineæ, ad quadratum diffe-rentiæ illarum e&longs;t, uelut totius lineæ ad differentiam.<emph.end type="italics"/></cell><cell>142</cell></row><row><cell>CLII.</cell><cell>S<emph type="italics"/>i linea in duas partes æquales, duasque inæquales diuidatur, fueritque proportio ag-gregati ex maiore, & dimidio ad ip&longs;am maiorem, uelut ex minore, & ali-qua linea ad ip&longs;am minorem, & rur&longs;us aggregati ex minore, & dimidio ad ip&longs;am minorem, uelut aggregati ex maiore, & alia addita ad ip&longs;am maiorem, erit proportio dimidij ad partem unam inæqualem, uelut alterius partis inæ-qualis ad &longs;uam additam mutuò, & etiam proportio additarum inuicem, uelut proportio <expan abbr="parti&utilde;">partium</expan> <expan abbr="inæquali&utilde;">inæqualium</expan> duplicata, & rur&longs;us ip&longs;um <expan abbr="dimidi&utilde;">dimidium</expan> lineæ a&longs;&longs;um-ptæ <expan abbr="medi&utilde;">medium</expan>, erit proportione inter additas.<emph.end type="italics"/> D<emph type="italics"/><expan abbr="em&utilde;">emum</expan> proportio dimidij <expan abbr="c&utilde;">cum</expan> addita maiore ad <expan abbr="dimidi&utilde;">dimidium</expan>, cum addita minore, uelut maioris partis ad <expan abbr="minor&etilde;">minorem</expan>.<emph.end type="italics"/></cell><cell>142</cell></row><row><cell>CLIII.</cell><cell>V<emph type="italics"/>im quamcunque manus multiplicare.<emph.end type="italics"/></cell><cell>144</cell></row><row><cell>CLIIII.</cell><cell>S<emph type="italics"/>i lineæ datæ alia linea adiungatur, ab extremitatibus autem prioris lineæ duæ rectæ in unum punctum concurrant proportionem habentes, quam mediam inter tota m & adiectam, & adiectam erit punctus, concur&longs;us à puncto extre-mo lineæ adiectæ di&longs;tans per lineam mediam.<emph.end type="italics"/> Q<emph type="italics"/>uod &longs;i ab extremo alicuius li-neæ æqua'is mediæ, &longs;eu peripheria circuli, cuius &longs;emidiameter &longs;it media linea duæ lineæ ad prædicta puncta producantur, ip&longs;æ erunt in proportione mediæ ad adiectam.<emph.end type="italics"/></cell><cell>145</cell></row><row><cell>CLV.</cell><cell>Q<emph type="italics"/>uadr atorum numerum proportionem & inuentionem con&longs;iderare.<emph.end type="italics"/></cell><cell>147</cell></row><row><cell>CLVI.</cell><cell>H<emph type="italics"/>orologiorum tempus multiplicare.<emph.end type="italics"/></cell><cell>152</cell></row><row><cell>CLVII.</cell><cell>H<emph type="italics"/>orologiorum molarium rationem o&longs;tendere.<emph.end type="italics"/></cell><cell>154</cell></row><row><cell>CLVIII.</cell><cell>R<emph type="italics"/>ationem indicis mobilis cum rota, qua horarum numerus per ictus indicatur ex-plicare.<emph.end type="italics"/></cell><cell>156</cell></row><row><cell>CLIX.</cell><cell>N<emph type="italics"/>ullus angulus rectilineus æqualis e&longs;&longs;e pote&longs;t alicui angulo contento recta, & cir culi portione.<emph.end type="italics"/></cell><cell>158</cell></row><row><cell>CLX.</cell><cell>P<emph type="italics"/>ropo&longs;ita linea tribusque in ea &longs;ignis punctum inuenire, ex quo ductæ tres lineæ ad &longs;igna &longs;int in proportionibus datis.<emph.end type="italics"/></cell><cell>162</cell></row><row><cell>CLXI.</cell><cell>S<emph type="italics"/>i fuerint duo trianguli, quorum ba&longs;es in eadem linea &longs;int con&longs;tituti, & æquales ad unum punctum terminati, & latus unum commune inter reliqua quantita-te medium nece&longs;&longs;e e&longs;t angulum à maioribus lineis <expan abbr="content&utilde;">contentum</expan> minorem e&longs;&longs;e.<emph.end type="italics"/></cell><cell>162</cell></row><row><cell>CLXII.</cell><cell>P<emph type="italics"/>roportionem duorum orbium, quorum diametrorum conuexæ partis, & conca-uæ proportiones datæ &longs;int inue&longs;tigare.<emph.end type="italics"/></cell><cell>164</cell></row><row><cell>CLXIII.</cell><cell>P<emph type="italics"/>roportionem uirium &longs;tellarum per motus &longs;uos indagare.<emph.end type="italics"/></cell><cell>165</cell></row><row><cell>CLXIIII.</cell><cell>S<emph type="italics"/>yderum proportionem in magnitudine o&longs;tendere.<emph.end type="italics"/></cell><cell>166</cell></row><row><cell>CLXV.</cell><cell>P<emph type="italics"/>roportionem motuum omnium &longs;tellarum ad<emph.end type="italics"/> S<emph type="italics"/>olem con&longs;iderare.<emph.end type="italics"/></cell><cell>167</cell></row><row><cell>CLXVI.</cell><cell>P<emph type="italics"/>roportiones mu&longs;icas &longs;uperpartientes in eas, quæ particulá una tantum abundant reducere.<emph.end type="italics"/></cell><cell>168</cell></row><pb/><row><cell>CLXVII.</cell><cell>P<emph type="italics"/>roportionem mu&longs;icam ad &longs;apores & odores coaptare.<emph.end type="italics"/></cell><cell>176</cell></row><row><cell>CLXVIII.</cell><cell>P<emph type="italics"/>icturarum proportiones explicare.<emph.end type="italics"/></cell><cell>179</cell></row><row><cell>CLXIX.</cell><cell>P<emph type="italics"/>roportionem mu&longs;icam in in&longs;trumentis declarare iuxta compo&longs;itionis ra-tionem.<emph.end type="italics"/></cell><cell>182</cell></row><row><cell>CLXX.</cell><cell>C<emph type="italics"/>oniugationes cuiu&longs;uis numeri breuiter inuenire.<emph.end type="italics"/></cell><cell>185</cell></row><row><cell>CLXXI.</cell><cell>P<emph type="italics"/>ropo&longs;itis duobus quibuslibet numeris, quotuis alios &longs;eu in continuum &longs;eu medios in continua proportione arithmetica, geometrica & mu&longs;ica in-uenire.<emph.end type="italics"/></cell><cell>187</cell></row><row><cell>CLXXII.</cell><cell>P<emph type="italics"/>roportiones<emph.end type="italics"/> S<emph type="italics"/>tiphelij de&longs;cribere.<emph.end type="italics"/></cell><cell>191</cell></row><row><cell>CLXXIII.</cell><cell>C<emph type="italics"/>irculum &longs;uper centro &longs;uo mouere æqualiter, ita quod omnia illius puncta per rectam lineam moueantur ultro citroque.<emph.end type="italics"/></cell><cell>192</cell></row><row><cell>CLXXIIII.</cell><cell>P<emph type="italics"/>rogre&longs;&longs;us & regre&longs;&longs;us, tam &longs;ine latitudine quàm cum latitudine in planetis per &longs;olos concentricos circulos æqualiter motos demon&longs;trare.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell>CLXXV.</cell><cell>C<emph type="italics"/>au&longs;am uarietatis diametrorum ex &longs;uppo&longs;itis concentricis demon&longs;tra-re.<emph.end type="italics"/></cell><cell>195</cell></row><row><cell>CLXXVI.</cell><cell>R<emph type="italics"/>ationem centri grauitatis declarare.<emph.end type="italics"/></cell><cell>197</cell></row><row><cell>CLXXVII.</cell><cell>S<emph type="italics"/>i proportio aliqua ex duabus proportionibus eiu&longs;dem quantitatis ad alias duas componatur, erit proportio illarum duarum eadem proportioni producti ex proportione in primam duarum quantitatum, detracta prio-re illa quantitate, quæ ad duas comparatur, ad eandem priorem quanti-tatem.<emph.end type="italics"/></cell><cell>198</cell></row><row><cell>CLXXVIII.</cell><cell>P<emph type="italics"/>roportionem mi&longs;tionis metallorum, maximè auri & argenti declara-re.<emph.end type="italics"/></cell><cell>199</cell></row><row><cell>CLXXIX.</cell><cell>S<emph type="italics"/>i duobus totis duæ portiones &longs;imiles ab&longs;cindantur ab ei&longs;dem denuò, & ab-&longs;cißis portionibus partes eædem auferantur, denuoque ac denuò quoties libuerit à portionibus, & ù re&longs;iduis ip&longs;arum quantitatum partes eædem auferantur, erit re&longs;iduí ad re&longs;iduum, ueluti totius ad totum.<emph.end type="italics"/></cell><cell>200</cell></row><row><cell>CLXXX.</cell><cell>S<emph type="italics"/>i aliqua quantitas in duas partes diuidatur, fueritque alicuius quantitatis ad partes illas compo&longs;ita proportio, non poterit eiu&longs;dem quantitatis ad par-tes alias quantitatis diui&longs;a, aliter proportio eadem componi.<emph.end type="italics"/></cell><cell>202</cell></row><row><cell>CLXXXI.</cell><cell>C<emph type="italics"/>um fuerit aliqua proportio, compo&longs;ita ex proportionibus primæ ad &longs;ecun-dam & tertiam, & rur&longs;us quartæ ad quintam & &longs;extam: ita &longs;e habebit proportio &longs;ecundæ ad tertiam, ad proportionem quintæ ad &longs;extam, uelut producti ex proportione in &longs;ecundam detracta prima ad primam ad pro-ductum ex proportione in quintam, detracta quarta ad quartam.<emph.end type="italics"/></cell><cell>203</cell></row><row><cell>CLXXXII.</cell><cell>P<emph type="italics"/>ropo&longs;ita differentia proportionum partium &longs;imilium ad partes a&longs;&longs;umptas, propo&longs;itaque proportione totius ad re&longs;idua eadem, differentiam propor-tionum totius ad reliquum re&longs;idui inuenire.<emph.end type="italics"/></cell><cell>203</cell></row><row><cell>CLXXXIII.</cell><cell>S<emph type="italics"/>pacium uitæ naturalis per &longs;pacium uitæ fortuitum declarare.<emph.end type="italics"/></cell><cell>204</cell></row><row><cell>CLXXXIIII.</cell><cell>Q<emph type="italics"/>uæcunque grauia in uorticibus aquarum, merguntur, in medio uorticis, pri-mum uer&longs;a mergantur.<emph.end type="italics"/></cell><cell>211</cell></row><row><cell>CLXXXV.</cell><cell>C<emph type="italics"/>ur homo &longs;edens quanto altius &longs;edet, & quanto magis crura ad f&oelig;mora, & f&oelig;mora ad pectus reclinata habet, facilius con&longs;urgat, cum tamen hæc op-po&longs;ito modo inuicem &longs;e habeant, declarare.<emph.end type="italics"/></cell><cell>213</cell></row><row><cell>CLXXXVI.</cell><cell>S<emph type="italics"/>i fuerit proportio primæ & &longs;ecundæ quantitatis ad tertiam, ut primæ & quartæ ad quintam, fueritque quarta &longs;ecunda maior, erit proportio quar-tæ ad quintam maior quàm &longs;ecundæ ad tertiam.<emph.end type="italics"/> Q<emph type="italics"/>uod &longs;i fuerit maior<emph.end type="italics"/></cell><cell/></row><pb/><row><cell/><cell><emph type="italics"/>quartæ ad quintam quàm &longs;ecundæ ad tertiam, nece&longs;&longs;e e&longs;t quartam &longs;ecunda e&longs;&longs;e maiorem.<emph.end type="italics"/></cell><cell>214</cell></row><row><cell>CLXXXVII.</cell><cell>S<emph type="italics"/>i ei&longs;dem uiribus & ‘eadem’ proportione cum auxilio ponderis tertij quar-tum pondus moueatur quibus &longs;ecundum, auxilio primi nece&longs;&longs;e e&longs;t <expan abbr="quart&utilde;">quartum</expan> pon dus tardius & maiore cum difficultate moueri quàm &longs;ecundum.<emph.end type="italics"/></cell><cell>214</cell></row><row><cell>CLXXXVIII.</cell><cell>S<emph type="italics"/>i uires aliquæ moueant cum ponderibus aliqua pondera, ut compo&longs;ita pro-portio &longs;it eadem proportioni uirium & duorum ponderum mouentium ag-gregatum æquale duorum ponderum, ubi maior fuerit partium in æqualitas, ibi erit maior difficultas.<emph.end type="italics"/></cell><cell>214</cell></row><row><cell>CLXXXIX.</cell><cell>S<emph type="italics"/>i pondus minus ad longitudinem minorem &longs;ub æquali proportione coapte-tar, facilius deor&longs;um trahetur quàm quod maius e&longs;t & propius.<emph.end type="italics"/></cell><cell>215</cell></row><row><cell>CXC.</cell><cell>S<emph type="italics"/>i fuerit primum graue minus &longs;ecundo, & &longs;ecundum minus tertio, proportio autem primi ad &longs;ecundum multo maior quàm &longs;ecundi ad tertium, po&longs;ibile erit propo&longs;itis uiribus ei&longs;dem addere pondus <expan abbr="&longs;ec&utilde;do">&longs;ecundo</expan>, ut ip&longs;um & tertium mouea-tur faciliùs ab ei&longs;dem uiribus, & primo uel &longs;ecundo quàm antea.<emph.end type="italics"/></cell><cell>215</cell></row><row><cell>CXCL.</cell><cell>C<emph type="italics"/>um fuerint duo pondera & uires, duxerisque aggregatum ex uiribus & mi-nore pondere in maius, addiderisque in&longs;uper quantum e&longs;t productum dimidij ui rium in &longs;e latus aggregati detracto dimidio uirium, dicetur pondus auxiliare æqualis proportionis.<emph.end type="italics"/></cell><cell>215</cell></row><row><cell>CXCII.</cell><cell>S<emph type="italics"/>i ex medio diametri linea ad perpendiculum erigatur ad circuli peripheri-am, ex eo puncto autem quotlibet lineæ ducantur &longs;eu intus ad circun ferentiam u&longs;que, &longs;eu extra ad diametrum, erit proportio totius lineæ ad totam uelut mu-tuo partis ad partem.<emph.end type="italics"/></cell><cell>217</cell></row><row><cell>CXCIII.</cell><cell>R<emph type="italics"/>ationem ponderis triplicem explicare.<emph.end type="italics"/></cell><cell>218</cell></row><row><cell>CXCIIII.</cell><cell>P<emph type="italics"/>roportionem ponderis longioris in medio &longs;u&longs;pen&longs;i, ad breuius illi æquale & in medio &longs;u&longs;pen&longs;um declarare.<emph.end type="italics"/></cell><cell>219</cell></row><row><cell>CXCV.</cell><cell>S<emph type="italics"/>i lectus fiat dupla longitudine ad latitudinem, melius &longs;uffulcietur re&longs;tibus ex medio ad angulos & eius æquidi&longs;tantibus quàm &longs;ecundum longitudinem & latitudinem.<emph.end type="italics"/></cell><cell>220</cell></row><row><cell>CXCVI.</cell><cell>S<emph type="italics"/>i duo circuli &longs;uper eodem centro eodem motu trans feruntur, æquale &longs;pacium &longs;uperant.<emph.end type="italics"/></cell><cell>221</cell></row><row><cell>CXCVII.</cell><cell>C<emph type="italics"/>ur lances ad locum &longs;uum &longs;u&longs;pen&longs;i redeant, impendentes <expan abbr="nõ">non</expan>, <expan abbr="demõ&longs;trare">demon&longs;trare</expan>.<emph.end type="italics"/></cell><cell>224</cell></row><row><cell>CXCVIII.</cell><cell>C<emph type="italics"/>ur &longs;olidum quod cubus uocatur<emph.end type="italics"/> P<emph type="italics"/>yramide &longs;tabilius &longs;it o&longs;tendere.<emph.end type="italics"/></cell><cell>225</cell></row><row><cell>CXCIX.</cell><cell>R<emph type="italics"/>ationem remorum nauim impellentium inuenire.<emph.end type="italics"/></cell><cell>227</cell></row><row><cell>CC.</cell><cell>C<emph type="italics"/>ur temo cum paruus &longs;it, magnam nauim agere pote&longs;t, & cur cùm uarietas &longs;it in prora, ip&longs;e con&longs;tituatur in puppi.<emph.end type="italics"/> E<emph type="italics"/>t cum transuer&longs;im ab aqua prematur rectà nauim dirigat.<emph.end type="italics"/></cell><cell>228</cell></row><row><cell>CCI.</cell><cell>S<emph type="italics"/>i duæ lineæ non &longs;ecantes circuli peripheriam in unum punctum ex ea coe-ant exterius, nece&longs;&longs;e e&longs;t illas peripheria contenta e&longs;&longs;e maiores.<emph.end type="italics"/></cell><cell>229</cell></row><row><cell>CCII.</cell><cell>R<emph type="italics"/>ationem &longs;trepitus o&longs;tendere.<emph.end type="italics"/></cell><cell>232</cell></row><row><cell>CCIII.</cell><cell>C<emph type="italics"/>ur &longs;cytalis onera portentur faciliùs, explorare.<emph.end type="italics"/></cell><cell>233</cell></row><row><cell>CCIIII.</cell><cell>C<emph type="italics"/>ur pluribus trochleis, pondera facilius eleuentur o&longs;tendere.<emph.end type="italics"/></cell><cell>233</cell></row><row><cell>CCV.</cell><cell>S<emph type="italics"/>uper uerbis<emph.end type="italics"/> P<emph type="italics"/>latonis de fine<emph.end type="italics"/> R<emph type="italics"/>eipublicæ.<emph.end type="italics"/></cell><cell>234</cell></row><row><cell>CCVI.</cell><cell>R<emph type="italics"/>hombi paßiones qua&longs;dam declarare.<emph.end type="italics"/></cell><cell>235</cell></row><row><cell>CCVII.</cell><cell>P<emph type="italics"/>roportionem agentium naturalium in tran&longs;mutatione con&longs;iderare.<emph.end type="italics"/></cell><cell>238</cell></row><row><cell>CCVIII.</cell><cell>M<emph type="italics"/>ota res à centro grauitatis per <expan abbr="prior&etilde;">priorem</expan> motum, in reditu uelocius mouetur quam &longs;i quieuerit.<emph.end type="italics"/></cell><cell>238</cell></row><pb/><row><cell>CCIX.</cell><cell>S<emph type="italics"/>i &longs;uperficies rectangula in duas partes æquales diui&longs;a intelligatur, quæ am-bæ quadratæ &longs;int, itemque in duas inæquales, erit parallelipedum ex latere mediæ partis in totam &longs;uperficiem maius aggregato parallelipedorum ex partibus inæqualibus in latera alterius partis mutuo, in eo, quod fit ex dif ferentia lateris minoris partis à mediæ latere in differentiam maioris par-tis &longs;uperficiei à media &longs;uperficie bis, & ex differentia amborum laterum inæqualium iunctorum ad ambo latera, æqualia iuncta in minorem par-tem &longs;uperficiei.<emph.end type="italics"/></cell><cell>241</cell></row><row><cell>CCX.</cell><cell>S<emph type="italics"/>i duæ lineæ ad æquales angulos ab eodem puncto peripheriæ circuli refle-ctantur, nece&longs;&longs;e e&longs;t angulos cum dimetiente factos æquales e&longs;&longs;e.<emph.end type="italics"/> V<emph type="italics"/>nde ma-nife&longs;tum e&longs;t, protractam diametrum angulum &longs;uppo&longs;itum per æqualia di-uidere.<emph.end type="italics"/></cell><cell>242</cell></row><row><cell>CCXI.</cell><cell>S<emph type="italics"/>i duæ lineæ ex duobus punctis peripheriam contingentes, in eandem par-tem protrahantur, &longs;emper magis di&longs;tabunt inuicem ea ex parte, & nun-quam concurrent.<emph.end type="italics"/></cell><cell>243</cell></row><row><cell>CCXII.</cell><cell>S<emph type="italics"/>i ab eodem puncto ad circuli peripheriam lineæ quotuis ducantur, tres inue-nire lineas, quæ non in alium punctum reflectentur.<emph.end type="italics"/></cell><cell>244</cell></row><row><cell>CCXIII.</cell><cell>P<emph type="italics"/>ropo&longs;ito circulo, atque in eius peripheria puncto &longs;ignato, lineas contingentes ultra cítraque, & eam ab ip&longs;omet deducere.<emph.end type="italics"/></cell><cell>245</cell></row><row><cell>CCXIIII.</cell><cell>S<emph type="italics"/>i extra circulum duo puncta æqualiter à centro di&longs;tantia &longs;ignentur, erit pun-ctum reflexionis æqualis in medio arcus intercepti inter lineas, quæ à cen tro ducuntur ad illa puncta.<emph.end type="italics"/> S<emph type="italics"/>i uerò unum centro proximius fuerit altero, punctum æqualitatis in peripheria tantò longius, uer&longs;us breuiorem line-am, quantò punctum aliud à centro magis di&longs;teterit.<emph.end type="italics"/></cell><cell>245</cell></row><row><cell>CCXV.</cell><cell>P<emph type="italics"/>unctum reflexionis punctorum inæqualiter di&longs;tantium à centro, æqualiter di&longs;tat à lineis, ductis à centro ad puncta æqualiter di&longs;tantia alterutrin-que.<emph.end type="italics"/></cell><cell>246</cell></row><row><cell>CCXVI.</cell><cell>S<emph type="italics"/>i fuerint circuli duo inæquales, & extra utrunqúe punctum ad illud ex mi-nore reflexè per magnam partem minoris à maiore perueuire pote-runt.<emph.end type="italics"/></cell><cell>247</cell></row><row><cell>CCXVII.</cell><cell>O<emph type="italics"/>culus uidet partem &longs;uperficiei<emph.end type="italics"/> L<emph type="italics"/>unæ illuminatam à<emph.end type="italics"/> S<emph type="italics"/>ole per radios reflexos à<emph.end type="italics"/> S<emph type="italics"/>olis corpore: nec tamen pote&longs;t uidere imaginem ip&longs;ius in<emph.end type="italics"/> L<emph type="italics"/>una tan quam in &longs;peculo.<emph.end type="italics"/></cell><cell>248</cell></row><row><cell>CCXVIII.</cell><cell>R<emph type="italics"/>ationem maculæ<emph.end type="italics"/> L<emph type="italics"/>unæ indagare.<emph.end type="italics"/></cell><cell>248</cell></row><row><cell>CCXIX.</cell><cell>R<emph type="italics"/>ationem eorum quæ apparent circa<emph.end type="italics"/> S<emph type="italics"/>olem &longs;peculo in aqua po&longs;ito decla-rare.<emph.end type="italics"/></cell><cell>150</cell></row><row><cell>CCXX.</cell><cell>C<emph type="italics"/>au&longs;am cur<emph.end type="italics"/> S<emph type="italics"/>ol æ&longs;tiuis diebus exoriens umbram ad meridiem, cum in meridie ad boream mittat, explorare.<emph.end type="italics"/></cell><cell>252</cell></row><row><cell>CCXXI.</cell><cell>M<emph type="italics"/>agnitudo<emph.end type="italics"/> L<emph type="italics"/>unæ & cæterorum a&longs;trorum digno&longs;citur ex proportione alio-rum ad eam iuxta di&longs;tantiam: ip&longs;ius uerò iuxta rationem pupillæ ad<emph.end type="italics"/> L<emph type="italics"/>u-nam di&longs;tantiæ ratione.<emph.end type="italics"/></cell><cell>354</cell></row><row><cell>CCXXII.</cell><cell>Q<emph type="italics"/>uantitates quæ æquales e&longs;&longs;e non po&longs;&longs;unt in eodem genere, maius tamen & minus recipiunt, &longs;unt in proportione pote&longs;tatis.<emph.end type="italics"/></cell><cell>255</cell></row><row><cell>CCXXIII.</cell><cell>Q<emph type="italics"/>uantitates quæ actu æquales e&longs;&longs;e non po&longs;&longs;unt, in nulla proportione actu e&longs;&longs;e po&longs;&longs;unt.<emph.end type="italics"/></cell><cell>256</cell></row><row><cell>CCXXIIII.</cell><cell>N<emph type="italics"/>eque temporis totius, ut imaginamur, ip&longs;um e&longs;&longs;e infinitum, neque æui ui-tarum proportio ulla e&longs;t ad tempus, quod pote&longs;tate e&longs;t, utpotè diem<emph.end type="italics"/></cell><cell/></row><pb/><row><cell/><cell><emph type="italics"/>uel men&longs;em.<emph.end type="italics"/></cell><cell>256</cell></row><row><cell>CCXXV.</cell><cell>P<emph type="italics"/>roportio media non e&longs;t ex ratione agentis, &longs;ed patientis.<emph.end type="italics"/></cell><cell>256</cell></row><row><cell>CCXXVI.</cell><cell>P<emph type="italics"/>roportio &longs;ublimis non con&longs;i&longs;tit in magnitudine, &longs;ed ordine, iuxta quem diffe-rentia e&longs;t eius quod e&longs;t ante & po&longs;t.<emph.end type="italics"/></cell><cell>257</cell></row><row><cell>CCXXVII.</cell><cell>V<emph type="italics"/>itæ iuxta numerum perfectionum in comparatione ad cogitationem no-&longs;tram proportionem quand am habent.<emph.end type="italics"/></cell><cell>259</cell></row><row><cell>CCXXVIII.</cell><cell>P<emph type="italics"/>roportionem &longs;cientiæ futurorum & cæterorum occultorum con&longs;idera-re.<emph.end type="italics"/></cell><cell>260</cell></row><row><cell>CCXXIX.</cell><cell>I<emph type="italics"/>ncorporea omnia unum &longs;unt, neque numerus e&longs;t eorum.<emph.end type="italics"/></cell><cell>261</cell></row><row><cell>CCXXX.</cell><cell>P<emph type="italics"/>roportio incorporeorum a&longs;cendentium &longs;emper maior e&longs;t.<emph.end type="italics"/></cell><cell>262</cell></row><row><cell>CCXXXI.</cell><cell>T<emph type="italics"/>res e&longs;&longs;e mundos atque inter ip&longs;os nullam e&longs;&longs;e proportionem: nec numero cos definiri.<emph.end type="italics"/></cell><cell>263</cell></row><row><cell>CCXXXII.</cell><cell>O<emph type="italics"/>mnis motus naturalis quanto uelocior e&longs;t tanto propior e&longs;t & magis &longs;imil limus quieti.<emph.end type="italics"/></cell><cell>264</cell></row><row><cell>CCXXXIII.</cell><cell>Q<emph type="italics"/>uod e&longs;t in mundo incorporeo æternum e&longs;t, beatum, &longs;ecurum, immutabile &longs;ecundum locum, &longs;olum iuxta e&longs;&longs;entiam fit: iuxta quod uelut à leui &longs;u-&longs;urro aquæ & aura æ&longs;tiua demulcetur.<emph.end type="italics"/></cell><cell>270</cell></row></table><p type="head">

<s>FINIS.</s></p></section><section><pb pagenum="1"/><p type="head">

<s>FINIS.</s></p></section></front> <body> <chap> <pb pagenum="1"/><p type="head">

<s>HIERONYMI CAR <lb/>DANI MEDIOLANENSIS, CI<lb/>VI'SQVE BONONIENSIS, MEDICI<lb/>de Proportionibus, &longs;eu Ope<lb/>ris Perfecti <lb/>LIBER QVINTVS.</s></p></section></front> <body> <chap>

<s>HIERONYMI CAR <lb/>DANI MEDIOLANENSIS, CI<lb/>VI'SQVE BONONIENSIS, MEDICI<lb/>de Proportionibus, &longs;eu Ope<lb/>ris Perfecti <lb/>LIBER QVINTVS.</s></p>

<p type="main"><s>Prima diffinitio.</s></p><p type="main">

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