Vitruvius, De architectura libri decem, 1567

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            <pb o="290" file="514.01.322" n="322" rhead="LIBER"/>
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              <s xml:id="echoid-s21962" xml:space="preserve">œqualiter moueretur, ſeruando in utroque defectu eandem motus diuerſitatem, ita ut certi fierent Lunam eſſe
                <lb/>
              in eodem epicycli loco. </s>
              <s xml:id="echoid-s21963" xml:space="preserve">Ex ea obſeruatione certiores facti ſunt, quod interuallo geminorum defectuum Luna
                <lb/>
              numerum integrarum uerſationis abſoluerat, quoniam in eundem locum epicycli redierat, & </s>
              <s xml:id="echoid-s21964" xml:space="preserve">pariter Luna-
                <lb/>
              rium menſium numerum perfectum finierat, iam reuerſa ad locum Soli oppoſitum. </s>
              <s xml:id="echoid-s21965" xml:space="preserve">Tunc igitur uerſationum
                <lb/>
              numer um cognouerimus, cum unius uerſationis ſpatium nobis cognitum fuerit, licet non penitus exacte, neq;
                <lb/>
              </s>
              <s xml:id="echoid-s21966" xml:space="preserve">propterea nobis latere poteſt Lunaris menſis ſpatium, cum coitum, & </s>
              <s xml:id="echoid-s21967" xml:space="preserve">oppoſitionem Lunœ habere poterimus,
                <lb/>
              & </s>
              <s xml:id="echoid-s21968" xml:space="preserve">ex interuallo defectuum in menſium Lunarium numerum diuiſum Lunaris menſis quantitas colligetur. </s>
              <s xml:id="echoid-s21969" xml:space="preserve">
                <lb/>
              Verum quia in Lunari menſe Luna long itudinis uerſationem perficit, tantumq́; </s>
              <s xml:id="echoid-s21970" xml:space="preserve">interualli apponit, quantum
                <lb/>
              Sol eodem menſe mouetur, ideo integer ille circulus cum additamento illo, qui fit ex Solis motu in numerum
                <lb/>
                <note position="left" xlink:label="note-514.01.322-01" xlink:href="note-514.01.322-01a" xml:space="preserve">10</note>
              dierum menſis Lunaris diuiſus cum ſuis minutijs, nos in notitiam diurni motus Lunœ deducet. </s>
              <s xml:id="echoid-s21971" xml:space="preserve">Est etiam & </s>
              <s xml:id="echoid-s21972" xml:space="preserve">
                <lb/>
              alia uia noſcendi quantum Luna ſingulis diebus mouetur. </s>
              <s xml:id="echoid-s21973" xml:space="preserve">Nam ſi noueris numerum verſationum Lunœ in-
                <lb/>
              ter duos defectus, Solisq́; </s>
              <s xml:id="echoid-s21974" xml:space="preserve">motum addideris eodem tempore factum, collegerisq́; </s>
              <s xml:id="echoid-s21975" xml:space="preserve">Lunœ motum eo ſpatio pera-
                <lb/>
              ctum, ſi totum illud diuiſeris in numerum dierum eiuſdem ſpatij, babebis Lunœ motum diurnum. </s>
              <s xml:id="echoid-s21976" xml:space="preserve">Prœterea
                <lb/>
              ſcies etiam quantum Luna ſingulis diebus a Sole recedit, ſi integrum circulum diuiſeris in numerum dierum
                <lb/>
              Lunaris menſis cum ſuis minutijs, quas fractiones uocant. </s>
              <s xml:id="echoid-s21977" xml:space="preserve">itemq; </s>
              <s xml:id="echoid-s21978" xml:space="preserve">numerum graduum uerſationum, & </s>
              <s xml:id="echoid-s21979" xml:space="preserve">inter-
                <lb/>
              uallo peractarum partire in numerum ipſius interualli, & </s>
              <s xml:id="echoid-s21980" xml:space="preserve">babebis eundem Lunœ motum, quantum ſcilicet
                <lb/>
              ſingulis diebus a Sole recedit, ſuperatq́; </s>
              <s xml:id="echoid-s21981" xml:space="preserve">Solis diurnum motum. </s>
              <s xml:id="echoid-s21982" xml:space="preserve">non minus numerus uerſationum in epicyclo
                <lb/>
              uerſus in gradus, & </s>
              <s xml:id="echoid-s21983" xml:space="preserve">ſectus in numerum graduum interualli dierum eundem diurnum Lunœ motum metiri
                <lb/>
              ostendet. </s>
              <s xml:id="echoid-s21984" xml:space="preserve">His rationibus ba betur longitudinis motum ſingulis diebus eſſe partium tredecim, particularum
                <lb/>
                <note position="left" xlink:label="note-514.01.322-02" xlink:href="note-514.01.322-02a" xml:space="preserve">20</note>
              decem, & </s>
              <s xml:id="echoid-s21985" xml:space="preserve">ſecundarum ( ut appellant ) 35. </s>
              <s xml:id="echoid-s21986" xml:space="preserve">Et epicycli motum eſſe partium. </s>
              <s xml:id="echoid-s21987" xml:space="preserve">13. </s>
              <s xml:id="echoid-s21988" xml:space="preserve">particularum. </s>
              <s xml:id="echoid-s21989" xml:space="preserve">3. </s>
              <s xml:id="echoid-s21990" xml:space="preserve">ſecun-
                <lb/>
              darum. </s>
              <s xml:id="echoid-s21991" xml:space="preserve">54. </s>
              <s xml:id="echoid-s21992" xml:space="preserve">Longum eſſet omnia recenſere, quæ a ſcriptoribus in Lunæ motu conſiderata ſunt, quare ad
                <lb/>
              eos ſtudioſos remittam, excutiamq́; </s>
              <s xml:id="echoid-s21993" xml:space="preserve">quàm breuiſſime potero eorum ſyderum motiones, quæ Soli ſubijciun-
                <lb/>
              tur, Mercurij ſcilicet & </s>
              <s xml:id="echoid-s21994" xml:space="preserve">Veneris. </s>
              <s xml:id="echoid-s21995" xml:space="preserve">Aio Aſtronomos percepiſſe duo illa ſydera, a Sole digredi, cer-
                <lb/>
              tis tamen terminis utraque ex parte, & </s>
              <s xml:id="echoid-s21996" xml:space="preserve">in medio acceſſus, & </s>
              <s xml:id="echoid-s21997" xml:space="preserve">receſſus eorum ad Solem cum eo coniungi, & </s>
              <s xml:id="echoid-s21998" xml:space="preserve">
                <lb/>
              cum ab lateribus Solis eſſent, in eorum ſtationibus longiſſime abeſſe, quare collegerunt buiuſmodi progreſſum,
                <lb/>
              & </s>
              <s xml:id="echoid-s21999" xml:space="preserve">regreſſum epicyclo tueri oportere. </s>
              <s xml:id="echoid-s22000" xml:space="preserve">ita ut epicycli centrum cum Sole circumuolueretur, & </s>
              <s xml:id="echoid-s22001" xml:space="preserve">utrunque ſydus
                <lb/>
              tantum ab Sole abeſſe poſſet, quantum epicycli latitudo pateretur. </s>
              <s xml:id="echoid-s22002" xml:space="preserve">Verum quia colligentes geminas contra-
                <lb/>
              rias, & </s>
              <s xml:id="echoid-s22003" xml:space="preserve">maximas eorum ſyderum a Sole diſtantias, inuenerunt non eandem in omni loco quantitatem ſerua-
                <lb/>
              ri, & </s>
              <s xml:id="echoid-s22004" xml:space="preserve">eam ſummam exercere non poſſe, niſiacceſſu, nec decreſcere niſireceſſu epicycli ab orbis centro:</s>
              <s xml:id="echoid-s22005" xml:space="preserve">ideo
                <lb/>
                <note position="left" xlink:label="note-514.01.322-03" xlink:href="note-514.01.322-03a" xml:space="preserve">30</note>
              duobus inferioribus his & </s>
              <s xml:id="echoid-s22006" xml:space="preserve">eccentricum, & </s>
              <s xml:id="echoid-s22007" xml:space="preserve">epicyclum dedere, ea conditione, ut eccentricum ſemper epicy-
                <lb/>
              clum cum Sole in orbem ferret, & </s>
              <s xml:id="echoid-s22008" xml:space="preserve">idem eſſet medius motus Solis & </s>
              <s xml:id="echoid-s22009" xml:space="preserve">ſyderis. </s>
              <s xml:id="echoid-s22010" xml:space="preserve">Epicyclus uero ſydus binc inde
                <lb/>
              a Sole abeſſe faceret, acregreſſibus, & </s>
              <s xml:id="echoid-s22011" xml:space="preserve">latitudinem motibus quàm aptiſſime reſponderet. </s>
              <s xml:id="echoid-s22012" xml:space="preserve">Nunc ut ſciamus
                <lb/>
              qua ratione motus quantitatem metiamur; </s>
              <s xml:id="echoid-s22013" xml:space="preserve">dico eſſe obſeruandum locum ſyderis in ſignifero, & </s>
              <s xml:id="echoid-s22014" xml:space="preserve">expectare
                <lb/>
              donec in eundem reuerſum fuerit, ea conditione, ut ſit æque a loco media Solis in utroque loco, nam tunc ſy-
                <lb/>
              dus integras utriuſque motus uerſationes perfecrit: </s>
              <s xml:id="echoid-s22015" xml:space="preserve">tum in eccentrico, quoniam epicycli centrum ad priorẽ
                <lb/>
              locum redietit, tum in epicyclo, quoniam ſydus reuerſum ad eandem ab Sole diſtantiam, idem quoque pun-
                <lb/>
              ctum epicycli repetierit. </s>
              <s xml:id="echoid-s22016" xml:space="preserve">his obſeruationibus elicietur tempus elapſum, & </s>
              <s xml:id="echoid-s22017" xml:space="preserve">uerſationum numerus, quoniam in
                <lb/>
              tribus ſuperioribus quot fuerint uerſationes epicycli, & </s>
              <s xml:id="echoid-s22018" xml:space="preserve">uerſationes eccentrici, unam in ſummam collectæ, tot
                <lb/>
              in eodem tempore erunt Solis uerſationes tranſactæ. </s>
              <s xml:id="echoid-s22019" xml:space="preserve">Sed in duobus inferioribus numerus uerſationum eccen-
                <lb/>
                <note position="left" xlink:label="note-514.01.322-04" xlink:href="note-514.01.322-04a" xml:space="preserve">40</note>
              trici idem eſt cum numero uerſationum epicycli, ubi propè uerum nobis notum fuerit unius uer ſationis tempus,
                <lb/>
              unde numerus uerſationum ductus per 360, reddet gradus: </s>
              <s xml:id="echoid-s22020" xml:space="preserve">graduum uerò numerus per numerum dierum
                <lb/>
              ſpatij obſeruationum diuiſus, not am faciet ſummam diurni motus. </s>
              <s xml:id="echoid-s22021" xml:space="preserve">ſed quis ordo in progreſſibus, & </s>
              <s xml:id="echoid-s22022" xml:space="preserve">regreſſio-
                <lb/>
              nibus, & </s>
              <s xml:id="echoid-s22023" xml:space="preserve">quœ neceßitas eos cogat, breuiter dicam. </s>
              <s xml:id="echoid-s22024" xml:space="preserve">Si prius monuero diuerſitatem, aut contr arietatem
                <lb/>
              iſtius uiſionis altero duorum modorum tueri nos poſſe, aut ſiſyderi detur ſolum deferens eccentricum, aut epi-
                <lb/>
              cyclus cum deferente concentrico: </s>
              <s xml:id="echoid-s22025" xml:space="preserve">ſcilicet eo modo quod in ſingulis tribus ſuperioribus: </s>
              <s xml:id="echoid-s22026" xml:space="preserve">ſi colligantur in unum
                <lb/>
              motus epicycli in concentrico, & </s>
              <s xml:id="echoid-s22027" xml:space="preserve">ſyderis in epicyclo, & </s>
              <s xml:id="echoid-s22028" xml:space="preserve">inueniantur æquales medio motui Solis, ſed ea lege
                <lb/>
              ut centrum eccentrici ſecundum ordinem ſignorum ſimul cum Sole moueatur, & </s>
              <s xml:id="echoid-s22029" xml:space="preserve">ſydus ea uelocitate mouea-
                <lb/>
              tur, qua epicyclus in concentrico mouetur, ita ut linea illa, quœ a centro prouenit, quœ œquidistat lineæ du-
                <lb/>
              ctæ a centro eccentrici ad centrum ſyderis, ſiniat in medium ſyderis motum. </s>
              <s xml:id="echoid-s22030" xml:space="preserve">atque hoc in tribus ſuperioribus
                <lb/>
              obſeruatur: </s>
              <s xml:id="echoid-s22031" xml:space="preserve">ſed in duobus inferioribus ponatur motus epicycli in concentrico œqualis medio motui Solis, & </s>
              <s xml:id="echoid-s22032" xml:space="preserve">
                <lb/>
                <note position="left" xlink:label="note-514.01.322-05" xlink:href="note-514.01.322-05a" xml:space="preserve">50</note>
              motus ſyderis in epicyclo unà cum motu centri eccentrici œqualis ſit ſummæ illi, quœ ex medio motu Solis, & </s>
              <s xml:id="echoid-s22033" xml:space="preserve">
                <lb/>
              motu ſyderis in epicyclo colligitur, & </s>
              <s xml:id="echoid-s22034" xml:space="preserve">ſydus pari celeritate moueatur, qua epicyclus in concentrico moue-
                <lb/>
              tur, eadem ( qua dictum est ſupra ) conditione, ſcilicet ut linea illa a centro ducta æque diſtans lineæ a centro
                <lb/>
              eccentrici ductæ ad ſyderis centrum, terminet in medio motu ſyderis, & </s>
              <s xml:id="echoid-s22035" xml:space="preserve">etiam addita ea lege in omnibus, quœ
                <lb/>
              diametri eccentrici, & </s>
              <s xml:id="echoid-s22036" xml:space="preserve">concentrici proportione reſpondeant ſemidiametris epicycli, & </s>
              <s xml:id="echoid-s22037" xml:space="preserve">egreſſioni ab centro,
                <lb/>
              atque ita utroque modo tueripoſſumus in ſyderibus rationem progreſſionis, & </s>
              <s xml:id="echoid-s22038" xml:space="preserve">regreßionis, quantum ad di-
                <lb/>
              uerſitatem, & </s>
              <s xml:id="echoid-s22039" xml:space="preserve">uarietatem pertinet, quemadmodum longa experientia Aſtronomi obſeruarunt, ideo neceſſe
                <lb/>
              fuit primam diuerſitatem epicyclo, ſecundam deferenti tribuere: </s>
              <s xml:id="echoid-s22040" xml:space="preserve">ſed unum illud ſatis erat ad probibendum ne
                <lb/>
              ſyderum omnium deferentes unum centrum efficerent, ſcilicet motuum ſingularitas, quoniam concentrici or-
                <lb/>
                <note position="left" xlink:label="note-514.01.322-06" xlink:href="note-514.01.322-06a" xml:space="preserve">60</note>
              bes alter alteriſuum motum præbet, id eſt ſuperior inferiori, & </s>
              <s xml:id="echoid-s22041" xml:space="preserve">quoniam buiuſmodi communio non ſuit </s>
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