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  <info>
    <author>Guevara, Giovanni di</author>
    <title>In Aristotelis mechanicas commentarii</title>
    <date>1627</date>
    <place>Roma</place>
    <translator></translator>
    <lang>la</lang>
    <cvs_file>gueva_mecha_005_la_1627.xml</cvs_file>
    <cvs_version></cvs_version>
    <locator>005.xml</locator>
  </info>
  <text>
    <front>          </front>
    <body>
      <chap id="N10019">
        <pb id="p.0001" xlink:href="005/01/001.jpg"></pb>
        <p id="N1001E" type="head">
          <s id="N10020">IOANNIS <lb></lb>DE GVEVARA <lb></lb>CLER. REG. MIN. <lb></lb>IN ARISTOTELIS MECHANICAS <lb></lb>Commentarij.</s>
        </p>
        <p id="N1002B" type="head">
          <s id="N1002D"><emph type="italics"></emph>VNA CVM ADDITIONIBVS QVIBVSDAM <lb></lb>Ad eandem materiam pertinentibus.<emph.end type="italics"></emph.end></s>
        </p>
        <figure id="id.005.01.001.1.jpg" xlink:href="005/01/001/1.jpg"></figure>
        <p id="N1003B" type="head">
          <s id="N1003D">ROMAE, Apud Iacobum Maſcardum, MDCXXVII. <lb></lb>SVPERIORVM PERMISSV.</s>
        </p>
        <pb xlink:href="005/01/002.jpg"></pb>
        <p id="N10045" type="main">
          <s id="N10047">Imprimatur ſi videbitur Reuerendiſs. P. Mag. Sac. Pal. Apoſt. <emph type="italics"></emph>A. Epiſc. Hieracen. Viceſg.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1005B" type="main">
          <s id="N1005D"><emph type="italics"></emph>Imprimatur<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N10064" type="main">
          <s id="N10066">Fr. </s>
          <s id="N1006A">Paulus Palumbara Socius Reuerendiſs. P. Fr. </s>
          <s id="N10070">Nicolai Ro<lb></lb>dulfij Sac. Pal. Apoſt. Mag. Ord. Prædic. </s>
        </p>
        <pb xlink:href="005/01/003.jpg"></pb>
        <p id="N10081" type="head">
          <s id="N10083">ILLVSTRISS^{MO} PRINCIPI</s>
        </p>
        <p id="N10086" type="head">
          <s id="N10088">FRANCISCO <lb></lb>BARBERINO <lb></lb>S. R. E. CARDINALI <lb></lb>AMPLISSIMO <lb></lb><emph type="italics"></emph>IOANNES DE GVEVARA.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N10097" type="main">
          <s id="N10099">Q<emph type="italics"></emph>vod olim opus in Ari<lb></lb>ſtotelis Mechanicas, dum <lb></lb>Philoſophiæ, &amp; Mathe<lb></lb>maticis vacarem inter<lb></lb>mittere coegit nouæ con<lb></lb>templationis occaſio, hoc <lb></lb>ipſum præteritis diebus <lb></lb>(Illuſtriſsime Princeps) dum publicis nego<lb></lb>tijs, <expan abbr="grauioribusq.">grauioribusque</expan> ſtudijs implicatus, ægrè <lb></lb>aut vix, vt decet aggredi potuiſſem, breuiter vt<lb></lb>cunque perficere, ac prælis mandare, tua me <lb></lb>compulit ampliſsima gratia. </s>
          <s id="N100B9">Cum enim te pri<lb></lb>mò Magni Patrui, <expan abbr="Summiq.">Summique</expan> Pontificis Lega<lb></lb>tum ampliſsimum, in Galliam nauigantem, <lb></lb>ac nuper ex Hiſpania redeuntem ad afferen<pb xlink:href="005/01/004.jpg"></pb>dam pacem animis, profligandumque maxi<lb></lb>morum Regum auctoritate exortum in Italia <lb></lb>bellum, quo poteram obſequio, atque opera eiuſ<lb></lb>dem Pontificis iuſſu proſequerer, nobiliſsimo <lb></lb>in comitatu innumeræ excitabantur quæſtio<lb></lb>nes, tùm circa rem nauticam, tùm circa ma<lb></lb>chinariam, atque vectoriam in vniuerſum; <lb></lb>quarum ſolutiones è mechanicis principijs pe<lb></lb>tere operæ pretium erat. </s>
          <s id="N100DC"><expan abbr="Cumq.">Cumque</expan> hinc orta fuiſ<lb></lb>ſet mentio de meis hiſce lucubrationibus eodem <lb></lb>in genere partis, gratum fore cognoui, ſi vlti<lb></lb>mam ipſis manum imponens legendas eas ti<lb></lb>bi litterarum amantiſsimo pro animi refectio<lb></lb>ne obtuliſſem. </s>
          <s id="N100EC">Infatigabiles namque animi eo<lb></lb>rum qui in rebus maximis occupantur, non <lb></lb>ocio, ſed varietate reficiuntur, &amp; oblectantur: <lb></lb>præſertim cum à grauioribus ad leuiora (di<lb></lb>gna tamen, &amp; aliquo in genere præſtantia) vel <lb></lb>ab agilibus ad ſpeculabilia, &amp; è contra, oppor<lb></lb>tuna quadam viciſsitudine conuertuntur. </s>
          <s id="N100FB">Sed <lb></lb>nec ſemper leuiora, aut minoris ex ſe conditio<lb></lb>nis dixerim, quæ in contemplationem mecha<lb></lb>nicam cadunt, vtpotè quæ non modò ad res per <lb></lb>magni momenti, ac neceſſarium humanæ vi<lb></lb>tæ vſum, ſplendoremque ordinantur: quæque <lb></lb>proinde apud Reges, ac Principes ex quo ge-<pb xlink:href="005/01/005.jpg"></pb>nus hominum capit, incomparabilem obtinue<lb></lb>runt extimationem; verùm quæ ſpeciali qua<lb></lb>dam ratione, in aliam ampliorem, <expan abbr="diuinioremq.">diuinioremque</expan> <lb></lb>contemplationem, ſummi videlicet rerum ma<lb></lb>chinatoris nos conducant. </s>
          <s id="N1011A">Quippe qui talia hu<lb></lb>mano ingenio excogitare dedit molimina, qui<lb></lb>bus multaque ſupra naturam ſunt, naturam ip<lb></lb>ſam emulando perficeret, arte ſuperando ea à <lb></lb>quibus natur a vincimur, (vt Antipho ſcribit <emph.end type="italics"></emph.end><arrow.to.target n="marg1"></arrow.to.target><lb></lb><emph type="italics"></emph>Poeta) &amp; cæleſtem machinam eiuſque mul<lb></lb>tiplicem, ac inuariabilem motum, orbiſque to<lb></lb>tius molem imitaretur: vt Archimedes alij<lb></lb>que permulti inſignes Mechanici opere præ<lb></lb>ſtiterunt, &amp; Cambray publico in foro li<lb></lb>cet videre. </s>
          <s id="N1013A">Nimirum arte manum dirigente <lb></lb>tamquam potentiam executiuam, &amp; inſtru<lb></lb>mentariam, effectricemque omnium excogi<lb></lb>tabilium machinarum. </s>
          <s id="N10143">Quæ ſolis homini<lb></lb>bus iccirco data eſt, vt perhibet Philoſophus,<emph.end type="italics"></emph.end><arrow.to.target n="marg2"></arrow.to.target><lb></lb><emph type="italics"></emph>quia ſoli inter omnia animalia ſumma pru<lb></lb>dentia, in qua ars tota fundatur præditi ſunt. <lb></lb></s>
          <s id="N10154">Vnde ſicut mens ipſa humana imaginem <lb></lb>diuinæ ſapientiæ, ac prouidentiæ refert dum <lb></lb>cuncta rectè diſponit; ita, &amp; manus homi<lb></lb>nis, omnipotentiam quodammodo exprimit <lb></lb>Creatoris, dum tam varia, ac mira, Me-<pb xlink:href="005/01/006.jpg"></pb>chanica cognitione duce patratur. </s>
          <s id="N10163">Quæ ſi <lb></lb>cunctis ob ſui generis excellentiam maximo <lb></lb>cum animarum prouentu, atque decore con<lb></lb>ſideranda ſe offerunt: quàm dignè interdùm <lb></lb>hac in contemplatione morabitur, quem fru<lb></lb>ctum non ex ea iucundè decerpet, qui diuina<lb></lb>rum rerum meditationibus aſſuetus, pium<lb></lb>que in Deum affectum exercens ipſum ſum<lb></lb>mum moderatorem veneratur, ac iugiter in <lb></lb>mundi regimine imitatur; dum non modo <lb></lb>firmum ſe Eccleſiæ Cardinem præbet, in <lb></lb>quo eius circumuertitur, ac fulcitur machi<lb></lb>na gubernationis. </s>
          <s id="N1017E">Sed ei qui ipſius vniuer<lb></lb>ſalis Eccleſiæ nauem ſummo imperio Chriſti <lb></lb>vice moderatur, ac regit tanta obſeruantia, <lb></lb>atque virtute miniſtrat, tali ope atque conſi<lb></lb>lio adeſt, vt vnica veluti vtriuſque manu mi<lb></lb>ſticæ huius nauis gubernaculum cenſeatur <lb></lb>inflecti? </s>
          <s id="N1018D">Tibi igitur Cardinalis Ampliſsi<lb></lb>me dum talia tuum erga Sanctiſsimum <lb></lb>Patruum ter optimum Pontificem agis, mu<lb></lb>neraque penè diuina perſoluis, non mediocris <lb></lb>prouentus ſimul, ac iucunditatis offertur <lb></lb>occaſio in his, quos dicaui præſtantiſsimæ <lb></lb>ſcientiæ Commentarijs. </s>
          <s id="N1019D">Nam, &amp; motus <lb></lb>orbis, vel cuiuſque globi circa cardines, ac <pb xlink:href="005/01/007.jpg"></pb>circuli circa centrum, admirabileſque eius <lb></lb>proprietates in ipſis patebunt; &amp; modus quo <lb></lb>paruo gubernaculo ingentia circumferuntur <lb></lb>nauigia: quod etiam Iacobus Apoſtolus mi-<emph.end type="italics"></emph.end><arrow.to.target n="marg3"></arrow.to.target><lb></lb><emph type="italics"></emph>ratus eſt, &amp; ad martalia tranſtulit. </s>
          <s id="N101B5">Inſuper <lb></lb>&amp; quo pacto vela dare liceat, ac remigio vti <lb></lb>contingat ad nauis progreſſum: Quod Petri <lb></lb>nauim quam in altum ducere Saluator præ<lb></lb>cepit ob oculis ponit: Et qua denique ratione <emph.end type="italics"></emph.end><arrow.to.target n="marg4"></arrow.to.target><lb></lb><emph type="italics"></emph>exiguo pondere ingentia leuentur onera, vt <lb></lb>vniuerſaliter diſcamus; cum Paulo, quan-<emph.end type="italics"></emph.end><arrow.to.target n="marg5"></arrow.to.target><lb></lb><emph type="italics"></emph>tumuis magnum, ac diuturnum in ſe ſit, <lb></lb>quod pro Chriſti nomine patimur in hac vi<lb></lb>ta, momentaneum tamen, ac leue in fide<lb></lb>lium ſtatera inueniri, ſolo pondere eius quam <lb></lb>ſperamus futuræ gloriæ, ac retributionis: <lb></lb>Aliaque permulta id genus licebit ſpectare, <lb></lb>non minus fortaſſe ad moralem, ac politi<lb></lb>cam inſtructionem, quàm ad vtilem in reli<lb></lb>quis, iucundamque Principis exercitatio<lb></lb>nem. </s>
          <s id="N101E6">Quod ſi Amplitudini tuæ inter has tem<lb></lb>porum anguſtias, non ſatis digna obtulerim, <lb></lb>mentiſque propoſitum haud plenè aſſecutus <lb></lb>fuerim, obſequentiſsimum, gratiſsimumque <lb></lb>ſaltem in eis aſpice votum, dum vix è Tri<lb></lb>remibus poſt longam nauigationem tecum <pb xlink:href="005/01/008.jpg"></pb>egreſſus, multis, ac varijs honoribus au<lb></lb>ctus, vt quo poteram pacto obſequium erga <lb></lb>te meum illicò præſtarem, perpetuoque ani<lb></lb>mo inſeruirem, ea detuli prout iacent; morem <lb></lb>putans gerere tuæ voluntati.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N10201" type="margin">
          <s id="N10203"><margin.target id="marg1"></margin.target>Apud Ariſ<lb></lb>tot. in <lb></lb>quęſt. </s>
          <s id="N1020E">Mec.<margin.target id="marg2"></margin.target>Lib. 4. de <lb></lb>part. </s>
        </p>
        <p id="N10217" type="margin">
          <s id="N10219">ani<lb></lb>mal. </s>
          <s id="N1021E">cap. <lb></lb>10.&amp; ma<lb></lb>gn. </s>
          <s id="N10225">Mo<lb></lb>ral. c. 33.</s>
        </p>
        <p id="N1022E" type="margin">
          <s id="N10230"><margin.target id="marg3"></margin.target>In epiſt. <lb></lb>cap.

3.</s>
        </p>
        <p id="N10239" type="margin">
          <s id="N1023B"><margin.target id="marg4"></margin.target>Luc. cap. <lb></lb>5.</s>
        </p>
        <p id="N10245" type="margin">
          <s id="N10247"><margin.target id="marg5"></margin.target>2. Cor. </s>
          <s id="N1024C">4.</s>
        </p>
        <figure id="id.005.01.008.1.jpg" xlink:href="005/01/008/1.jpg"></figure>
        <pb pagenum="1" xlink:href="005/01/009.jpg"></pb>
        <p id="N10259" type="head">
          <s id="N1025B">IOANNIS <lb></lb>DE GVEVARA <lb></lb>CLER. REG. MIN. <lb></lb>IN ARISTOTELIS MECHANICAS <lb></lb>Commentarii: <lb></lb><emph type="italics"></emph>VNA CVM ADDITIONIBVS QVIBVSDAM <lb></lb>Ad eandem materiam pertinentibus.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1026E" type="head">
          <s id="N10270">OPERIS ARGVMENTVM.</s>
        </p>
        <p id="N10273" type="main">
          <s id="N10275">Tota hæc Ariſtotelis Mechanica tra<lb></lb>ctatio in duas partes diuiditur, in qua<lb></lb>rum prima, vniuerſalis quædam do<lb></lb>ctrina traditur de natura &amp; obiecto <lb></lb>ipſius facultatis Mechanicæ, tum de <lb></lb>cauſis &amp; principijs earum <expan abbr="operationũ">operationum</expan> <lb></lb>ad quas facultas ipſa ordinatur in vni<lb></lb>uerſum; quæ ſanè principia vt præco<lb></lb>gnita, ſunt etiam ſpeciales rationes <expan abbr="aſſentiẽdi">aſſentiendi</expan> concluſionibus <lb></lb>in ſuis demonſtrationibus, præter vniuerſaliora illa Geome<lb></lb>trica elementa, ac theoremata, quibus paſſim quoque vtitur <lb></lb>in eiſdem demonſtrationibus. </s>
          <s id="N10296">Huiuſmodi autem cauſæ at<lb></lb>que principia, ſunt quæ de natura &amp; admirandis proprietati<lb></lb>bus circuli ab ipſo Ariſtotele afferuntur. </s>
          <s id="N1029D">Siquidem in reſo<lb></lb>lutione, ad ea reducuntur &amp; in ipſis fundantur quæcunque <lb></lb>de mechanicis inſtrumentis, <expan abbr="eorumq.">eorumque</expan> motionibus in progreſ<lb></lb>ſu demonſtrantur, vel quæcunque ad artificioſam motionem, <lb></lb>aut detentionem grauium &amp; leuium hìc oſtenduntur. </s>
          <s id="N102AC">Proin<pb pagenum="2" xlink:href="005/01/010.jpg"></pb><expan abbr="deq.">deque</expan> ex ipſis totam artem mechanicam tanquam ex proprijs <lb></lb>principijs intelligemus conſurgere. </s>
          <s id="N102B9">Quamuis huc etiam ſpe<lb></lb>ctent, &amp; inter eadem principia computari debeant, quæ Ar<lb></lb>chimedes, Hero, ac Pappus cum alijs tradiderunt de centro <lb></lb>grauitatis, in quibus pariter variæ, ac perplures demonſtra<lb></lb>tiones mechanicæ fundantur: quæ que propterea à nobis bre<lb></lb>uiſſimè colligentur, &amp; ad complementum doctrinæ inferius <lb></lb>in Additionibus afferentur. </s>
        </p>
        <p id="N102C8" type="main">
          <s id="N102CA">In ſecunda vero parte huius Mechanicæ tractationis tri<lb></lb>gintaquinque Ariſtoteles quæſtiones veluti problemata quę<lb></lb>dam proponit, in quarum ſolutionibus, ſingulis experimentis <lb></lb>obſeruatis ac ritè perſpectis, <expan abbr="ſingulisq.">ſingulisque</expan> difficultatibus occur<lb></lb>rendo, vniuerſam applicat doctrinam in priori parte traditam. </s>
        </p>
        <p id="N102D5" type="main">
          <s id="N102D7">Rurſus autem primam partem huius libri ſeu tractationis <lb></lb>in duo tantum veluti capita ſub duobus titulis Ariſtoteles di<lb></lb>ſtribuit. </s>
          <s id="N102DE">In quorum primo agitur de artis mechanicæ obie<lb></lb>cto ac facultate. </s>
          <s id="N102E3">In ſecundo verò de proprietatibus circuli <lb></lb>in quibus mechanicæ demonſtrationes penè omnes fundan<lb></lb>tur. </s>
          <s id="N102EA">Quoniam verò doctrina quæ in ipſo ſecundo capite <expan abbr="cõ-tinetur">con<lb></lb>tinetur</expan>, non modò fuſior eſt, ſed etiam obſcurior, vt commo<lb></lb>dius noſtris commentarijs dilucidetur, eam vlteriùs in textus <lb></lb>diuidendam eſſe cenſuimus, iuxta numerum proprietatum <lb></lb>circuli, de quibus ipſe philoſophus tractat; <expan abbr="primumq.">primumque</expan> caput <lb></lb>prædictum, etiam ſub textus nomine &amp; inſcriptione ad vni<lb></lb>formitatem ſermonis, ac diuiſionis comprehendere placuit. </s>
        </p>
        <p id="N10301" type="main">
          <s id="N10303">Tranſlationem denique Leonici elegimus tanquam com<lb></lb>muniorem, licet in quibuſdam deficiat, quoniam adhuc gre<lb></lb>cus textus mendis eſt plenus. </s>
          <s id="N1030A">Et quidem mirandum, <expan abbr="dolen-dumq.">dolen<lb></lb>dumque</expan> valde eſt, aureum hoc opus Philoſophi, diuinis propè <lb></lb>ſpeculationibus refertum, tot verborum tranſpoſitionibus &amp; <lb></lb>corruptionibus deprauari. </s>
          <s id="N10317">Qua de cauſa fortaſſe permulti il<lb></lb>lud exponere neglexerunt, ac difficile iuxtà verum ſenſum <lb></lb>Auctoris intellexerunt. </s>
          <s id="N1031E">Eſt enim in quibuſdam partibus di<lb></lb>minutum in alijs verò redundans, ac in multis confuſum. <lb></lb></s>
          <s id="N10324">Quapropter nonnullæ nobis permittendæ erunt tranſpoſitio<lb></lb>num reductiones, <expan abbr="verborumq.">verborumque</expan> reſecationes, aut additiones <pb pagenum="3" xlink:href="005/01/011.jpg"></pb>circa litteram ipſius textus, quam penitus &amp; in rigore ſemper <lb></lb>ſectari nequaquam liceret, ob præfatam corruptionem. <lb></lb></s>
          <s id="N10335">Pro viribus tamen eam ſectabimur, ſenſum enucleando, ac <lb></lb>exponendo, nunc per modum parafraſis, nunc vero per mo<lb></lb>dum interpretationis &amp; extenſionis. </s>
          <s id="N1033C">Multa in quibuſdam lo<lb></lb>cis addendo, prout opus fuerit ad complementum doctrinæ, <lb></lb><expan abbr="multaq.">multaque</expan> pariter ſub Additionum titulo, ſeorſum extra com<lb></lb>mentarios annectendo, vt ſiggillatim quæ ſcitu digna ſunt, &amp; <lb></lb>ad mechanicam contemplationem pertinent pleniùs eluce<lb></lb>ſcant. </s>
        </p>
        <figure id="id.005.01.011.1.jpg" xlink:href="005/01/011/1.jpg"></figure>
        <pb pagenum="4" xlink:href="005/01/012.jpg"></pb>
        <p id="N10355" type="head">
          <s id="N10357">PRIMA PARS <lb></lb>MECHANICES <lb></lb>ARISTOTELIS STAGIRITAE <lb></lb>IN QVA EA CONTINENTVR, <lb></lb>quæ ad naturam Mechanicæ facultatis, <lb></lb>&amp; principia operationum ipſius <lb></lb>pertinent.</s>
        </p>
        <p id="N10366" type="head">
          <s id="N10368"><emph type="italics"></emph>Quæ ſit artis Mechanicæ facultas.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1036F" type="head">
          <s id="N10371">Textus Primus.</s>
        </p>
        <p id="N10374" type="main">
          <s id="N10376">M<emph type="italics"></emph>iracvlo ſunt ea quidem quæ <lb></lb>natura contingunt, quorum ignoran<lb></lb>tur cauſæ: illa verò quæ præter natu<lb></lb>ram quæcunque ad hominum vtilita<lb></lb>tem arte fiunt. </s>
          <s id="N10384">In multis enim natu<lb></lb>ra ei, quod nobis vſui eſſe potest, con<lb></lb>trarium facit. </s>
          <s id="N1038B">Natura etenim eun<lb></lb>dem ſemper habet modum, &amp; ſimpli<lb></lb>citer: vtile autem multifariam commutatur. </s>
          <s id="N10392">Quando igitur <lb></lb>quippiam præter naturam oportuerit facere, difficultate ſua <lb></lb>hæſitationem præstat, <expan abbr="arteq.">arteque</expan> indiget: quamobrem eam artis <lb></lb>partem, quæ huiuſmodi ſuccurrit difficultatibus mechanicam <lb></lb>appellamus. </s>
          <s id="N103A1">Quemadmodum enim Antipho ſcribit Poeta, ſic <lb></lb>ſe res habet; arte enim ſuperamus ea à quibus natura vinci<lb></lb>mur. </s>
          <s id="N103A8">Huiuſmodi autem ſunt, in quibus &amp; minora ſuperant <lb></lb>maiora: &amp; quæcunque momentum paruum habentia, magna <lb></lb>movent pondera; &amp; omnia ferè illa, quæ mechanica nuncupa<lb></lb>mus &amp; problemata. </s>
          <s id="N103B1">Sunt autem hæc neque naturalibus om<lb></lb>nino quæſtionibus eadem, neque ſeiugata valde: verum ma<lb></lb>thematicarum contemplationum, <expan abbr="naturaliumq.">naturaliumque</expan> communia.<emph.end type="italics"></emph.end></s>
        </p>
        <pb pagenum="5" xlink:href="005/01/013.jpg"></pb>
        <p id="N103C2" type="head">
          <s id="N103C4">COMMENTARIVS.</s>
        </p>
        <p id="N103C8" type="main">
          <s id="N103CA">Ad colligendum quæ nam ſit artis mechanicæ facul<lb></lb>tas quantauè ſit eius dignitas, &amp; excellentia ex ma<lb></lb>gnis ac mirabilibus, quæ operatur; illud in primis <lb></lb>Ariſtoteles præmittit, eorum quæ miraculo habentur, alia <lb></lb>quidem natura contingere, vt inſueta &amp; peregrina, quorum <lb></lb>ignorantur cauſæ: alia verò præter naturam, vt quæ artificio <lb></lb>aliquo adhibito ſupra vires patrantur atque ad propriam ho<lb></lb>minum vtilitatem ordinantur. </s>
          <s id="N103DB">Siquidem natura <expan abbr="nõnunquam">nonnunquam</expan> <lb></lb>deficit in quibuſdam, quæ vſui nobis eſſe poſſunt, imò con<lb></lb>trarium facit, quia eundem ſemper, ac ſimpliciter ſeruat mo<lb></lb>dum in ſuis operationibus; vtile autem ad vſum hominum <lb></lb>diuerſimodè accommodatur, ac multifariam commutatur, <lb></lb>iuxtà ſcilicet varias exigentias, &amp; opportunitates. </s>
          <s id="N103EC">Quando <lb></lb>igitur quippiam præter naturam nos facere oportuerit, ob <lb></lb>difficultatem quam plerunque in ſe id, quod faciendum eſt <lb></lb>continet, hæſitare, &amp; cogitare nos cogit quomodo faciamus, <lb></lb><expan abbr="artemq.">artemque</expan> aliquam propterea quærere quæ difficultati ſuccur<lb></lb>rat, ae nos ad finem conſequendum opportunis, <expan abbr="aptisq.">aptisque</expan> me<lb></lb>dijs dirigat atque perducat. </s>
          <s id="N10402">Cum verum ſit quod Antipho <lb></lb>ſcribit Poeta, arte nos ſuperare ea, in quibus vincimur à na<lb></lb>tura. </s>
          <s id="N10409">Quamobrem concludit Ariſtoteles, eam artem, ſeu <lb></lb>artis vniuerſæ partem, quæ huiuſmodi ſuccurrit difficultati<lb></lb>bus, <expan abbr="nosq.">nosque</expan> adiuuat ad operandum &amp; <expan abbr="conſequendũ">conſequendum</expan> ea, quæ <lb></lb>ſunt præter naturam, Mechanicam appellamus. </s>
          <s id="N1041A">Hac enim <lb></lb>vtimur in his in quibus minora ſuperant maiora, &amp; quæcun<lb></lb>que paruam vim habentia, magna mouent pondera; inſuper <lb></lb>&amp; in omnibus ijs, quæ cadunt ſub problemata, quæ commu<lb></lb>niter vocantur mechanica. </s>
          <s id="N10425">Sunt autem (inquit) problema<lb></lb>ta mechanica, neque naturalibus quæſtionibus omnino ea<lb></lb>dem, neque ſeiuncta valde: verùm <expan abbr="mathematicarũ">mathematicarum</expan> contem<lb></lb>plationum, <expan abbr="naturaliumq.">naturaliumque</expan> communia. </s>
          <s id="N10436">Quia ſcilicet non eo<lb></lb>dem modo nec eadem ratione procedunt problemata me<lb></lb>chanica, ac naturalia ſeu phyſica. </s>
          <s id="N1043D">Siquidem diuerſis vtun<pb pagenum="6" xlink:href="005/01/014.jpg"></pb>tur principijs, vt fuſiùs infra explicabitur; <expan abbr="diuerſasq.">diuerſasque</expan> omnino <lb></lb>demonſtrationes efficiunt. </s>
          <s id="N1044B">Quoniam verò ea, circa quæ me<lb></lb>chanica facultas verſatur nempe pondus &amp; vis, qua illud mo<lb></lb>uetur, ſub obiecto adæquato phyſices materialiter contine<lb></lb>tur, ac non ſolùm geometricis, ſed naturalibus quoque ratio<lb></lb>nibus nonnulla de ipſis demonſtrantur; hinc eſt, vt mechani<lb></lb>ca problemata à phyſicis non dicantur valde ſeiuncta, nec <lb></lb>admodum diſtinguantur. </s>
          <s id="N1045A">Quare concludit Philoſophus, me<lb></lb>chanica problemata eſſe <expan abbr="naturaliũ">naturalium</expan>, <expan abbr="mathematicarumq.">mathematicarumque</expan> con<lb></lb>templationum communia, hoc eſt ratione ſubiecti materia<lb></lb>lis quod commune eſt phyſicæ ac mathematicæ, &amp; ratione <lb></lb>quarundam concluſionum quę quidem <expan abbr="vtrarumq.">vtrarumque</expan> ſcientia<lb></lb>rum principijs demonſtrantur. </s>
        </p>
        <p id="N10473" type="main">
          <s id="N10475">Verùm vt hęc omnia diſtinctiùs eluceſcant, <expan abbr="nihilq.">nihilque</expan> ad hu<lb></lb>ius textus Ariſtotelis, <expan abbr="naturæq.">naturæque</expan> artis mechanicæ <expan abbr="intelligentiã">intelligentiam</expan> <lb></lb>in vniuerſum quoad fieri poteſt deſideretur, nonnullas addi<lb></lb>tiones hìc ſubnectere opere pretium putauimus, in quibus ea<lb></lb>dem ſeorſum, ac luculentiùs, <expan abbr="aliaq.">aliaque</expan> permulta ad comple<lb></lb>mentum doctrinæ exponere conabimur. </s>
        </p>
        <p id="N10492" type="head">
          <s id="N10494"><emph type="italics"></emph>De Nomine, &amp; Origine facultatis <lb></lb>Mechanicæ.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1049E" type="head">
          <s id="N104A0">ADDITIO PRIMA.</s>
        </p>
        <p id="N104A4" type="main">
          <s id="N104A6">Nomen hoc mechanicæ facultatis, machinalem artem <lb></lb>aut ſcientiam ſignificat; ſumpta ethimologia à machi<lb></lb>na, ſeu inuentione qua aliquid molimur, &amp; quòd adiectiuum <lb></lb>mechanicus, vel mechanica deriuetur à græca voce <foreign lang="grc">μηκανικὸς</foreign>, <lb></lb>&amp; hæc <foreign lang="grc">μηκανη</foreign>, vel à <foreign lang="grc">μηκὰνηκα</foreign>, quæ inuentionem, &amp; machi<lb></lb>namentum ſignificat. </s>
          <s id="N104C1">Vnde etiam apud latinos machina, tam <lb></lb>animi quoddam inuentum aut molimen, quàm inſtrumentum <lb></lb>aliquod artificioſum quo moles leuantur, aut quocunque <lb></lb>modo pelluntur denotare vt plurimum conſueuit, iuxta illud <lb></lb><arrow.to.target n="marg6"></arrow.to.target> Taciti, Nihil tam ignarum barbaris quàm machinamenta, &amp; <lb></lb>aſtus oppugnationum. </s>
          <s id="N104D1"><expan abbr="Illudq.">Illudque</expan> Liuij, Turres contabulatas, <pb pagenum="7" xlink:href="005/01/015.jpg"></pb><expan abbr="machinamentaq.">machinamentaque</expan> alia quatiendis muris portabant. </s>
          <s id="N104DF">Nam ſiue <lb></lb>loquendo de machinis bellicis, ſiue de machinis nauticis aut <lb></lb>architectonicis, ſemper machina vtrumque ſignificatum in<lb></lb>uoluit, aut ſaltem admittit. </s>
        </p>
        <p id="N104E8" type="margin">
          <s id="N104EA"><margin.target id="marg6"></margin.target><emph type="italics"></emph><gap></gap>ac. lib.<emph.end type="italics"></emph.end> 12. <lb></lb><emph type="italics"></emph>lib.<emph.end type="italics"></emph.end> 4 <emph type="italics"></emph>de bel<lb></lb>lo Punico.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N10507" type="main">
          <s id="N10509">Ars igitur vel ſcientia, quæ ad huiuſmodi machinas<arrow.to.target n="marg7"></arrow.to.target> ſpe<lb></lb>ctat à Plinio dicitur machinalis, quaſi machinandi ſcientia, <lb></lb>vel peritia: Ab alijs vero communiter appellatur mechanica. <lb></lb></s>
          <s id="N10515">Quo ſenſu Archimedes, eo quòd ad debellandos hoſtes plu<lb></lb>ra adinuenerit machinamenta, apud Firmicum dicitur<arrow.to.target n="marg8"></arrow.to.target> Roma<lb></lb>nos exercitus mechanicis artibus ſæpe proſtraſſe. </s>
          <s id="N10520">Vſurpata <lb></lb>autem vel extenſa ſignificatione, ars quoque mechanica vul<lb></lb>go nuncupatur omnis illa quæ circa fabrilia verſatur, &amp; con<lb></lb>diſtinguitur ab arte liberali. </s>
          <s id="N10529">Nam &amp; mechanicus dicitur qui<lb></lb>libet faber vel opifex eorum, quæ ingenio ſimul ac manibus <lb></lb>fiunt. </s>
          <s id="N10530">Et machinator bellicorum inſtrumentorum appella<lb></lb>tur non ſolum qui bellicas machinas excogitauit, ſed is quo<lb></lb>que qui conficit; vt videre eſt apud Liuium, &amp; alios auctores.<arrow.to.target n="marg9"></arrow.to.target><lb></lb>Quamobrem Hero mechanicus, vt apud Pappum Alexandri, <lb></lb>num lib.

8. ſuarum collectionum refertur, mechanicam fa<lb></lb>cultatem in rationalem ac manualem diſtinxit, vtpote quæ in <lb></lb>genere ſumpta, vtramque rationem ſeu naturam videatur <lb></lb>amplecti. </s>
        </p>
        <p id="N10544" type="margin">
          <s id="N10546"><margin.target id="marg7"></margin.target><emph type="italics"></emph>Piin. lib.<emph.end type="italics"></emph.end>7. <lb></lb><emph type="italics"></emph>cap.<emph.end type="italics"></emph.end>37.</s>
        </p>
        <p id="N10559" type="margin">
          <s id="N1055B"><margin.target id="marg8"></margin.target><emph type="italics"></emph>Firmic. lib.<emph.end type="italics"></emph.end><lb></lb>6.<emph type="italics"></emph>cap.<emph.end type="italics"></emph.end>31.</s>
        </p>
        <p id="N1056E" type="margin">
          <s id="N10570"><margin.target id="marg9"></margin.target><emph type="italics"></emph>Liu.de bello <lb></lb>Punico.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1057C" type="main">
          <s id="N1057E">Propriè tamen hìc apud Ariſtotelem ſicut apud cœteros <lb></lb>omnes Philoſophos, ac Geometras, mechanica facultas tan<lb></lb>tùm ſignificat artem ſiue ſcientiam, quæ Geometricis princi<lb></lb>pijs circa ſtatum &amp; lationem grauium &amp; leuium verſatur, hoc <lb></lb>eſt circa grauia &amp; leuia prout artificiosè moueri, aut quieſce<lb></lb>re debent, vt clariùs infra ex Pappo, &amp; ex tradenda<arrow.to.target n="marg10"></arrow.to.target> defini<lb></lb>tione conſtabit. </s>
        </p>
        <p id="N10591" type="margin">
          <s id="N10593"><margin.target id="marg10"></margin.target><emph type="italics"></emph>Papp. lib.<emph.end type="italics"></emph.end>8. <lb></lb><emph type="italics"></emph><expan abbr="collectionũ">collectionum</expan><emph.end type="italics"></emph.end></s>
        </p>
        <p id="N105A7" type="main">
          <s id="N105A9">Iam verò ſi originem huius facultatis ſecundum latiſſimam <lb></lb>eius ſignificationem ſpectatæ conſideremus, eam non niſi <expan abbr="cũ">cum</expan> <lb></lb>ipſa natura humana ortum habuiſſe comperiemus. </s>
          <s id="N105B4">Quando<lb></lb>quidem nec in ipſis mundi primordijs defuerunt <expan abbr="machinamẽ-ta">machinamen<lb></lb>ta</expan> quibus arte quadam innata, vel infuſa primis parentibus, <lb></lb>ipſi ſeſe, &amp; à contrarijs defenderent, &amp; commoda conſecta<lb></lb>rentur ad vitam <expan abbr="incolumitatemq.">incolumitatemque</expan> tuendam; Nam &amp; corpora <pb pagenum="8" xlink:href="005/01/016.jpg"></pb>tegere, &amp; domos conſtruere, &amp; agros arare, &amp; commeatus <lb></lb>vehere, aliaue onera per aquas ac terras longius aſportare; <lb></lb><expan abbr="aquamq.">aquamque</expan> ipſam ex imis haurire, oleum exprimere, triticum <lb></lb>terere, ligna cedere, ferrum acuere, <expan abbr="aliaq.">aliaque</expan> huiuſmodi perage<lb></lb>re ad varios vſus ex neceſſitate, vel ab initio cœperunt; quæ <lb></lb>cum inſtrumenta nonnulla mechanica, tùm artem ipſam ma<lb></lb>chinandi ſupponunt. </s>
        </p>
        <p id="N105DF" type="main">
          <s id="N105E1">Quòd ſi ſecundum propriam acceptionem loquamur de <lb></lb>facultate mechanica, quatenus vt diximus ars quædam eſt, <lb></lb>vel ſcientia, quæ geometricis nixa principijs peculiari <expan abbr="quadã">quadam</expan> <lb></lb>ratione circa ſuum obiectum per demonſtrationes verſatur, <lb></lb>ac præcepta tradit, quibus homo in vſu ac motione grauium, <lb></lb>&amp; leuium dirigitur ac iuuatur; ſic nullum extat monimentum <lb></lb>quo ante tempora Eudoxij Architæ, ac Platonis illam cępiſſe <lb></lb>aſſereremus. </s>
          <s id="N105F6">Eudoxius enim Gnidius, &amp; Archita Tarentinus <lb></lb>primò geometrica principia ad vſum mechanicum, ſeu me<lb></lb>chanicam contemplationem tranſtulerunt. </s>
          <s id="N105FD">Sed Archita eo <lb></lb>quòd ligneam columbam volantem exhibuerit, <expan abbr="aliaq.">aliaque</expan> præcla<lb></lb>ra, &amp; admiranda mechanicæ artis adminiculo patrauerit, ip<lb></lb>ſiuſmet artis inuentor eſt habitus, vt extat apud Eutocium; <lb></lb>niſi Democritum Meleſium qui iam antea opus quoddam fe<lb></lb>rè mechanicum Certamen Clepſydræ inſcriptum ediderat, <lb></lb>inter mechanicæ facultatis Auctores computare velimus. <lb></lb></s>
          <s id="N10611">Poſt Architam verò Tarentinum, vnum inuenimus Ariſtote<lb></lb>lem Stageritam non modo verioris, ac ſolidioris philoſophiæ <lb></lb>auctorem maximum, ſed &amp; mathematicarum diſciplinarum <lb></lb>inſtructiſſimum qui mechanicæ artis modo ſcientifico funda<lb></lb>menta iecerit, hunc quem exponimus libellum edens, in quo <lb></lb>præter ſubtiliſſimas quæſtiones quas acutiſſimè diluit, firmiſ<lb></lb>ſima, &amp; vniuerſaliſſima tradit principia quibus mechanici om<lb></lb>nes tractatus ac demonſtrationes eorum nituntur. </s>
          <s id="N10622">Exinde <lb></lb>igitur mechanica facultas propagari cœpit, nam Ariſtotelem <lb></lb>ſecuti, vel imitati ſunt multi, præſertim, qui ſequenti ſeculo <lb></lb>maximè claruerunt, vt Archimedes Siracuſanus, cuius do<lb></lb>ctrina, ac ſummo ingenio huiuſmodi facultas maxima incre<lb></lb>menta ſuſcepit. </s>
          <s id="N1062F">Item Cteſibus machinator præſtantiſſimus <pb pagenum="9" xlink:href="005/01/017.jpg"></pb>qui ſpiritalia &amp; hydraulicas machinas primus inuenit. </s>
          <s id="N10637">Dein<lb></lb>de vero Philo Bizantius, cuius mechanica peritia ab Herone <lb></lb>commemoratur. </s>
          <s id="N1063E">Hero ipſe Alexandrinus Philoſophus Cte<lb></lb>ſebij diſcipulus; qui multa ac eruditiſſima monumenta me<lb></lb>chanica protulit. </s>
          <s id="N10645">Hinc Athenæus, cuius duo extant <expan abbr="fragmẽ-ta">fragmen<lb></lb>ta</expan> græca de Machinis apud Vitruuium in fine. </s>
          <s id="N1064E">Vitruuius <expan abbr="etiã">etiam</expan> <lb></lb>ipſe celeberrimus Architectus. </s>
          <s id="N10657">Ptolemæus Alexandrinus <lb></lb>aſtronomorum Princeps, qui libros mechanicos præclariſſi<lb></lb>mos edidit. </s>
          <s id="N1065E">Pappus denique Alexandrinus, mechanicæ fa<lb></lb>cultatis propagator egregius, &amp; Hero mechanicus, qui de <lb></lb>Geodæſia ac de machinis bellicis diſſertiſſime ſcripſit. </s>
          <s id="N10665">Quos <lb></lb>authores enumeraſſe ſufficiat ad exiſtentiam, &amp; originem hu<lb></lb>ius facultatis innuendam, cœteris recenſioribus, breuitatis <lb></lb>gratia prætermiſſis, qui ad hæc vſque tempora eam magno<lb></lb>perè illuſtrarunt, <expan abbr="micantq.">micantque</expan> adhuc ipſi, operum ac ingeniorum <lb></lb>ſplendore. </s>
        </p>
        <p id="N10676" type="head">
          <s id="N10678"><emph type="italics"></emph>De obiecto circa quod Mechanica facultas <lb></lb>verſatur.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N10681" type="head">
          <s id="N10683">ADDITIO SECVNDA.</s>
        </p>
        <p id="N10687" type="main">
          <s id="N10689">Vt <expan abbr="autẽ">autem</expan> Mechanicæ facultatis natura ex proprio obie<lb></lb>cto, quemadmodum commune eſt omnibus artibus, <lb></lb>atque ſcientijs in doctrina Ariſtotelis 2. de anima text. </s>
          <s id="N10694">33. <lb></lb>præcipuè dignoſcatur, Obſeruandum in primis eſt, id quod <lb></lb>per mechanicam facultatem intendimus, &amp; ad quod tanquam <lb></lb>ad finem conſequendum omnis mechanica contemplatio or<lb></lb>dinatur, aliud non eſſe, quàm grauis aut leuis cuiuſque cor<lb></lb>poris motionem, vel quietem, quæ parua vt plurimum virtu<lb></lb>te, arte ipſa mirabiliter comparatur, ſiue motio ſit ſecundum <lb></lb>naturam, ſiue ſit præter aut contra naturam ipſius corporis <lb></lb>grauis aut leuis. </s>
          <s id="N106A7">Porro inductione conſtat, mechanicum om<lb></lb>nem conatum, <expan abbr="omnemq.">omnemque</expan> tractatum in admirabilem lationem, <lb></lb>aut ſtatum corporum ordinari ex ipſius artis proprio inſtitu<lb></lb>to, vt ad leuanda, vel detinenda etiam exigua virtute quæ-<pb pagenum="10" xlink:href="005/01/018.jpg"></pb>cunque pondera, ad aerem vel aquam artificiosè pellendam, <lb></lb>attrahendam, aut continendam, ad miſſilia proijcienda, <expan abbr="aliaq.">aliaque</expan> <lb></lb>ſecundum varias poſitiones locanda, vel de loco ad locum, <lb></lb>diuerſimodè transferenda, &amp; ſimilia, quæ per ſe nota erunt <lb></lb>mechanicamenta omnia ad id præſtandum accomodata, ac <lb></lb>ſpeculationes mechanicas recenſenti. </s>
        </p>
        <p id="N106C7" type="main">
          <s id="N106C9">Deinde obſeruandum eſt, ad prædictam motionem, aut <lb></lb>quietem arte conſequendam, duo potiſſimum conſiderari à <lb></lb>Mechanico; nimirum &amp; quantitatem ponderis ex parte cor<lb></lb>poris mouendi, &amp; quantitatem virtutis ex parte mouentis, ſi<lb></lb>ue immediatè ipſe moueat per virtutem intrinſecam, fiue per <lb></lb>impreſſionem impetus, aut per inſtrumenta. </s>
          <s id="N106D6">In hoc enim ars <lb></lb>ipſa mechanica ſita eſt, vt habita ratione ponderis, aut leui<lb></lb>tatis corporis mouendi aut detinendi, proportionalis vis ad id <lb></lb>præſtandum adhibeatur, <expan abbr="congruaq.">congruaque</expan> applicentur machina<lb></lb>menta, ad ſupplendum quod deeſt naturali virtuti. </s>
          <s id="N106E5">Quod <lb></lb>nequaquam fieri poſſet ſine conſideratione quantitatis vtriuſ<lb></lb>que, nempe ponderis mouendi, &amp; virtutis motiuæ vbi tota <lb></lb>fundari debet proportio vnius ad alteram. </s>
        </p>
        <p id="N106EE" type="main">
          <s id="N106F0">Denique obſeruandum etiam erit, prædictam quantitatem <lb></lb>ponderis, tum grauitatem, tum leuitatem reſpectu <expan abbr="diuerſorũ">diuerſorum</expan> <lb></lb>à Mechanicis appellari. </s>
          <s id="N106FB">Maior enim quantitas ponderis re<lb></lb>ſpectu minoris, ab ipſis dicitur grauitas; minor vero compa<lb></lb>ratione maioris, dicitur leuitas. </s>
          <s id="N10702">Sicut illud corpus ab ipſis <lb></lb>dicitur leue, quod minus habet pondus reſpectu alterius; il<lb></lb>lud vero graue, quod maius; etiam ſi per ſe ſimpliciter lo<lb></lb>quendo vtrumque graue ſit. </s>
          <s id="N1070B">Non enim Mechanicus accipit <lb></lb>graue aut leue ſimpliciter &amp; ſecundum ſe, quemadmodum vt <lb></lb>plurimum accipit Phyſicus (nempe per graue intelligendo, <lb></lb>quod nullam habet in ſe leuitatem, per leue autem quod nul<lb></lb>lam habet in ſe grauirtatem;) ſed ſemper vtrumque accipit <lb></lb>reſpectiue; ita vt idem dicatur graue &amp; leue reſpectu diuerſo<lb></lb>rum, vt habetur etiam apud Ariſtotelem lib.

4. de cœlo tex. <lb></lb>27. vbi aer &amp; aqua reſpectu terræ dicuntur leuia, reſpectu ve<lb></lb>ro ignis, grauia. </s>
        </p>
        <p id="N1071F" type="main">
          <s id="N10721">His ergo præmiſſis facile primo intelligetur, ſubiectum ma-<pb pagenum="11" xlink:href="005/01/019.jpg"></pb>teriale adæquatum facultatis mechanicæ eſſe grauia &amp; leuia, <lb></lb>ſeu quantitatem ponderis ipſorum, ac virtutis qua moueri <lb></lb>debent aut detineri. </s>
          <s id="N1072D">Ratio autem eſt, quia in ſcientijs, illud <lb></lb>dicitur ſubiectum materiale adæquatum, quod complectitur <lb></lb>omnia de quibus in ſcientia tractatur; omne autem de quo in <lb></lb>hac ſcientia tractatur, reducitur ad corpus aliquod graue, aut <lb></lb>leue mouendum aut detinendum, ſiue ad quantitatem virtu<lb></lb>tis qua moueri debet aut detineri; <expan abbr="Proindeq.">Proindeque</expan> ipſa grauia &amp; <lb></lb>leuia vt ſic, <expan abbr="ſimulq.">ſimulque</expan> virtus motiua ac detentiua illorum, me<lb></lb>ritò huius facultatis mechanicæ materiale ſubiectum adæ<lb></lb>quatum deſignatur. </s>
        </p>
        <p id="N10748" type="main">
          <s id="N1074A">Secundo vero non minus facile conſtabit, obiectum forma<lb></lb>le eiuſdem facultatis eſſe admirabilem, &amp; artificioſam mobi<lb></lb>litatem, aut quietèm ipſorum grauium, &amp; leuium, abſtrahen<lb></lb>do à motione &amp; quiete naturali aut violenta, vt quæ per im<lb></lb>petum impreſſum, aut detentionem fieri conſueuit. </s>
          <s id="N10755">Conſtat <lb></lb>autem ex eo quod obiectum formale cuiuſque facultatis, aut <lb></lb>ſcientiæ, eſt ipſa ratio ſub qua de proprio ſubiecto materiali <lb></lb>agitur in tali ſcientia: ratio autem ſub qua in mechanica fa<lb></lb>cultate agitur de graui &amp; leui, <expan abbr="virtuteq.">virtuteque</expan> motiua aut detentiua <lb></lb>eorum, eſt ipſa artificioſa mobilitas ſecundum <expan abbr="locũ">locum</expan>, &amp; quies <lb></lb>conſequenda ipſorum, mediantibus præceptis tradendis in <lb></lb>eadem ſcientia, vt per ſe patet ex fine explicato, ad quem <lb></lb>tota hæc ſcientia dirigitur, &amp; ordinatur. </s>
          <s id="N10770">Ea ergo admirabi<lb></lb>lis, <expan abbr="artificioſaq.">artificioſaque</expan> mobilitas, iure cenſeri debet formale obie<lb></lb>ctum huius facultatis mechanicæ. </s>
        </p>
        <p id="N1077B" type="main">
          <s id="N1077D">Quo tandem fit tertio, vt obiectum totale, &amp; adæquatum <lb></lb>mechanicæ facultatis in vniuerſum, ſint ipſa grauia &amp; leuia <lb></lb>prout artificiosè mobilia, &amp; vt ita dicam quieſcibilia, <expan abbr="ſimulq.">ſimulque</expan> <lb></lb>omnia quæ de ipſis demonſtrantur in hac eadem ſcientia. <lb></lb></s>
          <s id="N1078B">Quod certe non obſcurè ſumitur ex Pappo Alexandrino lib. <lb></lb>8. ſuarum Collectionum, vbi mechanicam contemplationem <lb></lb>docet verſari circa ſtatum &amp; lationem corporum, <expan abbr="motumq.">motumque</expan> <lb></lb>ſecundum locum in vniuerſo, vt eorum quæ natura fiunt, cau<lb></lb>ſas reddat; eorum verò quæ à natura ſua diſcedere coguntur <lb></lb>extra propria loca, in contrarios motus per ſua theoremata <pb pagenum="12" xlink:href="005/01/020.jpg"></pb>transferat. </s>
          <s id="N107A2">Ratio vero eſt manifeſta, nam huiuſmodi <expan abbr="obiectũ">obiectum</expan> <lb></lb>totale &amp; adæquatum in qualibet ſcientia coaleſcere debet <expan abbr="tũ">tum</expan> <lb></lb>ex ſubiecto materiali etiam adæquato, ac formalitate ſub qua <lb></lb>de illo agitur; tum etiam ex omnibus ijs quæ de ipſo demon<lb></lb>ſtrantur in ſcientia. </s>
          <s id="N107B5">Explicatum ergo ſubiectum materiale <lb></lb>ſub illa formalitate cum omnibus quæ de illo demonſtrantur <lb></lb>per theoremata ac problemata mechanica, conſtituetur to<lb></lb>tale &amp; adæquatum huius facultatis obiectum, in ordine ad <lb></lb>quod tota eius eſſentia, ac ratio ſpecifica deſumenda eſt, ac <lb></lb>paulatim inferius explicanda. </s>
        </p>
        <p id="N107C2" type="head">
          <s id="N107C4"><emph type="italics"></emph>Qua ratione facultas Mechanica conſtituatur <lb></lb>Ars &amp; Scientia.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N107CD" type="head">
          <s id="N107CF">ADDITIO TERTIA.</s>
        </p>
        <p id="N107D3" type="main">
          <s id="N107D5">Hviuſque ad ſignificandum habitum intellectualem <expan abbr="cõ-templationis">con<lb></lb>templationis</expan> mechanicæ, vt plurimum vſi ſumus no<lb></lb>mine facultatis mechanicæ, eo quod nomen facultas abſtra<lb></lb>hat à propria ſignificatione artis, aut ſcientiæ, <expan abbr="latiusq.">latiusque</expan> pateat <lb></lb>ſecundum communem omnium conceptionem. </s>
          <s id="N107E4">Quare de<lb></lb>terminandum nunc eſt, vtrum talis habitus vel facultas, ſit ve<lb></lb>rè in ſe, ac propriè vocari poſſit tum ars, tum ſcientia. </s>
          <s id="N107EB">Quod <lb></lb>ſanè auſpicari debet à communi ratione artis atque ſcientiæ <lb></lb>ab Ariſtotele ſæpius explicata, <expan abbr="aptèq.">aptèque</expan> paſſim licet non ſem<lb></lb>per diſtincta. </s>
          <s id="N107F8">Nam 6 Ethicorum cap.

4. artem docet eſſe <lb></lb>habitum quendam vera cum ratione <expan abbr="effectiuũ">effectiuum</expan> circa id quod <lb></lb>aliter eſſe atque aliter poteſt; &amp; cuius principium ſit in eo <lb></lb>quod efficitur. </s>
          <s id="N10805">Vnde eorum quæ ex neceſſitate ſunt, vel fiunt <lb></lb>ſecundum naturam, nullam ait eſſe artem, cum hæc in ſe prin<lb></lb>cipium habeant. </s>
          <s id="N1080C">Ac proinde ſequenti capite diſtinguit artem <lb></lb>à ſcientia, eo quod ſcientia ſit de rebus quæ non poſſunt ali<lb></lb>ter ſe habere. </s>
          <s id="N10813">Nihilominus 1. Metaphiſices cap.

1. idem <lb></lb>Philoſophus artem videtur confundere cum ſcientia ſaltem <lb></lb>practica; ait enim, artem eſſe de vniuerſalibus, ac propter <lb></lb>cauſam ea quæ ſfiunt cognoſcere, exemplum adhibens tum <pb pagenum="13" xlink:href="005/01/021.jpg"></pb>medicinæ, tum architecturæ; imò ipſas mathematicas diſci<lb></lb>plinas indefinitè loquendo, quas conſtat eſſe ſcientias, artes <lb></lb>appellat. </s>
        </p>
        <p id="N10825" type="main">
          <s id="N10827">Ex quibus primò dicendum erit, mechanicam facultatem <lb></lb>verè &amp; propriè eſſe artem, prout in hoc libello, &amp; in explica<lb></lb>to textu aſſumitur ab Ariſtotele. </s>
          <s id="N1082F">Nam procul dubio huiuſ<lb></lb>modi facultas eſt habitus intellectualis vera cum ratione effe<lb></lb>ctiuus; qui nimirum pro ratiocinationem verſatur circa facti<lb></lb>bilia, vt ſunt grauia &amp; leuia, quæ aliter atque aliter ſe poſſunt <lb></lb>habere ſecundum artificioſam motionem, aut quietem illis <lb></lb>tribuendam ab eodem principio in quo eſt ipſe habitus intel<lb></lb>lectualis, ac directiuus mechanicæ operationis. </s>
        </p>
        <p id="N1083E" type="main">
          <s id="N10840">Secundò dicendum eſt, eandem facultatem mechanicam <lb></lb>verè etiam ac propriè eſſe ac vocari poſſe ſcientiam. </s>
          <s id="N10845">Id quod <lb></lb>implicitè docet Ariſtoteles loco citato metaphiſices, dum <lb></lb>eodem pacto ſub nomine artis, de hac facultate ac de medi<lb></lb>cina loquitur, <expan abbr="eisq.">eisque</expan> competere ait rationem ſcientiæ; &amp; in <lb></lb>ſpecie Architectos (qui ſanè mechanici ſunt) honorabilio<lb></lb>res, &amp; doctiores eſſe ait ijs qui manibus propter ſolam <expan abbr="cõſue-tudinem">conſue<lb></lb>tudinem</expan> &amp; experientiam operantur: quoniam (inquit) cauſas <lb></lb>eorum quæ fiunt, ſciunt; &amp; ſignum ſcientis eſt poſſe docere.<arrow.to.target n="marg11"></arrow.to.target><lb></lb>Vnde Pappus Mechanicam <expan abbr="ſcientiã">ſcientiam</expan> ſimul &amp; artem appellat. </s>
        </p>
        <p id="N10867" type="margin">
          <s id="N10869"><margin.target id="marg11"></margin.target><emph type="italics"></emph>Paip.Alex, <lb></lb>lib<emph.end type="italics"></emph.end> 8.<emph type="italics"></emph>math. <lb></lb></s>
          <s id="N10879">collat.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1087E" type="main">
          <s id="N10880">Ratio autem eſt eadem quam citatis verbis indicauit Ari<lb></lb>ſtoteles; quia nempe ſi ſcire non eſt aliud niſi rem per cau<lb></lb>ſam cognoſcere propter quam res ipſa eſt, &amp; non poteſt ali<lb></lb>ter ſe habere, vt alibi ipſemet Philoſophus definit 1. Poſter. <lb></lb>cap.

2. iure &amp; quidem optimo mechanica facultas ſeu noti<lb></lb>tia, ſcientia eſſe debet, ac dici: quandoquidem hæ omnes <lb></lb>conditiones illi proprijſſimè conueniunt. </s>
          <s id="N10890">In primis enim eſt <lb></lb>intellectualis cognitio eorum quæ circa motionem localem, <lb></lb>aut quietem grauium ac leuium contingunt, orta ex præexi<lb></lb>ſtenti alia cognitione principiorum, quæ ſiue ſint per ſe nota, <lb></lb>ſiue demonſtrentur in alia ſuperiori ſcientia, vt infra dicetur, <lb></lb>omnino tamen ſunt cauſa eius quod aſſeritur in concluſione. <lb></lb></s>
          <s id="N1089E">Ideo <expan abbr="namq.">namque</expan> dicimus in motu circulari, partem diametri, quæ <lb></lb>magis diſtat à centro circuli, velocius moueri; quia hæc ma-<pb pagenum="14" xlink:href="005/01/022.jpg"></pb>gis participat de motu recto, ac naturali à quo prouenit ipſa <lb></lb>maior velocitas tanquam à cauſa intrinſeca, &amp; hoc ita ſe ha<lb></lb>bere demonſtratur ex principijs geometricis. </s>
          <s id="N108B0">Similiter non <lb></lb>ex alio dicimus rotunda corpora ſuper planum, facilius mo<lb></lb>ueri, niſi quia parua vel minima ſui parte planum contingám, <lb></lb>ac minus offenſant. </s>
          <s id="N108B9"><expan abbr="Idq.">Idque</expan> probatur eo quòd circulus tangat in <lb></lb>puncto, ac magis à plano ſemotum efficiat angulum. </s>
          <s id="N108C1">Quæ <lb></lb>deſumuntur ex geometricis, <expan abbr="ſuntq.">ſuntque</expan> veræ cauſæ ipſius mobili<lb></lb>taris facilioris quæ de rotundis corporibus aſſeueratur. </s>
          <s id="N108CC">Quod <lb></lb>cum in omnibus concluſionibus mechanicis obſeruetur, vt <lb></lb>per ſe conſtat, palàm conuincitur, eas conſtituere notitiam <lb></lb>quandam rerum ſiue effectuum procedentem ex cognitione <lb></lb>cauſæ illorum, ac proinde per diſcurſum &amp; illationem virtute <lb></lb>medij, nempe ipſius cauſæ præcognitæ, ex notitia <expan abbr="antecedẽ-tis">anteceden<lb></lb>tis</expan> deueniendo in notitiam conſequentis, quod eſt ſecundum <lb></lb>hanc conditionem participare propriam rationem ſcientiæ. </s>
        </p>
        <p id="N108E1" type="main">
          <s id="N108E3">Deinde probatur, nam ea quæ per mechanicam notitiam <lb></lb>ex cauſis proprijs cognoſcuntur, tàm neceſſario ab ipſis cau<lb></lb>ſis procedunt, vt non poſſint aliter ſe habere, quæ erat altera <lb></lb>conditio propriæ ſcientiæ. </s>
          <s id="N108EC">Neque enim contingenter pon<lb></lb>dus libræ aut vectis magis grauitat in parte remotiori à fulci<lb></lb>mento ex eo quòd pars diametri, quæ plus à centro circuli <lb></lb>diſceſſerit, magis ab eadem virtute moueri ſuapte natura <lb></lb>præualeat: ſed neceſſariò ac ineffabiliter, cùm neceſſariò li<lb></lb>bra aut vectis in ſuo proprio motu conſtituatur veluti diame<lb></lb>ter circuli; &amp; hoc quod eſt pondus in parte diſtantiori à ful<lb></lb>cimento quod eſt centrum, magis grauitare ſeu efficaciùs de<lb></lb>orſum impellere eſſentialiter dependeat ab eo, quod eſt par<lb></lb>tem illam diſtantiorem à centro aptiorem eſſe ad motum, vt <lb></lb>apertiſſimè ex geometricis principijs demonſtrabitur. </s>
          <s id="N10903">Nec <lb></lb>per accidens eſt, longiùs ferri miſſilia funda, quàm manu miſ<lb></lb>ſa, quia in motu circulari qui fit per emiſſionem, ſeu proie<lb></lb>ctionem, magis illa diſtant à centro per fundæ vſum, quàm ſi <lb></lb>ſola manu proijcerentur, vt per ſe conſtat; ſed neceſſariò ex <lb></lb>tali cauſa talis procedit effectus, qui proinde aliter non poteſt <lb></lb>ſe habere propter eandem rationem, vt in cœteris quoque <pb pagenum="15" xlink:href="005/01/023.jpg"></pb>facilè erit inductione probare. </s>
          <s id="N10917">Cumque ipſæ cauſæ ex qui<lb></lb>bus mechanica facultas ſuas elicit concluſiones, vel ſint per <lb></lb>ſe notæ, vt citius ferri, quod facilius mouetur; Aequalia ab <lb></lb>æqualibus non moueri, &amp; ſimilia; vel fundentur in principijs <lb></lb>demonſtratis in alia ſuperiori ſcientia, de quibus habetur ve<lb></lb>ra certitudo, &amp; euidentia hinc vlterius fit, vt ipſa pariter co<lb></lb>gnitio mechanicarum concluſionum, eandem participet, ac <lb></lb>ſortiatur euidentiam, vt commune eſt omnibus ſcientijs, quæ <lb></lb>nimirum euidentiam non niſi ex principijs obtinent per reſo<lb></lb>lutionem vſque ad elementa, vt ſæpè docet Philoſophus in <lb></lb>Analiticis. </s>
        </p>
        <p id="N1092E" type="main">
          <s id="N10930">Quòd ſi mechanica facultas ſimul à nobis <expan abbr="cõſtituatur">conſtituatur</expan> ars, <lb></lb>&amp; hæc iuxta doctrinam allegatam Ariſtotelis 6. Ethic. cap.

4. <lb></lb>ſemper verſetur circa aliquid quod aliter eſſe atque aliter po<lb></lb>teſt; Id ſanè non obſtat; nam ibi apud Philoſophum ſermo <lb></lb>eſt de arte ſumpta pro arte ſeruili, quæ verſatur circa ſingu<lb></lb>laria, ac varia corporum accidentia, vt circa fabrilia, hoc eſt <lb></lb>varias corporum formas manibus <expan abbr="effingẽdas">effingendas</expan>, &amp; artificiosè in<lb></lb>troducendas, quæ certè aliter atque aliter ſe poſſunt habere, <lb></lb>ac proinde de illis dari non poteſt vera ſcientia. </s>
          <s id="N1094F">Alioquin <expan abbr="cũ">cum</expan> <lb></lb>diximus huiuſmodi facultatem eſſe pariter artem, artem ſum<lb></lb>pſimus cum Ariſtotele 1. Metaphiſices cap.

1. pro habitu in<lb></lb>tellectuali qui verſatur circa vniuerſalia factibilia, &amp; ex cauſis <lb></lb>ea dignoſcendo, ac tradendo modum quo fieri debent; quo <lb></lb>ſenſu diximus, artem cum ſcientia quaſi confundere, ſaltem <lb></lb>loquendo de ſcientia practica. </s>
          <s id="N10962">Quamobrem. </s>
        </p>
        <p id="N10966" type="main">
          <s id="N10968">Tertio dicendum eſt, mechanicam facultatem non eſſe <lb></lb>ſcientiam ſpeculatiuam, ſed practicam. </s>
          <s id="N1096D">In quo nulla poteſt <lb></lb>eſſe difficultas præſertim in doctrina Ariſtotelis, nam vt ipſe <lb></lb>docet lib.

2. Met. cap.

1. Scientia ſpeculatiua eſt illa cuius <lb></lb>finis eſt veritas, <expan abbr="quæq.">quæque</expan> in ſe ipſa ſiſtit, nullum includens ordi<lb></lb>nem ad aliud præter veritatem ipſius obiecti ſcibilis. </s>
          <s id="N10980">Practi<lb></lb>ca verò ſcientia eſt, cuius finis eſt opus; nempè quæ ex ſe or<lb></lb>dinatur ad opus, vel operationem aliquam exercendam præ<lb></lb>ter ipſam ſcientiam. </s>
          <s id="N10989">Mechanica autem facultas nullo modo <lb></lb>abſtrahere poteſt ab ordine quem eſſentialiter dicit ad <expan abbr="motũ">motum</expan> <pb pagenum="16" xlink:href="005/01/024.jpg"></pb>localem, aut quietem mobilibus impertiendam, &amp; ad <expan abbr="modũ">modum</expan> <lb></lb>quo moueri debent vel quieſcere. </s>
          <s id="N1099D">Nam licet nonnullæ pro<lb></lb>poſitiones mechanicæ, ſi per ſe ſumantur, ſint ſpeculatiuæ, eo <lb></lb>quod præciſe ſiſtere poſſent in ſola veritate, nihilominus pro<lb></lb>pter connexionem quam habent cum alijs practicis, &amp; ordi<lb></lb>nem quem ſimul includunt ad praxim, verè conſtituunt <expan abbr="vnã">vnam</expan> <lb></lb>ſcientiam totalem practicam. </s>
          <s id="N109AE">Quod confirmari etiam poteſt <lb></lb>ex eo: nam verè ac propriè huiuſmodi ſcientia cadit ſub illa <lb></lb>diuiſione generica ſcientiæ practicæ, cum Philoſophus 6. <lb></lb>Metaph.

cap.

1. eam diuidit in actiuam &amp; factiuam. </s>
          <s id="N109B7"><expan abbr="Quoniã">Quoniam</expan> <lb></lb>ſub actiua optimè intelligitur contineri ſcientias, quæ verſan<lb></lb>tur circa actus immanentes intellectus ac voluntatis, prout <lb></lb>dirigibiles per ipſas met ſcientias; cuiuſmodi ſunt Logica, &amp; <lb></lb>Philoſophia moralis, quarum finis &amp; opus, eſt ipſa rectitudo <lb></lb>actionis internæ, ſeu actuum immanentium intellectus &amp; vo<lb></lb>luntatis, ſiuè in genere moris in ordine ad honeſtatem, ſiuè in <lb></lb>genere cognitionis in ordine ad veritatem: ſub factiua verò <lb></lb>contineri omnes illas artes, ſiuè ſcientias, quæ verſantur cir<lb></lb>ca factionem aliquam ſeu opus extrinſecus faciendum, nem<lb></lb>pe genere diſtinctum ab ipſo actu ſcientifico per quem opus <lb></lb>ſit aut dirigitur, vt quælibet operatio corporea, vel opus ex <lb></lb>tali operatione relictum, vt perſpicuè docet idem Ariſtoteles <lb></lb><gap></gap> Met. tex. 16. &amp; 1. magn. </s>
          <s id="N109DC">moral. </s>
          <s id="N109DF">cap.

33. Et huiuſmodi <lb></lb>dicimus eſſe facultatem mechanicam, cum verè pro fine ha<lb></lb>beat opus externum, vt diximus, nempe motum localem &amp; <lb></lb>artificioſum, vel quietem grauibus &amp; leuibus impertiendam, <lb></lb>non ſecus ac medicina conſtituitur ſcientia practica, <lb></lb>eo quod eius finis, ad quem ordinatur <lb></lb>tanquam ad proprium opus <lb></lb>ſit ſanitas anima<lb></lb>lis ho<lb></lb>minibus im<lb></lb>pertien<lb></lb>da. </s>
        </p>
        <pb pagenum="17" xlink:href="005/01/025.jpg"></pb>
        <p id="N109FE" type="head">
          <s id="N10A00"><emph type="italics"></emph>Mechanicam facultatem vere ac proprie eſſe <lb></lb>ſcientiam Mathematicam.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N10A09" type="head">
          <s id="N10A0B">ADDITIO QVARTA.</s>
        </p>
        <p id="N10A0E" type="main">
          <s id="N10A10">Vtrum autem Mechanica facultás pertineat ad ſcien<lb></lb>tiam phyſicam, an ad mathematicam, vel potius di<lb></lb>cenda ſit partim phyſica, partim mathematica, non leuem <lb></lb>habet difficultatem. </s>
          <s id="N10A19">Etenim eſſe ſcientiam phyſicam, illud <lb></lb>primo loco ſuadet, quia nimirum leius ſubiectum eſt phyſi<lb></lb>cum, vt graue, &amp; leue, <expan abbr="virtusq.">virtusque</expan> motium, ac detentiua, qua ſe<lb></lb>cundum locum ipſa cientur aut detinentur. </s>
          <s id="N10A2C">Secundo <expan abbr="quoniã">quoniam</expan> <lb></lb>de huiuſmodi ſubiecto agitur ſub ratione phyſica, prout ſcili<lb></lb>cet eſt mobile ſecundum locum natura ſua aut violentia; quæ <lb></lb>certè fit per impreſſionem impetus, eleuationem, vel tractio<lb></lb>nem, aut proiectionem, quæ ſunt operationes phyſicæ. </s>
          <s id="N10A3F">Ter<lb></lb>tio, quia ſiſtendo in puris principijs phyſicis, fatis <expan abbr="vidẽtur">videntur</expan> de<lb></lb>monſtrari omnia quæ pertractantur in ipſa mechanica ſcien<lb></lb>tia quoad propoſitiones vniuerſales, ac propriè ſcientificas. <lb></lb></s>
          <s id="N10A4D">Vt exempli gratia, grauia æqualia ex æqualibus <expan abbr="diſtãtijs">diſtantijs</expan> ęquè <lb></lb>ponderare, nec vnum poſſe in libra aliud vincere; nam ratio <lb></lb>huius eſt, quia actio debet eſſe ab inæquali proportione, vt ex <lb></lb>Ariſt.

habetur in phyſicis 1. de Generat. tex. 48. Similiter; <lb></lb>grauia faciliùs tolli beneficio trocleæ, aut vectis, quàm ſola <lb></lb>manu; &amp; id genus alia, reducuntur ad principium phyſicum <lb></lb>de maiori facilitate motus circularis, <expan abbr="maioreq.">maioreque</expan> velocitate <lb></lb>partium, quæ magis diſtant à centro circuli, eo quod maius <lb></lb>ſpatium percurrant in æquali tempore ac minus fulciantur. <lb></lb></s>
          <s id="N10A6D">Quapropter ipſemet Ariſtoteles phyſicè hic videtur tractate <lb></lb>quidquid ad vniuerſalem doctrinam mechanicam pertinet, <lb></lb>nec adhibere principia mathematica, niſi aliquando ad cla<lb></lb>riùs &amp; euidentiùs demonſtrandum, non ſecus ac in alijs quo<lb></lb>que tractationibus phyſicis conſueuit. </s>
          <s id="N10A78">Nihil enim prohibet, <lb></lb>idem diuerſis principijs plurium ſcientiarum oſtendi. </s>
        </p>
        <p id="N10A7D" type="main">
          <s id="N10A7F">Quarto, nam licet mechanica facultas, vt ab alijs traditur, <pb pagenum="18" xlink:href="005/01/026.jpg"></pb>paſſim vtatur demonſtrationibus mathematicis, id tamen fit, <lb></lb>vt deſcendat ad particularia, &amp; adaptetur ad praxim, vel vt <lb></lb>clarius innoteſcat veritas abſtractè conſiderata, cum per figu<lb></lb>ras obijcitur ſenſibus, ac metiri poſſumus magnitudinem &amp; <lb></lb>diſtantiam, vt appareat proportio requiſita ad motum ipſo<lb></lb>rum grauium. </s>
        </p>
        <p id="N10A91" type="main">
          <s id="N10A93">Quinto, nam eſtò Mechanica ſcientia pluries indigeat au<lb></lb>xilio mathematico, nec poſſit multa probare, niſi mutuetur <lb></lb>aliqua ex principijs geometricis, imò &amp; arithmeticis; non ta<lb></lb>men per hoc ſequitur, Mathematicis ſubalternari, ſicut nec <lb></lb>Phyſica, &amp; Theologia ſubalternantur Metaphyſicæ, quamuis <lb></lb>multa petant ex Metaphyſica. </s>
        </p>
        <p id="N10AA1" type="main">
          <s id="N10AA3">Ex alio verò capite, cum Philoſophi ac Mathematici om<lb></lb>nes, qui de hac facultate ſcripſerunt, eam ex Phyſica, &amp; Geo<lb></lb>metria ortam conſtituant, vt videre eſt apud Heronem, Pap<lb></lb>pum Alexandrinum, &amp; alios qui eos ſequuntur; potius ipſam <lb></lb>quaſi mixtam ex vtraque, ac tertiam quandam ſcientiam per <lb></lb>ſe eſſe videbitur, ſicut nonnullis hac tempeſtate viſum fuiſſe <lb></lb>affirmat Guidus Vbaldus in præfatione ſuorum mechanico<lb></lb>rum. </s>
          <s id="N10AB4">Et confirmari poſſet ex verbis illis Ariſtotelis iam ex<lb></lb>poſitis in fine huius textus, cum loquendo de mechanicis <lb></lb>problematibus ait: Sunt autem hæc neque naturalibus om<lb></lb>ninò quæſtionibus eadem, neque ſeiuncta valde, verùm ma<lb></lb>thematicarum contemplationum, <expan abbr="naturaliumq.">naturaliumque</expan> communia. <lb></lb></s>
          <s id="N10AC4">Quando quidem quod commune duobus eſt, vtriuſque natu<lb></lb>ram participat. </s>
        </p>
        <p id="N10AC9" type="main">
          <s id="N10ACB">Pro ſolutione tamen quæſtionis, notandum eſt, adhoc vt <lb></lb>vna ſcientia alteri ſubalternetur, duo præcipuè requiri, ad <lb></lb>quæ reducantur omnia quæ Ariſtoteles tradit 2. poſter. </s>
          <s id="N10AD2">tex. <lb></lb>58. &amp; ſequentibus. </s>
        </p>
        <p id="N10AD8" type="main">
          <s id="N10ADA">Primum eſt, vt quæ tractantur in ſcientia ſubalternata, non <lb></lb>poſſint <expan abbr="euidẽter">euidenter</expan> cognoſci, niſi ex ijs quæ traduntur ac <expan abbr="demõ-ſtrantur">demon<lb></lb>ſtrantur</expan> in ſcientia ſubalternante, à qua propterea ipſa ſcien<lb></lb>tia ſubalternata dicitur intrinſecè &amp; eſſentialiter dependere. <lb></lb></s>
          <s id="N10AEC">Ratio autem eſt, quia ſcientia ſubalternata cum non habeat <lb></lb>principia per ſe nota, &amp; immediata, ſicut illa quæ immediatè <pb pagenum="19" xlink:href="005/01/027.jpg"></pb>pendet ab habitu principiorum, loco illorum nititur conclu<lb></lb>ſionibus demonſtratis in ſuperiori ſcientia. </s>
          <s id="N10AF8">Et hac ratione <lb></lb>nihil demonſtratur in Perſpectiua, quod <expan abbr="nõ">non</expan> inferatur ex con<lb></lb>cluſionibus Geometriæ cui ipſa ſubordinatur; <expan abbr="nihilq.">nihilque</expan> in Mu<lb></lb>ſica, quod non nitatur concluſionibus ac principijs Arithme<lb></lb>ticæ cui ſimiliter ipſa ſubalternatur. </s>
        </p>
        <p id="N10B0B" type="main">
          <s id="N10B0D">Secundum requiſitum eſt, vt idem ſit obiectum ſubalter<lb></lb>natæ, ac ſubalternantis ſecundum aliquam rationem forma<lb></lb>lem. </s>
          <s id="N10B14">Quandoquidem ſi ſubiecta eſſent eſſentialiter diuerſa <lb></lb>ſecundum formalitatem qua cadunt ſub ſcientiam, non dare<lb></lb>tur tranſitus à ſcientia ſubalternata ad <expan abbr="ſubalternantẽ">ſubalternantem</expan>, vt do<lb></lb>cet Ariſtoteles; hoc eſt accipiendo ex illa propria principia <lb></lb>ac media ad probandum ſuas concluſiones; quia tam paſſio<lb></lb>nes demonſtrandæ de ſubiecto, quàm principia quæ ſunt <lb></lb>cauſæ intrinſecæ ipſarum <expan abbr="paſſionũ">paſſionum</expan>, debent eſſe maximè pro<lb></lb>pria &amp; connexa cum ipſo ſubiecto: nihil autem poteſt eſſe <lb></lb>maximè proprium duobus ſubiectis eſſentialiter diuerſis; ac <lb></lb>proinde ex connexione cum principijs vnius, inferri non po<lb></lb>teſt connexio alterius ad conficiendas demonſtrationes. </s>
          <s id="N10B33">Ea<lb></lb>dem ergo eſſentialiter debent eſſe ſubiecta ſubalternantis, ac <lb></lb>ſubalternatæ, ſaltem ſecundum aliquam rationem formalem, <lb></lb>quamuis alia ratione differant inter ſe. </s>
          <s id="N10B3C">Semper enim ratio <lb></lb>illa formalis ſub qua agitur de aliquo in ſcientia, vniuerſaliori <lb></lb>ac ſimpliciori modo conſideratur in ſubalternante, quàm in <lb></lb>ſubalternata, in qua ſemper contrahitur ab aliqua differentia <lb></lb>accidentali ſuperaddita, vt conſtat in Muſica reſpectu Arith<lb></lb>meticæ, &amp; in Perſpectiua reſpectu Geometriæ. </s>
          <s id="N10B49">Siquidem in <lb></lb>Arithmetica ſimpliciter conſideratur numerus ſecundum ſe, <lb></lb>in Muſica vero conſideratur numerus in ſono. </s>
          <s id="N10B50"><expan abbr="Similiterq.">Similiterque</expan> in <lb></lb>Geometria ſolum conſiderantur lineæ, in Perſpectiua vero <lb></lb>conſiderantur in viſu, quæ differentiæ putantur accidentales; <lb></lb>nam vt docet Ariſtoteles locis citatis, &amp; 13 metaph. </s>
          <s id="N10B5C">ſum. 1. <lb></lb>cap.

3. Muſica &amp; Perſpectiua non verſantur formaliter circa <lb></lb>ſonum &amp; viſum ſed circa numerum &amp; lineam de quibus agi<lb></lb>tur abſolutè in Arithmetica, &amp; Geometria. </s>
        </p>
        <p id="N10B68" type="main">
          <s id="N10B6A">Quibus poſitis, dicendum eſt, Mechanicam <expan abbr="facultatẽ">facultatem</expan> ab<pb pagenum="20" xlink:href="005/01/028.jpg"></pb>ſolutè ac totaliter non ſubalternari Philoſophiæ naturali, ſed <lb></lb>Mathematicæ; Ita ſenſit expreſsè Ariſtoteles in principio iam <lb></lb>explicato huius opuſculi, cum ait, ſubiectum quidem huius <lb></lb>facultatis eſſe Phyſicum, conſiderationem verò eſſe mathe<lb></lb>maticam. </s>
          <s id="N10B7E">Quod poſtea omnes Philoſophi, ac Mathematici <lb></lb>vniuerſaliter ſupponunt in diſtributione, ac ſub alternatione <lb></lb>Mathematicarum diſciplinarum, ſubordinando hanc ſcien<lb></lb>tiam Geometricæ. </s>
        </p>
        <p id="N10B88" type="main">
          <s id="N10B8A">Ratione verò probatur, nam quælibet ſcientia ſubalterna, <lb></lb>illi ſcicntiæ dicitur ſubalternari, cuius idem ſubiectum ſecun<lb></lb>dum aliquam rationem formalem conſiderat, cuiuſque con<lb></lb>cluſionibus vtitur tanquam principijs ad conficiendas pro<lb></lb>prias demonſtrationes; ſed ſcientia Mechanica circa idem <lb></lb>ſubiectum ſecundum aliquam rationem formalem verſatur <lb></lb>ac Geometria, ex <expan abbr="eaq.">eaque</expan> vt plurimum ſumit ſua principia ad <lb></lb>demonſtrandas mechanicas concluſiones. </s>
          <s id="N10B9F">Ergo Mechanica <lb></lb>facultas ſubalternatur Geometriæ &amp; non alteri ſcientiæ. </s>
          <s id="N10BA4">Ma<lb></lb>ior pater ex ſupra notatis. </s>
          <s id="N10BA9">Minor in qua eſt difficultas, pro<lb></lb>batur quoad priorem partem, ex eo; Nam cettum eſt, ipſum <lb></lb>corpus mobile graue, aut leue, quod conſtituitur ſubiectum <lb></lb>huius ſcientiæ, non conſiderari niſi ſecundum quantitatem, <lb></lb>ponderis quam habet, &amp; prout moueri aut detineri poteſt <lb></lb>tanta vel tanta virtute, ac mediante aliquo artificio. </s>
          <s id="N10BB6">Quo <lb></lb>fit vt proxima ratio ſecundum quam de illo agitur, ſit tum <lb></lb>quantitas ponderis illius, abſtrahendo à materia ponderante, <lb></lb>tùm quantitas virtutis mouentis aut detinentis, prout ſcilicet <lb></lb>vtraque quantitas coaptari, ac proportionari debet in ordine <lb></lb>ad motionem aut quietem artificioſam: ſeu prout quantitas <lb></lb>ponderis ſubſtat motioni, aut quieti artificioſæ, quam pro<lb></lb>pterea diximus, vltimò complere, &amp; <expan abbr="cõſtituere">conſtituere</expan> obiectum for<lb></lb>male huius ſcientiæ. </s>
          <s id="N10BCD">At huiuſmodi ratio formalis ſic expli<lb></lb>cata, manifeſtè inuoluit quantitatem abſtractam à materia, <lb></lb>ac ſpecialiter paſſionem quandam quantitatis continuæ ac <lb></lb>permanentis, quæ eſt obiectum Geometriæ; nempe artifi<lb></lb>cioſam mobilitatem &amp; quietem; imò talis mobilitas attendi<lb></lb>tur iuxta dimenſionem quantitatiuam ipſius mobilis, ac pro-<pb pagenum="21" xlink:href="005/01/029.jpg"></pb>portionem quam habet cum mouente, in tanta propinquita<lb></lb>te vel diſtantia; ac perſæpe fundatur in ipſa figura quantitatis <lb></lb>mobilis aut mouendæ. </s>
          <s id="N10BE3">Ergo ratio formalis ſub qua Mecha<lb></lb>nica facultas circa proprium ſubiectum verſatur, eandem eſ<lb></lb>ſentialiter rationem ſubiecti Geometriæ participat. </s>
        </p>
        <p id="N10BEA" type="main">
          <s id="N10BEC">Quod autem Mechanica facultas vtatur principijs. </s>
          <s id="N10BEF">proba<lb></lb>tis in Geometria, palam oſtendunt ipſæ demonſtrationes me<lb></lb>chanicæ, quæ ferè omnes immediatè nituntur propoſitioni<lb></lb>bus, ac theorematibus demonſtratis in illa, deinde reſoluun<lb></lb>tur in eadem principia geometrica; <expan abbr="ſiquidẽ">ſiquidem</expan> præcipuè fundan<lb></lb>tur in proprietatibus, ac paſſionibus circuli quæ ſanè demon<lb></lb>ſtrantur principijs geometricis, vt pręſertim patet ex tertio ac <lb></lb>ſexto <expan abbr="elementorũ">elementorum</expan> Euclidis. </s>
          <s id="N10C09">Rurſus principia Mechanica, quæ <lb></lb>traduntur ab Archimede, <expan abbr="alijsq.">alijsque</expan> Mechanicis, vel ſunt omninò <lb></lb>geometrica, vel ſumuntur ex geometricis. </s>
          <s id="N10C14">Vt grauia æqua<lb></lb>lia ex æqualibus diſtantijs æquè ponderare: Aequalia verò <lb></lb>grauia ex inæqualibus diſtantijs, non æquè ponderare, ſed <lb></lb>præponderare ad graue ex maiori diſtantia. </s>
          <s id="N10C1D">Et æqualibus ſi<lb></lb>milibusque, figuris planis inter ſe coaptatis, centra quoque <lb></lb>grauitatum inter ſe coaptari oportere. </s>
          <s id="N10C24">Et ſimilia vt vi<lb></lb>dere eſt apud ipſum Archimedem, Pappum, &amp; alios <lb></lb>Auctores. </s>
        </p>
        <p id="N10C2B" type="main">
          <s id="N10C2D">Ad primum igitur argumentum in contrarium Reſponde<lb></lb>tur, ſubiectum Mechanicæ facultatis eſſe quidem phyſicum <lb></lb>in genere entis, non tamen in genere ſcibilis, nempe ſub ra<lb></lb>tione qua de illo agitur in hac ſcientia. </s>
          <s id="N10C36">Quare licet <expan abbr="ſubiectũ">ſubiectum</expan> <lb></lb>materiale huius facultatis, quod eſt graue, &amp; leue, ſeu quan<lb></lb>titas ponderis cuiuſque corporis mobilis ſecundum locum, <lb></lb>connotet paſſionem quamdam corporis naturalis, quod con<lb></lb>ſtituitur ſubiectum adæquatum Phyſicæ; cum tamen non <expan abbr="cõ-ſideretur">con<lb></lb>ſideretur</expan> hic per habitudinem ad illud, pertinere non poteſt <lb></lb>ad ſcientiam phyſicam; ſicut nec ipſa quantitas, quæ conſti<lb></lb>tuitur ſubiectum adæquatum totius facultatis mathematicæ, <lb></lb>quamuis in ſe ſit affectio corporis naturalis, &amp; paſſio ſubſtan<lb></lb>tiæ corporeæ, de <expan abbr="illaq.">illaque</expan> abundè etiam tractetur in Phyſica. <lb></lb></s>
          <s id="N10C58"><expan abbr="Idemq.">Idemque</expan> exemplificari poteſt in Muſica &amp; Perſpectiua, quarum <pb pagenum="22" xlink:href="005/01/030.jpg"></pb>ſubiecta materialia non minus ſunt phyſica, conſideratio ve<lb></lb>rò mathematica. </s>
          <s id="N10C65">Ac tandem apertiſſimè conſtare poteſt in<lb></lb>ductione partium eiuſdem facultatis Mechanicæ. </s>
          <s id="N10C6B">Nam licet <lb></lb>Centrobarica verbi gratia, vel Machinaria, non agat niſi de <lb></lb>ſubiectis phyſicis, tota tamen eorum conſideratio eſt mathe<lb></lb>matica, geometricè procedendo ad <expan abbr="demonſtrãdas">demonſtrandas</expan> dimenſio<lb></lb>nes, ſiguras, diſtantias, ponderoſitatem, vires, ac motum ip<lb></lb>ſorum. </s>
          <s id="N10C7C">Similites ſpiritalis tractatio quamuis agat de aere, ac <lb></lb>de coniunctione aeris cum alijs elementis ad multos vitæ no<lb></lb>ſtræ vſus, quæ res phyſicæ in ſe ſunt, nihilominus ad mathe<lb></lb>maticam contemplationem pertinet, &amp; ab Herone mathe<lb></lb>maticè cum ſuis demonſtrationibus traditur, contemplando <lb></lb>proportionem, numerum, magnitudinem, diſtantiam, ordi<lb></lb>nem, figuram, &amp; cauſas effectuum, qui ex incluſo aere profi<lb></lb>ciſcuntur. </s>
          <s id="N10C8D">Quorum omnium ratio eſt, quia in his non atten<lb></lb>ditur ſubiectum materialiter ſumptum in eſſe rei, ſed formali<lb></lb>tas qua cadit ſub ſcientiam, ſeu ratio ſub que agitur de ille, <lb></lb>quæ dicitur ſubiectum, vel obiectum formale; <expan abbr="cumq.">cumque</expan>, hoc in <lb></lb>propoſito pertineat ad Mathematicum, ſequitur, facultatem <lb></lb>ipſam ſiue ſcientiam mechanicam, eſſe verè mathematicam. </s>
        </p>
        <p id="N10C9A" type="main">
          <s id="N10C9C">Ad ſecundum Reſpondetur, motionem &amp; quietem <expan abbr="grauiũ">grauium</expan> <lb></lb>&amp; leuium, ſiue ex natura ſua, ſiue ex aliqua violentia vtraque <lb></lb>proficiſcatur, eſſe quidem paſſiones phyſicas eorum prout <lb></lb>corpora naturalia ſunt, non tamen conſiderari à Mechanicis <lb></lb>vt tales paſſiones ſunt, ſed prout obtineri poſſum ab illis tan<lb></lb>quam finis intentus, mediante aliquo artificio. </s>
          <s id="N10CAD">Vnde ratio <lb></lb>formalis ſub qua grauia &amp; leuia conſtituuntur obiecta huius <lb></lb>ſcientiæ, non eſt prout mobilia ſunt ſecundum locum, aut <lb></lb>quieſcere poſſunt, abſolutè loquendo; ſed prout artificiosè <lb></lb>moueri aut quieſcere poſſunt, loquendo modum quo mo<lb></lb>uenda ſunt, vel detinenda, &amp; circa quem formaliter ors ipſa <lb></lb>verſatur ad finem intentum. </s>
        </p>
        <p id="N10CBE" type="main">
          <s id="N10CC0">Ad tertium Reſpondetur, nec omnia, nec ſatis demonſtra<lb></lb>ri poſſe ex principijs phyſicis in hac ſcientia. </s>
          <s id="N10CC5">Porrò licet non<lb></lb>nulla de graui &amp; leui ſupponantur, vel etiam probentur ex <lb></lb><gap></gap>is, cætera tamen vt plurimum &amp; exactè non <expan abbr="demonſtrãtus">demonſtratus</expan> <pb pagenum="23" xlink:href="005/01/031.jpg"></pb>niſi ex principijs geométricis, quare ficat de lride multa <lb></lb>pertractantur in Phyſica, quod ramen non tollit omnimodam <lb></lb>eius cognitionem ad Perſpectiuam referri, ita quamuis mul<lb></lb>ta de graui &amp; leui ſumantur ex phyſicis, hoc non obſtat quo<lb></lb>minus prout artificiosè mobilia ſunt, ex profeſſo &amp; omnino <lb></lb>ſolum cognoſcantur in hac ſcientia ex principijs mathemati<lb></lb>cis. </s>
          <s id="N10CE7">Et ſic, grauia æqualia ex æqualibus diſtantijs æquè pon<lb></lb>derare, <expan abbr="vnumq.">vnumque</expan> in libra non poſſe aliud vincere, non ſatis <lb></lb>probatur ex illo principio physico, quod àctio debeat eſſe ab <lb></lb>inæquali proportione. </s>
          <s id="N10CF4">Quando quidem inæqualitas diſtan<lb></lb>tiæ non tollit æqualitatem ponderis, nec proportionem illius <lb></lb>ad alterum, ſi ſecundum ſe ac phyſicis conſideretur, tollit <lb></lb>autem ſe mathematicè demonſtratur, maiorem diſtantiam à <lb></lb>centro, vbi grauia falciantur, grauitatem, vel potiùs effe<lb></lb>ctum illius, <expan abbr="actumq.">actumque</expan> ponderandi in ipſis grauibus augere. <lb></lb></s>
          <s id="N10D08">Item maior velocitas, ac facilitas quam experimur in motu <lb></lb>circulari earum partium, quæ magis diſſant à centro, non <lb></lb>probatur à priori, nec demonſtratur ex eo quod maius ſpa<lb></lb>tium percurrant in æquali tempore, nam hoc eſt idem per <lb></lb>diuerſa explicare. </s>
          <s id="N10D13">Demonſtratur autem per cauſam, &amp; à <lb></lb>priori, ex illo principio mathematico, quod quanto magis li<lb></lb>neæ à centro diſceſſerint, magis participant de motu recto <lb></lb>ac naturali, <expan abbr="minusq.">minusque</expan> retrahuntur in circumuolutione circull, <lb></lb>at ſuo lo eo explicabitur ex Ariſtotele qui ſanè in hoc <expan abbr="alijsq.">alijsque</expan> <lb></lb>dogmatibus mechanicis non vtitur demonſtrationibus geo<lb></lb>metricis ad exemplum, vt in logica vel phyſica, neque ad <lb></lb>confirmationem veritatis probatæ; ſed ve abſolutè probet <lb></lb>quod aſſumpſerat, <expan abbr="quodq.">quodque</expan> aliter omninò probare nequiret. </s>
        </p>
        <p id="N10D32" type="main">
          <s id="N10D34">Ex quibus fæcile apparet quid reſpaondendum ſit ad quar<lb></lb>tum &amp; quintum argumentum, nempe principia mathemati<lb></lb>ca non modo in mechanica ſcientia deſeruire ad maiorem <lb></lb>claritatem doctrinæ, &amp; vt hæc aptetur ad praxim circa parti<lb></lb>cularia, ſed abſolutè ad demonſtrandas ſuas concluſiones in <lb></lb>vniuerſum, quas quippe aliter non poſſet omninò probare. <lb></lb></s>
          <s id="N10D44">Id quod non ſolum verificatur in vni vel altera concluſione, <lb></lb>ſed ferè in omnibus, vt in progreſſu conſtabit. </s>
        </p>
        <pb pagenum="24" xlink:href="005/01/032.jpg"></pb>
        <p id="N10D4D" type="main">
          <s id="N10D4F">Quod <expan abbr="tandẽ">tandem</expan> afferebatur de ortu Mechanices ex Phyſica, <lb></lb>&amp; Mathematica ad probandum eſſe ſcientiam ex vtraque <lb></lb>conflatam, ſi rectè conſideretur, nullius eſt momenti; nam <lb></lb>vere dicitur ex Phyſica ſumpſiſſe ſubiectum, &amp; ex Geome<lb></lb>tria principia quibus in ſuis demonſtrationibus procederet; <lb></lb>ex quo tamen non ſequitur, ipſam veluti mixtam quandam <lb></lb>reſultare ſcientiam, partim ſcilicet Phyſicam, partim verò <lb></lb>Mathematicam; tum quia ſpecificatio ſcientiarum vt diximus <lb></lb>non attenditur ex ſubiecto materiali, ſed ex obiecto formali; <lb></lb>tum etiam, quia nequit vna eademque ſcientia, pluribus ſcien<lb></lb>tijs omnino diuerſis ſubalternari, cum vnitas ipſius attenda<lb></lb>tur penes vnitatem eiuſdem obiecti formalis, quod mutuari <lb></lb>debet vel ex vna, vel ex altera ſuperiori ſcientia. </s>
          <s id="N10D6E">Quare cum <lb></lb>Ariſtoteles ait, Mechanica problemata eſſe Mathematicarum <lb></lb>quæſtionum, naturaliumque communia, non intellexit eſſe <lb></lb>veluti aggregata &amp; <expan abbr="cõflata">conflata</expan> ex illis vtriſque. </s>
          <s id="N10D7B">Non enim <expan abbr="cõmu-nia">commu<lb></lb>nia</expan> conflantur ex particularibus, ſed particularia ex commu<lb></lb>nibus ac vniuerſalibus. </s>
          <s id="N10D86">Vnde potius ſenſit Philoſophus, Me<lb></lb>chanicam facultatem de his rebus agere, quæ communes ſunt <lb></lb>naturalibus ac Mathematicis quæſtionibus (quamuis ſub di<lb></lb>uerſa ratione formali) cuiuſmodi ſunt quantitas ponderis, ſeu <lb></lb>ipſa ponderantia, quæ dicuntur grauia &amp; leuia, ac virtus qua <lb></lb>ipſa mouentur aut detinentur. </s>
          <s id="N10D93">Siquidem de his omnibus <lb></lb>multa quæruntur in phyſicis, prout ſunt affectiones corporis <lb></lb>naturalis, vel corpora quædam naturalia; <expan abbr="multaq.">multaque</expan> pa<lb></lb>riter in mathematicis, prout dimenſionem habent <lb></lb>quantitatiuam, aut virtutis, abſtrahendo <lb></lb>ab hac vel illa materia, <expan abbr="peculiaresq.">peculiaresque</expan> <lb></lb>fortiuntur paſſiones in ordine <lb></lb>ad motum artifi<lb></lb>cioſum. </s>
        </p>
        <pb pagenum="25" xlink:href="005/01/033.jpg"></pb>
        <p id="N10DB2" type="head">
          <s id="N10DB4"><emph type="italics"></emph>Quæ nam deſcriptio quidditatiua huius facul<lb></lb>tatis colligatur ex dictis, &amp; quo pacto <lb></lb>ab alijs ſcientijs diſtinguatur.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N10DBF" type="head">
          <s id="N10DC1">ADDITIO QVINTA.</s>
        </p>
        <p id="N10DC4" type="main">
          <s id="N10DC6">Qvæ dicta ſunt recapitulantes, hanc huius facultatis de<lb></lb>ſcriptionem colligere poſſumus ad explicandam to<lb></lb>tam quidditatem ipſius. </s>
          <s id="N10DCD">Mechanica facultas, eſt <lb></lb>practica ſcientia, quæ geometricis demonſtrationibus nixa <lb></lb>verſatur circa quantitatem ponderis grauium &amp; leuium, <expan abbr="vir-tutiſq.">vir<lb></lb>tutiſque</expan> qua artificiosè ac mirabiliter moueri debent, aut quie<lb></lb>ſcere ad finem intentum ab Artifice. </s>
          <s id="N10DDD">In qua deſcriptione <lb></lb>ponitur (practica ſcientia) loco generis, in quo conuenit cum <lb></lb>Philoſophia morali, cum Logica, ac Medicina; per idemque <lb></lb>diſtinguitur à ſcientijs ſpeculatiuis, quæ ſane non ordinantur <lb></lb>ad praxim, &amp; à ſeruilibus artibus, quæ nullam includunt ratio<lb></lb>nem ſcientiæ, vt ſupra explicuimus. </s>
          <s id="N10DEA">Per particulam verò <lb></lb>(geometricis demonſtrationibus nixa) explicatur quædam <lb></lb>differentia, qua talis ſcientia conuenit quidem cum ſcientijs <lb></lb>Mathematicis ſubalternatis Geometriæ, vt Perſpectiua, Geo<lb></lb>deſia, &amp; Aſtronomia; diſtinguitur autem ab illis quæ vel <lb></lb>non ſubalternantur Geometriæ, vt Muſica &amp; Arithmetica, <lb></lb>vel nullo modo ſunt Mathematicæ, vt Metaphyſica, Philoſo<lb></lb>phia naturalis aut moralis, Medicina ac Logica. </s>
          <s id="N10DFC">Denique <lb></lb>per cæteras particulas explicatur vltima differentia, ex pro<lb></lb>prio obiecto ac fine deſumpta, qua certè huiuſmodi ſcientia <lb></lb>optimè diſtinguitur ab illis quæ non verſantur circa quantita<lb></lb>tem aliquam; tum ab illa contemplatione Logica, aut Me<lb></lb>taphiſica, quæ tantum verſatur circa quantitatem prædica<lb></lb>mentalem; item à Phyſica quæ circa quantitatem ſolum <lb></lb>verſatur in quantum eſt affectio corporis naturalis, &amp; in ordi<lb></lb>ne ad principium motus &amp; quietis naturalis. </s>
          <s id="N10E0F">Rurſus non <lb></lb>minus diſtinguitur, eadem differentia, à reliquis diſciplinis <lb></lb>Mathematicis, nam licet conueniat cum illis in hoc quod eſt <pb pagenum="26" xlink:href="005/01/034.jpg"></pb>verſari circa quantitatem modo quodam abſtracto à materia, <lb></lb>illam tamen contrahit ad quantitatem ponderis grauium, &amp; <lb></lb>leuium, ac virtutis qua debent moueri, ſicet non determi<lb></lb>net materiam ponderantem, aut virtutis mouentis. </s>
          <s id="N10E21">Per <lb></lb>quod ſanè primo diſtinguitur ab Arithmetica &amp; Muſica, quæ <lb></lb>verſatur circa quantitatem diſcretam; non autem continuam <lb></lb>ſicut grauium ac lenium; deinde à Geometria propriè dicta, <lb></lb>&amp; a Stereometria quæ verſantur circa quantitatem <expan abbr="cõtinuam">continuam</expan> <lb></lb>planorum ac ſolidorum, abſtrahendo à grauitate aut ſeuitate, <lb></lb>&amp; à quocunque motu illorum. </s>
          <s id="N10E34">Denique diſtinguitur à Per<lb></lb>ſpectiua quæ ſanè quantitatem conſideran in lineis viſualibus, <lb></lb>&amp; à Geodeſia quæ illam conſiderat in aceruis tanquam co<lb></lb>nis, vel in puteis tanquam cylindris; tandem ab Astronomias <lb></lb>quæ illam conſiderat in corporibus celeſribus eorumque <lb></lb>diſtantijs, ac motibus à natura præſcriptis. </s>
          <s id="N10E41">Cum igitur per <lb></lb>idem res <expan abbr="cõſtituatur">conſtituatur</expan> in eſſe ſui, per quod diſtinguitur ab alijs, <lb></lb>vt receptiſſimum eſt in doctrina Peripatetica, ſatis videtur <lb></lb>explicata conſtitutio &amp; eſſentia huius ſcientiæ per traditam <lb></lb>definitionem ſeu quidditatiuam deſcriptionem, cum per eam <lb></lb>conſtet ſufficienter ab alijs ſcientijs ac facultatibus diſtingui. </s>
        </p>
        <p id="N10E52" type="head">
          <s id="N10E54"><emph type="italics"></emph>De vnitate ſcientiæ Mechinicæ <lb></lb>eiuſque partibus.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N10E5D" type="head">
          <s id="N10E5F">ADDITIO SEXTA,</s>
        </p>
        <p id="N10E62" type="main">
          <s id="N10E64">Ex peditis ijs quæ ad quæſtionem, an ſit, &amp; quid ſit Hæc <lb></lb>ſcientia, pertinere videbantur, ſequitur inquirendum, <lb></lb>quotuplex ſit; vtrum ſcilicet ſit vna vel multiplex, &amp; quas <lb></lb>habeat partes. </s>
          <s id="N10E6D">Qua in re ſupponimus primo, ſermonem eſſe <lb></lb>de ſcientia totali, prout eſt aggregatum quoddam ex omni<lb></lb>bus ſcientijs partialibus, ſiue actualibus, ſiue habitualibus, <lb></lb>nempe ex omnibus concluſionibus demonſtratis de ſubiecto <lb></lb>adæquato, circa quod huiuſmodi facultas verſatur. </s>
          <s id="N10E78">Deinde <lb></lb>ſupponimus vnitatem ſcientiæ totalis de ſumi, tùm ex vnitate <lb></lb>ordinis quo concluſiones ac partes illius coaptantur inter ſe, <pb pagenum="27" xlink:href="005/01/035.jpg"></pb>ad componendam integram ſcientiam de eodem ſubiecto <lb></lb>materiali ac paſſionibus illius; tum ex vnitate obiecti form<lb></lb>lis circa quod omnes ſcientiæ partiales conueniunt. </s>
        </p>
        <p id="N10E88" type="main">
          <s id="N10E8A">Quibus poſitis dicendum eſt, Mechanicam facultatem eſ<lb></lb>ſe vnicam ſcientiam totalem vnitate ordinis, ac obiecti for<lb></lb>malis, ſub quà ſcientia totali tanquam ſub ſpecie atoma con<lb></lb>tinentur omnes concluſiones, vel ſcientiæ partiales Mecha<lb></lb>nicæ. </s>
          <s id="N10E95">Id quod facile probatur ex eo, quia omnis Mechani<lb></lb>ca cognitio verſatur circa eandem rationem formalem obie<lb></lb>cti adęquati, nempe quantitatem ponderis artificiosè mouen<lb></lb>di, aut detinendi, licet non de eodem pondere, vel de eiſdem F<lb></lb>ponderantibus in qualibet parte huius ſcientiæ persè agatur. <lb></lb>Deinde probatur, quia omnes concluſiones demonſtratæ in <lb></lb>hac ſcientia, <expan abbr="ordinãtur">ordinantur</expan> ad plenam cognitionem obiecti expli<lb></lb>cati, ſiue per contemplationem partium illius, agendo de <lb></lb>hoc, vel illo graui, aut leui quod moueri debet, aut quieſce<lb></lb>re, ſiue per contemplationem plurium paſſionum quas idem <lb></lb>ſubiectum patitur, quatenus cadit ſub artificioſam motionem <lb></lb>aut quietem. </s>
          <s id="N10EB3">Rurſus plurimæ concluſiones in ea demonſtra<lb></lb>tæ, deſeruiunt tanquam principia in demonſtrationibus reli<lb></lb>quarum; vnde talis apparet ordo &amp; connexio inter illas ad <lb></lb>inuicem, vt indubitanter ad eandem omninò ſcientiam tota<lb></lb>lem in ſpecie ſumptam pertinere ab omnibus dicantur. </s>
        </p>
        <p id="N10EBE" type="main">
          <s id="N10EC0">Diuiditur autem hæc ſcientia totalis in plures partes ve<lb></lb>luti integrantes, ratione ſubiecti. </s>
          <s id="N10EC5">Porrò cum eius ſubiectum <lb></lb>non ſit vna &amp; eadem indiuiſibilis entitas, ſed multiplex ſub <lb></lb>ratione illa communi iam explicata corporis artificiosè mo<lb></lb>bilis, tot erunt partes huius ſcientiæ, quot ſunt partes ipſius <lb></lb>adæquati ſubiecti de quo demonſtrat qua ratione moueri de<lb></lb>beat aut quieſcere. </s>
          <s id="N10ED2">Et licet partes ipſæ adæquati ſubiecti <lb></lb>comparari poſſent ad illud tanquam ſpecies ad genus, ſub <lb></lb>quo continentur, vt ſingula elementa, aut mixta reſpectu cor<lb></lb>poris in vniuerſum quod artificiosè moueri poteſt, aut quie<lb></lb>ſcere; nihilominus cum ratio ſpecificans ſcientiam, in præſenti <lb></lb>non attendatur penes propriam differentiam ſubiecti mate<lb></lb>rialis, ſed penes rationem formalem ſub qua conſideratur in <pb pagenum="28" xlink:href="005/01/036.jpg"></pb>ipſa ſcientia; hinc eſt, vt commodius ac magis propriè ſpe<lb></lb>cies ipſæ corporum grauium; ac leuium comparentur ad gra<lb></lb>ue &amp; leue in communi, tanquam partes integrantes ad totum <lb></lb>quod conſtituunt; præſertim cum etiam genus dicat totum <lb></lb>confusè in compoſitione Metaphyſica vt eſt communis do<lb></lb>ctrina ſumpta ex Ariſtotele lib.

5 Met. cap.

20. </s>
        </p>
        <p id="N10EF2" type="main">
          <s id="N10EF4">Iuxtà hæc igitur Mechanica ſcientia primò diuiditur in <lb></lb>Centrobaricam quæ quidem centrum grauitatis in quolibet <lb></lb>corpore ſpeculatur, &amp; in Machinariam quæ verſatur circa <lb></lb>machinamenta quibus ipſa corpora mouentur, aut detinen<lb></lb>tur, ſiue grauia ſint, ſiue leuia. </s>
          <s id="N10EFF">Rurſus Centrobaricam comi<lb></lb>tatur, ab <expan abbr="eaq.">eaque</expan> dependet Sphæropœia, quæ motum circa cen<lb></lb>trum ſphæricorum corporum contemplatur, <expan abbr="modumq.">modumque</expan> quo <lb></lb>ipſa conficienda ſunt exhibet ad imitationem corporum cœ<lb></lb>leſtium, prout Archimedem confeciſſe traditur; quem etiam <lb></lb><arrow.to.target n="marg12"></arrow.to.target> librum de Sphęropœia edidiſſe refert Carpus Antiochenſis <lb></lb>apud Pappum Alexandrinum. </s>
          <s id="N10F19">Machinaria verò diuiditur in <lb></lb>Manganariam, cuius ope, exigua virtute, ingentia transferun<lb></lb>tur pondera, &amp; in Organopeticam, quæ inſtrumenta omnia <lb></lb>ad corporum motionem, aut detentionem accommodata ac <lb></lb>fabrefacta conſiderat, <expan abbr="modumq.">modumque</expan> quo fieri debent rationabili<lb></lb>ter tradit. </s>
          <s id="N10F2A">Sub Manganaria continetur Mechanopætica, quæ <lb></lb>aquam ex imis facilè haurire ac in <expan abbr="altũ">altum</expan> tollere docet, &amp; ſiqua <lb></lb>eſt alia ſpeculatio quæ ad corpus aliquod <expan abbr="leuãdum">leuandum</expan> aut tranſ<lb></lb>ferendum ordinatur. </s>
          <s id="N10F3B">Sub Organopetica verò continetur Po<lb></lb>liorcetica, quæ verſatur circa bellicas machinas, vt Arietes ad <lb></lb>quatiendos muros, vel Catapultas &amp; alias quibus ſagittæ, la<lb></lb>pides, ac tela, in longiſſima viæ ſpatia emittuntur, &amp; videre <lb></lb>eſt apud Athenæum, Heronem mechanicum, &amp; Apolliodo<lb></lb>rum; &amp; in Thaumaturgicam, de qua Hero Alexandrinus, <lb></lb>quæque tandem diuiditur in tres partes, quarum prima ver<lb></lb>ſatur circa clepſydras, fiſtulas, varioſque ductus, quibus ex <lb></lb>vno vaſe in aliud aqua transfunditur, aut foris emittitur ad <lb></lb>conſtituendas fontes artificiales, aliaſque commoditates prę<lb></lb>ſtandas. </s>
          <s id="N10F52">Secunda verò docet quo pacto rotis, neruis, tim<lb></lb>panis, <expan abbr="alijsq.">alijsque</expan> inſtrumentis motus veluti animatus præſtetur <pb pagenum="29" xlink:href="005/01/037.jpg"></pb>inſenſibilibus, vt fertur de ſtatua Dedali ac Vulcani, de Ar<lb></lb>chitæ columba, ac ſimilibus. </s>
          <s id="N10F62">Tertia modum tradit, quo ex <lb></lb>incluſo aere varij emittantur ſonitus ad morum vel percuſſio<lb></lb>nem aquę, vt de ſerpentum ſibilis, ac volucrum cantibus, <expan abbr="hu-manisq.">hu<lb></lb>manisque</expan> vocibus imitatis, à pluribus enarratur: de que armo<lb></lb>nia quam reddebant argentei remi celeberrimi illius nauigij <lb></lb>Cleopatræ Aegypti Reginæ cum aquam offenderent, ob ſpi<lb></lb>ritum inter thecas eorum reſeratum, qui agitatione remigum, <lb></lb><expan abbr="aquarumq.">aquarumque</expan> percuſſione per varia <expan abbr="artificioſaq.">artificioſaque</expan> foramina exire <lb></lb>cogebatur. </s>
          <s id="N10F80">Et hæc de diuiſione ſeu partibus Mechanicæ fa<lb></lb>cultatis attigiſſe ſufficiat, vt omittamus alias, quæ non tàm <lb></lb>propriè partes illius, quàm annexæ, aut mixtæ facultates vi<lb></lb>dentur, vt Architectonica, quæ licet multum occupetur in <lb></lb>conſideratione artificioſæ motionis, aut quietis grauium &amp; <lb></lb>leuium, vlterius tamen huiuſmodi conſiderationem ordinat <lb></lb>ad opus conſtruendum ex illis, tanquam ad proprium finem, <lb></lb>&amp; obiectum primarium: Vnde Vitruuius potius ipſam Ma<lb></lb>chinariam facultatem, partem ſeu portionem facit Archite<lb></lb>ctonicæ. </s>
          <s id="N10F95">Item Nautica quæ licet contempletur artificioſam <lb></lb>motionem, aut quietem nauigij eiuſque membrorum, quæ <lb></lb>certè grauia aut leuia ſunt; quia tamen hæc conſiderat in or<lb></lb>dine ad incolumem tranſuectionem, inter Mechanicas abſo<lb></lb>lutè, &amp; communiter non connumeratur. </s>
          <s id="N10FA0">Verum cum talis <lb></lb>differentia valde accidentaria ſit &amp; ab extrinſeco fine deſum<lb></lb>pta, non minus fortaſſe inter Mechanicas facultates propriè <lb></lb>poterit <expan abbr="cõputari">computari</expan>. </s>
          <s id="N10FAD">Non enim apparet in quo eſſentialiter diffe<lb></lb>rat artificioſa tranſuectio quæ per nauim fit, ab ea, <lb></lb>quæ per plauſtrum, aut currum; neque <lb></lb>intereſt ſi per aquas, an per aera <lb></lb>moles aut pondera tran<lb></lb>sferantur. </s>
        </p>
        <pb pagenum="30" xlink:href="005/01/038.jpg"></pb>
        <p id="N10FBE" type="margin">
          <s id="N10FC0"><margin.target id="marg12"></margin.target><emph type="italics"></emph>Lib.<emph.end type="italics"></emph.end> 8. <emph type="italics"></emph>Ma<lb></lb>th. <gap></gap>.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N10FD3" type="head">
          <s id="N10FD5"><emph type="italics"></emph>Quem gradum perfectionis, aut dignitatis fa<lb></lb>cultas Mechanica obtineat inter ſcientias.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N10FDE" type="head">
          <s id="N10FE0">ADDITIO SEPTIMA.</s>
        </p>
        <p id="N10FE3" type="main">
          <s id="N10FE5">Svpereſt vt qualis hæc facultas ſit, quamque dignitatem <lb></lb>inter cæteras, artes ac ſcientias obtineat, videamus. </s>
          <s id="N10FEA">Et <lb></lb>quidem ſi receptiſſimam Philoſophi doctrinam ſpectemus, <lb></lb>triplici ex capite explorandum id eſſe comperiemus. </s>
          <s id="N10FF1">Nempe <lb></lb>ex fine ad quem ſcientia ex ſe ordinatur, &amp; obiecto circa <lb></lb>quod verſatur; &amp; ex certitudine aut euidentia qua procedit. <lb></lb></s>
          <s id="N10FF9">Nam primo Met. cap. <gap></gap>. </s>
          <s id="N11000">Scientiarum, illam, quæ gratia ſui ip<lb></lb>ſius eſt, &amp; propter ipſum ſcire, vt omnis ſcientia ſpeculatiua, <lb></lb>præferendam eſſe, ait, illi, quæ aliorum gratia eligitur, vt eſt <lb></lb>omnis ſcientia practica. </s>
          <s id="N11009">Deinde ibidem &amp; clarius lib.

p. </s>
          <s id="N1100C">de <lb></lb>anima cap.

1. Notitiarum vel ſcientiarum, alteram altera ait, <lb></lb>eſſe præſtantiorem, aut ſecundum certitudinem, aut ex eo <lb></lb>quod meliorum aut mirabiliorum ſit, quod etiam docuerat <lb></lb>lib.

8. Topic. cap.

2. Inquiens, ſcientiam ſcientia eſſe melio<lb></lb>rem, aut eo quod exactior eſt, aut quod meliorum. </s>
          <s id="N1101B">Per me<lb></lb>liora autem intelligit tum per ſe nobiliora, tum etiam ſupe<lb></lb>riora, quæ ſunt vniuerſaliora, ac ſimpliciora. </s>
        </p>
        <p id="N11022" type="main">
          <s id="N11024">Ex quo triplici capite facile intelligemus, <expan abbr="Mechanicã">Mechanicam</expan> facul<lb></lb><expan abbr="tatẽ">tatem</expan> <expan abbr="inferiorẽ">inferiorem</expan> <expan abbr="gradũ">gradum</expan> perfectionis obtinere inter Mathematicas <lb></lb>diſciplinas, ac ſcientias omnes merè ſpeculatiuas ſecundum <lb></lb>eam partem, qua merè ſpeculatiuæ, ac demonſtratiuæ ſcien<lb></lb>tiæ ſunt, vt Phyſica ac Metaphyſica: perfectiorem tamen eſſe <lb></lb>multis ſcientijs practicis, vt Agricultura, Architectura, Nau<lb></lb>tica, ſi modo ab illa diſtinguitur, &amp; alijs huiuſmodi. </s>
        </p>
        <p id="N11042" type="main">
          <s id="N11044">Id quod planum fieri poteſt ſigillatim diſcurrendo per ſin<lb></lb>gulas ſcientias enumeratas. </s>
          <s id="N11049">Nam quod attinet ad Mathema<lb></lb>ticas, Arithmeticam, Geometriam, Aſtrologiam, Muſicam, <lb></lb>ac Perſpectiuam, &amp; ſi quæ ſunt aliæ huiuſmodi; nulli dubium <lb></lb>eſt, eas omnes præſtantiores eſſe ſcientia Mechanica; tum <lb></lb>quia ſunt gratia ſui, hoc eſt merè ſpeculatiuæ, ac de nobilio-<pb pagenum="31" xlink:href="005/01/039.jpg"></pb>ribus, ſeu amplioribus, ac ſimplicioribus ſubiectis pertractant, <lb></lb>vt per ſe patet; tum etiam quia vel parem, vel maiorem cer-<lb></lb>titudinem, &amp; euidentiam habent, præſertim illæ, quibus ipſa <lb></lb>Mechanica ſubalternatur, &amp; à quibus accipit ſua principia, <lb></lb>vt Geometria ac Stereometria. </s>
          <s id="N11061">Quandoquidem immedia<lb></lb>tius attingunt primam rationem aſſentiendi, in qua fundatur <lb></lb>tota euidentia. </s>
          <s id="N11068">Vnde vniuerſaliter colligit Ariſtoteles primo <lb></lb>Metaphyſices cap.

2. Omnem ſcientiam ſubalternantem, per<lb></lb>fectiorem eſſe ſcientia ſubalternata. </s>
        </p>
        <p id="N1106F" type="main">
          <s id="N11071">Quod verò attinet ad Phyſicam, ac Metaphyſicam, idem <lb></lb>ſimiliter conſtat ex longe maiori nobilitate obiecti, <expan abbr="modoq.">modoque</expan> <lb></lb>indagandi ſpeculatiuo, quo ipſæ circa illud verſantur, etiamſi <lb></lb>non ſemper parem <expan abbr="obtineãt">obtineant</expan> certitudinem, &amp; euidentiam. <lb></lb></s>
          <s id="N11083">Quod nihil vtique obſtat, cum in ſententia Ariſtotelis lib.

1. <lb></lb>de par. </s>
          <s id="N11088">animal. </s>
          <s id="N1108C">cap.

5. hoc quod eſt, res illas ſuperiores leui<lb></lb>ter tantum nos poſſe attingere, non tollat eius cognoſcendi <lb></lb>generis excellentiam, qua certè amplius oblectamur, quàm <lb></lb>cum hæc nobis iuncta omnia tenemus. </s>
          <s id="N11095">Et ratio eſt, quia ex<lb></lb>cellentia cognitionis, quæ attenditur ex parte obiecti, ſumitur <lb></lb>ex propria differentia, <expan abbr="proindeq.">proindeque</expan> eſſentialiter <expan abbr="illã">illam</expan> ſibi vendicat <lb></lb>ipſa <expan abbr="ſciẽtia">ſcientia</expan>, vt talis cognitio eſt ex proprio ſuo genere. </s>
          <s id="N110AA">Perfe<lb></lb>ctio verò cognitionis, quæ attenditur ex maiori certitudine, <lb></lb>aut euidentia; licet maxima ſit, non eſt tamen eſſentialis, cum <lb></lb>ſupponat ſcientiam ipſam <expan abbr="conſtitutã">conſtitutam</expan> in eſſe talis ſcientiæ cum <lb></lb>ſufficienti certitudine, aut euidentia. </s>
        </p>
        <p id="N110B9" type="main">
          <s id="N110BB">Quod ſi comparemus Mechanicam facultatem cum parti<lb></lb>bus quibuſdam, ac ſubalternatis ſcientijs Phyſicæ, præſertim <lb></lb>practicis, vt Medicina, &amp; Agricultura, <expan abbr="alijsq.">alijsque</expan> annexis, mixtis, <lb></lb>vel ſubalternatis etiam Mathematicis, vt Architectura, &amp; <lb></lb>Nautica; diuerſa omnino ratio eſt. </s>
          <s id="N110C6">Nam vel ſubiectum illa<lb></lb>rum fecundum ſuam rationem ſpecificam ignobilius eſt gra<lb></lb>ui, &amp; leui, virtuteque eorum motrici in vniuerſum, vt multa <lb></lb>de quibus tanquam de ſubiectis partialibus agitur in Medici<lb></lb>na, &amp; Agricultura: Vel tanta eſt incertitudo, &amp; imperfectio <lb></lb>inferendi concluſiones in talibus ſcientijs, vt ex genere ſuo <lb></lb>vix ſcientiæ <expan abbr="nũcupari">nuncupari</expan> poſſint, potiuſque ex probabilibus, <expan abbr="quã">quam</expan> <pb pagenum="32" xlink:href="005/01/040.jpg"></pb>ex <expan abbr="demõſtratis">demonſtratis</expan> conſtare <expan abbr="videãtur">videantur</expan> magna <expan abbr="ſaltẽ">ſaltem</expan> ex parte. </s>
          <s id="N110EE">Vnde <lb></lb>licet de rebus præſtantioribus agant <expan abbr="ſecundũ">ſecundum</expan> <expan abbr="rationẽ">rationem</expan> obiecti <lb></lb>totalis, vt eſt corpus animale ſanabile; aut <expan abbr="vegetatiuũ">vegetatiuum</expan> germina<lb></lb>bile; nullatenus tamen <expan abbr="Mechanicã">Mechanicam</expan> <expan abbr="facultatẽ">facultatem</expan>, quæ de familia<lb></lb>rioribus omnimoda <expan abbr="cũ">cum</expan> <expan abbr="euidẽtia">euidentia</expan> tractat, antecellere <expan abbr="putabũtur">putabuntur</expan>. </s>
        </p>
        <p id="N11119" type="main">
          <s id="N1111B">Enim uero, vt Ariſtoteles adnotauit primo de partibus ani<lb></lb>mal. </s>
          <s id="N11120">cap.

5. etiam nobis propiora, &amp; natura familiariora ali<lb></lb>quid cum rerum diuinarum ſtudio rependunt, atque compen<lb></lb>ſant, modò cauſas perſpicere valeamus; cum in omnibus na<lb></lb>turæ numen, &amp; honeſtum, <expan abbr="pulchrumq.">pulchrumque</expan> inſit ingenium. </s>
        </p>
        <p id="N1112D" type="main">
          <s id="N1112F">Accedit, quod ſæpe vtilitas refunditur in dignitatem obie<lb></lb>cti; vtilitas enim attenditur ex fine, ad quem ordinatur ſcien<lb></lb>tia; qui profectò in ſcientijs practicis coincidit cum obiecto <lb></lb>formali. </s>
          <s id="N11138">Eadem namque ſanitas animalis, eſt finis medicinæ, <lb></lb>&amp; ratio, ſub qua Medicina agit de ſuis ſubiectis. </s>
          <s id="N1113D">Eademque <lb></lb>directio operationum intellectus, eſt finis Logicæ ſcientiæ, &amp; <lb></lb>ratio ſub qua de ipſis operationibus agitur in illa. </s>
          <s id="N11144">Cum igi<lb></lb>tur talis, ac tanta ſit vtilitas Mechanicæ ſcientiæ ad fines præ<lb></lb>ſtantiſſimos admirabili cum artificio conſequendos, vt ad le<lb></lb>uanda ingentia pondera, parua, &amp; exigua virtute, ad commo<lb></lb>ditates tam plurimas, <expan abbr="vrbiumq.">vrbiumque</expan> ornatum tam varium: ad ſub<lb></lb>miniſtrandas tot machinas, &amp; inſtrumenta in bello, vt belli<lb></lb>gerare potius Mechanica, quam armis ipſis, homines videan<lb></lb>tur: ad aptius mouenda Nauigia; ingentes paruo momento <lb></lb>excitandas moles, <expan abbr="immaniaq.">immaniaque</expan> euertenda ædificia: ad aquas ar<lb></lb>tificioſiſſimè <expan abbr="ſublimãdas">ſublimandas</expan>, <expan abbr="aeremq.">aeremque</expan> perpetuis follibus emitten<lb></lb>dum; voces tàm varias effingendas, concentum æquabiliter <lb></lb>efformandum, motum quaſi animalem inſenſibilibus imper<lb></lb>tiendum, &amp; ſimilia; ingenue fatendum eſt nec eſſe artem, <lb></lb>quæ ſe Mechanicæ arti in dignitate valeat comparari, nec <lb></lb>eſſe ſcientiam practicam, quam ipſa ex certitudine, &amp; euiden<lb></lb>tia, qua procedit, &amp; ex dignitate, ac præſtantia finis, non an<lb></lb>tecellat; ita vt in quo ſuperatur ex parte ſubiecti nobilioris à <lb></lb>Medicina, vel Logica, compenſetur, aut vincatur ex parte <lb></lb>digniſſimi finis, &amp; obiecti formalis, dum admirabili artificio <lb></lb>intendit ipſos naturæ fines Naturam emulando ſuperare. </s>
        </p>
        <pb pagenum="33" xlink:href="005/01/041.jpg"></pb>
        <p id="N11183" type="head">
          <s id="N11185"><emph type="italics"></emph>De Dignitatibus, <expan abbr="admirandisq.">admirandisque</expan> circuli <lb></lb>proprietatibus.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N11192" type="head">
          <s id="N11194">Textus Secundus.</s>
        </p>
        <p id="N11197" type="main">
          <s id="N11199">D<emph type="italics"></emph>e numero autem eorum quæ hoc in genere du<lb></lb>bitantur, illa eſſe dicuntur, quæ circa vectem <lb></lb>fiunt: Abſurdum enim eſſe videtur, magnum <lb></lb>moueri pondus ab exigua virtute <expan abbr="cũ">cum</expan> pluri præ<lb></lb>ſertim pondere. </s>
          <s id="N111AB">Quod enim vna vecte <expan abbr="quiſpiã">quiſpiam</expan> <lb></lb>mouere non poteſt, idipſum ponderis citiùs mouet, vectis ad <lb></lb>illud pondus adiungens. </s>
          <s id="N111B6">Omnium autem huiuſmodi cauſæ <lb></lb>principium habet circulus. </s>
          <s id="N111BB">Istud verò ratione contingit. </s>
          <s id="N111BE">Ex <lb></lb>admirabili etenim, mirandum accidere quippiam, non est ab<lb></lb>ſurdum.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N111C7" type="head">
          <s id="N111C9">COMMENTARIVS.</s>
        </p>
        <p id="N111CD" type="main">
          <s id="N111CF">Qvæcunque maxima omnium admiratione præter <lb></lb>naturam à Mechanicis patrantur, ea quippe non <lb></lb>niſi inſtrumentorum ac <expan abbr="machinarũ">machinarum</expan> beneficio con<lb></lb>ſequi, in præſentibus ſupponit Ariſtoteles, atque <lb></lb>inter ipſa inſtrumenta præcipue hic vectem commemorat. <lb></lb></s>
          <s id="N111DF">Præmittit autem exemplum de magno pondere quod ab exi<lb></lb>gua virtute admirandum in modum, ipſius vectis adminiculo <lb></lb>conſtat moueri. </s>
          <s id="N111E6"><expan abbr="Rationemq.">Rationemque</expan> admirationis ac dubitationis <lb></lb>annectit: Quia ſcilicet potius oppoſitum ex eo ſequi deberet, <lb></lb>cum vectis adminiculo, pondus ponderi adiungatur, <expan abbr="inquiẽs">inquiens</expan>. <lb></lb></s>
          <s id="N111F5">Quod enim ſine vecte quiſpiam mouere non poteſt, idipſum <lb></lb>citius mouet, vectis ad illud pondus adiungens. </s>
          <s id="N111FA">Verum enim <lb></lb>uero huius ac ſimilium miraculorum omnium cauſas refert <lb></lb>ad naturam circuli. </s>
          <s id="N11201">Nam vt inferius docet, quæ circa libram <lb></lb>fiunt, ad circulum rediguntur; quæ vero circa vectem, ad ip<lb></lb>ſam libram; alia autem fere omnia quæ circa Mechanicas <pb pagenum="34" xlink:href="005/01/042.jpg"></pb>ſunt motiones, ad vectem. </s>
          <s id="N1120D">Interim ex admirabili (inquiens) <lb></lb>mirandum accidere quippiam non eſſe abſurdum. </s>
          <s id="N11212">Subin<lb></lb>telligendo, admirabilem profecto eſſe ipſam naturam circuli <lb></lb>ex qua tot admiranda procedunt, vt ſtatim probare aggredi<lb></lb>tur in ſequentibus. </s>
        </p>
        <p id="N1121B" type="head">
          <s id="N1121D"><emph type="italics"></emph>De Prima Circuli admiranda Proprietate.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N11225" type="head">
          <s id="N11227">Textus Tertius.</s>
        </p>
        <p id="N1122A" type="main">
          <s id="N1122C">M<emph type="italics"></emph>axime autem eſt admirandum ſimul <lb></lb>contraria fieri; Circulus verò ex huiuſmo<lb></lb>di eſt conſtitutus: ſtatim enim ex commoto <lb></lb>effectus eſt &amp; manente, quorum natura ad <lb></lb>ſe inuicem est contraria. </s>
          <s id="N1123A">Quamobrem iſthæc <lb></lb>cernentes minùs admirari conuenit contingentes in illo con<lb></lb>trarietates.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N11243" type="head">
          <s id="N11245">COMMENTARIVS.</s>
        </p>
        <p id="N11249" type="main">
          <s id="N1124B">Ex quatuor igitur conditionibus ſeu proprietatibus <lb></lb>colligit, admirabilem eſſe naturam circuli. </s>
          <s id="N11250">Ac pri<lb></lb>mò quòd in fieri ex contrarijs conſtituatur, nempe ex <lb></lb>commoto &amp; manente. </s>
          <s id="N11257">Quandoquidem in deſcriptione cir<lb></lb>culi, alterum ſemidiametri extremum mouetur in gyrum, al<lb></lb>terum vero quieſcit, quod centrum denominatur. </s>
          <s id="N1125E">Imò ma<lb></lb>nente ipſo altero extremo, quod dicitur centrum, quod reli<lb></lb>quum eſt eiuſdem ſemidiametri, circumuehitur totum. </s>
        </p>
        <p id="N11265" type="main">
          <s id="N11267">Nec obſtat quod nonnulli obijciunt, centrum in rigore lo<lb></lb>quendo non eſſe partem ſemidiametri, ac proinde nec circuli, <lb></lb>nam ſufficit eſſe illius terminum intrinſecum, ſiue extremum, <lb></lb>quo immoto, ſi tota longitudo ſemidiametri circumducatur, <lb></lb>circulus conſtituatur. </s>
          <s id="N11272">Cum igitur admirandum valde ſit, ſi<lb></lb>mul contraria fieri, aut aliquid effici ex contrarijs, &amp; hoc con<lb></lb>tingat in ipſa conſtitutione circuli; minus admirandum eſſe <pb pagenum="35" xlink:href="005/01/043.jpg"></pb>relinquitur (concludit Ariſtoteles) ſi ex ipſo circulo conſti<lb></lb>tuto, aliæ poſtea oriantur contrarietates, vel alia contraria in <lb></lb>ipſo conſiderentur, vt mox ex dicendis patebit. </s>
        </p>
        <p id="N11282" type="head">
          <s id="N11284"><emph type="italics"></emph>De ſecunda circuli proprietate.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1128B" type="head">
          <s id="N1128D">Textus Quartus.</s>
        </p>
        <p id="N11290" type="main">
          <s id="N11292">I<emph type="italics"></emph>n primis enim lineæ illi, quæ circuli orbem am<lb></lb>plectitur, nullam habenti latitudinem contraria <lb></lb>quodammodo ineſſe apparans, concauum ſcilicet, <lb></lb>&amp; curuum. </s>
          <s id="N1129E">Hæc autem eo à ſe inuicem diſtant <lb></lb>modo, quo magnum, &amp; paricum, illorum etenim <lb></lb>medium eſt æquale: horum verò rectum; quapropter cum ad <lb></lb>ſe inuicem commutantur, illa <expan abbr="quidẽ">quidem</expan> prius æqualia fieri neceſſe <lb></lb>est, quam extremorum vtrumlibet: lineam vero rectam, <lb></lb>quando eſt curua, concaua, aut ex huiuſmodi rurſum curua ſit, <lb></lb>&amp; circularis. </s>
          <s id="N112B1">Vnum quidem igitur iſtuc abſurdum ineſt circulo.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N112B6" type="head">
          <s id="N112B8">COMMENTARIVS.</s>
        </p>
        <p id="N112BC" type="main">
          <s id="N112BE">Secundò admirabilem ſe natura circuli oſtendit, ſi ſu<lb></lb>matur infacto eſſe, quod cum in primis (inquit Ariſto<lb></lb>teles) linea, quæ ipſius circuli orbem complectitur, ac <lb></lb>peripheria, ſeu <expan abbr="circunferẽtia">circunferentia</expan> nuncupatur, ſit per ſe quoad la<lb></lb>titudinem, &amp; profunditatem indiuiſibilis, ſimul tamen tan<lb></lb>quam ex duobus contrarijs inter ſe coniunctis conſtituatur <lb></lb>concaua, &amp; curua, ſiuè conuexa. </s>
          <s id="N112D1">Etenim eſt verè terminus <lb></lb>extimus, &amp; conuexum ipſius circuli, ac ſimul ambiens, &amp; <lb></lb>complectens in ſua concauitate ipſam ſuperficilem circuli: <lb></lb>Concauum autem, &amp; conuexum ſe habent ſicut magnum, <lb></lb>&amp; paruum. </s>
          <s id="N112DC">Horum enim medium eſt æquale, illorum verò <lb></lb>rectum. </s>
          <s id="N112E1">Quarè ſicut cum magnum, &amp; paruum inuicem, <lb></lb>commutantur, prius perueniunt ad æquale, quàm ad hoc vt <lb></lb>magnum conſtituatur paruum, &amp; paruum conſtituatur ma<pb pagenum="36" xlink:href="005/01/044.jpg"></pb>gnum: ita quælibet linea curua, ſeu conuexa antequam fiat <lb></lb>concaua, prius debet fieri recta: abſurdum igitur apparet, ean<lb></lb>dem omnino circuli periferiam, ſimul conſtitui concauam, <lb></lb>&amp; conuexam. </s>
        </p>
        <p id="N112F3" type="main">
          <s id="N112F5">Nec difficultatem euadunt, qui dicunt, concauum, &amp; con<lb></lb>uexum realiter non eſſe idem in circulo, ſeu curuitatem, &amp; <lb></lb>concauitatem non reperiri in eadem linea, ſed in diuerſis, ità <lb></lb>vt in circunferentia ſit tantum curuitas, ſeù conuexum, con<lb></lb>cauitas verò ſit potius in corpore extrinſeco ambiente per li<lb></lb>neam illi correſpondentem. </s>
          <s id="N11302">Etenim cum linea corporis con<lb></lb>tinentis ambiens circulum, penetretur in eodem ſpacio cum <lb></lb>circunferentia ipſius circuli, <expan abbr="conſidereturq.">conſidereturque</expan> ſola quantitas <lb></lb>abſtracta, &amp; figura vtriuſque lineæ coincidentis, eadem ſem<lb></lb>per difficultas obſtabit; nempè quo pacto fieri poſſit, vt <expan abbr="eadẽ">eadem</expan> <lb></lb>longitudo latitudinis expers, circulum terminans, ſeù circu<lb></lb>lariter extenſa, ſimul ſit concaua, &amp; conuexa. </s>
          <s id="N11319">Sed nihil pro<lb></lb>hibet eandem circumferentiam indiuisibilem quoad latitudi<lb></lb>nem, &amp; profunditatem, ſimul eſſe concauam, &amp; conuexam <lb></lb>reſpectu diuerſorum, vt in alijs etiam linearum figuris, ac ſu<lb></lb>perficiebus poterit exemplificari: &amp; vt eadem via dicitur <lb></lb>acliuis, &amp; decliuis; idemque magnum, &amp; paruum rei pectu di<lb></lb>uerſorum, quæ cum illo comparantur. </s>
          <s id="N11328">Quo fit, vt admiran<lb></lb>dam quidem eſſe huiuſmodi proprietatem circuli iure dica<lb></lb>mus, nullam tamen in ſe <expan abbr="repugnantiã">repugnantiam</expan> inuoluere admittamus. </s>
        </p>
        <p id="N11333" type="head">
          <s id="N11335"><emph type="italics"></emph>De tertia Circuli proprietate.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1133C" type="head">
          <s id="N1133E">Textus Quintus.</s>
        </p>
        <p id="N11341" type="main">
          <s id="N11343">A<emph type="italics"></emph>ltervm autem, quod ſimul contrarijs <lb></lb>mouetur motionibus: ſimul enim ad anterio<lb></lb>rem mouetur locum, &amp; ad poſteriorem. </s>
          <s id="N1134D">Et <lb></lb>ea, quæ circulum deſcribit, linea eodem ſe <lb></lb>habet modo: Ex que enim incipit loco, illius <lb></lb>extremum, ad eundem rurſus redit: Illa <lb></lb>enim continuò commota, extremum rurſus efficitur primum.<emph.end type="italics"></emph.end><pb pagenum="37" xlink:href="005/01/045.jpg"></pb><emph type="italics"></emph>Quamobrem manifeſtum, quod inde mutatum eſt. </s>
          <s id="N11361">Quaprop<lb></lb>ter (vt dictum eſt prius) non eſt inconueniens, ipſum miraculo<lb></lb>rum omnium eſſe principium.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1136A" type="main">
          <s id="N1136C"><emph type="italics"></emph>Ea igitur, quæ circa libram fiunt, ad circulum referuntur: <lb></lb>“quæ vero circa vectem, ad ipſam libram; alia autem ferè om-<emph.end type="italics"></emph.end><arrow.to.target n="marg13"></arrow.to.target><lb></lb><emph type="italics"></emph>nia, quæ circa Menbanicas ſunt motiones, ad vectem. </s>
          <s id="N1137C">Prae<lb></lb>tereà etiam quoniam vnica exiſtente, quæ ex centro eſt linea, <lb></lb>nullum aliud alij, quæ in illa ſunt, punctorum æqua velocitate <lb></lb>feratur; ſed citius ſemper, quod à manente termino eſt remo<lb></lb>tius, <expan abbr="pleraq.">pleraque</expan> miraculorum accidunt in circuli motionibus: de <lb></lb>quibus in ijs, quæ poſthac adducentur, quæſtionibus erit ma<lb></lb>nifeſtam.”<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N11391" type="margin">
          <s id="N11393"><margin.target id="marg13"></margin.target>Verba re<lb></lb>ſecanda.</s>
        </p>
        <p id="N1139A" type="main">
          <s id="N1139C"><emph type="italics"></emph>Quoniam autem secundum contrarias ſimul motiones mo<lb></lb>uetur circulus; &amp; alienum quidem diametri extremum, vbi A, <lb></lb>in ante mouetur, alterum verò vbi B, ad retro; efficiunt non<lb></lb>nulli, vt ab vnica motione multi contrario ſimul moueantur <lb></lb>circuli; quemadmodum ſunt illi, quos in locis proponunt ſacris, <lb></lb>æneos, &amp; ferreos fabricantes orbiculos. </s>
          <s id="N113AB">Si enim AB, circu<lb></lb>lum alier contingerit, circulus in quo CD, mota circuli, in quo <lb></lb>AB, diametro in ante, mouebitur CD, ad retro diametro cir<lb></lb>culi, vbi eſt A, circà idem mota, In contrarium igitur moue<lb></lb>bitur circulus vbi CD, ad illum, vbi AB, El rurſus ipſe con<lb></lb>tiguum vbi EF, in contrarium ſibi ipſi mouebitur propter ean<lb></lb>dem cauſam. </s>
          <s id="N113BA">Eodem etiam modo ſi plures fuerint, idem <lb></lb>facient, vno ſolo commoto. </s>
          <s id="N113BF">Hanc lgitur in circulo exiſtentem <lb></lb>animaduertens naturam Architecti, inſtrumentum fabricant, <lb></lb>celantes principium, vt machinæ ſolum manifeſtum ſit illud, <lb></lb>quod admirationem præſtat, cauſa verò lateat.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N113CA" type="head">
          <s id="N113CC">COMMENTARIVS.</s>
        </p>
        <p id="N113D0" type="main">
          <s id="N113D2">Tertio illud quoque admiratione dignum ſeſe offert in <lb></lb>circulo, quod, inquit Ariſtoteles, contrarijs ſimul fe<lb></lb>ratur motionibus, antrorſum videlicet, ac retrorſum, <lb></lb>ſurſum, ac deorſum. </s>
          <s id="N113DB">Dum enim pars circuli ſuperior deſcen<lb></lb>dit, ac mouetur antrorſum, v. g. ad dexteram, altera pars illi <pb pagenum="38" xlink:href="005/01/046.jpg"></pb>oppoſita, quæ eſt inferior, aſcendit, ac mouetur retrorſum ad <lb></lb>leuam. </s>
          <s id="N113EB">Quod ſi huiuſmodi poſitiones formaliter non con<lb></lb>ſtituantur niſi in quadam relatione, ac reſpectu vnius partis ad <lb></lb>alteram, hoc parum refert, cum fundamentaliter ſemper im<lb></lb>portent realem oppoſitionem, ac diuerſitatem loci, in quo <lb></lb>ipſe partes relatæ conſtituuntur, vel ad quem tendunt <expan abbr="tanquã">tanquam</expan> <lb></lb>ad terminum ſui motus. </s>
          <s id="N113FC">Quapropter idem Philoſophus ſu<lb></lb><figure id="id.005.01.046.1.jpg" xlink:href="005/01/046/1.jpg"></figure><lb></lb>biungit ex hac contra<lb></lb>rietate fieri, vt vnius <lb></lb>circuli motione, alij cir<lb></lb>culi in contrarium mo<lb></lb>ueantur. </s>
          <s id="N1140F">Vt ſi conſti<lb></lb>tuatur circulus, qui pri<lb></lb>mò moueri debeat in<lb></lb>ter alios quaruor, <expan abbr="ſintq.">ſintque</expan> <lb></lb>omnes denticulati, <lb></lb>quem admodum videre <lb></lb>eſt in horologijs, <expan abbr="alijsq.">alijsque</expan> <lb></lb>ſimilibus machinis, vt <lb></lb>in hac figura: Nam pars <lb></lb>ſuperor medij circuli, <lb></lb>quæ deſcendit, impellit partem inferiorem ſuperioris circuli, <lb></lb>facitque eam aſcendere. </s>
          <s id="N11430">Et pars inferior eiuſdem medij cir<lb></lb>culi, aſcendendo facit deſcendere partem ſuperiorem circuli <lb></lb>inferioris. </s>
          <s id="N11437">Deinde ſimiliter idem circulus medius dum dex<lb></lb>trorſum mouetur, mouet circulum dexterum ſiniſtrorſum, &amp; <lb></lb>ſiniſtrum dextrorſum. </s>
        </p>
        <p id="N1143E" type="main">
          <s id="N11440">Eodem que modo ſe habet, ſubiungit Ariſtoteles, linea illa <lb></lb>quæ in vno extremo manens, altero circumlata, circulum <lb></lb>deſcribit; nempe ſemidiameter. </s>
          <s id="N11447">Quandoquidem contraria <lb></lb>ſimiliter admittit; nimirum primum &amp; extremum ſimul; ſeu <lb></lb>principium ac terminum ſui motus in eodem loco. </s>
          <s id="N1144E">Ex quo <lb></lb>enim puncto incipit circunduci, ad idem poſtremo reuertitur <lb></lb>tanquam ad terminum ſui motus. </s>
          <s id="N11455">Et ſic <expan abbr="extremũ">extremum</expan> rurſus effici<lb></lb>tur <expan abbr="primũ">primum</expan>. </s>
          <s id="N11462">Quapropter concludit: Non eſt inconueniens ex <lb></lb>ipſa ſemidiametro <expan abbr="deſcriptũ">deſcriptum</expan>, <expan abbr="miraculorũ">miraculorum</expan> <expan abbr="pluriũ">plurium</expan> eſſe <expan abbr="principiũ">principium</expan>. </s>
        </p>
        <pb pagenum="39" xlink:href="005/01/047.jpg"></pb>
        <p id="N1147B" type="main">
          <s id="N1147D">Quæ autem de libra ac vatia punctorum ſemidiametri ve<lb></lb>locitate hìc docet Ariſtoteles, fruſtra interpoſita ſunt ac præ<lb></lb>ter Auctoris intentum, cum ad rem de qua agitur non perti<lb></lb>neant, ac alibi proprijs in locis repetantur. </s>
          <s id="N11486">Quare ex hoc <lb></lb>textu reſecanda eſſent, incipiendo à particula (Ea igitur) <lb></lb>vſque ad (erit manifeſtum) incluſiue, prout lineis consi<lb></lb>gnauimus. </s>
        </p>
        <p id="N1148F" type="head">
          <s id="N11491"><emph type="italics"></emph>De Quarta Circuli Proprietate.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N11499" type="head">
          <s id="N1149B">Textus Sextus.</s>
        </p>
        <p id="N1149E" type="main">
          <s id="N114A0">I<emph type="italics"></emph>n primis igitur quæ accidunt circa libram du<lb></lb>bitare faciunt, quam nam ob cauſam exactio<lb></lb>res minoribus maiores ſunt libræ. </s>
          <s id="N114AA">Huius au<lb></lb>tem rei principium est quamobrem in ipſo cir<lb></lb>culo, quæ plus à centro diſtat linea eadem vi <lb></lb>commota, citius fertur, quàm illa quæ minus distat. </s>
          <s id="N114B3">Citius <lb></lb>enim bifariam dicitur: ſiue enim in minori tempore æqualem <lb></lb>pertranſit locum, citius feciſſe dicimus: ſeu in æquali maio<lb></lb>rem. </s>
          <s id="N114BC">Maior autem in æquali tempore, maiorem deſcribit cir<lb></lb>culum: qui enim extra eſt, maior eo qui intus eſt. </s>
          <s id="N114C1">Horum <lb></lb>autem cauſa, quoniam duas fertur lationes ea quæ circulum <lb></lb>deſcribit linea. </s>
          <s id="N114C8">Quandoquidem igitur in proportione fertur <lb></lb>aliqua id quod fertur, ſuper rectam ferri neceſſe: Et hæc dia<lb></lb>meter efficitur figuræ quam faciunt illæ quæ in huiuſmodi pro<lb></lb>portione coaptantur lineæ. </s>
          <s id="N114D1">Sit enim proportio ſecundum quam <lb></lb>latum fertur, quam habet AB ad AC. &amp; A quidem fertur <lb></lb>verſus B: A B vero ſubterſeratur verſus MC: latum au<lb></lb>tem ſit A quidem ad D. </s>
          <s id="N114DB">Vbi autem est A B verſus E: quo<lb></lb>niam igitur lationis erat proportio, quam A B habet ad A C, <lb></lb>neceſſe eſt &amp; A D ad A E hanc habere proportionem. </s>
          <s id="N114E2">Simile <lb></lb>igitur est proportione paruum quadrilaterum maiori: quam<lb></lb>obrem &amp; eadem illorum eſt diameter, &amp; A erit ad F. </s>
          <s id="N114EA">Eodem <lb></lb>etiam oſtendetur modo, vbicunque latio deprahendatur; ſem-<emph.end type="italics"></emph.end><pb pagenum="40" xlink:href="005/01/048.jpg"></pb><emph type="italics"></emph>per enim ſupra diametrum erit. </s>
          <s id="N114F8">Manifeſtum igitur, quod id <lb></lb>quod ſecundum diametrum duabus fertur lationibus, neceſſa<lb></lb>riò ſecundum laterum proportionem fertur. </s>
          <s id="N114FF">Si enim ſecun<lb></lb>dum aliam quampiam, non fertur ſecundam diametrum. <lb></lb></s>
          <s id="N11505">Si autem in nulla fertur proportione ſecundum duas lationes <lb></lb>nullo in tempore, rectam eſſe lationem, eſt impoſſibile. </s>
          <s id="N1150A">Sit enim <lb></lb>recta. </s>
          <s id="N1150F">Poſita igitur hac pro diametro, &amp; circumrepletis late<lb></lb>ribus, illud quod fertur, ſecundum laterum proportionem fer<lb></lb>ri neceſſe eſt: hoc enim demonſtratum eſt prius. </s>
          <s id="N11516">Non igitur <lb></lb>rectam efficiet id quod ſecundum nullam proportionem, in nul<lb></lb>lo fertur tempore. </s>
          <s id="N1151D">Si autem ſecundum quampiam feratur <lb></lb>proportionem, &amp; in tempore quopiam, hoc neceſſe est tempus <lb></lb>rectam e&lt;32&gt;e lationem, per ea quæ retro ſunt dicta. </s>
          <s id="N11524">Quamob<lb></lb>rem circulare eſt id, quod ſecundum nullam proportionem nul<lb></lb>lo in tempore duas fertur lationes.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1152D" type="head">
          <s id="N1152F">COMMENTARIVS.</s>
        </p>
        <p id="N11533" type="main">
          <s id="N11535">Qvartò denique occaſione ſumpta ex eo, cur maio<lb></lb>res libræ exactiores ſint minoribus, vt huius rei <lb></lb>principium vel cauſa innoteſcat, aliam circuli pro<lb></lb>prietatem non minus ad mitandam Ariſtoteles <lb></lb>proponit, quam in ſuperiori etiam textu interpoſitè inſinua<lb></lb>uerat: Nempe in vna <expan abbr="eademq.">eademque</expan> linea quæ eſt à centro ad cir<lb></lb>cumferentiam, nullum eſſe punctum, quod æquali velocitate <lb></lb>moueatur reſpectu aliorum, quæ ſunt in eadem linea; ſed <lb></lb>citius ſemper feratur punctum quod à manente termino, ſci<lb></lb>licet centro, eſt remotius. </s>
          <s id="N1154E">Quamobrem ait in ipſo circulo <lb></lb>quæ plus à centro diſtat linea, eadem vi commota, citius fer<lb></lb>tur, quàm illa, quæ minus diſtat &amp;c. </s>
          <s id="N11555">Quod ita ſe habere <lb></lb>oſtendit ex eo, quia dupliciter aliquid intelligimus velocius <lb></lb>alio moueri; nempe, vel quia in minori tempore, æquale <lb></lb>ſpatium pertranſit; vel quia eodem tempore, maius interual<lb></lb>lum percurrit. </s>
          <s id="N11560">Et hoc pacto inquit in deſcriptione circuli <lb></lb>contingere vt puncta quæ magis à centro diſtant, velocius <lb></lb>moueantur. </s>
          <s id="N11567">Siquidem eodem tempore maiorem deſcribunt <pb pagenum="41" xlink:href="005/01/049.jpg"></pb>ambitum. </s>
          <s id="N1156F">Maior enim eſt circum ſerentia circuli continentis, <lb></lb>quàm contenti. </s>
          <s id="N11574">Si autem circa idem centrum plures circuli <lb></lb>ducantur, ſemper ille qui coeteros continet, à remotiori pun<lb></lb>cto ſemidiametri deſcribetur, <expan abbr="proindeq.">proindeque</expan> quò remotiora erunt <lb></lb>ipſa puncta ſemidiametri à centro, eò velocius mouebuntur. </s>
        </p>
        <p id="N11581" type="main">
          <s id="N11583">Horum autem cauſam eſſe inquit Ariſtoteles, quoniam ſe<lb></lb>midiameter circulum deſcribens mouetur motu quodam <lb></lb>mixto ex duabus lationibus, nempe naturali, ac præternatu<lb></lb>rali, vt infra ſequenti textu probabitur; quam duplicem la<lb></lb>tionem partes ſemidiametri non æquè participant, hoc eſt <lb></lb>non participant ſecundum eandem proportionem. </s>
          <s id="N11590">Quando<lb></lb>quidem, vt infra pariter ipſe Philoſophus oſtendit, partes quæ <lb></lb>remotiores ſunt à centro, magis participant de latione natu<lb></lb>rali: contra verò quæ centro ſunt viciniores, magis partici<lb></lb>pant de motione præternaturali. </s>
          <s id="N1159B">Si enim ſecundum eandem <lb></lb>aliquam proportionem, duplicem illam lationem omnes ip<lb></lb>sæ participarent, non vtique mouerentur motu circulari, ſed <lb></lb>recto, vt ſtatim ipſe demonſtrat. </s>
          <s id="N115A4">Quare ſuppoſito quòd mo<lb></lb>bile tanto velocius monetur, quanto magis participat de mo<lb></lb>tu naturali, vt ex dicendis etiam tex. 8. conſtabit, a primo ad <lb></lb>vltimum conuincitur, puncta vel partes ſemidiametri quò <lb></lb>plus à centro diſtauerint in deſcriptione circuli, eò cœlerius <lb></lb>moueri, quò vero minus, eo tardius. </s>
        </p>
        <p id="N115B3" type="main">
          <s id="N115B5">Et confirmari poteſt argumento quod idem Philoſophus, <lb></lb>alijs interpoſitis, ſequenti textu adiecit; nimirum, quia ſi <lb></lb>duobus (inquit) ab eadem potentia latis, hoc quidem plus <lb></lb>repellatur vel impediatur ab aliquo, illud verò minus; ratio<lb></lb>ni conſentaneum eſt, tardius moueri id quod plus præpedi<lb></lb>tur, aut repellitur: Sed lineæ circumductæ in circulo, vel pun<lb></lb>cta quæ ſunt in eius diametro, quò magis appropinquantur <lb></lb>centro, eò magis repelluntur in motu circulari ac impediun<lb></lb>tur ab ipſo centro; ergo tardius mouentur. </s>
          <s id="N115C8">Minor propoſitio <lb></lb>huius argumenti probatur; quia cum centrum ſit fixum &amp; <lb></lb>immotum, <expan abbr="eiq.">eique</expan> colligatæ ſint omnes partes diametri per lon<lb></lb>gitudinem extenſæ, illæ quæ magis ei appropinquantur, ma<lb></lb>gis vinciuntur ac detinentur nè moueantur: quæ verò magis <pb pagenum="42" xlink:href="005/01/050.jpg"></pb>ab eo diſtant, magis relaxantur, <expan abbr="magisq.">magisque</expan> ſoluuntur à princi<lb></lb>pio detinente, ac propterea minus impediuntur nè ad im<lb></lb>pulſum vel motum alterius moueantur, &amp; ſic velocius fe<lb></lb>runtur. </s>
        </p>
        <p id="N115E6" type="main">
          <s id="N115E8">Verum enim uero, vt primum ac principale Ariſtotelis ar<lb></lb>gumentum omninò concludat id quod intendit, examinanda <lb></lb>ac probanda ſunt nonnulla quæ in eo aſſumuntur, ac difficul<lb></lb>tatem non paruam inuoluunt. </s>
          <s id="N115F1">Quorum vnum hic, reliqua <lb></lb>verò in ſequentibus ipſe pertractat. </s>
          <s id="N115F6">Illud igitur hic ſtatim <lb></lb>aggreditur probandum, quod de proportione duarum latio<lb></lb>num docuerat, eam ſcilicet ſolùm dari in eo quod fertur mo<lb></lb>tu recto. </s>
          <s id="N115FF">Quod quippe antequam probetur, ſano modo in<lb></lb>telligendum eſt. </s>
          <s id="N11604">Etenim in partibus etiam circuli, dum vni<lb></lb>formiter difformiter, geminata ac mixta quadam latione du<lb></lb>cuntur in gyrum, ſemper aliqua ſeruatur vtriuſque lationis <lb></lb>proportio; vt ſcilicet magis vel minus participent de motu <lb></lb>naturali, aut præternaturali, iuxta diſtantiam vel propinqui<lb></lb>tatem quam partes ipſæ habent cum centro. </s>
          <s id="N11611">Quare expli<lb></lb>candus eſt Ariſtoteles, vt loquatur de proportione eadem, <lb></lb>non vero de quacunque. </s>
          <s id="N11618">Nam reuera, vt etiam Baldus de <lb></lb>monſtrat, licet circulus fiat, proportionibus quidem duarum <lb></lb>lationum ſeruatis; nunquam tamen eadem erit proportio <lb></lb>vnius lationis ad alteram reſpectu cuiuſque partis ipſius cir<lb></lb>culi vel ſemidiametri, ſicut cum quippiam duabus lationibus <lb></lb>fertur ſuper rectam: &amp; hoc ſolum probat Ariſtoteles, vt ſta<lb></lb>tim videbimus; illud vtique intendens, quòd ſi eadem ſem<lb></lb>per proportio vtriuſque lationis ſeruaretur in deſcriptione <lb></lb>circuli, motus ille eſſet rectus, &amp; non circularis de quo <lb></lb>agitur. </s>
        </p>
        <p id="N1162F" type="main">
          <s id="N11631">Rurſus antequam ad exactam eius probationem ex Geo<lb></lb>metricis principijs accedamus, idem prælibare licebit exem<lb></lb>plo huius figuræ, quod non parum ad dilucidationem textus, <lb></lb><expan abbr="doctrinæq.">doctrinæque</expan> Ariſtotelis conducet. </s>
          <s id="N1163D">Sit enim corpus ſeu pon<lb></lb>dus quod moueri debeat conſtitutum ſuper planum vbi A, <lb></lb>mouentia verò vbi B, C. </s>
          <s id="N11645">Deinde ſupponamus æquali virtu<lb></lb>te &amp; æquali ſimul tempore vtrumque mouens ad ſe pondus <pb pagenum="43" xlink:href="005/01/051.jpg"></pb><figure id="id.005.01.051.1.jpg" xlink:href="005/01/051/1.jpg"></figure><lb></lb>ipſum trahere; quod eſt, eandem ſemper proportionem ad <lb></lb>inuicem ſeruare, vt beneficio trochlearum vel alterius inſtru<lb></lb>menti. </s>
          <s id="N11659">Tunc enim dicimus primo, corpus ipſum mobile A <lb></lb>moueri motu quodam mixto ex duabus lationibus, nempe <lb></lb>qua appropinquatur ad B, &amp; qua appropinquantur ad C. <lb></lb></s>
          <s id="N11662">Quia durante huiuſmodi motu, non datur inſtans in quo non <lb></lb>magis ipſum pondus A appropinquetur ad B, ac ſimul ad C. <lb></lb></s>
          <s id="N11669">Præterea dicimus, huiuſmodi motum neceſſariò eſſe rectum, <lb></lb>non verò circularem, ſeu pondus non niſi ſuper rectam tunc <lb></lb>ſemper moueri. </s>
          <s id="N11670">Etenim ſeruata eadem proportione, pon<lb></lb>dus ipſum, &amp; quælibet eius pars æqualiter vtrique mouenti in <lb></lb>æquali tempore deberet appropinquari: quia non eſſet maior <lb></lb>ratio cur magis aut citius appropinquaretur ad B, quàm ad C. <lb></lb></s>
          <s id="N1167B">At non poſſet æqualiter vtrique appropinquari, niſi feratur <pb pagenum="44" xlink:href="005/01/052.jpg"></pb>per diametrem quadranguli A B C D, quæ eſt recta A D; <lb></lb>ſiquidem in nulla alia parte interiecti ſpatij, diſtantia eſſet <lb></lb>æqualis, vt ſenſu conſtat: Ergo ſeruata eadem proportione in <lb></lb>ipſa duplici latione reſpectu mobilis &amp; cuiuſque partis ipſius, <lb></lb>motus neceſſariò erit rectus, ſeu <expan abbr="põdus">pondus</expan> &amp; quælibet eius pars, <lb></lb>non niſi per rectam lineam poterit moueri. </s>
        </p>
        <p id="N11691" type="main">
          <s id="N11693">Deinde quod infert Ariſtoteles, circulare eſſe id quod ſe<lb></lb>cundum nullam proportionem, nullo in tempore duas pati<lb></lb>tur lationes, falſum eſſet etiam iuxta præfatam explicationé <lb></lb>proportionis; niſi per circulare intelligeremus lato modo, id <lb></lb>quod eſt curuum. </s>
          <s id="N1169E">quia nimirum non ſequitur, aliquid eſſe <lb></lb>circulare, in rigore loquendo, aut moueri per lineam circula<lb></lb>rem, eo quòd moueri non poſſit per lineam rectam; cum plu<lb></lb>res ſint figuræ ac lineæ non rectæ, nec circulares, vt figura el<lb></lb>lipſis, ſectiones parabolicæ, ac lineæ ſpirales, <expan abbr="aliæq.">aliæque</expan> irregu<lb></lb>lares permultæ. </s>
          <s id="N116AF">Quæ omnia prænotaſſe, ipſa verborum am<lb></lb>biguitas poſtulabat, vt clarius ad probationem doctrinæ pro<lb></lb>cederemus. </s>
        </p>
        <p id="N116B6" type="main">
          <s id="N116B8">Iam vero vt Geometricis principijs quæ dicta ſunt pateát, <lb></lb>ſic probat Ariſtoteles, quidquid fertur duabus lationibus ad <lb></lb>inuicem proportionatis, ſuper rectam neceſſariò ferri, ac pro<lb></lb>inde non circulariter. </s>
          <s id="N116C1">Sit inquit proportio ipſarum lationum <lb></lb><figure id="id.005.01.052.1.jpg" xlink:href="005/01/052/1.jpg"></figure><lb></lb>quam habent inter <lb></lb>ſe latera A B &amp; AC <lb></lb>in dato rectangulo <lb></lb>A B C D. </s>
          <s id="N116D3">Et A <lb></lb><expan abbr="quidẽ">quidem</expan> duplici motu <lb></lb>feratur, vno quo <lb></lb><expan abbr="tẽdat">tendat</expan> verſus B, qua<lb></lb>ſi ex ſe incedendo <lb></lb>ſuper lineam A B: <lb></lb>altero verò, quo ſimul cum ipſa linea A B ſubterferatur ver<lb></lb>ſus C, ſeu verſus lineam C D cum eadem ſemper proportio<lb></lb>ne. </s>
          <s id="N116EC">Tunc dicimus punctum A motu ipſo mixto, neceſſariò <lb></lb>ferri per rectam A D, quæ eſt diameter eiuſdem quadrilateri <lb></lb>A B C D. </s>
          <s id="N116F4">Etenim ſi <expan abbr="cõſtituatur">conſtituatur</expan> rectangulus minor A E F G <pb pagenum="45" xlink:href="005/01/053.jpg"></pb>proportionalis maiori A B C D, ac per motum proprium <lb></lb>verſus B, ipſum punctum A peragrauerit quantum eſt vſque <lb></lb>ad E; &amp; per motum totius lineæ A B, verſus lineam C D, <lb></lb>peragrauerit quantum eſt ab A, vſque ad F, ſeruata eadem <lb></lb>proportione ipſorum laterum; certe punctum A reperiri non <lb></lb>poſſet in E, neque in F; ſiquidem non fuiſſet latum duabus <lb></lb>lationibus, nec peragraſſet ſpacium ſecundum vtramque po<lb></lb>ſitionem, ſimul accedendo quantum fieri poteſt ad B &amp; ad <lb></lb>C; ſed vna tantùm latione, alterum ſolum ſpacium percur<lb></lb>riſſet. </s>
          <s id="N11712">Reperietur ergo ipſum. </s>
          <s id="N11715">punctum A vbi vtraque pro<lb></lb>greſſio poteſt verificari, vt in puncto G. </s>
          <s id="N1171B">Quia nimirum F G <lb></lb>eſt æqualis ipſi A E, &amp; E G æqualis ipſi A F, cum ſint latera <lb></lb>oppoſita eiuſdem rectanguli, vt patet per 34. primi Elemen<lb></lb>torum Euclidis. </s>
          <s id="N11725">Sed punctum G non poteſt eſſe niſi in recta <lb></lb>A D, quæ eſt vtriuſque rectanguli diameter, vt patet per 26. <lb></lb>ſexti, &amp; eodem modo quodlibet aliud punctum, in quo vtra<lb></lb>que latio ac latera depræhendantur eadem proportione pro<lb></lb>portionalia, vt in H, reſpectu I &amp; K: igitur punctum A, dua<lb></lb>bus lationibus proportionalibus latum, neceſſariò mouebi<lb></lb>tur ſuper rectam A D, quod erat probandum. </s>
        </p>
        <p id="N11734" type="main">
          <s id="N11736">Quod quidem clarius adhuc probari poſſet exemplo hu<lb></lb>ius quadrati A B C D, cuius latera diuiſa ſint in quatuor par<lb></lb>tes æquales, <expan abbr="efficiantq.">efficiantque</expan> ex illis minora quadrata contenta in <lb></lb>maiori. </s>
          <s id="N11743">Nam ſi ſup<lb></lb><figure id="id.005.01.053.1.jpg" xlink:href="005/01/053/1.jpg"></figure><lb></lb>ponatur punctum A ex <lb></lb>ſe moueri tanquam na<lb></lb>turali ac proprio motu <lb></lb>verſus B, ſuper rectam <lb></lb>A B, &amp; eodem tempo<lb></lb>re ſimul cum ipſa A B, <lb></lb>quaſi motu alieno de<lb></lb>ſcendere verſus C D, <lb></lb>ac ſeruata eadem pro<lb></lb>portione vtriuſque mo<lb></lb>tus, quæ ſit æqualita<lb></lb>tis: abſque dubio, eo-<pb pagenum="46" xlink:href="005/01/054.jpg"></pb>dem tempore quo A, peragrauerit ſpacium AE, ſimul pera<lb></lb>grabit ſpacium AF, &amp; reperietur in G, quandoquidem ſunt <lb></lb>latera eiuſdem quadrati AG, ac proinde æqualia. </s>
          <s id="N1176D">Et ſicut to<lb></lb>ta linea AB, coincideret cum linea FH, ita punctum E, coin<lb></lb>cideret cum puncto G. </s>
          <s id="N11775">Similiterque cum A, peruenerit in I, <lb></lb>ſimul reperietur in K, propter eandem rationem, &amp; ſic de <lb></lb>ſingulis. </s>
          <s id="N1177C">Ex quibus conſtabit, ipſum A, moueri per rectam <lb></lb>diagonalem ſeu diametrum AD, quod erat oſtendendum. </s>
        </p>
        <p id="N11781" type="head">
          <s id="N11783"><emph type="italics"></emph>Quo pacto linea circulum deſcribens, duabus <lb></lb>feratur lationibus.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1178C" type="head">
          <s id="N1178E">Textus Septimus.</s>
        </p>
        <p id="N11791" type="main">
          <s id="N11793">Q<emph type="italics"></emph>vod quidem igitur ea quæ circulum deſcri<lb></lb>bit, duas ſimul feratur lationes, manifestum <lb></lb>eſt cùm ex istis, tùm quia ſecundum rectum <lb></lb>lata ad perpendiculum peruenit, vt ſit rurſus <lb></lb>ipſa à centro <expan abbr="perpendiculũ">perpendiculum</expan>. </s>
          <s id="N117A5">Sit circulus ABCD, <lb></lb>extremum autem vbi eſt B. feratur ad ipſum <lb></lb>D, peruenit ſane aliquando ad ipſum C. </s>
          <s id="N117AD">Siquidem igitur in <lb></lb>proportione feratur, quam habet BE, EC, fertur vtique ſecun<lb></lb>dum diametrum BC. </s>
          <s id="N117B5">Nunc autem, <expan abbr="quoniã">quoniam</expan> in nulla proportione, <lb></lb>in circunferentia certè fertur vbi BEC. </s>
          <s id="N117BE">Si autem duobus ab <lb></lb><expan abbr="eadẽ">eadem</expan> potentia latis, hoc <expan abbr="quidẽ">quidem</expan> plus repellatur, illud vero minus, <lb></lb>rationi <expan abbr="conſentaneũ">conſentaneum</expan> eſt, tardius moueri id quod plus repellitur <lb></lb>eo quod repellitur minus. </s>
          <s id="N117D2">Quod videtur accidere maiori &amp; mi<lb></lb>nori illarum quæ ex centro circulos deſcribunt. </s>
          <s id="N117D7"><expan abbr="Quoniã">Quoniam</expan> enim <lb></lb>propius eſt manenti, eius quæ minor eſt, <expan abbr="extremũ">extremum</expan>, quam id quod <lb></lb>eſt maioris, veluti rectum in contrarium, ad medium, tardius <lb></lb>fertur minoris extremum. </s>
          <s id="N117E7">Omne quidem igitur circulum de<lb></lb>ſcribenti iſtud accidit: <expan abbr="ferturq.">ferturque</expan> eam quæ ſecundum naturam <lb></lb>eſt lationem, ſecundum circumferentiam: illam vero quæ præ<lb></lb>ter naturam, in tranſuerſum &amp; ſecundum centrum. </s>
          <s id="N117F6">Maio-<emph.end type="italics"></emph.end><pb pagenum="47" xlink:href="005/01/055.jpg"></pb><emph type="italics"></emph>rem autem ſemper eam quæ præter naturam eſt ipſa minor <lb></lb>fertur: quia enim centro eſt vicinior quod trahit, vincitur <lb></lb>magis.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N11808" type="head">
          <s id="N1180A">COMMENTARIVS.</s>
        </p>
        <p id="N1180E" type="main">
          <s id="N11810">Qvamuis Philoſophus ſuperiori textu ſemel atque <lb></lb>iterum aſſumpſerit, ſemidiametrum, ſeu lineam <lb></lb>circulum deſcribentem, duabus ferri lationibus, <lb></lb>prout explicuimus; huc tamen illud probandum <lb></lb>reliquit, &amp; ex dictis etiam de motu antrorſum &amp; retrorſum <lb></lb>manifeſtum eſſe docet. </s>
          <s id="N1181D">Id igitur hic probat ex eo. </s>
          <s id="N11820">Nam ſi <lb></lb>in deſcriptione circuli, ſemidiameter vnam tantum lationem <lb></lb>pateretur, vt verbi gratia naturalem, qua rectà tenderet ver<lb></lb>ſus, vnam aliquam differentiam ſitus, nunquam ad ipſius dia<lb></lb>metri perpendiculum perueniret. </s>
          <s id="N1182B">Implicat enim vnica la<lb></lb>tione, aliquid ſimul rectà tendere, ac in tranſuerſum, quem<lb></lb>admodum ſe habet perpendiculum ad diametrum à qua pro<lb></lb>pendit: At ſemidiameter circulum deſcribendo, aliquando <lb></lb>peruenit ad ſuum perpendiculum, ita vt coincidat cum illo: <lb></lb>Ergo non vnica, ſed duplici latione conuincitur ferri. </s>
        </p>
        <figure id="id.005.01.055.1.jpg" xlink:href="005/01/055/1.jpg"></figure>
        <p id="N1183D" type="main">
          <s id="N1183F">Sit enim circulus de<lb></lb>ſcribendus ABCD, circa <lb></lb>centrum E. </s>
          <s id="N11847">Sitque dia<lb></lb>meter AC, ſemidiameter <lb></lb>vero circulum deſcribens <lb></lb>AE. </s>
          <s id="N11851">Si igitur ipſa recta <lb></lb>A E, altero eius extremo <lb></lb>manente in centro E, al<lb></lb>tero vero nempè A, cir<lb></lb>cumferatur, aliquando <lb></lb>abſque dubio erit in ED, <lb></lb>quæ eſt perpendicularis <lb></lb>diametro AC. </s>
          <s id="N11863">Per <expan abbr="motũ">motum</expan> <lb></lb>autem naturalem ipſa AE, deſcendiſſet in FD, vel aliò rectè <lb></lb>tranſlata fuiſſet. </s>
          <s id="N1186E">Non ergo linea circulum deſcribens fertur, <pb pagenum="48" xlink:href="005/01/056.jpg"></pb>vnico tantum modo motu verſus vnicam differentiam ſitus, <lb></lb>ſed duplici motu, nempe mixto ex naturali &amp; præternaturali; <lb></lb>verſus duplicem differentiam ſitus. </s>
          <s id="N1187A">Naturali quippe, quo in <lb></lb>propoſita figura fertur verſus latus F D, præternaturali verò, <lb></lb>quo retrahitur in tranſuerſum verſus latus E D, eo quòd alte<lb></lb>rum eius extremum detineatur in centro E, vt clarius infra <lb></lb>patebit. </s>
        </p>
        <p id="N11885" type="main">
          <s id="N11887">Quibus ita conſtitutis, reuertitur Ariſtoteles ad <expan abbr="probandũ">probandum</expan>, <lb></lb>partes vel puncta ſemidiametri, eò velocius moueri, quò plus <lb></lb>à centro diſtauerint; eò verò tardius, quò magis ad centrum <lb></lb>acceſſerint. </s>
          <s id="N11896">Quod cum ad doctrinam in ſuperiori textu tra<lb></lb>ditam ſpectet, <expan abbr="illucq.">illucque</expan> propterea à nobis tranſlatum ſit, ac ſa<lb></lb>tis expoſitum, non eſt cur hic rurſus idem repetatur ac denuo <lb></lb>exponatur. </s>
          <s id="N118A3">Acceptionem autem &amp; explicationem motus <lb></lb>naturalis ac præternaturalis, qua vſi ſumus, ſumpſimus ex co<lb></lb>dem Philoſopho textu ſequenti, &amp; lib.

1. Metheororum c. 5. <lb></lb>Vbi diſcurrentium ſyderum ac fulminum motum quem in <lb></lb>ſublimi aere obliquè fieri conſpicimus, ex duabus pariter la<lb></lb>tionibus docet conſtare. </s>
          <s id="N118B2">Vna quidem naturali, qua prout <lb></lb>accenſa ac leuia corpora, ſurſum rectà tendere debent: <lb></lb>altera verò præternaturali, qua prout à conſtipan<lb></lb>te frigore extruduntur ac propelluntur (in<lb></lb>ſpiſſata ſcilicet ac grauitante magis eo<lb></lb>rum exhalationis materia) deor<lb></lb>ſum inclinant. </s>
          <s id="N118C1">Ex his enim <lb></lb>duabus lationibus <lb></lb>medius qui<lb></lb>dam mo<lb></lb>tus <lb></lb>reſultat, quo vt ipſe inquit, ſydera <lb></lb>videntur volare, &amp; obliquè <lb></lb>tanquam proiecta <lb></lb>per aera <lb></lb>ferri. </s>
        </p>
        <pb pagenum="49" xlink:href="005/01/057.jpg"></pb>
        <p id="N118DA" type="head">
          <s id="N118DC"><emph type="italics"></emph>Qua ratione partes diametri a centro remotio<lb></lb>res magis participent de motu naturali, <lb></lb>propinquiores verò magis de præ<lb></lb>ternaturali.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N118E9" type="head">
          <s id="N118EB">Textus Octauus</s>
        </p>
        <p id="N118EE" type="main">
          <s id="N118F0">Q<emph type="italics"></emph>vod autem magis quod præter naturam <lb></lb>eſt mouetur ipſa minor, quam maior illarum, <lb></lb>quæ ex centro circulos deſcribunt, ex ijs est <lb></lb>manifestum. </s>
          <s id="N118FC">Sit circulus vbi B C D E, &amp; <lb></lb>alter in hoc minor, vbi M N O P, circà <lb></lb>idem centrum A, &amp; projiciantur diametri <lb></lb>in magno quidem, in quibus C D, B E, in minori verò ipſæ <lb></lb>M O, N P: &amp; altera parte longius quadratum ſuppleatur <lb></lb>D K R C: ſiquidem A B circulum deſcribens ad id perue<lb></lb>niet, vnde eſt egreſſa; manifeſtum eſt, quod ad ipſam fertur <lb></lb>AB. </s>
          <s id="N1190E">Similiter etiam A M ad ipſam A M perueniet. </s>
          <s id="N11911">T ardiùs <lb></lb>autem fertur A M, quam A B quemadmodum dictum <lb></lb>eſt: quia maior fit repulſio, &amp; magis retrabitur A M. </s>
          <s id="N11918">Du<lb></lb>catur igitur ipſa A L F, &amp; ab ipſo L perpendiculum ad ip<lb></lb>ſam AB, ipſa LQ in minore circulo: &amp; rurſum ab L du<lb></lb>catur iuxtà A B L S, &amp; S T ad ipſam A B perpendicu<lb></lb>lum, &amp; ipſa FX: ipſæ igitur vbi ſunt ST, &amp; LQ, æqua<lb></lb>les: ipſa ergò B T minor est, quam M <expan abbr="q.">que</expan> Aequales enim <lb></lb>rectæ lineæ in ęqualibus coniecta circulis perpendiculares à <lb></lb>diametro, minorem diametri reſecant ſectionem in maioribus <lb></lb>circulis. </s>
          <s id="N1192F">Est autem ipſa S T æqualis ipſi L <expan abbr="q.">que</expan> In quan<lb></lb>to autem tempore ipſa AL ipſam ML lata eſt, in tanto tem<lb></lb>poris ſpatio in maiori circulo, maiorem, quam ſit B S, latum <lb></lb>erit extremum ipſis AB. </s>
          <s id="N1193D">Latio quidem igitur ſecundum na<lb></lb>turam æqualis: Ea autem, quæ præter naturam eſt minor, <lb></lb>videlicet B T, quam M <expan abbr="q.">que</expan> Oportet autem proportiona-<emph.end type="italics"></emph.end><pb pagenum="50" xlink:href="005/01/058.jpg"></pb><emph type="italics"></emph>biliter eſſe, ſicut quod est fecundum naturam, ita quod est <lb></lb>præter naturam, ad id, quod est præter naturan; maiorem <lb></lb>igitur circumferentiam pertranſiuit, quam ſit ipſa S B. </s>
          <s id="N11955">Ne<lb></lb>ceſſe autem eſt ipſam F B. in hoc tempore pertranſi&lt;32&gt;e: hic <lb></lb>enim erit, quando proportionabiliter vtrinque accidis, quod eſt <lb></lb>præter naturam, ad id quod eſt ſecundum naturam. </s>
          <s id="N1195E">Si igi<lb></lb>tur maius eſt, quod ſecundum naturam in maiori, &amp; quod eſt <lb></lb>præter naturam, magis vtique hic coincidit vno modo: ita <lb></lb>quod B ſit latum per ipſam B F in tanto tempore, in quo <lb></lb>M punctum per ipſam M L. </s>
          <s id="N1196A">Hic enim ſeeundum naturam <lb></lb>quidem ſigno B fit X F: eſt enim ab ipſo F perpendiculum: <lb></lb>præter naturam verò ad ipſam X B. </s>
          <s id="N11971">Eſt autem quem ad<lb></lb>modum FX ad X B, ſic L Q ad M <expan abbr="q.">que</expan> Manifeſtum <lb></lb>autem ſi coniunguntur ab ipſa B M ad FL. </s>
          <s id="N1197C">Si autem mi<lb></lb>nor, aut maior, quam ſit FB erit illa, quam latum eſt B, <lb></lb>non ſimiliter erit, neque proportionale in vtriſque quod eſt ſe<lb></lb>cundum naturam ad id quod eſt præter naturam. </s>
          <s id="N11985">Quam igi<lb></lb>tur ob cauſam ab eadem potentia celerius fertur id quod plus <lb></lb>à centro diſtat punctum ex ijs, quæ dicta ſunt eſt mani<lb></lb>feſtum.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N11990" type="head">
          <s id="N11992">COMMENTARIVS.</s>
        </p>
        <p id="N11996" type="main">
          <s id="N11998">Ex aſſumptis ab Ariſtotele in illo priori argumento <lb></lb>iam ſupra textu 6. à nobis expoſito ad oſtenden<lb></lb>dum in ipſo circulo, quæ plus à centro diſtat linea <lb></lb>eadem vi commota citius ferri quàm illa, quæ minus diſtat; <lb></lb>illud dumtaxat ci probandum remanſerat, videlicet partes <lb></lb>lineæ circulum deſcribentis, quò viciniores centro ſunt, eò <lb></lb>magis detrahi à motu naturali, <expan abbr="magisq.">magisque</expan> participare de motu <lb></lb>præternaturali; E contrà verò quo remotiores ſunt à cen<lb></lb>tro, magis participare de motu naturali, vt inde inferatur ve<lb></lb>locius moueri. </s>
          <s id="N119B3">Probat autem hoc modo; ſit enim, inquit, <lb></lb>Circulus B C D E; &amp; alter in hoc minor vbi M N O P <lb></lb>circà idem centrum A. <expan abbr="Sintq.">Sintque</expan> Diametri maioris quidem C. <lb></lb>D, &amp; B E; minoris verò M O, &amp; N P. </s>
          <s id="N119C1">Deinde complea-<pb pagenum="51" xlink:href="005/01/059.jpg"></pb><figure id="id.005.01.059.1.jpg" xlink:href="005/01/059/1.jpg"></figure><lb></lb>tur quadrangulum rectangulum D K R C nempe ducen<lb></lb>do lineam K R. paralellam, &amp; æqualem ipſi D C. per pun<lb></lb>ctum B, &amp; claudendo ipſas K R &amp; D C per lineas D K <lb></lb>&amp; C R. </s>
          <s id="N119D6">Cum igitur motus naturalis cuiuſlibet lineæ dica<lb></lb>tur ille, quo recta fertur verſus eam partem in quam tendit, <lb></lb>ſi linea A B ſtantis circuli deſcripti deorſum tenderet ſim<lb></lb>plici motu naturali, abſque dubio rectè, ac perpendiculari<lb></lb>ter tota ſimul caderet, &amp; coincideret cum C R. </s>
          <s id="N119E4">Quoniam <lb></lb>vero non poteſt ita ferri ſimplici motu naturali, eò quod al<lb></lb>terum eius extremum detineatur in centro, illæ partes ip<lb></lb>ſius dicentur magis participare de motu naturali, quæ re<lb></lb>ctius tendunt in ipſam C R; hoc eſt per lineam magis appro<lb></lb>pinquantem ad perpendiculum; ſicut è contrà illæ dicentur <lb></lb>magis detrahi à motu naturali, quæ magis incuruantur ten<lb></lb>dendo verſus lineam C D. </s>
          <s id="N119F6">Itaque progreſſas perpendicu<lb></lb>laris verſus C R erit motus naturalis, verſus autem C D erit <lb></lb>præternaturalis Quod certè videtur ſupponere Ariſtoteles. <lb></lb></s>
          <s id="N119FF">Nunc autem ſic procedit ad oſtenden lum propoſitum, <lb></lb>nempè partem diametri propinquiorem centro, vt A M <pb pagenum="52" xlink:href="005/01/060.jpg"></pb>magis detrahi à motu naturali, ac tardiùs moueri, quàm <lb></lb>M B quæ magis diſtat ab illo. </s>
          <s id="N11A0B">Ducatur inquit à centro li<lb></lb>nea A L F; &amp; à puncto L perpendicularis ipſi A B quæ <lb></lb>ſit L Q, &amp; rurſus ab eodem L ducatur L S paralella ei<lb></lb>dem A B. </s>
          <s id="N11A14">Deinde à puncto S excitetur alia perpendicu<lb></lb>laris eidem AB. <expan abbr="Sitq.">Sitque</expan> ST; &amp; ab F item eidem perpendicu<lb></lb>laris F X. </s>
          <s id="N11A20">His poſitis linea QL erit æqualis lineæ T S, vt <lb></lb>patet ex 34. primi Euclidis, cum ſint latera oppoſita rectan<lb></lb>guli T L. </s>
          <s id="N11A28">Cumque ſpacium, quod naturali motu tranſcur<lb></lb>runt puncta M, &amp; B menſuretur ipſis perpendicularibus. <lb></lb></s>
          <s id="N11A2E">QL &amp; T S, vt dictum eſt, motus naturalis per lationem ip<lb></lb>ſius B vſque ad S æqualis erit motui naturali per lationem <lb></lb>ipſius M vſque ad L. </s>
          <s id="N11A36">At motus præternaturales eorundem <lb></lb>punctorum M, &amp; B tunc erunt inæquales. </s>
          <s id="N11A3B">Nam ſpacium <lb></lb>quod præternaturaliter percurriſſet punctum M eſſet ipſa <lb></lb>M <expan abbr="q;">que</expan> &amp; ſpatium, quod præternaturaliter percurriſſet <lb></lb>punctum B eſſet ipſa B T. </s>
          <s id="N11A49">Maior autem eſt M Q, quàm <lb></lb>ſit B T. </s>
          <s id="N11A4F">Siquidem ex æqualibus rectis lineis perpendicula<lb></lb>riter cadentibus à communi diametro ad circumferentias <lb></lb>totidem circulorum inæqualium, ea, quæ eſt in minori <lb></lb>circulo maiorem reſecat diametri portionem, vt conſtat <lb></lb>ex doctrina de Sinibus, &amp; patere poteſt in perpendicularibus <lb></lb>QL T S, &amp; HI; quæ cum ſine æquales inter duas paralel<lb></lb>las, inæquales reſecant portiones diametri E G; nempe tan<lb></lb>to maiorem, quanto in minori circulo, vt eſt QM reſpectu <lb></lb>T B, &amp; ipſa T B reſpectu H G. </s>
          <s id="N11A63">Igitur punctum M quod ſa<lb></lb>nè propinquius eſt centro, magis mouetur motu præterna<lb></lb>turali, quàm punctum B, quod remotius eſt ab illo. </s>
          <s id="N11A6A">Id quod <lb></lb>primo loco erat probandum. </s>
        </p>
        <p id="N11A6F" type="main">
          <s id="N11A71">Vlterius verò quod punctum B magis moueatur motu <lb></lb>ſecundum naturam, quam ipſum punctum M probatur ex <lb></lb>eo; Nam quo tempore punctum M latum fuerit vſque ad <lb></lb>L; punctum B eodem tempore perueniet vſque ad F. </s>
          <s id="N11A7B">Ete<lb></lb>nim cum ita ſe habere debeat motus naturalis ipſius B ad <lb></lb>motum præter naturam eiuſdem B quemadmodum ſe ha<lb></lb>bet motus naturalis ipſius M ad motum præter naturam <pb pagenum="53" xlink:href="005/01/061.jpg"></pb>eiuſdem M talis proportio ſolum verificari poteſt in F, <lb></lb>nam proportio, quam habet linea F X referens ſpacium <lb></lb>tranſactum ſecundum naturam ad B X, quod ab eodem <lb></lb>puncto B tranſactum eſt præter naturam in maiori circulo, <lb></lb>eadem eſt, ac proportio lineæ QL tranſactæ ſecundum <lb></lb>naturam ad lineam M Q tranſactam præter naturam in mi<lb></lb>nori circulo. </s>
          <s id="N11A95">Quod inde patere poteſt, nam ſi ducantur re<lb></lb>ctæ B F, &amp; M L efficientur duo triangula æquiangula <lb></lb>B X F, &amp; M Q L quæ per 4. ſexti habebunt latera pro<lb></lb>portionalia circà æquales angulos: Vnde ſicut ſe habet F X <lb></lb>ad X B circa angulum. </s>
          <s id="N11AA0">rectum X, ita ſe habet L Q ad <lb></lb>QM circà angulum rectum <expan abbr="q.">que</expan> Et permutando, ſicut ſe <lb></lb>habet F X ad L Q, ità X B ad QM per 16. Quinti. </s>
          <s id="N11AAB">Ita<lb></lb>que proportionabiliter punctum B, vel quodlibet aliud, <lb></lb>quanto magis diſtat à centro, tanto magis mouebitur motu <lb></lb>naturali; ſiquidem F X maior eſt, quam L Q, <expan abbr="proindeq.">proindeque</expan> <lb></lb>velociùs feretur, ſeù maius ſpatium in eodem tempore per<lb></lb>curret, quam punctum M, vel aliud, quod propinquius <lb></lb>ſit centro; Et hoc erat probandum, vt omnino conſtaret <lb></lb>quidquid aſſumptum fuerat ex eodem Ariſtotele in explica<lb></lb>tione quartæ proprietatis circuli, &amp; aſſignatione cauſæ illius, <lb></lb>vt ibidem commonuimus. </s>
        </p>
        <p id="N11AC8" type="head">
          <s id="N11ACA"><emph type="italics"></emph>De Inſtrumentis, ac Machinis naturam cir<lb></lb>culi in motione participantibus.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N11AD3" type="head">
          <s id="N11AD5">ADDITIO PRIMA.</s>
        </p>
        <p id="N11AD9" type="main">
          <s id="N11ADB">Attenta natura circuli cum ſuis proprietatibus modò <lb></lb>explicatis ad hoc acumen humani ingenij iam pridem <lb></lb>peruenit, vt machinas quaſdam excogitaret, quæ naturam <lb></lb>ipſius circuli participantes, motricem potentiam in motu <lb></lb>grauium ac leuium iuuarent. </s>
          <s id="N11AE6">Huiuſmodi autem machinas <lb></lb>inſtrumenta mechanica communiter appellamus, vtpotè <lb></lb>quæ mechanica ſpeculatione adinuenta ſunt, <expan abbr="eademq.">eademque</expan> arte <pb pagenum="54" xlink:href="005/01/062.jpg"></pb>adhibentur tanquam inſtrumenta ad leuanda pondera, vel <lb></lb>quomodolibet mouenda grauia, quæ reſpectiuè dicuntur <lb></lb>etiam leuia. </s>
          <s id="N11AFA">Sunt autem hæc inſtrumenta præcipua ſex, ad <lb></lb>quæ cætera omnia reducuntur: nempè Libra. </s>
          <s id="N11B00">Vectis, Tro<lb></lb>chlea, Axis in Peritrochio, Cuneus, &amp; Cochlea Et licet Ari<lb></lb>ſtoteles diſtinctam eorum tractationem prætermiſerit, ac <lb></lb>non niſi quatuor ex ipſis hic, vel in ſequentibus quæſtionibus <lb></lb>pro opportunitate meminerit, ſupponit nihilominus <expan abbr="tanquã">tanquam</expan> <lb></lb>certum, illa omnia ac ſimilia participare naturam circuli, <lb></lb>eorumque vim qua motricem augent potentiam in hoc ip<lb></lb>ſo conſiſtere, vt circuli proprietatem ſapiendo, faciliùs &amp; <lb></lb>mouerentur, &amp; motum præſtarent oneribus ac ponderibus <lb></lb>mouendis, cum circularis ſine orbicularis figura ſit omnium <lb></lb>mouentiſſima. </s>
          <s id="N11B1B">Ait enim ſupra tex. 5. Ea igitur quæ circa <lb></lb>libram fiunt, ad circulum referuntur: quæ verò circa vectem, <lb></lb>ad ipſam libram: alia autem ferè omnia, quæ circa mecha<lb></lb>nicas ſunt motiones, ad vectem. </s>
          <s id="N11B26">Ex quibus infertur ſiue im<lb></lb>mediate, ſiue mediante, alia quadam abſtracta ratione quam <lb></lb>ipſa participent, mechanica penè omnia inſtrumenta in ſuis <lb></lb>motionibus ad circuli naturam referri. </s>
          <s id="N11B2F">Quod vt clarius te<lb></lb>neatur, pauca ſaltem de ſingulis ipſis inſtrumentis hic adij<lb></lb>cere opere pretium putauimus, ea ſcilicet tantum mo<lb></lb>do, quæ ad inſtitutam textus dilucidationem no<lb></lb>uerimus pertinere; Cum exacta huiuſmodi <lb></lb>inſtrumentum tractatio habeatur apud <lb></lb>Heronem, Pappum, &amp; alios ve<lb></lb>teres, nouiſsimè verò &amp; <lb></lb>accuratiſsimè apud <lb></lb>Guidum Vbal<lb></lb>dum <lb></lb>ex Marchionibus Montis, qui ſi<lb></lb>gillatim de illis præcla<lb></lb>rum librum in<lb></lb>ſtituit. </s>
        </p>
        <pb pagenum="55" xlink:href="005/01/063.jpg"></pb>
        <p id="N11B53" type="head">
          <s id="N11B55">DE LIBRA.</s>
        </p>
        <p id="N11B58" type="main">
          <s id="N11B5A">Libra, quæ inter mechanica inſtrumenta iure <lb></lb>primum ſibi vendicat locum, eo quod imme<lb></lb>diatius, ac magis participet <expan abbr="naturã">naturam</expan> circuli in <lb></lb>ſuis motionibus, eſt <expan abbr="iugũ">iugum</expan> <expan abbr="quoddã">quoddam</expan> ex medio <lb></lb>liberè ſuſpenſum, <expan abbr="axeq.">axeque</expan> <expan abbr="ſuffultũ">ſuffultum</expan>, ac plano ho<lb></lb>rizontis <expan abbr="parallelũ">parallelum</expan>, ex cuius <expan abbr="vtraq;">vtraque</expan> extremitate gemina lanx <lb></lb>pendet, <expan abbr="cuiusq.">cuiusque</expan> conuerſione circa ipſum axem, dum altera <lb></lb>eleuatur, altera deprimitur, póndus vel exceſſus <expan abbr="põderis">ponderis</expan> cu<lb></lb>iuſlibet, deprehenditur, ac menſuratur. </s>
          <s id="N11B91">Qua in deſcriptione <lb></lb>ſupponitur <expan abbr="iugũ">iugum</expan> ex medio, trutina, ſeu axe ſuſpenſum, conſti<lb></lb>tui, ac manere parallelum plano horizontis propter <expan abbr="æqui-ponderantiã">æqui<lb></lb>ponderantiam</expan> vtriuſque medietatis: <expan abbr="motumq.">motumque</expan> circularem, ſeu <lb></lb><expan abbr="conuerſionẽ">conuerſionem</expan> circa fulcimentum tanquam circa <expan abbr="centrũ">centrum</expan> im<lb></lb>motum, non niſi ratione <expan abbr="inæqualiũ">inæqualium</expan> <expan abbr="ponderũ">ponderum</expan> in gemina lance <lb></lb>vtrinque pendentium illi competere: vnde ſi pondera ſint <lb></lb>æqualia, libra ſemper maneat, &amp; in æquilibrio conſtituatur, <lb></lb>ſeu æquidiſtans à plano horizontis. </s>
          <s id="N11BBF">Deinde ita ſupponitur, <lb></lb>pondera in lancibus impoſita, ex vtraque iugi extremitate <lb></lb><expan abbr="pẽdere">pendere</expan>, vt hoc non ſit <expan abbr="neceſſariũ">neceſſarium</expan>, <expan abbr="neq;">neque</expan> eſſentialiter pertineat <lb></lb>ad <expan abbr="conſtitutionẽ">conſtitutionem</expan> libræ, ſed potius ad <expan abbr="commoditatẽ">commoditatem</expan> ponde<lb></lb>randi, cum ſatis intelligatur libra eſſentialiter conſtituta <lb></lb>etiam abſque lancibus, ponderibus in ipſis iugi extremita<lb></lb>tibus, adiacentibus, vt cernere eſt in ſequentibus figuris. </s>
        </p>
        <p id="N11BE1" type="main">
          <s id="N11BE3">Quo autem pacto libra in ſui motione participet natu<lb></lb>ram circuli per ſe conſtat conſideranti, iugum, diametri vi<lb></lb>cem gerere, axem verò ſeu trutinam, aut <expan abbr="fulcimentũ">fulcimentum</expan> quod<lb></lb>libet, centri locum tenere, circa quod immotum, ipſa dia<lb></lb>meter vertitur dum circulum deſcribit; ſiquidem immoto <lb></lb>axe, ſeu fulcimento ipſius libræ, iugum, alterius extremita<lb></lb>tis depreſsione ob exuperantiam <expan abbr="põderis">ponderis</expan>, alterius verò ele<lb></lb>uatione, circumagitur, non ſecus ac diameter circulum <lb></lb>conficiendo. </s>
          <s id="N11BFE">Quod ſi partes iugi vtrinque à centro produ<lb></lb>ctæ, non ſint inter ſe <expan abbr="lõgitudine">longitudine</expan> æquales, quamuis æquipon<lb></lb>derantes; tunc quidem in ipſis iugi conuerſione, ac circum<pb pagenum="56" xlink:href="005/01/064.jpg"></pb>latione duo circuli deſcribentur alter altero maior, <expan abbr="tanquã">tanquam</expan> <lb></lb>à duplici ſemidiametro circumlato, vt hic erit inſpicere. </s>
        </p>
        <figure id="id.005.01.064.1.jpg" xlink:href="005/01/064/1.jpg"></figure>
        <p id="N11C19" type="head">
          <s id="N11C1B">DE VECTE.</s>
        </p>
        <p id="N11C1E" type="main">
          <s id="N11C20">Vectis ſimplex <expan abbr="quoddã">quoddam</expan> <expan abbr="inſtrumentũ">inſtrumentum</expan> eſt ligneum, <lb></lb>vel <expan abbr="ferreũ">ferreum</expan> ſatis oblongum veluti palus, aut fuſtis <lb></lb>grandior, ad promouenda pondera; cuius vt <expan abbr="plu-rimũ">plu<lb></lb>rimum</expan> altera extremitas <expan abbr="põderi">ponderi</expan> eleuando ſubijci<lb></lb>tur, altera verò manu, ſeu <expan abbr="potẽtia">potentia</expan> præmitur, ſub<lb></lb>ſtrato inter <expan abbr="vtramq;">vtramque</expan> aliquo fulcimento, cui inni<lb></lb>tatur, quòd græcè hypomochlion appellatur, <expan abbr="quodq">quoque</expan> <expan abbr="quãto">quanto</expan> pro<lb></lb>pinquius ponderi locatur, tanto facilius ipſo vecte leuatur. </s>
          <s id="N11C52">Ali<lb></lb>quando verò altera extremitas <expan abbr="nõ">non</expan> ponderi, ſed fulcimento ſubij<lb></lb>citur, vel ei quoquo modo innititur <expan abbr="tanquã">tanquam</expan> manenti valido, pon-<pb pagenum="57" xlink:href="005/01/065.jpg"></pb><expan abbr="dusq.">dusque</expan> eleuatur, aut deprimitur per vectis <expan abbr="partẽ">partem</expan> mediam, quæ eſt <lb></lb>inter <expan abbr="vtramq.">vtramque</expan> <expan abbr="extremitatẽ">extremitatem</expan> iuxta <expan abbr="eleuationẽ">eleuationem</expan>, aut <expan abbr="depreſſionẽ">depreſſionem</expan> al<lb></lb>terius extremitatis vbi applicatur <expan abbr="potẽtia">potentia</expan>: vel certè <expan abbr="põdus">pondus</expan> ele<lb></lb>uatur per <expan abbr="alterã">alteram</expan> extremitatem, ſi in illa locetur, <expan abbr="manusq.">manusque</expan> aut po<lb></lb>tentia in medio adhibeatur. </s>
          <s id="N11C95">Vnde tres nonnulli ſpecies <expan abbr="vectiũ">vectium</expan> di<lb></lb>ſtinguunt, quas iuxta prædicta figuris <expan abbr="etiã">etiam</expan> hic ſtuduimus expri<lb></lb>mere; Illud interim admonendo, eas omnes facilè in ſuis motio<lb></lb>nibus ad <expan abbr="circulũ">circulum</expan> referri, cum ipſæ non niſi <expan abbr="diametrũ">diametrum</expan>, vel <expan abbr="ſemidia-metrũ">ſemidia<lb></lb>metrum</expan> <expan abbr="circulũ">circulum</expan> circa <expan abbr="immotũ">immotum</expan> <expan abbr="fulcimentũ">fulcimentum</expan> <expan abbr="deſcribentẽ">deſcribentem</expan> referant, vt <lb></lb>per ſe patet, ac prima quæ ſanè vtilior &amp; frequentius in vſu eſt, <lb></lb>ad <expan abbr="librã">libram</expan> à <expan abbr="fulcimẽto">fulcimento</expan> inæquales vtrinque partes <expan abbr="habentẽ">habentem</expan> euiden<lb></lb>tiſsimè reducatur, vt amplius deinceps <expan abbr="cõſtabit">conſtabit</expan>. </s>
          <s id="N11CDA"><expan abbr="Nã">Nam</expan> hoc quod eſt <lb></lb>fulciri per <expan abbr="ſuſpenſionẽ">ſuſpenſionem</expan> beneficio trutinæ, vel per <expan abbr="ſubiectionẽ">ſubiectionem</expan> al<lb></lb>terius corporis, quod non minus axis, ac centri <expan abbr="vicẽ">vicem</expan> ſubeat, eſt <lb></lb>differentia valde accidentalis. </s>
        </p>
        <figure id="id.005.01.065.1.jpg" xlink:href="005/01/065/1.jpg"></figure>
        <pb pagenum="58" xlink:href="005/01/066.jpg"></pb>
        <p id="N11CFB" type="head">
          <s id="N11CFD">DE TROCHLEA.</s>
        </p>
        <p id="N11D00" type="main">
          <s id="N11D02">Trochlea eſt inſtrumentum veluti conce<lb></lb>ptaculum quoddam, aut capſula, vnum, vel <lb></lb>plures ſtriatos orbiculos, ſeu rotulas in ſe <lb></lb>continens, axiculis per rotulas traiectis, circa <lb></lb>quos illæ vertuntur, quibus admoto fune du<lb></lb>ctario eleuantur, aut remittuntur onera. </s>
          <s id="N11D0F">Conſtare autem <lb></lb>ſolet Trochlea ex vno, vel pluribus orbiculis tanquam inter <lb></lb>thecas inſertis, non quidem æqualibus, ſed maioribus ſuper <lb></lb>minores adiectis, ne vnius funis circumductus funem alte<lb></lb>rius impediat. </s>
          <s id="N11D1A">Inſuper ipſi orbiculo, modò bini ſuper binos <lb></lb>locari conſueuerunt, ita vt in trochlea quatuor, vel ſex or<lb></lb>biculi, duplici, vel triplici ordine <expan abbr="reperiãtur">reperiantur</expan> diſpoſiti; modo <lb></lb>verò non niſi ſinguli ſuper ſingulos, totidem ordinibus con<lb></lb>tinentur, vt quo potuimus modò hic figuris expreſsimus. </s>
        </p>
        <figure id="id.005.01.066.1.jpg" xlink:href="005/01/066/1.jpg"></figure>
        <p id="N11D2E" type="main">
          <s id="N11D30">Reducitur autem Trochlea ad Vectem, &amp; conſequen<lb></lb>ter ad libram, quia vnuſquiſque orbiculus illius per diame<lb></lb>trum nititur proprio axiculo tanquam fulcimento, quod in<lb></lb>ter onus leuandum, aut ſuſtinendum, &amp; potentiam eleuan<lb></lb>tem locatur, ita vt ad depreſsionem vnius extremitatis dia-<pb pagenum="59" xlink:href="005/01/067.jpg"></pb>metri, vbi mouentis potentia applicatur, altera extremitas, <lb></lb>quæ onus ſuſtinet, eleuetur; licet hoc non immediatè fiat; <lb></lb>ſed mediante fune ductario, vt hic ad oculos ſpectandum <lb></lb>proponetur ac infra fuſiùs explicabitur quæſt. </s>
          <s id="N11D46">18. Sit enim <lb></lb>trochleae orbiculus ABC, dia<lb></lb><figure id="id.005.01.067.1.jpg" xlink:href="005/01/067/1.jpg"></figure><lb></lb>meter verò orbiculi linea ho<lb></lb>rizonti parallela AB, &amp; axicu<lb></lb>lus C, tanquam centrum lo<lb></lb>catum in medio: Deinde per <lb></lb>funem ductarium ab extremo <lb></lb>A propendeat onus D, &amp; ab <lb></lb>extremo B idem funis demit<lb></lb>tatur, cui applicata ſit poten<lb></lb>tia motiua in E. </s>
          <s id="N11D64">Dicimus er<lb></lb>go totum orbiculum incum<lb></lb>bere, ac niti axiculo C tan<lb></lb>quam fulcimento per diame<lb></lb>trum eius AB in cuius medio <lb></lb>axiculus eſt locatus, &amp; in cuius <lb></lb>extremis AB, vtrinque ſit tota <lb></lb>compreſsio, nempe oneris ac potentiæ; <expan abbr="proindeq.">proindeque</expan> ipſam <lb></lb>diametrum AB, vectis vicem in motione gerere, qua<lb></lb>tenus nixa in præfato fulcimento C, ad depreſ<lb></lb>ſionem extreminitatis B per vim trahen<lb></lb>tem in E, extremitas A neceſſario <lb></lb>eleuatur, ac ſimul cum illa <lb></lb>pondus D pendens ex <lb></lb>ipſa, vt per ſe <lb></lb>patet. </s>
        </p>
        <pb pagenum="60" xlink:href="005/01/068.jpg"></pb>
        <p id="N11D8D" type="head">
          <s id="N11D8F">DE AXE IN PERITROCHIO.</s>
        </p>
        <p id="N11D92" type="main">
          <s id="N11D94">Axis in Peritrochio eſt oblongus quidam <lb></lb>cylindrus Peritrochio firmiter infixus, ac pa<lb></lb>rallelus horizontis plano locatus, cuius ex<lb></lb>trema in rotundis foraminibus immoti peg<lb></lb>matis expeditè vertuntur. </s>
          <s id="N11D9F">Peritrochium ve<lb></lb>rò, eſt machina rotunda, ad rotæ ſeu tympani ſimilitudi<lb></lb>nem efformata, in cuius conuexa peripheria ſtipites qui &amp; <lb></lb>Scytalæ vocantur, tanquam radij infinguntur; quibus admo<lb></lb>ta manu tota machina ſimul cum axe verſatur, ac funibus <lb></lb>circa axem conuolutis, trahuntur pondera illis alligata; vt <lb></lb>hic licebit inſpicere. </s>
        </p>
        <figure id="id.005.01.068.1.jpg" xlink:href="005/01/068/1.jpg"></figure>
        <p id="N11DB3" type="main">
          <s id="N11DB5">Reducitur <expan abbr="autẽ">autem</expan> <lb></lb>tota huiuſmodi ma <lb></lb>china, ſeu inſtru<lb></lb>mentum ad <expan abbr="vectẽ">vectem</expan>; <lb></lb>Nam ſi conſidere<lb></lb>mus <expan abbr="conſtitutũ">conſtitutum</expan> ex <lb></lb>diametro axis, ac <lb></lb>ſemidiametro Pe<lb></lb>ritrochij <expan abbr="coincidẽ-te">coinciden<lb></lb>te</expan> cum illa non ali<lb></lb>ter in circumuolu<lb></lb>tione ſe habere <expan abbr="cõ-perimus">com<lb></lb>perimus</expan>, ac <expan abbr="Vectẽ">Vectem</expan>, <lb></lb>qui circa ſuum ful<lb></lb>cimentum vertitur, <lb></lb>tanquam circa pro<lb></lb>prium centrum. <lb></lb></s>
          <s id="N11DF1">Eſto enim Axis ſimul, ac Peritrochij immobile centrum <lb></lb>A, circa quod vtriuſque circumferentia deſcripta ſit, nem<lb></lb>pe tàm Axis, quàm Tympani ipſius Peritrochij cum ſcyta<lb></lb>lis; Diameter verò Axis ſit linea BC; ac ſemidiameter Pe<lb></lb>titrochij AD, conſtituentes integram lineam BD. </s>
          <s id="N11DFD">Tum <pb pagenum="61" xlink:href="005/01/069.jpg"></pb>ex Axe per funem BE propendeat onus F; <expan abbr="virtusq.">virtusque</expan> mo<lb></lb>uentis applicetur in ſcytala vbi eſt ipſum D. </s>
          <s id="N11E0C">Ad motum <lb></lb>igitur deorſum ipſius D, linea BD, non aliter ſe poteſt <lb></lb>habere, ac vectis firmiter innixa immobili centro A, tan<lb></lb>quam fulcimento, ac dum pars AD deprimitur, altera. <lb></lb></s>
          <s id="N11E16">nempe AB, eleuabitur ſimulque cum puncto B, pondus <lb></lb>F, quod ab eodem puncto extremo dependet. </s>
        </p>
        <figure id="id.005.01.069.1.jpg" xlink:href="005/01/069/1.jpg"></figure>
        <p id="N11E20" type="head">
          <s id="N11E22">DE CVNEO.</s>
        </p>
        <p id="N11E25" type="main">
          <s id="N11E27">Cvnevs eſt ſimplex quoddam inſtrumen<lb></lb>tum ad findenda, ſeu ſcindénda corpora aptiſ<lb></lb>ſimum accedente percuſſione. </s>
          <s id="N11E2E">Eſt enim ſoli<lb></lb>dum, quod ex quadrangulari baſe <expan abbr="conſurgẽs">conſurgens</expan>, <lb></lb>quatuor ſuperficiebus in peracutam aciem <lb></lb>terminantibus, clauditur. </s>
          <s id="N11E3B">Duabus videlicet ſibi oppoſitis <lb></lb>quadrangularibus, ac altera parte longioribus; duabus verò <lb></lb>ſimiliter oppoſitis, ſed triangularibus in prædictam acutam, <lb></lb>&amp; oblongam aciem terminantibus. </s>
          <s id="N11E44">Quæ ſanè acies cum in <lb></lb>rimulam quamlibet <expan abbr="ſcindẽdæ">ſcindendæ</expan> molis ſe inſinuare præualeat, <pb pagenum="62" xlink:href="005/01/070.jpg"></pb>adueniente valida percuſſione, vt quæ per malleúm ſuper ba<lb></lb>ſim adactum fieri conſueuit, facilè totum cuneum cogit ad<lb></lb>mittere, <expan abbr="proindeq.">proindeque</expan> partes molis ab inuicem ſecedere, quod <lb></lb>eſt molem ipſam ſcindi, ac diuidi. </s>
          <s id="N11E5E">Cunei ergo figura ſic de<lb></lb>lineanda cenſuimus ex quadrata baſi ABCD, excitando <lb></lb>ſuperficiem quadrangularem DBEF, ac aliam triangula<lb></lb>rem CDE, quæ ſimul cum ſuis oppoſitis omnes quatuor <lb></lb>deſinant, ac terminentur in aciem EF. </s>
        </p>
        <figure id="id.005.01.070.1.jpg" xlink:href="005/01/070/1.jpg"></figure>
        <p id="N11E6E" type="main">
          <s id="N11E70">Refertur auté hoc quoque inſtru<lb></lb>mentum ad vecté, eo quod ex duplici <lb></lb>vecte videatur conſtare, vt infra quęſt. <lb></lb></s>
          <s id="N11E78">17. ex Ariſtotele magis ex profeſſo <lb></lb>probabitur. </s>
          <s id="N11E7D">Etenim ſi conſiderentur <lb></lb>duo eius latera, quæ ex baſi in aciem <lb></lb>terminantur, vt CE, &amp; DE non ſe<lb></lb>cus ac duo vectes ſibi inuicem obuer<lb></lb>ſi, &amp; cóntra conantes reperientur, quo<lb></lb>rum <expan abbr="vtiq;">vtique</expan> fulcimenta ſunt partes ſcin<lb></lb>dendi corporis vtrinque conſtitutæ vt <lb></lb>GH, quibus intrando cuneus innititur. </s>
          <s id="N11E92">Onera verò ſunt re<lb></lb><figure id="id.005.01.070.2.jpg" xlink:href="005/01/070/2.jpg"></figure><lb></lb>reliquæ eiuſdem corporis partes <lb></lb>ſucceſsiuè dimouendę, &amp; adinui<lb></lb>cem ſeparándæ per aciem intran<lb></lb>tem vbi E, vt in propoſita figu<lb></lb>ra eſt l, &amp; K. </s>
          <s id="N11EA6">Nam pars vbi K <lb></lb>eſt onus reſpectu vectis CE in<lb></lb>nixæ in G; &amp; pars vbi I, eſt <lb></lb>onus reſpectu vectis DE innixæ <lb></lb>in H. </s>
          <s id="N11EB2">Et extrema in quibus ap<lb></lb>plicatur potentia ſunt initia ipſo<lb></lb>rum laterum ex parte baſis vbi <lb></lb>fit tota percuſſio, nempe vbi C <lb></lb>&amp; D, quæ omnia apertiſſimè <lb></lb>citata quæſtione amplius conſta<lb></lb>bunt. </s>
        </p>
        <pb pagenum="63" xlink:href="005/01/071.jpg"></pb>
        <p id="N11EC5" type="head">
          <s id="N11EC7">DE COCHLEA.</s>
        </p>
        <p id="N11ECA" type="main">
          <s id="N11ECC">Cochlea inſtrumentum eſt veluti com<lb></lb>poſitum ex cuneo, &amp; cylindro, ſeu eſt ſtria<lb></lb>tus quidam cylindrus ſtrigas habens admo<lb></lb>dum helicis ſpirulatim circumuolutas, cuius <lb></lb>vertigine pondera helici <lb></lb><figure id="id.005.01.071.1.jpg" xlink:href="005/01/071/1.jpg"></figure><lb></lb>congruè applicata, facillimè mouentur. <lb></lb></s>
          <s id="N11EE0">Exemplum ſit erectus cylindrus AB, <lb></lb>cuius helices, vel ſtrigæ circumuolutæ, <lb></lb>ſint CD, EF; manubrium verò cylin<lb></lb>dri G. </s>
          <s id="N11EEA">Etenim ſi in principio helicis <lb></lb>vbi C, onus congruè applicetur, vt <lb></lb>pila ſuperſignata H; ita tamen vt ex <lb></lb>aduerſo non poſſit moueri, niſi ſuper <lb></lb>rectam IK, quaſi intercepta inter cy<lb></lb>lindrum &amp; planum quoddam paralle<lb></lb>lum cylindro; abſque dubio, ad cir<lb></lb>cumuolutionem manubrij totiuſque <lb></lb>cylindri, pondus H paulatim aſcendet <lb></lb>ex C ad D, deinde ad E &amp; F, &amp; ſic <lb></lb>deinceps. </s>
        </p>
        <p id="N11F01" type="main">
          <s id="N11F03">Idemque poteſt exemplificari in. <lb></lb></s>
          <s id="N11F07">alia ipſius cochleæ figura æquidiſtantis <lb></lb>ab horizonte, vt AB, ſi apponatur <lb></lb>illi onus CD, tanquam cylindri con<lb></lb>caui ac ſtriati, qui &amp; Tylum à Pappo, &amp; alijs Mechanicis, <lb></lb><figure id="id.005.01.071.2.jpg" xlink:href="005/01/071/2.jpg"></figure><pb pagenum="64" xlink:href="005/01/072.jpg"></pb>&amp; Cochleæ fœmina vulgò appellatur. </s>
          <s id="N11F1B">Nam ad conuerſio<lb></lb>nem manubrij totiuſque cylindri ſuper proprium axem, <lb></lb>mouebitur etiam ipſum Tylum CD. </s>
          <s id="N11F23">Quæ omnia fusè Gui<lb></lb>dus Vbaldus demonſtrat. </s>
          <s id="N11F28">Ex cuius doctrina illud tandem <lb></lb>hic relinquitur adnotandum, ac ſimul in propoſito conclu<lb></lb>dendum, Cochleæ helices, aliud non eſſe, quàm latus <lb></lb>cunei circa idem cylindrum iterum atque iterum circumuo<lb></lb>lutum. </s>
          <s id="N11F33">Vnde apparet quomodo etiam cochlea reducatur <lb></lb>ad vectem; nimirum eodem prorſus pacto, quo cuneus, vt <lb></lb>latius ipſe proſequitur. </s>
        </p>
        <p id="N11F3A" type="head">
          <s id="N11F3C"><emph type="italics"></emph>De Centro grauitatis <expan abbr="naturaliq.">naturalique</expan> mobilitate <lb></lb>grauium, &amp; leuium.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N11F49" type="head">
          <s id="N11F4B">ADDITIO SECVNDA.</s>
        </p>
        <p id="N11F4F" type="main">
          <s id="N11F51">Poſt conſiderationem inſtrumentorum, ac machinarum <lb></lb>circuli naturam participantium, vt aptam ac debitam <lb></lb>eorum applicationem ad motum <expan abbr="grauiũ">grauium</expan>, &amp; leuium cogno<lb></lb>ſcamus, conſideranda nobis erit mobilitas ipſa tàm natu<lb></lb>ralis, quàm præternaturalis, &amp; artificioſa illorum, cui ada<lb></lb>ptari debent inſtrumenta, &amp; ad quam ex inſtituto ordinan<lb></lb>tur. </s>
          <s id="N11F64">Cumque naturalis mobilitas grauium ſit penes cen<lb></lb>trum grauitatis illorum, aliquid primò dicendum occurrit <lb></lb>de centro grauitatis in communi, vt quàm breuiſſimè quæ <lb></lb>neceſſaria ſunt ad intelligentiam præfatæ motionis expe<lb></lb>diantur. </s>
        </p>
        <p id="N11F6F" type="main">
          <s id="N11F71"><arrow.to.target n="marg14"></arrow.to.target> Centrum igitur grauitatis vniuſcuiuſque corporis iuxta <lb></lb>doctrinam Heronis, ac Pappi Alexandrini, eſt punctum il<lb></lb>lud intra poſitum, à quo ſi ipſum corpus graue ſuſpendatur, <lb></lb>vel etiam ſuſpenſum feratur, <expan abbr="eãdem">eandem</expan> ſemper ſuarum partium <lb></lb>ſeruat poſitionem quippe quæ in ipſa ſuſpenſione, aut latio<lb></lb>ne corporis minimè circumuertuntur, cum vndique ſint <lb></lb>æqualium momentorum. </s>
          <s id="N11F87">Quod præclarè explicat Federi<lb></lb>cus Commandinus. </s>
          <s id="N11F8C">Si enim, inquit, per tale centrum du-<pb pagenum="65" xlink:href="005/01/073.jpg"></pb>catur planum, figuram ipſius corporis quomodocunque<arrow.to.target n="marg15"></arrow.to.target> ſe<lb></lb>cans, ſemper in partes æqueponderantes ipſam diuidet, <lb></lb>quamuis aliquando ſint inæqualis dimentionis. </s>
          <s id="N11F9C">Porrò in <lb></lb>diuiſione corporis per eius centrum grauitatis, partes diui<lb></lb>ſæ non ſemper ſunt eiuſdem magnitudinis, ſeu dimentionis, <lb></lb>ſunt tamen eiuſdem ponderis, &amp; grauitatis, vt Guidus<arrow.to.target n="marg16"></arrow.to.target> Vbal<lb></lb>dus ſatis demonſtrat. </s>
          <s id="N11FAB">Quod ſanè, vt idem animaduertit, in<lb></lb>telligendum eſt de partibus mente tantum diuiſis, non au<lb></lb>tem re, ac ſeorſum conſtitutis, vt quæ ab inuicem ſeiunctæ <lb></lb>ponderantur in libra: Cum alia tunc ſit ratio grauitandi, <lb></lb>iuxta ſcilicet propriam magnitudinem maiorem, aut mino<lb></lb>rem, quæ in propoſito quando partes coniunctæ ſunt com<lb></lb>penſatur à poſitione, ac ſitu vnius reſpectu alterius iuxta di<lb></lb>ſtantiam à centro, à quo totum corpus ſuſpenditur. </s>
        </p>
        <p id="N11FBC" type="margin">
          <s id="N11FBE"><margin.target id="marg14"></margin.target>Lib.8. Me<lb></lb>them. col<lb></lb>lection.</s>
        </p>
        <p id="N11FC9" type="margin">
          <s id="N11FCB"><margin.target id="marg15"></margin.target>Lib.

de <expan abbr="Cẽ-tro">Cen<lb></lb>tro</expan> grauit. <lb></lb></s>
          <s id="N11FD7">ſolidorum.</s>
        </p>
        <p id="N11FDA" type="margin">
          <s id="N11FDC"><margin.target id="marg16"></margin.target>In primum <lb></lb>l.b. </s>
          <s id="N11FE3"><expan abbr="Aequi-põder">Aequi<lb></lb>ponder</expan>. Ar<lb></lb>chimedis. <lb></lb></s>
          <s id="N11FF0">propoſ<gap></gap>lt.</s>
        </p>
        <p id="N11FF5" type="main">
          <s id="N11FF7">Quapropter ſi punctum <lb></lb>A fuerit centrum grauita<lb></lb><figure id="id.005.01.073.1.jpg" xlink:href="005/01/073/1.jpg"></figure><lb></lb>tis corporis BCD <expan abbr="quo-modocumq;">quo<lb></lb>modocumque</expan> diuiſi per <expan abbr="pla-nã">pla<lb></lb>nam</expan> EF tranſeuntem per ip<lb></lb>ſummet centrum, atque <lb></lb>idem corpus ex eodem <lb></lb>puncto ſuſpenderetur, cer<lb></lb>tè quo ad poſitionem ac <lb></lb>diſpoſitionem ſuarum par<lb></lb>tium inuariatum omnino maneret; ita vt nullo pacto ipſum <lb></lb>B, ac D verterentur circa punctum A tanquam circa cen<lb></lb>trum, ſed eadem qua prius poſitione manerent, ſiue pars <lb></lb>BEFC æqualis dimentionis inueniretur parti EDF, ſiue <lb></lb>inæqualis: ſemper enim ſic coniunctæ æqueponderaret, eſ<lb></lb>ſentque æqualium momentorum. </s>
          <s id="N12026">Cumque in his, quæ ſu<lb></lb>ſpenduntur ex aliquo puncto, vel etiam ſic ſuſpenſæ ferun<lb></lb>tur non detur motus circumuolutionis abſque exuperantia <lb></lb>alterius partis eorum, nec vna poſſit aliam ſuperare niſi per <lb></lb>exceſſum ponderis ipſius; hinc eſt, vt immotæ ambæ ipſæ <lb></lb>partes perſeuerarent tanquam in æquilibrio conſtitutæ. <lb></lb></s>
          <s id="N12034">Idemque contingeret quocunque alio modo ipſum corpus <pb pagenum="66" xlink:href="005/01/074.jpg"></pb>ſuſpenſum, aut etiam latum à principio conſtitueretur. </s>
        </p>
        <p id="N1203C" type="main">
          <s id="N1203E">Quod ſi contra definitionem, ſeu deſcriptionem tradi<lb></lb>tam afferatur, multa dari poſſe corpora talis figuræ, vt cen<lb></lb>trum grauitatis illorum non ſit intra, ſed extra, quemadmo<lb></lb>dum exempli gratia in rota AB cuius quidem centrum <lb></lb>eſſet in C. </s>
          <s id="N1204A">Sicut etiam in corpore irregulari DE cuius <lb></lb><figure id="id.005.01.074.1.jpg" xlink:href="005/01/074/1.jpg"></figure><lb></lb>centrum eſſet in F. </s>
          <s id="N12056">Occurrit Guidus Vbaldus dicens, etiam <lb></lb>prædicta centra intra figuram eſſe quatenus verè continen<lb></lb>tur ab ambitu eiuſdem figuræ ipſorum corporum. </s>
        </p>
        <p id="N1205D" type="main">
          <s id="N1205F">His autem ſic ſtabilitis de centro grauitatis, dicendum <lb></lb>eſt naturalem mobilitatem grauium, &amp; leuium reſpectiuè <lb></lb>(hoc eſt corporum magis, aut minus grauium, vt explicui<lb></lb>mus) eſſe innatam quandam aptitudinem, ac propenſionem <lb></lb>ad motum deorſum ex principio intrinſeco tum actiuo, tum <lb></lb>paſſiuo per rectam lineam, quæ centrum grauitatis ipſius <lb></lb>grauis, <expan abbr="centrumq.">centrumque</expan> mundi connectit. </s>
          <s id="N12072">Id quod apertiſſimè <lb></lb>conſtabit conſideranti graue quodcumque ſecluſo omni <lb></lb>impedimento, ac detentione, ſtatim ſuo pondere, &amp; ex ſe <lb></lb>centrum vniuerſi expetere, nec vnquam quieſcere donec <lb></lb>ad illud ſi fieri poſſet, perueniat. </s>
        </p>
        <p id="N1207D" type="main">
          <s id="N1207F">Diximus autem huiuſcemodi aptitudinem eſſe ex prin<lb></lb>cipio intrinſeco tum actiuo tum paſſiuo; nam id per quod <lb></lb>grauia formaliter conſtituuntur apta, &amp; in actu primo ad <lb></lb>motum localem deorſum, non modò eſt potentia paſſiua <lb></lb>ipſis innata, ſicut cuilibet corpori ad recipiendum talem <lb></lb>motum, ſiue producatur à ſe ipſo ſiue ab alio: ſed præcipuè <pb pagenum="67" xlink:href="005/01/075.jpg"></pb>eſt intrinſeca ipſa grauitas, quæ tanquam proprium ope<lb></lb>randi principium eſt illis ratio, vt moueantur deorſum, ſeu <lb></lb>forma qua in ſe ſecluſis impedimentis, talem motum pro<lb></lb>ducunt. </s>
          <s id="N12097">Quod optimè expreſſit Ariſtoteles lib.

8. Phyſic. <lb></lb>tex. 32. &amp; lib.

1. de Cœlo, tex. 17. &amp; lib.

4. tex. 6. Ratio au<lb></lb>tem eſt manifeſta, quia ſenſu conſtat, efficaciam, ac celeri<lb></lb>tatem in motu deorſum creſcere creſcente grauitate cor<lb></lb>poris, ac minui ad diminutionem illius (vt idem Philoſo<lb></lb>phus obſeruauit 1. de Cœlo tex. 89.) quod non poſſet con<lb></lb>tingere ſi in ipſo corpore graui grauitas non eſſet propria <lb></lb>cauſa effectiua ipſius motus, quæ ſimul cum effectu creſce<lb></lb>ret, ac decreſceret. </s>
          <s id="N120B3">Sicut calor, qui dum intenditur, aut re<lb></lb>mittitur, efficacius aut remiſſius operatur, <expan abbr="maioremq.">maioremque</expan> aut <lb></lb>minorem calefactionis motum producit, eo quod ſimiliter <lb></lb>eſt ratio formalis calefaciendi, ſicut grauitas ſe deorſum <lb></lb>mouendi. </s>
          <s id="N120C2"><expan abbr="Nullumq.">Nullumque</expan> eſt inconueniens, idem corpus eſſe <lb></lb>poſſe mouens &amp; motum, cum in corpore graui ſit potentia <lb></lb>receptiua motus, &amp; grauitas, quæ eſt <expan abbr="potẽtia">potentia</expan> effectiua illius. </s>
        </p>
        <p id="N120D0" type="main">
          <s id="N120D2">Diximus verò grauia moueri deorſum per <expan abbr="rectã">rectam</expan> lineam, <lb></lb>quæ centrum grauitatis ipſorum, <expan abbr="centrumq.">centrumque</expan> mundi conne<lb></lb>ctit: Nam ſenſu pariter conſtat, illa non tendere ad ipſum <lb></lb>mundi centrum per lineam aliquam obliquam, neque per <lb></lb>lineam rectam, quæ ab extremo quoddam, vel quauis alia <lb></lb>parte ipſius ad mundi centrum extendatur, ſed per <expan abbr="eã">eam</expan>, quam <lb></lb>diximus <expan abbr="lineã">lineam</expan>, quæ ab eius centro grauitatis rectà ad mun<lb></lb>di centrum propendet. </s>
          <s id="N120F3">Omnis enim grauitas cuiuſque <lb></lb>grauis ita in ipſo grauitatis centro colligitur, &amp; coacerua<lb></lb>tur, vt extra ipſum nihil grauitare propemodum in corpori<lb></lb>bus videatur: <expan abbr="proindeq.">proindeque</expan> non niſi ipſomet centro rectà deor<lb></lb>ſum eadem corpora ferri conſpicimus naturali propenſio<lb></lb>ne. </s>
          <s id="N12104">Quo pariter fit, vt ſi aliundè quàm ab ipſius grauitatis <lb></lb>centro graue aliquod ſuſpendatur, ſtatim grauitatis centro <lb></lb>deorſum tendente conuertatur, nec manere vnquam poſſit <lb></lb>donec ipſum grauitatis centrum ſub puncto ſuſpenſionis per <lb></lb>lineam horizonti perpendicularem conſtituatur. </s>
          <s id="N1210F">Quando<lb></lb>quidem tunc idem eſt, ac ſi corpus per ipſummet grauita<pb pagenum="68" xlink:href="005/01/076.jpg"></pb>tis centrum ſuſpenderetur, cum per eandem lineam ei li<lb></lb>ceat grauitare, vt latius ac rectè proſequitur Guidus Vbal<lb></lb>dus loco citato. </s>
        </p>
        <p id="N1211D" type="head">
          <s id="N1211F"><emph type="italics"></emph>De præternaturali, &amp; artificioſa mobilitate <lb></lb>grauium, &amp; leuium.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N12128" type="head">
          <s id="N1212A">ADDITIO TERTIA.</s>
        </p>
        <p id="N1212E" type="main">
          <s id="N12130">Iam verò præternaturalis mobilitas grauium, &amp; leuium <lb></lb>in eo relinquitur conſiſtere, quod eſt, ipſa grauia, &amp; le<lb></lb>uia ſecundum quamcumque poſitionem, etiam repugnanti<lb></lb>bus naturæ legibus, moueri poſſe arte ac violentia, à princi<lb></lb>pio extrinſeco: ita tamen vt <expan abbr="quandoq.">quandoque</expan> eadem grauitas in<lb></lb>trinſeca, quæ ſuperatur à violentia, non parum ad ſe ipſam <lb></lb>euincendam, &amp; ad ſui motionem præternaturalem, &amp; artifi<lb></lb>cioſam augendam concurrat. </s>
        </p>
        <p id="N12145" type="main">
          <s id="N12147">Conſtat enim hoc cum aperta deductione ex dictis de <lb></lb>mobilitate naturali, tùm clara ac patenti experientia; <lb></lb>ita vt nulla ferè indigeat probatione, aut explicatione, præ<lb></lb>ſertim in doctrina Ariſtotelis, qui quantum attinet ad prin<lb></lb>cipium extrinſecum, à quo prouenire diximus præternatu<lb></lb>ralem motionem, cum 8 Phyſicor. tex. 33. dixiſſet: Omnia, <lb></lb>quæ mouentur, aut natura moueri, aut præter naturam, ac <lb></lb>violentia; mox addit: Et quæ vi &amp; præter naturam, omnia <lb></lb>à quodam, &amp; ab alio. </s>
          <s id="N1215E">Iuxta commune illud pronuntiatum <lb></lb>à ſe prius traditum, &amp; ab omnibus receptum nimirum, om<lb></lb>ne quod mouetur, ab alio moueri. </s>
          <s id="N12165">Quod quippè loquendo <lb></lb>ſaltem de motu præternaturali in rebus inanimatis, eſt ir<lb></lb>refragabile. </s>
        </p>
        <p id="N1216C" type="main">
          <s id="N1216E">Illud tamen apud nonnullos adhuc non eſt omnino ex<lb></lb>ploratum, ac non paruam habet difficultatem, quo videli<lb></lb>cet pacto violentia ipſa corporibus ab extrinſeco inferatur; <lb></lb>quauè ratione, eadem corpora poſtquam ab impulſore, vel <lb></lb>proijciente receſſerint, ex ſe præternaturaliter moueantur. <pb pagenum="69" xlink:href="005/01/077.jpg"></pb>Quod cum partim ad merè phyſicam ſpeculationem perti<lb></lb>neat in 7. &amp; 8. de phyſico auditu; partim verò infra cum <lb></lb>Ariſtotele quæſt. </s>
          <s id="N12182">32. &amp; 33. explicandum ſit, hìc non erit <lb></lb>diſcutiendum, ſed tantum ex dicendis, ac probandis ſuppo<lb></lb>nere oportet, nullam vnquam inferri poſſe violentiam per <lb></lb>motum localem abſque productione, ac impreſſione quali<lb></lb>tatis cuiuſdam in ipſo mobili, quæ communiter appellari ſo<lb></lb>let impetus ſiue impulſus, ac de qua ſæpe nobis redibit ſer<lb></lb>mo in ijs quæſtionibus. </s>
        </p>
        <p id="N12191" type="main">
          <s id="N12193">Diximus autem grauitatem <expan abbr="quandoq.">quandoque</expan> ad ſui motionem <lb></lb>violentam concurrere, quia cum deorſum magna vi ponde<lb></lb>ra extruduntur, vis illata, &amp; impetus incuſſus, grauitate mo<lb></lb>bilis intenditur, &amp; augetur, vt quæſt. </s>
          <s id="N121A0">32. probabitur. </s>
          <s id="N121A3">Vnde <lb></lb>licet quoad velocitatem, &amp; modum tunc motus ipſe deor<lb></lb>ſum <expan abbr="cõſtituatur">conſtituatur</expan> præternaturalis, ad eum tamen grauitas ip<lb></lb>ſa non minus, ac impetus concurrit. </s>
          <s id="N121B0">Quod contra ſe habet <lb></lb>cum ſurſum, vel ad latera graue transfertur; quia grauitas <lb></lb>ſicut ſemper tendit deorſum, ita <expan abbr="cuicumq;">cuicumque</expan> alio motui ſem<lb></lb>per obſiſtit, quamuis propriè non contrarietur virtuti, à qua <lb></lb>talis motus procedit, nec ſit incompoſſibilis cum illa in eo<lb></lb>dem ſubiecto, vt ibidem explicabitur. </s>
        </p>
        <p id="N121C1" type="main">
          <s id="N121C3">Deinde moueri poſſe diximus ipſa grauia <expan abbr="ſecundũ">ſecundum</expan> quam<lb></lb>cumque poſitionem atte, ac violentia; quia nec violentiæ <lb></lb>præſcripta eſt poſitio ſecundum quam duntaxat mouere <lb></lb>valeat, non verò ſecundum aliam, nec arti deficiunt præce<lb></lb>pta, &amp; inſtrumenta, quibus ita vis eis applicetur; vt quoquò <lb></lb>verſum, etiam contra naturæ leges grauia transferantur. </s>
          <s id="N121D4">Vn<lb></lb>de pluribus, ac innumeris penè modis arte comparatis vio<lb></lb>lentia poteſt inferri. </s>
          <s id="N121DB">Quos tamen Ariſtoteles 7. Phyſic. tex. <lb></lb>10. ad quatuor tantum reducit, iuxta quos to idem ſpecies <lb></lb>motus violenti conſtituit: Quadrifariam, inquiens, moueri <lb></lb>quidquid ab alio per violentiam ſecundum locum mouetur. <lb></lb></s>
          <s id="N121E8">Nimirum vel per Pulſionem, vel per Tractionem, vel per <lb></lb>Vectionem, vel per Vertiginem. </s>
          <s id="N121ED">Pulſionem autem diſtin<lb></lb>guit in Impulſionem, &amp; Expulſionem. </s>
          <s id="N121F2">Impulſionem ait eſſe <lb></lb>cum pellens ita pellit, vt pulſum non deſerat, ſed comite<pb pagenum="70" xlink:href="005/01/078.jpg"></pb>tur: Expulſionem verò, tum vbi pepulit, pulſum ipſum re<lb></lb>linquit, de quo genere eſt proiectio. </s>
          <s id="N121FE">Tractionem deinde ait <lb></lb>eſſe motum trahentis non ſeparatum à motu eius, quod <lb></lb>trahitur: <expan abbr="ideoq.">ideoque</expan> eſſe motum ad ſe ipſum, &amp; ad alterum. </s>
          <s id="N12209">Ve<lb></lb>ctionem verò eſſe motum per accidens; nam id quod vehi<lb></lb>tur ex co mouetur, quia eſt in eo, quod mouetur. </s>
          <s id="N12210">Quoniam <lb></lb>verò id quod vehit mouetur aut pulſum, aut tractum, aut <lb></lb>vertigine actum, ex hoc infert, vt &amp; Vectio tripliciter fieri <lb></lb>poſsit, iuxta triplicem motum prædictum. </s>
          <s id="N12219">Denique Verti<lb></lb>ginem ait eſſe motum compoſitum ex tractione, &amp; pulſio<lb></lb>ne. </s>
          <s id="N12220">Ad quas quippe quatuor ſpecies reuocari poſſunt aliæ <lb></lb>quam plures motiones præternaturales, ac violentæ, quibus <lb></lb>accommodata ſunt inſtrumenta, ac machinamenta, de qui<lb></lb>bus Additione prima egimus, cunctaquè alia, quæ ex illis <lb></lb>conſtantur, vel ad ea reducuntur. </s>
        </p>
        <p id="N1222B" type="main">
          <s id="N1222D">Quamobrem præternaturalis mobilitas grauium, ac le<lb></lb>nium pluries vocatur etiam artificioſa. </s>
          <s id="N12232">Nam licet interdum <lb></lb>à cauſis naturalibus, nulla interueniente hominum induſtria <lb></lb>aut violentia, vis aliqua corporibus inferatur, qua præterna<lb></lb>turaliter ipſa compelluntur moueri, vt cum ignitos lapides <lb></lb>è montibus quibuſdam videmus erumpere, &amp; in altum ſu<lb></lb>ſtolli; vel ferrea corpora à magnete ſurſum attrahi, ac pen<lb></lb>dentia ſuſtineri. </s>
          <s id="N12241">Sæpius tamen corpora non niſi artificioſa <lb></lb>violentia ex induſtria ipſis illata præternaturaliter, vt dice<lb></lb>bamus conſtat moueri. </s>
          <s id="N12248">Ita vt etiam motus eorum præter<lb></lb>naturales, qui ab aliqua cauſa naturali oriuntur, <expan abbr="aliosq.">aliosque</expan> ſimi<lb></lb>les, ad imitationem naturæ, ars ipſa violentiam applicando, <lb></lb>augendo, minuendo, ac diſtinguendo producat. </s>
          <s id="N12255">Vt perſpi<lb></lb>cuè obſeruare eſt in motibus violentis ſulfurei pulueris <lb></lb>virtute, ac artis magiſterio productis ad euerrendas moles, <lb></lb>explodendas ingentes pilas, ac diruendas portas vrbium, <lb></lb>ac munitionum: nec non in motibus, qui aéris, vel aquæ <lb></lb>beneficio multimoda cum arte diſpoſito fiunt, ad nauium <lb></lb>admirabilem lationem, <expan abbr="earumq.">earumque</expan> curſus moderationem; &amp; <lb></lb>ad tam varios machinarum ſe mouentium, ſeu ſpiritalium <lb></lb>vſus, de quibus ſcripſit Hero, cum in iis omnibus ars natu-<pb pagenum="71" xlink:href="005/01/079.jpg"></pb>ram æmulando, vel eam comitando magnopere elucear, <lb></lb>nec minus ad ipſam vim præternaturaliter inferendam con<lb></lb>ducat. </s>
        </p>
        <p id="N12275" type="main">
          <s id="N12277">Ad hanc igitur motionem artificioſam, ac præternatura<lb></lb>lem vniuerſa facultas Mechaniça ordinatur, vt ſupra expli<lb></lb>cuimus: quatenus mirabili ſuo magisterio rationabiliter per <lb></lb>cauſas procedendo, docet quo pacto grauia cuncta, aut le<lb></lb>uia poſſint ſecundum omnem poſitionem moueri, &amp; cuius <lb></lb>virtute, quauè proportione illius ad pondus; in qua diſtan<lb></lb>tia, <expan abbr="quibusq.">quibusque</expan> adminiculis, machinis, &amp; inſtrumentis, &amp; id ge<lb></lb>nus alia; quæ non parua ex parte conſtabunt ex is, quæ <lb></lb>Ariſtoteles vltra ſuperius allata, &amp; à nobis expoſita, in ſe<lb></lb>quentibus quæſtionibus tradit. </s>
          <s id="N12290">Cum alias exacta, &amp; pe<lb></lb>culiaris vniuſcuiuſque grauis, aut leuis prout artificiosè mo<lb></lb>ueri debeat conſideratio, ad diſtinctas Mechanicæ facul<lb></lb>tatis partes iam enumeratas, quas ipſe Philoſophus non eſt <lb></lb>aggreſſus; quippe qui vniuerſalia duntaxat principia huius <lb></lb>admirabilis diſciplinę in hac prima parte afferre ſtatuerit, <lb></lb>cauſas poſtea in ſecunda parte allaturus eorum, quæ in ſe<lb></lb>quentibus quæſtionibus proponuntur ad maiorem explica<lb></lb>tionem, &amp; applicationem eorundem principiorum, ex qui<lb></lb>bus aliæ infinitæ penè concluſiones poſſunt deduci. </s>
        </p>
        <p id="N122A5" type="main">
          <s id="N122A7">Sed illud hic ſummopere animaduertendum putauimus <lb></lb><expan abbr="Archimedẽ">Archimedem</expan>, quem iure inter huius diſciplinæ parentes opti<lb></lb>mos literæ omnes maxima cum laude commemorant, non <lb></lb>diuerſa ab ijs, quę Ariſtoteles tradidit principia aſſumpſiſſe, <lb></lb>ac in ſuis de æqueponderantibus libris protuliſſe, vt falsò <lb></lb>nonnulli comminiſcuntur; quin imò tradita ab ipſo Philoſo<lb></lb>pho ſuppoſuiſſe, &amp; amplius, ad particularia deſcendendo, <lb></lb>extendiſſe, ac planiora reddidiſſe, vt ingenuè fatetur Guidus <lb></lb>Vbaldus in Præfatione primi de æqueponderantibus libri <lb></lb><expan abbr="eiuſdẽ">eiuſdem</expan> Archimedis. </s>
          <s id="N122C3">Ariſtoteles enim (vt vel vno vtar exem<lb></lb>plo) loquendo de motione circulati, ad quam reducuntur <lb></lb>penè omnes motiones, quæ mechanicis inſtrumentis, atque <lb></lb>artibus fiunt, præſtantiſsimum illud conſtituit principium, <lb></lb>quæ ſunt in maiori à centro diſtantia, maiorem quoque ha<pb pagenum="72" xlink:href="005/01/080.jpg"></pb>bere virtutem ad motum, <expan abbr="velociusq.">velociusque</expan> moueri, vt ſupra vidi<lb></lb>mus tex. 6. Quod ſanè principium non ſolum admittit Ar<lb></lb>chimedes, at que ſupponit, ſed conſequenter ad illud vlte<lb></lb>rius inquirit, <expan abbr="tradiditq.">tradiditque</expan> quanto maior ſit virtus, quæ habe<lb></lb>tur in maiori illa diſtantia, <expan abbr="eamq">eamque</expan> ab ipſius diſtantiæ pro<lb></lb>portione indagando, receptiſsimum aliud fundamentum <lb></lb><arrow.to.target n="marg17"></arrow.to.target> mechanicum ſtatuit, nimirum, it a ſe habere pondus ad pon<lb></lb>dus, vt diſtantia ad diſtantiam à puncto vnde pondera ſu<lb></lb>ſpenduntur, permutata videlicet ratione, vt infra quæſt. </s>
          <s id="N122F0">3. <lb></lb>explicabitur. </s>
          <s id="N122F5">Cui fundamento tota Archimedis doctrina, <lb></lb><expan abbr="veraq.">veraque</expan> mechanica innititur contemplatio. </s>
          <s id="N122FD">Illud tamen an<lb></lb>tea patefecerat Ariſtoteles in ſuis mechanicis, quæſt. </s>
          <s id="N12302">3. illis <lb></lb>verbis, quod igitur motum pondus ad mouens, longitudo <lb></lb>patitur ad longitudinem. </s>
          <s id="N12309">Quem locum miror non animad<lb></lb>uertiſſe Guidum Vbaldum in confirmationem ſuæ <expan abbr="veræq.">veræque</expan> <lb></lb>ſententiæ; cum planè animaduertiſſet Archimedem in con<lb></lb>ſtituendis ſuis mechanicis poſtulatis ſuppoſuiſſe ea, quæ de <lb></lb>mechanicis principijs Philoſophus tradiderat. </s>
          <s id="N12318">Sed iam ad <lb></lb>exponendas ipſius Philoſophi quæſtiones accedamus. </s>
        </p>
        <p id="N1231D" type="margin">
          <s id="N1231F"><margin.target id="marg17"></margin.target>Lib. 1. <lb></lb>Atqui <expan abbr="põd">pond</expan>. <lb></lb></s>
          <s id="N1232D">propoſit. 6.</s>
        </p>
        <figure id="id.005.01.080.1.jpg" xlink:href="005/01/080/1.jpg"></figure>
        <pb pagenum="73" xlink:href="005/01/081.jpg"></pb>
        <p id="N1233B" type="head">
          <s id="N1233D">SECVNDA PARS <lb></lb>MECHANICES <lb></lb>ARISTOTELIS STAGIRITAE <lb></lb>IN QVA PLVRES QVAESTIONES <lb></lb>continentur, ac ſoluuntur iuxta principia in <lb></lb>priori parte tradita.</s>
        </p>
        <p id="N1234A" type="main">
          <s id="N1234C"><emph type="italics"></emph>Explicata vniuerſali doctrina principiorum, <lb></lb>ex quibus tanquam ex iactis fundamen<lb></lb>tis inconficiendis demonſtrationibus omnis <lb></lb>mechanica ſtructura conſurgit, particulares <lb></lb>quæſtiones Philoſophus proponit, in qua<lb></lb>rum ſolutionibus ipſa vniuerſalis doctrina, <lb></lb>vt præmonuimus, applicatur.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1235F" type="head">
          <s id="N12361">Quæſtio Prima.</s>
        </p>
        <p id="N12364" type="main">
          <s id="N12366">C<emph type="italics"></emph>vr autem maiores libræ exactio<lb></lb>res ſunt minoribus, palam eſt ex ijs. <lb></lb></s>
          <s id="N1236F">Spartum enim fit centrum, id <expan abbr="namq.">namque</expan> <lb></lb>manet. </s>
          <s id="N12374">Quod autem libræ vtrinque <lb></lb>eſt, exeuntes à centro.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1237B" type="main">
          <s id="N1237D"><emph type="italics"></emph>Ab eodem igitur pondere citius mo<lb></lb>ueri nece&lt;32&gt;e eſt extremum libræ, quo <lb></lb>plus à ſparto diſceſſerit. </s>
          <s id="N12386">Et nonnulla <lb></lb>quidem in paruis libris impoſita non manifeſta ſenſui ſunt <lb></lb>pondera: in magnis autem manifeſta. </s>
          <s id="N1238D">Nihil enim prohibet <lb></lb>minorem moueri magnitudinem, quàm vt viſioni ſit mani<lb></lb>feſta. </s>
          <s id="N12394">In magna autem libra idem pondus viſibile efficit ma-<emph.end type="italics"></emph.end><pb pagenum="74" xlink:href="005/01/082.jpg"></pb><emph type="italics"></emph>gnitudo. </s>
          <s id="N123A0">Quædam verò manifesta quidem ſunt in vtriſque, <lb></lb>ſed multò magis in maioribus, quoniam multò maior inclina<lb></lb>tionis fit magnitudo ab eodem pondere in maioribus. </s>
          <s id="N123A7">Quam<lb></lb>obrem machinantur ÿ, qui purpuram vendunt. </s>
          <s id="N123AC">vt pendendo <lb></lb>defraudent, tum ad medium ſpartum non ponentes, tum plum<lb></lb>bum in alterutram libræ partem infundentes, aut ligni, quod <lb></lb>ad radicem vergebat, in eam, quam deferri volunt partem <lb></lb>conſtituentes: aut ſi nodum habuerit. </s>
          <s id="N123B7">Ligni enim grauior il<lb></lb>la est pars, in qua est radix. </s>
          <s id="N123BC">Nodus verò radix quædam eſt.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N123C1" type="head">
          <s id="N123C3">COMMENTARIVS.</s>
        </p>
        <p id="N123C7" type="main">
          <s id="N123C9">Tanquam exploratiſſimum ſupponitur hic ab Ariſto. <lb></lb>tele experimentum, maiores libras, exactiores eſſe <lb></lb>minoribus: hoc eſt exactè magis oſtendere pondus <lb></lb>grauium, quæ ponderantur, <expan abbr="eiuſq.">eiuſque</expan> differentias per motum <lb></lb>ſurſum, ac deorſum, aut ſtatum ſuarum lancium. </s>
          <s id="N123D9"><expan abbr="Cauſamq.">Cauſamque</expan> <lb></lb>ipſe ſtatim afferens, docet ſpartum, quo ſuſpenditur libra, <lb></lb>ſeu trutinam quamlibet, ſecundum eam partem, ſcilicet <lb></lb>quæ intra foramen bilancis exiſtens in medio iugi, axis vi<lb></lb>cem gerit, ſe habere tanquam centrum in circulo, quod per <lb></lb>motum circularem eiuſdem circuli non mouetur: partes <lb></lb>autem ipſius iugi vtrinque productas, quæ &amp; brachia nun<lb></lb>cupantur, è quorum extremis lances propendunt, conſtitui <lb></lb>tanquam lineas à centro in peripheriam deductas, quæ cir<lb></lb>ca idem centrum conuertantur, &amp; aliquantulum per eleua<lb></lb>tionem vnius, ac depreſſionem alterius circumferantur, vt <lb></lb>videre eſt in ſequenti figura. </s>
          <s id="N123F5">At, inquit, quò plus lineæ à <lb></lb>centro circuli diſceſſerint, eo magis, quamuis ab eadem vel <lb></lb>æquali virtute, valent moueri, maius nempe ſpacium eo<lb></lb>dem tempore percurrendo, vt idemmet Ariſtoteles proba<lb></lb>uerat. </s>
          <s id="N12400">Ergo idem pondus ab extremo libræ propendens <lb></lb>eò magis illam conuertere, aut mouere valebit, quò maior <lb></lb>fuerit ipſa libra, ſeu quò longioribus brachijs conſtabit. </s>
          <s id="N12407">Si<lb></lb>quidem extremum vbi appenditur pondus, magis diſtabit <lb></lb>à centro, <expan abbr="maioremq.">maioremque</expan> proinde portionem circuli eodem <pb pagenum="75" xlink:href="005/01/083.jpg"></pb>tempore, <expan abbr="eademq.">eademque</expan> vi peraget, vt perſpicuum eſt in hac fi<lb></lb>gura ſi brachia libræ AB protrahantur vſque ad CD. </s>
          <s id="N1241E">Quia <lb></lb>nimirum, ſicut maio<lb></lb><figure id="id.005.01.083.1.jpg" xlink:href="005/01/083/1.jpg"></figure><lb></lb>rem efficerent circu<lb></lb>lum, videlicet conti<lb></lb>nentem, maioremque <lb></lb>diametrum; ita maio<lb></lb>rem arcum eorum ex<lb></lb>trema percurrerent. <lb></lb></s>
          <s id="N12436">Nam quo tempore <lb></lb>ac vi A moueretur vſ <lb></lb>que ad F, ipſum C <lb></lb>moueretur <expan abbr="vſq;">vſque</expan> ad E <lb></lb>Maior autem eſt CE <lb></lb>quàm AF, eo quod <lb></lb>ſicut diameter ad dia<lb></lb>metrum, ita portio ad <lb></lb>portionem circuli ſe <lb></lb>habeat. </s>
          <s id="N1244F">Cum igitur <lb></lb>facilius ſit cernere ac <lb></lb>diſcernere, quod maius eſt, quàm quod minus; ſequitur, eò <lb></lb>euidentius apparere motum libræ, quò maior fuerit ipſa li<lb></lb>bra: ac propterea per motum ipſum maioris libræ exactius<lb></lb>præponderantiam grauium, ſeu differentiam ponderis in<lb></lb>dicati. </s>
        </p>
        <p id="N1245E" type="main">
          <s id="N12460"><expan abbr="Atq;">Atque</expan> hinc euenire, ait Ariſtoteles, vt in paruis libris non<lb></lb>nulla pondera ſenſum omnino ferè lateant, quæ in magnis, <lb></lb>illi apertiſſimè innoteſcunt. </s>
          <s id="N1246A">Non quidem ex eo, quod ipſa <lb></lb>pondera moueant magnas libras, non autem paruas; ſed <lb></lb>quia motus ab ipſis productus, cum maior ſit in maioribus, <lb></lb>facilius, ac euidentius à ſenſu percipitur. </s>
          <s id="N12473">Vnde quæ mani<lb></lb>feſta ſunt in vtriuſque libris, multo magis (vt idem inquit) <lb></lb>manifeſta ſe præbent in meioribus, quoniam in illis multo <lb></lb>maior inclinatio cauſatur ab eodem pondere. </s>
          <s id="N1247C">Id quod in <lb></lb>omnibus inſtrumentis verificatur, quæ ad menſurandum de-<pb pagenum="76" xlink:href="005/01/084.jpg"></pb>ſeruiunt: Nam quo ampliora eò minus obtutum fallunt, &amp; <lb></lb>euidentius menſuratorum differentias manifeſtant. </s>
        </p>
        <p id="N12488" type="main">
          <s id="N1248A">Denique ex ijs animaduertit Atiſtoteles modum, quo <lb></lb>nonnulli vendentes purpuram, vel crocum, aut aliud huiuſ<lb></lb>modi, emptores defraudant. </s>
          <s id="N12491">Ita namque (vt ipſe ait) con<lb></lb>ſtruunt libram, vt ſpartum quo illa ſuſpenditur, ſeu axis cir<lb></lb>ca quem illa conuertitur, non ſit prorſus in medio iugi, ac <lb></lb>proinde vnum brachium illius, ſit longius altero, æquè ta<lb></lb>men grauitet, vt tegatur deceptio. </s>
          <s id="N1249C">Infundunt enim plum<lb></lb>bum in brachium, quod minorem habet longitudinem, vel <lb></lb>illud ex grauiori ligno conficiunt, vt puta nodoſo, aut ad ra<lb></lb>dicem vergente: &amp; ſic minorem habens longitudinem <lb></lb>æqueponderat habenti maiorem, <expan abbr="libraq.">libraque</expan> ipſa haud quaquam <lb></lb>apparet vitioſa ſiue iniuſta. </s>
          <s id="N124AD">Deinde verò mercem in eam <lb></lb>lancem imponunt, quæ ex longiori brachio pendet; vbi cer<lb></lb>tè quodlibet pondus magis grauitare neceſſe eſt, quàm in <lb></lb>oppoſita lance. </s>
          <s id="N124B6">Siquidem brachij extremum ex quo pen<lb></lb>det, magis diſtat a centro; <expan abbr="ideoq.">ideoque</expan> quamuis adulterinæ non <lb></lb>ſint <expan abbr="ponderũ">ponderum</expan> notæ, merces maioris ponderis putatur, quàm <lb></lb>reuera ſit, ac tanti ex fraude venditur. </s>
          <s id="N124C9">Vnde etiam ſi libra <lb></lb>lancibus vacuis æquilibrium demonſtret, &amp; æqualibus in <lb></lb>pondere, æqualia addantur, æquè illa ponderare non ſequi<lb></lb>tur, dum æquè à centro libræ non diſtant. </s>
          <s id="N124D2">Nàm ratione ſi<lb></lb>tus quælibet additio ponderis poſtea in ipſis lancibus facta, <lb></lb>ſemper eandem ſeruare debet proportionem, vt magis gra<lb></lb>uitet in loco diſtantiori, quàm in propinquiori; vt exactius <lb></lb>adhuc conſtare poteſt ex Archimede in primo lib. Aeque<lb></lb>ponderan. poſtulat. </s>
          <s id="N124E3">2. &amp; explicatione Guidi Vbaldi è Mar<lb></lb>chionibus Montis ibidem ac tract. de libra prop.

6. </s>
        </p>
        <p id="N124EB" type="main">
          <s id="N124ED">Illud tamen hic minimè prætereundum eſt, non rectè <lb></lb>Blancanum, hunc Ariſtotelis locum expoſuiſſe, <expan abbr="cũ">cum</expan> ex men<lb></lb>te illius ait, purpurarios fraudulentos, plumbum in lancem <lb></lb>illam infundere in quam merces imponitur. </s>
          <s id="N124FA"><expan abbr="Quãdoquidem">Quandoquidem</expan> <lb></lb>ſi ita eſſet, lanx illa maiorem longitudinem brachij non re<lb></lb>quireret ad magis grauitandum. </s>
          <s id="N12504">Quod ſi vtroque ex capi-<pb pagenum="77" xlink:href="005/01/085.jpg"></pb>te magis grauitaret, nempe ex plumbo adiuncto, &amp; ex ma<lb></lb>iori longitudine brachij, nunquam libra ponderibus, ac mer<lb></lb>cibus vacua, in æquilibrio poſſet conſtitui, fed ſatis apertè <lb></lb>huiuſmodi lanx ſemper deorſum tenderet, altera verò ſur<lb></lb>ſum; <expan abbr="ideoq.">ideoque</expan> nulla ex hoc oriretur deceptio, <expan abbr="nullaq.">nullaque</expan> fraus, <lb></lb>quæ ex deceptione conſequitur. </s>
          <s id="N1251E">Quando igitur Ariſtote<lb></lb>les ait, purpurarios plumbum, vel quid ſimile in eam, quam <lb></lb>deferri volunt partem conſtituere, intelligendus eſt de par<lb></lb>te, ſeu de brachio libræ minori, quod certè ſurſum aſcende<lb></lb>ret ad deſcenſum maioris, ac deferri non poſſet ad conſti<lb></lb>tuendum Aequilibrium, niſi ſimilibus adiumentis quantum <lb></lb>opus eſt deprimeretur; vt rectè etiam notat Cardanus lib. <lb></lb>1. de principijs prope finem. </s>
        </p>
        <p id="N12530" type="head">
          <s id="N12532">Quæſtio Secunda.</s>
        </p>
        <p id="N12535" type="main">
          <s id="N12537">C<emph type="italics"></emph>vr ſiquidem curſum ſuerit ſpartum, quan<lb></lb>do deorſum lato pondere quiſpiam id amouet, <lb></lb>rurſum aſcendit libra: ſi autem deorſum con<lb></lb>ſtitutum fuerit, non aſcendit, ſed manet? </s>
          <s id="N12543">An <lb></lb>quia ſurſum quidem ſparto existente plus li<lb></lb>bræ extra perpendiculum fit: quare neceſſe <lb></lb>eſt deorſum ferri id quod plus eſt, donec aſcendat, quæ bifa<lb></lb>riam libram diuidit, ad ipſum perpendiculum, cùm onus in<lb></lb>cumbat ad libræ partem ſurſum raptum.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N12554" type="main">
          <s id="N12556"><emph type="italics"></emph>Sit libra recta, vbi BC, ſpartum autem AD. </s>
          <s id="N1255C">Hoc igi<lb></lb>tur deorſum proiecto perpendiculum erit, vbi ADM. </s>
          <s id="N12562">Si igi<lb></lb>tur in ipſo B ponatur onus, B quidem erit, vbi E, C autem <lb></lb>vbi H s quamobrem ea, quæ bifariam libram ſecat, primò <lb></lb>quidem erit DM ipſius perpendiculi: incumbente autem <lb></lb>onere DG, quare libræ ipſius vbi EH, quòd extra perpen<lb></lb>diculum eſt AM, vbi eſt PQ, maius eſi dimidio. </s>
          <s id="N12571">Si igitur <lb></lb>amoueatur onus ab ipſo E, neceſſe eſt deorſum ferri H mi<lb></lb>nus enim eſt E. </s>
          <s id="N12579">Siquidem igitur ſurſum habuerit ſpartum,<emph.end type="italics"></emph.end><pb pagenum="78" xlink:href="005/01/086.jpg"></pb><emph type="italics"></emph>rurſum propter hoc aſcendit libra. </s>
          <s id="N12585">Si autem deorſum fuerit <lb></lb>in quod ſubſtat, contrarium facit. </s>
          <s id="N1258A">Plus enim dimidio fit li<lb></lb>bræ, quæ deorſum eſt pars, quàm quod per pendiculum ſecet: <lb></lb>quapropter non aſcendit. </s>
          <s id="N12591">Eleuata enim pars leuior eſt.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N12596" type="main">
          <s id="N12598"><emph type="italics"></emph>Sit libra recta vbi NG: perpendiculum autem KLM. <lb></lb></s>
          <s id="N1259F">Bifariam igitur ſecatur KG. </s>
          <s id="N125A2">Impoſito autem onere in ipſo <lb></lb>N, erit quidem N vbi O, ipſum autem G, vbi R, KL <lb></lb>autem vbi LP. </s>
          <s id="N125A9">Quare maius eſt KO, quam LR, ipſo <lb></lb>PKL. </s>
          <s id="N125AE">Et ablato igitur onere, nete&lt;32&gt;e eſt manere; incumbit <lb></lb>enim ceu onus exceſſus medietatis eius vbi eſt F.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N125B6" type="head">
          <s id="N125B8">COMMENTARIVS.</s>
        </p>
        <p id="N125BC" type="main">
          <s id="N125BE">Cvm axis vel ſpartum, quod gerit vicem axis, &amp; quo <lb></lb>ſuſpenditur libra, locari poſſit tum ſupra, tum infra <lb></lb>iugum ipſius libræ, quærit modo Ariſtoteles quid <lb></lb>cauſæ ſit, vt ſi locetur ſupra, appoſito in alteram lancem <lb></lb>pondere, deſcendat quippe illa, ſed eo amoto ex ſe iterum <lb></lb>in priſtinum locum aſcendat: ſi verò axis locetur infra, lanx <lb></lb>illa maneat, &amp; non reuertatur. </s>
        </p>
        <p id="N125CD" type="main">
          <s id="N125CF">Porrò prima huius quæſtionis pars ſi phyſicè conſidere<lb></lb>tur, non paruam videtur inuoluere difficultatem. </s>
          <s id="N125D4">Etenim <lb></lb>nullum apparet agens, à quo talis aſcenſus depreſſæ lancis <lb></lb>procedat. </s>
          <s id="N125DB">Cum enim quodlibet graue tendat deorſum, cau<lb></lb>ſa huiuſmodi eleuationis, &amp; aſcenſionis non poteſt eſſe for<lb></lb>ma aliqua intrinſeca; nec pro extrinſeca aſſignari poteſt <lb></lb>alia, niſi grauitas alterius lancis, qua ſcilicet illa deſcen<lb></lb>dendo, hanc faciat aſcendere. </s>
          <s id="N125E6">Verum cum vtraque lanx <lb></lb>æqualis molis, &amp; grauitatis conſtituatur, nequit altera alteri <lb></lb>præponderare, <expan abbr="deſcenſuq.">deſcenſuque</expan> proprio eam eleuare. </s>
          <s id="N125F1">Simile <lb></lb><expan abbr="namq.">namque</expan> in intenſione per eandem qualitatem agere non po<lb></lb>teſt in ſimile; cum omnis actio procedere debeat ab inæ<lb></lb>quali proportione, vt cum Ariſtotele ſentiunt omnes Phi<lb></lb>loſophi 1. de generat. </s>
          <s id="N125FF">tex. 48. </s>
        </p>
        <pb pagenum="79" xlink:href="005/01/087.jpg"></pb>
        <p id="N12608" type="main">
          <s id="N1260A">Nihilominus etiam phyſicis principijs inhærendo ex ijs, <lb></lb>quæ Ariſtoteles in præſentibus docet, optimè huic difficul<lb></lb>tati poteſt occurri, <expan abbr="primaq.">primaque</expan> pars quæſtionis reſolui. </s>
          <s id="N12615">Nam <lb></lb>ſuppoſito, quod pars iugi, quę eleuatur diſtinguatur à parte, <lb></lb>quæ deprimitur per lineam perpendicularem cadentem à <lb></lb>centro circa quod conuertitur libra, ſeu ab axe, vel ſparto <lb></lb>ad centrum terræ, vt senſu conſtabit in ſequenti figura: ſi<lb></lb>quidem quidquid libræ eſt ad leuam, v.g. talis lineæ, rapi<lb></lb>tur deorſum; quidquid verò eſt ad dexteram attollitur ſur<lb></lb>ſum: hoc inquam ſuppoſito, ait Ariſtoteles, quod ſi libra <lb></lb>axem, ſeu centrum habeat ſupra iugum, ac per depreſſio<lb></lb>nem alterius partis illius, altera eleuetur, plus quippe libræ <lb></lb>eſſet ex parte eleuata, quàm ex parte depreſſa: <expan abbr="proindeq.">proindeque</expan> <lb></lb>pars eleuata neceſſeriò deſcendet, &amp; ad deſcenſum illius, <lb></lb>ſequitur depreſſam aſcendere, quouſque vtraque conſtitua<lb></lb>tur æqualis, ac reuertatur ad æquilibrium. </s>
          <s id="N12634">Id quod ita ſe <lb></lb>habere ſic probat. </s>
          <s id="N12639">Nam ſi iugum libræ ſit BC in æquilibrio <lb></lb><figure id="id.005.01.087.1.jpg" xlink:href="005/01/087/1.jpg"></figure><lb></lb>conſtitutum: ſpartum <lb></lb>autem quo <expan abbr="ſuſpẽditur">ſuſpenditur</expan>, <lb></lb>AD, ita videlicet, vt <lb></lb>axis ſit ipſum D, quod <lb></lb>eſt punctum ſupra lati<lb></lb>tudinem iugi. </s>
          <s id="N12652">Dein<lb></lb>de ſpartum proijciatur <lb></lb>deorſum, <expan abbr="efficiatq.">efficiatque</expan> per<lb></lb>pendicularem ADM. <lb></lb></s>
          <s id="N12661">Tunc ſi in ipſo B ponatur onus, B quidem deſcendet in <lb></lb>E, C autem aſcendet vbi H. </s>
          <s id="N12667">Quamobrem linea, quæ in <lb></lb>priori ſitu libram diuidebat bifariam, eſt ipſa perpendicu<lb></lb>laris DM. </s>
          <s id="N1266F">Illa verò quæ poſtea eodem pacto diuidit in, <lb></lb>poſteriori ſitu propter onus, quod incumbit in E, erit <lb></lb>DG. </s>
          <s id="N12677">Quare ea pars libræ, ſeu iugi. </s>
          <s id="N1267A">EH, quæ eſt extra <lb></lb>perpendiculum AM verſus H maior erit dimidio nem<lb></lb>pe quantum importat triangulus DGM, quod ſpatium <lb></lb>Ariſtoteles ſignauit <expan abbr="Pq.">PQ</expan> Si igitur amoueatur onus, quod <pb pagenum="80" xlink:href="005/01/088.jpg"></pb>deprimit in E, neceſſe eſt deorſum ferri partem vbi H. <lb></lb><figure id="id.005.01.088.1.jpg" xlink:href="005/01/088/1.jpg"></figure><lb></lb><expan abbr="Siquidẽ">Siquidem</expan> pars illa ma<lb></lb>ior eſt quàm hæc vbi <lb></lb>E, quæ per <expan abbr="conſequẽs">conſequens</expan> <lb></lb>ſurſum aſcendet, &amp; ſic <lb></lb>rurſus libra conſtitue<lb></lb>tur in æquilibrio quod <lb></lb>erat probandum. </s>
          <s id="N126A7">Se<lb></lb>cunda verò pars huius <lb></lb>quæſtionis facilius ab <lb></lb>eodem Ariſtotele probatur. </s>
          <s id="N126B0">Quoniam ſi ſpartum, ſeu axis <lb></lb>infra iugum locetur, maior pars librę eſſet illa, quę deor<lb></lb>ſum ex impoſito pondere reperiretur depreſſa, quàm quę <lb></lb>ſurſum eſſet elata. </s>
          <s id="N126B9">Porrò plus dimidio contineret, <expan abbr="proin-deq.">proin<lb></lb>deque</expan> etiam ablato pondere adhuc magis grauitaret, ac pro<lb></lb>pterea ad equilibrium redire minimè poſſet. </s>
          <s id="N126C4">Id quod ſic <lb></lb>oſtendit Ariſtoteles ſit libra in ęquilibrio conſtituta NG <lb></lb><figure id="id.005.01.088.2.jpg" xlink:href="005/01/088/2.jpg"></figure><lb></lb><expan abbr="perpendiculũ">perpendiculum</expan> verò bi<lb></lb>fariam libram ipſam <lb></lb>ſecans, ac tendens ad <lb></lb>centrum mundi, ſit ca<lb></lb>dens KLM. </s>
          <s id="N126DD">Axis verò <lb></lb>infra <expan abbr="iugũ">iugum</expan> locatus vbi <lb></lb>L. </s>
          <s id="N126E9">Impoſito poſt hęc <lb></lb>onere in ipſo N, de<lb></lb>ſcendet plane ipſum <lb></lb>N, <expan abbr="eritq.">eritque</expan> exempli gratia, vbi O. </s>
          <s id="N126F6">Et per conſequens ipſum <lb></lb>G aſcendet ad R. </s>
          <s id="N126FC">Linea verò KL, quę bifariam diuide<lb></lb>bat libram in ſitu NG declinabit in PL. <expan abbr="Cumq.">Cumque</expan> maius ſit <lb></lb>KO, quàm KR eo quod vltra dimidium contineat etiam <lb></lb>triangulum PKL; ſequitur vt ablato onere, adhuc nequeat <lb></lb>pars iſta librę ſurſum attolli. </s>
          <s id="N1270B">Quandoquidem exceſſus il<lb></lb>le ſupra medietatem, tanquam onus quoddam ei ſemper in<lb></lb>cumbit. </s>
        </p>
        <p id="N12712" type="main">
          <s id="N12714">Huic autem Ariſtotelis demonſtrationi addi etiam po-<pb pagenum="81" xlink:href="005/01/089.jpg"></pb>teſt alia ſumpta ex centro grauitatis, vt proprium eſt me<lb></lb>chanicarum ſpeculationum. </s>
          <s id="N1271E">Porrò libræ iam explicatæ cen<lb></lb>trum grauitatis eſt punctum in medio iugi intrapoſitum, vt <lb></lb>patet ex definitione. </s>
          <s id="N12725">Nam circa illud <expan abbr="vndiq.">vndique</expan> partes æqua<lb></lb>lium ſunt momentorum. </s>
          <s id="N1272E">Quando autem libra eſt in Aequi<lb></lb>librio conſtituta, huiuſmodi centrum coincidit in eandem <lb></lb>lineam perpendiculatem, in qua eſt centrum circumuolu<lb></lb>tionis, ſeu axis ipſius libræ, ac centrum mundi; ſiue axis po<lb></lb>natur ſupra, ſiue infra <expan abbr="iugũ">iugum</expan>, vt videre eſt in deſcriptis figuris. <lb></lb></s>
          <s id="N1273E">Quo fit, vt libra in tali poſitione quieſcat; nam centrum <lb></lb>grauitatis per breuiorem lineam, qua fieri poteſt tendit ad <lb></lb>centrum mundi; nulla autem breuior eſt recta in ipſum ca<lb></lb>dente. </s>
          <s id="N12747">Quando verò libra per depreſſionem vnius, &amp; ele<lb></lb>uationem alterius partis ipſius, <expan abbr="nõ">non</expan> manet in æquilibrio, tunc <lb></lb>centrum grauitatis conſtituitur extra perpendiculum, ſeu li<lb></lb>neam prædictam cadentem ad centrum mundi per <expan abbr="cẽtrum">centrum</expan> <lb></lb>circumuolutionis ipſius libræ; ac propterea neceſſario ipſum <lb></lb>centrum grauitatis ſi ſupra eſt in parte eleuata, ablato pon<lb></lb>dere partis oppoſitæ deſcendet, ac reuertetur in locum pri<lb></lb>ſtinum, vt magis centro mundi appropinquetur per viam <lb></lb>qua poteſt. </s>
          <s id="N12762">Si verò infra eſt in parte depreſſa, etiam ſi pon<lb></lb>dus ab illa auferatur, manebit; quia in illo ſitu ſimiliter &amp; <lb></lb>adhuc magis appropinquatur centro mundi quo tendit. </s>
          <s id="N12769">Quę <lb></lb>omnia abſque alia figura perſpicua eſſe poſſunt ex deſcri<lb></lb>ptis, ac fuſiùs, &amp; exactiùs traduntur, cum à Guidone Vbaldo <lb></lb>tractatu de libra, tum à Bernardino Baldo in hac quæſtione, <lb></lb>qui tantam in centro grauitatis vim eſſe animaduertit ad <lb></lb>præponderandum, vt hinc colligat, libras quæ axem habent <lb></lb>ſupra iugum, non à quouis paruo pondere moueri, vel peni<lb></lb>tus declinare, ſed ab eo <expan abbr="tantũ">tantum</expan>, quod ſuperet <expan abbr="reſiſtentiã">reſiſtentiam</expan> cen<lb></lb>tri grauitatis, quę reſiſtentia proportionaliter eo maior ex<lb></lb>peritur, quo minus grauitatis <expan abbr="cẽtrũ">centrum</expan> diſtat ab axe, ſeu centro <lb></lb>circa quod ipſa libra conuertitur, vt <expan abbr="ibidẽ">ibidem</expan> ipſe demonſtrat. </s>
        </p>
        <p id="N12790" type="main">
          <s id="N12792">Verum quamuis prædicta omnia vera ſint, adhuc tamen <lb></lb>aliquod deſideratur ad adæquatam omnino rationem tra<lb></lb>dendam, cur axe exiſtente ſupra iugum, ſi eleuetur vna pars <pb pagenum="82" xlink:href="005/01/090.jpg"></pb>illius ad depreſſionem alterius, <expan abbr="cauſaq.">cauſaque</expan> depreſſionis remo<lb></lb>ueatur, ſtatim pars illa eleuata præcipiti curſu deſcendat, <lb></lb><expan abbr="redeatq.">redeatque</expan> in priſtinum locum. </s>
          <s id="N127A9">Siquidem exceſſus ille partis <lb></lb>eleuatæ, quem ex Ariſtotele explicuimus, <expan abbr="rurſumq.">rurſumque</expan> ratio <lb></lb>centri grauitatis prædicta non videntur ſufficere, nec tanti <lb></lb>eſſe momenti, vt <expan abbr="tantã">tantam</expan> motionem <expan abbr="tamquã">tamquam</expan> præcipitem de<lb></lb>ſcenſum cauſare præualeant. </s>
          <s id="N127C0">Cum &amp; centrum grauitatis <lb></lb>parum, aut imperceptibiliter remoueatur à linea illa ca<lb></lb>dente ab axe ad centrum mundi; &amp; exceſſus partis eleuatæ <lb></lb>non modo paruus ſit, ſed paruum etiam ab eadem linea di<lb></lb>ſtet vbi minus præponderantia experitur. </s>
          <s id="N127CB">Etenim ſi huiuſ<lb></lb>modi exceſſus appenderetur tanquam onus in libra, quæ in <lb></lb>æquilibrio ſit conſtituta, ac prope axem in ſimili ſitu, ac eſt <lb></lb>ille, quem in caſu noſtro retinet, abſque dubio parum, aut <lb></lb>nihil præponderaret brachium in quo appenderetur. </s>
        </p>
        <p id="N127D6" type="main">
          <s id="N127D8">Dicendum ergo eſt vltra cauſas prædictas præcipuè de<lb></lb>ſcenſionem illam cauſari à maiori grauitate, quam eleuatæ, <lb></lb>ac pondus lancis ab illo pendentis obtinere videtur in eo <lb></lb>loco. </s>
          <s id="N127E1">Nam licet in æquilibrio lances conſtitutæ, ſupponan<lb></lb>tur in grauitate æquales: non tamen in quocumque ſitu, &amp; <lb></lb>poſitione, æque poſſunt grauitare. </s>
          <s id="N127E8">Quodlibet enim libran<lb></lb>dum pondus alias inuariatum, quantò magis elongatur à li<lb></lb>nea perpendiculari, quæ per punctum axis inſtrumenti ca<lb></lb>dit ad centrum terræ (quam lineam Geometrici vocant ca<lb></lb>thectum) tanto magis grauitat, vt cernere eſt in ſtatera, <lb></lb>vel in alio ſimili ad ponderandum apto inſtrumento. </s>
          <s id="N127F5">Non <lb></lb>quia ratione ſitus re vera maiorem, aut minorem grauita<lb></lb>tem acquirat, ſed quia magis, vel minus ſuſtinetur ab in<lb></lb>ſtrumento in illo ſitu iuxta maiorem, aut minorem propin<lb></lb>quitatem, quam ſitus habet cum linea explicata, vt Guido <lb></lb>Vbaldus animaduertit, tractatu de Libra, prop.

4. ante med. <lb></lb></s>
          <s id="N12803">Cum igitur pondus ſuperioris lancis in eo loco magis diſtet <lb></lb>aliena perpendiculari prædicta, quàm pondus inferioris, ſe<lb></lb>quitur magis grauitare ſuperiorem lancem, quàm grauitet <lb></lb>inferior, atque adeo hæc ab illa tanquam ab inæquali pro<lb></lb>portione virtutis moueri, &amp; ſurſum ferri vſquequo ad æqua-<pb pagenum="83" xlink:href="005/01/091.jpg"></pb>lem cum illa à cathectu diſtantiam, ac proinde grauitatem <lb></lb>perueniat, vt in æquilibrio contingit</s>
        </p>
        <p id="N12815" type="main">
          <s id="N12817">Superiorem autem lancem modo prædicto à linea ca<lb></lb>thectus magis remoueri, ſic poteſt <expan abbr="demõſtrari">demonſtrari</expan> exemplo hu<lb></lb>ius figuræ. </s>
          <s id="N12822">Sit cathectus cadens linea AB, quæ tranſeat <lb></lb>per punctum axis propoſitæ libræ vbi C. </s>
          <s id="N12828">Deinde ducatur <lb></lb>recta DE per longum diuidens iugum libræ, <expan abbr="ipſaq.">ipſaque</expan> DE bi<lb></lb>fariam diuidatur in F, &amp; punctum in quo ſecat lineam AB, <lb></lb>ſignetur G. </s>
          <s id="N12836">Poſtea excitentur à puncto D, &amp; à puncto E <lb></lb>duæ paralellæ perpendiculariter tendentes ad lineam AB, <lb></lb>ita vt efficiantur duo triangula AEG, &amp; DGB. </s>
          <s id="N1283D">In his au<lb></lb><figure id="id.005.01.091.1.jpg" xlink:href="005/01/091/1.jpg"></figure><lb></lb>tem triangulis, an<lb></lb>gulus DGB ęqua<lb></lb>lis eſt angulo EGA <lb></lb>cum ſint ad verti<lb></lb>cem per 15. primi <lb></lb>Eucl. </s>
          <s id="N12853">Angulus <expan abbr="etiã">etiam</expan> <lb></lb>D. ęqualis eſt an<lb></lb>gulo E cum ſint al<lb></lb>terni intra eaſdem <lb></lb>paralellas, vt patet <lb></lb>per 29. primi eiuſ<lb></lb>dem Euclidis. </s>
          <s id="N12867">Si<lb></lb>militer etiam angu<lb></lb>lus B æqualis eſt <lb></lb>angulo A, quia <lb></lb>vterque ponitur re<lb></lb>ctus. </s>
          <s id="N12874">Cum igitur <lb></lb>tres anguli vnius <lb></lb>trianguli æquales <lb></lb>ſint tribus angulis alterius trianguli ſequitur per 4. prop.

ſex<lb></lb>ti, latera eorundem triangulorum, quę circum ęquales an<lb></lb>gulos ſunt, eſſe inter ſe proportionalia. </s>
          <s id="N12881">Vnde fit vt cum <lb></lb>vnum latus ex duobus, quibus angulus E continetur, vide<lb></lb>licet GE ſit maius <expan abbr="quã">quam</expan> latus GD ęqualis anguli D. </s>
          <s id="N1288D">Siqui<lb></lb>dem GE eſt pluſquam dimidium lineę DE continet enim <pb pagenum="84" xlink:href="005/01/092.jpg"></pb>amplius <expan abbr="diſtantiã">diſtantiam</expan> GF, eo quod in F ipſa linea DE bifariam <lb></lb>diuiſa ſit, <expan abbr="proindeq.">proindeque</expan> latus GD ſit minus dimidio, ad quod <lb></lb>deeſt ſpatium GF. Ex. hoc inquam fit, vt alterum latus <lb></lb>eiuſdem anguli E ſit etiam maius altero latere ęqualis an<lb></lb>guli D, nempe vt AE, maius ſit quàm BD. </s>
          <s id="N128AA">Iam ergo <lb></lb>per longiorem perpendicularem ſuperior lanx, quàm infe<lb></lb>rior à cathectu diſtabit, quod erat demonſtrandum, vt hanc <lb></lb>magis quam illam in eo ſitu grauitare aſſeramus. </s>
        </p>
        <p id="N128B3" type="main">
          <s id="N128B5">Vnum tandem hic ſupereſt explicandum, de quo non <lb></lb>meminit Ariſtoteles; Cur nimirum ſi axis non conſtituatur <lb></lb>ſupra, nec infra, ſed prorſus in puncto medio longitudinis, <lb></lb>ac magnitudinis iugi, vt in puncto A propoſitę librę BC <lb></lb>in æquilibrio conſtitutę; &amp; alterum extremum illius manu, <lb></lb>vel pondere deorſum trahatur, ablato pondere, vel ceſſante <lb></lb>detentione, rurſus ad ęquilibrium ipſa libra non reuertatur, <lb></lb>ſed maneat quomodocumque relinquatur. </s>
        </p>
        <p id="N128C6" type="main">
          <s id="N128C8">Id quod ex eo prouenire comperiemus, quoniam in hu<lb></lb>iuſmodi conſtitutione librę, centrum grauitatis coincidit <lb></lb>cum centro circumuolutionis, ſeu axis ipſius librę, <expan abbr="proin-deq.">proin<lb></lb>deque</expan> habere non poteſt, quo declinet, aut vergat etiam ſi <lb></lb>libra quomodolibet ſituetur, aut moueatur, ſed manebit <lb></lb><figure id="id.005.01.092.1.jpg" xlink:href="005/01/092/1.jpg"></figure><lb></lb>ſemper in illo <lb></lb>tanquam in ſuo <lb></lb>fulcimento, à <lb></lb>quo ſuſtentatur. <lb></lb></s>
          <s id="N128E6">Idem enim <expan abbr="pũ-ctum">pun<lb></lb>ctum</expan> A eſt cen<lb></lb>trum grauitatis <lb></lb>cum ſit in me<lb></lb>dio iugi BC, &amp; <lb></lb>eſt <expan abbr="cẽtrum">centrum</expan> axis <lb></lb>ex conſtructio<lb></lb>nis ſuppoſitio<lb></lb>ne. </s>
          <s id="N12901">Quare ſi in <lb></lb>illo iugum diui<lb></lb>datur per lineam perpendicularem DE, in quo cumque ſi-<pb pagenum="85" xlink:href="005/01/093.jpg"></pb>tu ponatur, ſiue in ęquilibrio, vt vbi BC, ſiue alibi vt in F G <lb></lb>ſemper diuidetur bifariam, atque adeo in duas partes ęqui<lb></lb>ponderantes, quarum altera, alteram mouere non poteſt, <lb></lb>cum propter ęquiponderantiam, tum propter <expan abbr="æquidiſtãtiam">æquidiſtantiam</expan> <lb></lb>quam ſemper <expan abbr="retinerẽt">retinerent</expan> à perpendiculo, ſeu linea cathectus. </s>
        </p>
        <p id="N1291D" type="head">
          <s id="N1291F">Quæſtio Tertia.</s>
        </p>
        <p id="N12923" type="main">
          <s id="N12925">C<emph type="italics"></emph>vr exiguæ vires (quemadmodum à principio<lb></lb>dictum eſt) vecte, magna mouent pondera, <lb></lb>vectis inſuper onus accipientes? </s>
          <s id="N12930">cum faci<lb></lb>lius ſit minorem mouere grauitatem: minor <lb></lb>autem eſt ſine vecte. </s>
          <s id="N12937">An quoniam ipſe ve<lb></lb>ctis eſt in cauſa libra exiſtens, ſpartum infer<lb></lb>nè habens, in inæqualia diuiſa. </s>
          <s id="N1293E">Hypomochlion enim est ſpar<lb></lb>tum: ambo namque stant vt centrum. </s>
          <s id="N12943">Quoniam autem ab <lb></lb>æquali pondere celeriùs mouetur maior earum, quæ à centro <lb></lb>ſunt: duo verò pondera, quod mouet, &amp; quod mouetur: quod <lb></lb>igitur motum pondus ad mouens, longitudo patitur ad longi<lb></lb>tudinem. </s>
          <s id="N1294E">Semper autem quanto ab hypomochlio diſtabit ma<lb></lb>gis, tantò faciliùs mouebit. </s>
          <s id="N12953">Cauſa autem eſt, quæ retrò com<lb></lb>memorata est: quoniam quæ plus à centro distat, maiorem <lb></lb>deſcribit circulum: quare ab eadem potentia plus ſeparabitur <lb></lb>mouens illud, quod plus ab hypomochlio diſtabit. </s>
          <s id="N1295C">Sit vectis <lb></lb>vbi AB, pondus vbi C, quod mouet autem, vbi D, hypo<lb></lb>mochlion vbi E, quod autem vbi eſt D, mouens vbi F. mo<lb></lb>tum autem vbi C. pondus vbi G.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N12968" type="head">
          <s id="N1296A">COMMENTARIVS.</s>
        </p>
        <p id="N1296E" type="main">
          <s id="N12970">Qvod Ariſtoteles tanquam admirandum, ac vnum <lb></lb>de numero eorum, quę pręter naturam accidunt in <lb></lb>principio huius libri textu 2. propoſuerat, hic mo<lb></lb>do ad inueſtigandam eius cauſam, iterum proponit, quęrens <pb pagenum="86" xlink:href="005/01/094.jpg"></pb>cur exiguę vires adhibito vecte, magna moueant pondera, <lb></lb>quę abſque vecte mouere minimè poſſent, cum tamen ip<lb></lb>ſum quoque onus vectis. </s>
          <s id="N12982">dimouendum ſuſcipiant? </s>
          <s id="N12985">Facilius <lb></lb>enim eſt, minorem quàm maiorem ſuperare grauitatem <lb></lb>ponderis: minor autem eſt grauitas ponderis abſque vecte, <lb></lb>quàm cum vecte. </s>
          <s id="N1298E">Vnde contrarium fortaſſe videtur debe<lb></lb>re contingere ab eo, quod de facto contingit. </s>
        </p>
        <p id="N12993" type="main">
          <s id="N12995">At ſtatim Ariſtoteles quæſtioni reſpondet dicens, ve<lb></lb>ctem quippe habere rationem libræ, cuius axis, ſeu truti<lb></lb>na ſit infra iugum, vt explicuimus, brachia verò ſint inæ<lb></lb>qualia. </s>
          <s id="N1299E">Hypomochlion enim, ſeu fulcimentum vectis, axis <lb></lb>vicem gerit. </s>
          <s id="N129A3">Similiter namque circa ipſum conuertitur ve<lb></lb>ctis, ſimiliterque ſemper manet immotum. </s>
          <s id="N129A8">Longitudo au<lb></lb>tem vectis vtrinque ex fulcimento protenſa, iugum refert <lb></lb>libræ, in brachia, ſeu partes inæquales diuiſum; quarum <lb></lb>illa, quæ ad pondus leuandum applicatur, ſit breuior, illa <lb></lb>verò in cuius, extremitate virtus adhibetur potentiæ mo<lb></lb>tricis ſit longior, vt cernere eſt in hac figura, quam tamen <lb></lb>Ariſtoteles exibuit in fine. </s>
          <s id="N129B7">Sit enim vectis. </s>
          <s id="N129BA">AB, pondus <lb></lb>verò vbi C, &amp; potentia mouens vbi D; inter quæ me<lb></lb>diet fulcimentum in E. </s>
          <s id="N129C2">Tunc ſi conſideretur, eadem erit <lb></lb><figure id="id.005.01.094.1.jpg" xlink:href="005/01/094/1.jpg"></figure><pb pagenum="87" xlink:href="005/01/095.jpg"></pb><figure id="id.005.01.095.1.jpg" xlink:href="005/01/095/1.jpg"></figure><lb></lb>ratio ac de libra, cuius iugum ſit AB, lances verò C, D, <lb></lb>&amp; axis, ſeu fulcimentum E. </s>
          <s id="N129D9">Siquidem ipſum D pendens <lb></lb>ex longiori brachio libræ, præponderat ipſi C. </s>
          <s id="N129DF">Quemad<lb></lb>modum potentia applicata in vecte vbi D, ſuperat graui<lb></lb>tatem ponderis C. </s>
          <s id="N129E7">Axis verò <expan abbr="cũ">cum</expan> ponatur infra iugum, ſiue <lb></lb>ipſum iugum ſit ſuſpenſum per trutinam, aut ſpartum, ſiue <lb></lb>innixum ſit alteri corpori immobili, idem ſemper præſtat, <lb></lb>ac fulcimentum vectis vbi E. </s>
        </p>
        <p id="N129F5" type="main">
          <s id="N129F7">Quoniam autem (proſequitur Ariſtoteles) ab æquali <lb></lb>pondere celerius, ſiue facilius mouetur brachium libræ, <lb></lb>quod magis à centro diſceſſerit, vt explicatum eſt de libra, <lb></lb>quæ alterum brachium longius obtinet, eam ad circulum <lb></lb>reducendo: hinc fit, vt cum duo ſint, quæ in ambis extre<lb></lb>mitatibus vectis præsunt, vel ponderant, nempe mouens <lb></lb>in vna, &amp; motum in alia; illud magis præponderet, quod <lb></lb>longiorem vectis extremitatem præſſerit; ſeu quanto magis <lb></lb>à fulcimento diſceſſerit, quamuis aliàs ipſa ponderantia in <lb></lb>ſe ſint æqualia, hoc eſt virtus mouentis æqualis ſit moto <lb></lb>ponderi, &amp; longior pars vectis æquè grauitet, ac breuior. <lb></lb></s>
          <s id="N12A0F">Quod totum, vt ipſemet Ariſtoteles inquit, deſumitur ab <pb pagenum="88" xlink:href="005/01/096.jpg"></pb>explicato illo principio; quoniam ſcilicet, quæ plus à cen<lb></lb>tro diſtat linea, ſeu extremitas ſemidiametri, maiorem de<lb></lb>ſcribit circumferentiam, quæ ſanè cum magis ad rectam li<lb></lb>neam accedat, facilius, ac velocius per ipſam fertur ſemidia<lb></lb>meter, tanquam per viam magis connaturalem, vt ibidem <lb></lb>explicuimus. </s>
        </p>
        <p id="N12A21" type="main">
          <s id="N12A23">Illud autem, quod Ariſtoteles interpoſuit, nempe: Quod <lb></lb>igitur motum pondus admouens, longitudo patitur ad lon<lb></lb>gitudinem: idem eſt, ac dicere, eandem proportionem ha<lb></lb>bere motricem potentiam ad pondus leuandum, quam ha<lb></lb>bet eius longitudo, ſeu diſtantia à centro vectis ad longitu<lb></lb>dinem, ſeu diſtantiam ponderis ab eodem centro vbi eſt <lb></lb>fulcimentum. </s>
          <s id="N12A32">Quare ſubiungit: Semper autem quanto ab <lb></lb>hypomochlio, id eſt fulcimento, diſtabit magis, tanto facilius <lb></lb>mouebit. </s>
          <s id="N12A39">Hæc ille, quæ poſtea exactius tradita ſunt ab <lb></lb>Archimede in ſuo primo libro æqueponderantium propo<lb></lb>ſitione ſexta; &amp; acutiſſimè probantur à Guido Vbaldo è <lb></lb>Marchionibus Montis in ſuis Mechanicis tractatu de libra <lb></lb>propoſitione ſexta; ac de vecte propoſitione quarta. </s>
          <s id="N12A44">De<lb></lb>monſtrant enim in æquilibrijs, tàm vectis, quàm libræ, ita ſe <lb></lb>habere pondus ad pondus, vt brachium ad brachium ex <lb></lb>commutata proportione. </s>
          <s id="N12A4D">Sit enim vectis, aut libra AB ſuf<lb></lb>fulta, aut ſuſpenſa in C. </s>
          <s id="N12A53">Brachium autem CA ſit verbi <lb></lb><figure id="id.005.01.096.1.jpg" xlink:href="005/01/096/1.jpg"></figure><lb></lb>gratia vnius <lb></lb>palmi. </s>
          <s id="N12A60">Bra<lb></lb>chium verò <lb></lb>CB ſit qua<lb></lb>tuor palmo<lb></lb>rum. </s>
          <s id="N12A6B">Dein<lb></lb>de <expan abbr="appẽda-tur">appenda<lb></lb>tur</expan> in <expan abbr="Apõ-dus">A pon<lb></lb>dus</expan> D, quod <lb></lb><expan abbr="põderet">ponderet</expan>, vt <lb></lb>quatuor; &amp; <lb></lb>in B appen<lb></lb>datur pondus E, ponderans vt vnum; ita vt ipſum pondus <pb pagenum="89" xlink:href="005/01/097.jpg"></pb>E ſe habeat ad pondus D eadem proportione, qua bra<lb></lb>chium CA ſe habet ad brachium CB. </s>
          <s id="N12A8F">Tunc quippe dici<lb></lb>mus vectem, aut libram manſuram in æquilibrio propter <lb></lb><expan abbr="cõmutatam">commutatam</expan> proportionem. </s>
          <s id="N12A99">Etenim quadruplum ponderis <lb></lb>D commutatur cum quadruplo longitudinis CB. </s>
          <s id="N12A9F">Et pon<lb></lb>dus E compenſatur à longitudine CA, quæ eſt quarta. <lb></lb></s>
          <s id="N12AA5">pars longitudinis CB: ſicut pondus E eſt quarta pars pon<lb></lb>deris D. </s>
          <s id="N12AAB">Quare promiſcue ſumendo partes ipſas ponde<lb></lb>rantes ſiue ratione propriæ grauitatis, ſiue ratione diſtan<lb></lb>tiæ quam habent à fulcimento, quinque erunt partes ad le<lb></lb>uam, &amp; quinque ad dexteram, <expan abbr="vtræq.">vtræque</expan> vtriſque in pondere <lb></lb>æquales, vel æquè ſimul grauitantes. </s>
          <s id="N12ABA">Siquidem nec pondus <lb></lb>D, quod eſt vt quatuor: nec pondus E, quod eſt vt vnum, <lb></lb>ſuperare poteſt longitudinem CA, quæ pariter eſt vt vnum. <lb></lb></s>
          <s id="N12AC2">Et ſic vnum ſupra quatuor ex vtraque parte conſtituunt <lb></lb>quinquenarium æquale ex commutata proportione longi<lb></lb>tudinis, &amp; grauitatis. </s>
        </p>
        <p id="N12AC9" type="main">
          <s id="N12ACB">Cæterum cum Ariſtoteles totam vin ſui argumenti ſum<lb></lb>pſerit ex eo, quod ab æquali pondere celerius mouetur bra<lb></lb>chium, ſeu partem libræ, quæ magis à centro diſtenditur; <lb></lb>cauſam ipſam cur exiguæ vires adhibito vecte magna mo<lb></lb>ueant pondera conſtituere videtur in velocitate, quæ bra<lb></lb>chij longitudinem conſequitur, vt ait Baldus. </s>
          <s id="N12AD9">Quod qui<lb></lb>dem ipſe minime approbat. </s>
          <s id="N12ADE">Quæ enim, ait, velocitas in re <lb></lb>ſtante? </s>
          <s id="N12AE3">Stant autem vectis, &amp; libra dum manent in æquili<lb></lb>brio, &amp; nihilominus parua potentia ingens ſuſtinet pondus. </s>
        </p>
        <p id="N12AE8" type="main">
          <s id="N12AEA">Veruntamen ſi verba Ariſtotelis exactius penſentur non <lb></lb>id ſignificant, nec ille talem cauſam formaliter in maiori <lb></lb>velocitate, ſed in maiori grauitate, aut virtute conſtituit, <lb></lb>quæ brachij maiorem longitudinem conſequitur. </s>
          <s id="N12AF3">Etenim <lb></lb>cum dixit: <emph type="italics"></emph>Quoniam autem ab æquali pondere celerius mo<lb></lb>uetur maior earum, quæ à centro ſunt.<emph.end type="italics"></emph.end></s>
          <s id="N12AFF"> Idem per <emph type="italics"></emph>celerius<emph.end type="italics"></emph.end> ac <lb></lb>per <emph type="italics"></emph>facilius<emph.end type="italics"></emph.end> intellexit. </s>
          <s id="N12B10">Quandoquidem paulo poſt id ipſum <lb></lb>repetens, ait. <emph type="italics"></emph>Semper autem quanto ab hypomochlio dicta<lb></lb>bit magis, tanto facilius mouebit.<emph.end type="italics"></emph.end></s>
          <s id="N12B20"> Et quidem in motu locali <lb></lb>velocitas ſemper facilitatem inuoluit, aut ſupponit, <expan abbr="ipſaq.">ipſaque</expan> <pb pagenum="90" xlink:href="005/01/098.jpg"></pb>maior velocitas, ac facilitas motus, maiorem grauitatem, aut <lb></lb>maiorem virtutem motiuam neceſſario indicat, vt palam eſt <lb></lb>in motibus tàm naturalibus, quàm violentis. </s>
          <s id="N12B32">Nam corpus <lb></lb>quò grauius, eò velocius deſcendit, ſi non detineatur; &amp; <lb></lb>proiecta, eò velocius inter medium percurrunt, quo maio<lb></lb>rem impulſum à proijciente recipiunt. </s>
          <s id="N12B3B"><expan abbr="Ipſaq.">Ipſaque</expan> animalia tan<lb></lb>to progrediuntur velocius, <expan abbr="citiusq.">citiusque</expan> per incuſſionem impul<lb></lb>ſus grauia mouent, quanto maiorem virtutem motiuam <lb></lb>adepta fuerit cum pari diſpoſitione inſtrumentorum. </s>
          <s id="N12B4B">Itaque <lb></lb>in propoſito, hoc ipſo quod extremum longiori brachij ve<lb></lb>locius mouetur, magis grauitat in illo ſitu, ſeu maiore in in<lb></lb>dicat ſe ibi adipiſci virtutem motiuam, maiuſque pondus <lb></lb>præualet ſuſtinere etiam ſi non moueatur. </s>
        </p>
        <p id="N12B56" type="head">
          <s id="N12B58">Quæſtio Quarta.</s>
        </p>
        <p id="N12B5B" type="main">
          <s id="N12B5D">C<emph type="italics"></emph>vr ij, qui in nauis medio ſunt remiges, ma<lb></lb>ximè nauem mouent? </s>
          <s id="N12B65">an quia remus vectis <lb></lb>est, hypomochlion autem fit ſcalmus? </s>
          <s id="N12B6A">ſtat <lb></lb>enim ille: pondus verò mare est, quod propel<lb></lb>lit remus: vectem autem mouens est ipſe re<lb></lb>mex. </s>
          <s id="N12B73">Semper autem plus mouet ponderis, <lb></lb>quantò magis ab hypomochlio distabit quicumque id mouet. <lb></lb></s>
          <s id="N12B79">Maior enim ita fit, quæ ex centro. </s>
          <s id="N12B7C">Scalmus autem hypomo<lb></lb>chlion exiſtens, centrum eſt. </s>
          <s id="N12B81">In medio autem nauis plurimum <lb></lb>remi intus eſt: illa enim parte latiſſima eſi nauis: quare ma<lb></lb>ior vtrinque remi pars vtrorumque nauis parietum intrinſe<lb></lb>cus eſi. </s>
          <s id="N12B8A">Mouetur autem nauis, quoniam appellente ad ma<lb></lb>re remo, extremum illius, quod intus eſt, in ante promouetur: <lb></lb>nauem verò ſcalmo alligatam ſimul promoueri contingit, <lb></lb>quo remi extremum. </s>
          <s id="N12B93">Vbi enim plurimum maris diuidit re<lb></lb>mus, eò maximè propelli neceſſe eſi. </s>
          <s id="N12B98">Plurimùm autem diuidit, <lb></lb>vbi pars plurima remi à ſcalmo eſt. </s>
          <s id="N12B9D">Et eam ob cauſam remi<lb></lb>ges, qui in media ſunt naui, mouent illam maximè. </s>
          <s id="N12BA2">Maxima <lb></lb>enim remi pars à ſcalmo in nauis medio intus eſt.<emph.end type="italics"></emph.end></s>
        </p>
        <pb pagenum="91" xlink:href="005/01/099.jpg"></pb>
        <p id="N12BAD" type="head">
          <s id="N12BAF">COMMENTARIVS.</s>
        </p>
        <p id="N12BB3" type="main">
          <s id="N12BB5">Svpponit hic Ariſtoteles ab experientia, quod nos in<lb></lb>fra ratione probabimus, remiges in nauis medio remi<lb></lb>gantes, magis nauem mouere, quàm ſi in prora, vel <lb></lb>puppi remigarent, ſiue quàm alij, qui æquali conatu, ac vir<lb></lb>tute ſimul remigant in alio ſitu. </s>
          <s id="N12BC0"><expan abbr="Cauſamq.">Cauſamque</expan> problematicè <lb></lb>ſciſcitando, vt ſolet præmittit, Remum vectem eſt, ſcal<lb></lb>mum verò fulcimentum, &amp; mare conſtitui pondus, quod per <lb></lb>remum propellitur à remige tanquam à vectem mouente. <lb></lb></s>
          <s id="N12BCF">Deinde ſic argumentatur: Tanto magis mouens adhibito <lb></lb>vecte pondus mouet, quanto magis extremum vectis vbi <lb></lb>virtutem applicat diſtat a centro, ſeu fulcimento: At in <lb></lb>medio nauis, remi manubrium ſiue extremum, in quo vir<lb></lb>tus remigis applicatur, magis diſtat à ſcalmo, qui conſtitui<lb></lb>tur fulcimentum: Ergo magis pariter nauem mouebit re<lb></lb>miger in illo ſitu, quàm in alio, vt in prora, vel puppi. </s>
          <s id="N12BDE">Quod <lb></lb>autem manubrium remi exiſtentis in medio nauis, magis <lb></lb>diſtet à ſcalmo, probat ex eo, quòd nauis in medio, latior <lb></lb>eſt, quàm verſus proram, vel puppim; <expan abbr="proindeq.">proindeque</expan> pars remi, <lb></lb>quæ intus eſt, ſiue vbi manubrium, longior pariter eſt iuxta <lb></lb>proportionem, quam habere debet cum ſitu. </s>
        </p>
        <p id="N12BEF" type="main">
          <s id="N12BF1">Ex quo Ariſtoteles aliam quoque rationem deſumit, <lb></lb>quam cum priori (perobſcurè tamen) connectit: Quia ni<lb></lb>mirum adhuc foris pars remi in medio nauis conſtituti, lon<lb></lb>gior eſt iuxta proportionem prædictam, quæ ad commodi<lb></lb>tatem remigationis ſemper ſeruatur in vſu. </s>
          <s id="N12BFC">Longior autem <lb></lb>remi pars externa, ſeu palmula, maiorem aquæ portionem <lb></lb>diuidit, ac propellit, magiſque propterea nauem promouet, <lb></lb>quàm quæ breuior eſt ratione proportionis, ac ſitus. </s>
          <s id="N12C05">Quare <lb></lb>obſeruandum eſt, eam eſſe debitam remorum proportio<lb></lb>nem inter ſe, quæ eſt inter ſitum, &amp; ſitum nauis vbi conſti<lb></lb>tuuntur, ita vt vbi latior fuerit nauis, ibi productiores remi <lb></lb>conſtituantur ex vtraque parte ipſorum, quæ eſt vtrinque à <lb></lb>scalmo. </s>
          <s id="N12C12">Hoc eſt tam intus ex parte manubrij, quàm foris <pb pagenum="92" xlink:href="005/01/100.jpg"></pb>ex parte palmulæ. </s>
          <s id="N12C1A">Et ſic qui in medio ſunt remi, eo quod ibi <lb></lb>latiſsima ſit nauis, longiſſimi ſunt, <expan abbr="maximèq.">maximèque</expan> proinde nauim <lb></lb>promouent; qui verò puppim verſus, aliquantulum breuio<lb></lb>res; ac breuiſſimi, qui conſtituuntur ad proram, propter ean<lb></lb>dem rationem; <expan abbr="ideoq.">ideoque</expan> minus, ac minus proportionaliter na<lb></lb>uem ipſam valent mouere, ſeu vniformiter difformiter. </s>
        </p>
        <p id="N12C2F" type="main">
          <s id="N12C31">Exploratiſſimum eſt hoc experimentum, <expan abbr="ratioq.">ratioque</expan> vt vidi<lb></lb>mus manifeſta. </s>
          <s id="N12C3A">Sed contra Ariſtotelem obijciunt Blanca<lb></lb>nus, &amp; Baldus, quòd mare potius, quàm ſcalmus rationem <lb></lb>habere videatur fulcimenti. </s>
          <s id="N12C43">Siquidem ſcalmus eo quod af<lb></lb>fixus ſit naui, non manet, vt <expan abbr="propriũ">proprium</expan> eſt fulcimenti, ſed fer<lb></lb>tur cum illa. </s>
          <s id="N12C4E">Quare in ipſorum ſententia, ita remus conſti<lb></lb>tuitur vectis, vt <expan abbr="centrũ">centrum</expan> habeat in extremitate palmulæ, qua <lb></lb>mari adhæret, atque innititur tanquam fulcimento; pondus <lb></lb><expan abbr="autẽ">autem</expan> ſit nauis, &amp; <expan abbr="potẽtia">potentia</expan> mouentis applicetur in manubrio. </s>
        </p>
        <p id="N12C62" type="main">
          <s id="N12C64">Veruntamen non video cur mobilitas ac latio nauis cum <lb></lb>ſcalmo, obſtet quominus ipſe ſcalmus habeat rationem ful<lb></lb>cimenti, <expan abbr="eaq.">eaque</expan> concedatur mari, quod non minus mouetur <lb></lb>per impulſum acceptum à palmula. </s>
          <s id="N12C71">Quapropter vel neu<lb></lb>trum horum <expan abbr="dicendũ">dicendum</expan> eſt, habere poſſe rationem fulcimen<lb></lb>ti, hoc eſt nec mare, nec ſcalmum; vel dicendum eſt vtrum<lb></lb>que illorum participare huiuſmodi rationem, vt exempli <lb></lb>gratia, ſi ponamus vectem AB interpoſitam eſſe inter <lb></lb><figure id="id.005.01.100.1.jpg" xlink:href="005/01/100/1.jpg"></figure><lb></lb>duos lapides CD, quorum C ſit verſus extremitatem B <lb></lb>retrorſum, D verò circa medium ipſius vectis antrorſum; <lb></lb>&amp; potentia applicetur in extremitate A. </s>
          <s id="N12C8D">Etenim ſi extre<lb></lb>mum A impellatur antrorſum verſus E, D quidem <lb></lb>ſimul feretur in F &amp; C retrocedet in G, vt cuilibet expe<lb></lb>riri fas eſt. </s>
          <s id="N12C96">Quapropter nulla eſſet maior ratio cur potius <pb pagenum="93" xlink:href="005/01/101.jpg"></pb>lapis C. quàm lapis D conſtitueretur fulcimentum in hac <lb></lb>latione vectis. </s>
          <s id="N12CA0">Ideoque vtrumque aliquo modo, illam par<lb></lb>ticipare dicendum erit. </s>
          <s id="N12CA5">Cum igitur obijcit Baldus, quod <lb></lb>tunc Philoſophi ratio procederet ſi ſtante naui immobili, re<lb></lb>miges in ipſo remigandi actu, mare pulſarent, quia tunc verè <lb></lb>ſcalmus fieret fulcimentum mare autem pondus. </s>
          <s id="N12CAE">Reſpon<lb></lb>detur retorquendo illi argumentum: quod tunc procederet <lb></lb>ratio ab ipſo adducta, ſi ſtante mare immobili ſicut terra, <lb></lb>remiges appulſa palmula, nauem ſcalmo alligatam, antror<lb></lb>ſum impellerent, vt cum Romani <expan abbr="cõtræ">contræ</expan> Carthaginenſes na<lb></lb>uales copias primo eſſent traducturi, ad remigium in arena <lb></lb>exercebantur; quia tunc verè mare fieret fulcimentum, ſcal<lb></lb>mus verò cum naui, pondus. </s>
        </p>
        <p id="N12CC3" type="main">
          <s id="N12CC5">Quoniam verò tàm mare, quàm ſcalmum diximus<arrow.to.target n="marg18"></arrow.to.target> habe<lb></lb>re rationem fulcimenti aliquo modo, non autem ſimpliciter <lb></lb>propter mobilitatem vtriuſque; examinan dum eſſet, quod<lb></lb>nam ex his, minus moueatur, vt hoc potius quàm alterum <lb></lb>dicatur magis participare rationem fulcimenti. </s>
          <s id="N12CD4">Sed fortaſ<lb></lb>ſe difficile poterit hoc penitus determinari. </s>
          <s id="N12CD9">Pendet enim <lb></lb>non modo à proportione partium remi, nempe quomodo <lb></lb>ſe habeat pars, quæ eſt à ſcalmo ad extremum manubrij ad <lb></lb>eam, quæ eſt à ſcalmo ad extremum palmulæ; verùm etiam <lb></lb>ab applicatione palmulæ in mare, vt ſi plus vel minus intro<lb></lb>mittatur, <expan abbr="maioremq.">maioremque</expan> portionem aquæ depellat. </s>
          <s id="N12CEA">Quando<lb></lb>quidem ſi profundè palmula immergatur, <expan abbr="magnamq.">magnamque</expan> por<lb></lb>tionem aquæ per illam remiger conetur depellere, tunc pro<lb></lb>cul dubio, minus mouebitur aqua retrorſum, quàm nauis an<lb></lb>trorſum. </s>
          <s id="N12CF9">Quod ex eo ſit palam, nam ſi nauis in mare me<lb></lb>diet inter duos ſcopulos, ad quos palmulæ poſſint pertinge<lb></lb>re, ſimili conatu remiges ſcopulos pulſando ac aquam pul<lb></lb>ſare conſueuerunt, magis profecto nauem ipſam mouebunt. <lb></lb></s>
          <s id="N12D07">Quod ſi alioquin palmulæ minimè immergantur, ſed veluti <lb></lb>ſolam ſuperficiem aquæ depellant, certum etiam eſt, magis <lb></lb>aquam illam depulſam <expan abbr="totamq.">totamque</expan> ferè in ſpumam redactam <lb></lb>abire, quam nauem vlterius progredi, aut moueri </s>
        </p>
        <p id="N12D14" type="margin">
          <s id="N12D16"><margin.target id="marg18"></margin.target>Polyb. lib. <lb></lb>1.longe an<lb></lb>te med.</s>
        </p>
        <p id="N12D22" type="main">
          <s id="N12D24">Tandem addit Baldus, falſum videri, quod aſſerit Ariſto-<pb pagenum="94" xlink:href="005/01/102.jpg"></pb>teles, eos qui in media naui ſunt remiges, maximè nauim <lb></lb>mouere, ſi per maximè denotet maximo ſpacio, aut velo. <lb></lb></s>
          <s id="N12D2F">cius. </s>
          <s id="N12D32">Etenim (inquit) tardius mouent, &amp; minori ſpatio, <lb></lb>quod ita probat. </s>
          <s id="N12D37">Eſto enim Remus AB, qui mari fulcitur <lb></lb><figure id="id.005.01.102.1.jpg" xlink:href="005/01/102/1.jpg"></figure><lb></lb>in B Scalmus remi, <lb></lb>qui ad proram, pup<lb></lb>pimve C, qui in <lb></lb>media naui D. </s>
          <s id="N12D49">Ma<lb></lb>ior autem remi pars <lb></lb>eſt à ſcalmo D ad <lb></lb>A, quàm ipſius C <lb></lb>ad A. </s>
          <s id="N12D55">Pellantur re<lb></lb>mi, &amp; ſtante ceu centro B; feratur ipſum A in E. </s>
          <s id="N12D5B">Eodem <lb></lb>igitur tempore C erit in F, &amp; D in G; ſed maius eſt ſpa<lb></lb>tium CF ſpatio DG: ergo vnica impulſione plus mouit <lb></lb>ſcalmum, hoc eſt nauim, potentia ad puppim proramve re<lb></lb>migans, quam ea, quæ operatur in media naui. </s>
          <s id="N12D66">Hæc ille. </s>
        </p>
        <p id="N12D69" type="main">
          <s id="N12D6B">Sed hoc ſchemate nihil demonſtratur contra <expan abbr="Ariſtotelẽ">Ariſtotelem</expan>. <lb></lb></s>
          <s id="N12D74">Nam ſi quid ex eo concluderetur, eſſet de motu circulari, <lb></lb>quo nauis duceretur circa punctum B per arcus CF &amp; DG. <lb></lb></s>
          <s id="N12D7B">Ariſtoteles autem loquitur de motu recto. </s>
          <s id="N12D7E">Deinde non ex <lb></lb>eo, quod punctum C eodem tempore maius ſpatium per<lb></lb>currat, quàm punctum D vtpotè magis diſtans à centro B, <lb></lb>iccirco ſequitur, magis mouere nauim remiges, qui ibi ſcal<lb></lb>mum habent affixum. </s>
          <s id="N12D89">Etenim alia, per quam plura ſunt pun<lb></lb>cta in ipſa naui, quæ maius adhuc ſpatium percurrunt, quam <lb></lb>C, tanquam à centro remotiora; in quibus tamen ſi conſti<lb></lb>tueretur ſcalmus, minus nauem remiges valerent mouere, <lb></lb>vt in cuſpide puppis, vel proræ. </s>
          <s id="N12D94">Quare motus ipſius C, &amp; <lb></lb>cuiuſlibet alterius puncti remotionis à centro, quamuis ve<lb></lb>locior ſit, quàm motus ipſius D, procedere poteſt magis <lb></lb>ab impulſu impreſſo in ipſo D, quàm ab impulſu impreſſo <lb></lb>in eodem C, &amp; ſic magis mouere nauim eos, qui in nauis <lb></lb>medio ſunt remiges, etiam loquendo de motu circulari. </s>
        </p>
        <p id="N12DA3" type="main">
          <s id="N12DA5">Rurſus ex ipſa Baldi probatione, atque concluſione ſe<lb></lb>queretur, ſcalmum vnius remi, magis diſtare à ſcalmo alte-<pb pagenum="95" xlink:href="005/01/103.jpg"></pb>rius poſt lationem nauis, quàm antea. </s>
          <s id="N12DB1">Quod ſic poteſt ex <lb></lb>proprijs diſtinctius expoſitis oſtendi. </s>
          <s id="N12DB6">Sint duo remi ante <lb></lb>motionem duæ <lb></lb><figure id="id.005.01.103.1.jpg" xlink:href="005/01/103/1.jpg"></figure><lb></lb>æquales para<lb></lb>lellæ, nempe <lb></lb>ADB in medio <lb></lb>nauis; &amp; ACB <lb></lb>verſus proram. <lb></lb></s>
          <s id="N12DCC"><expan abbr="Quorũ">Quorum</expan> <expan abbr="manu-briũ">manu<lb></lb>brium</expan> ſit A, pal<lb></lb>mula verò B <lb></lb>Sitque scalmus <lb></lb>vnius in D, al<lb></lb>terius verò in <lb></lb>C, magis <expan abbr="di-ſtãs">di<lb></lb>ſtans</expan> à B. </s>
          <s id="N12DE8">Dein<lb></lb>de poſt latio<lb></lb>nem <expan abbr="cõſtituan-tur">conſtituan<lb></lb>tur</expan> ijdem remi <lb></lb>ADB in EGB, &amp; ACB in EFB, vtrorumque extremis, <lb></lb>ſiue palmulis manentibus in eodem puncto B, &amp; vtrorum<lb></lb>que manubrijs æqualiter à priori loco <expan abbr="diſtãtibus">diſtantibus</expan> per æqua<lb></lb>les arcus AE vtriuſque remi. </s>
          <s id="N12E01">Scalmus verò D conſtitua<lb></lb>tur in G, &amp; ſcalmus C in F; ſitque maius ſpatium CF, <lb></lb>quam DG, vt rectè Baldus aſſumebat. </s>
        </p>
        <p id="N12E08" type="main">
          <s id="N12E0A">Dico igitur punctum G magis diſtare à puncto F (quæ <lb></lb>eſt diſtantia vnius scalmi ab altero poſt lationem) quàm <lb></lb>punctum D diſtet à puncto C, quæ erat diſtantia eorun<lb></lb>dem ante motionem. </s>
          <s id="N12E13">Ducantur enim rectæ CD &amp; FG <lb></lb>ſignantes vtramque diſtantiam. </s>
          <s id="N12E18">Et à puncto D, vbi prius <lb></lb>erat ſcalmus remi exiſtentis in medio nauis, excitetur alia <lb></lb>recta linea vſque ad G, vbi idem ſcalmus conſtituitur poſt<lb></lb>modum, atque ſuper ipſa latera CD, &amp; DG fiat paralel<lb></lb>logrammum CDGH. </s>
          <s id="N12E23">Tunc quippe latus GH erit æquale <lb></lb>lateri CD &amp; latus GD æquale erit lateri HC, eo quod <lb></lb>ſint oppoſita, vt patet per 34 primi Euclidis. </s>
          <s id="N12E2B">Quoniam <pb pagenum="96" xlink:href="005/01/104.jpg"></pb>verò ſpatium DG poſitum eſt minus, quam ſpatium CF, <lb></lb>ſequitur lineam CH pertingere non poſſe vſque ad pun<lb></lb>ctum F, cum ipſa ſit æqualis ad DG. </s>
          <s id="N12E38">Cumque ip<lb></lb><figure id="id.005.01.104.1.jpg" xlink:href="005/01/104/1.jpg"></figure><lb></lb>ſius extremum <lb></lb>vbi H, ſit pari<lb></lb>ter terminus li<lb></lb>neę, ſeu lateris <lb></lb>GH, ſequitur <lb></lb>vlterius, vt ne<lb></lb>que linea GH <lb></lb>pertingere poſ<lb></lb>ſit <expan abbr="vſq;">vſque</expan> ad pun<lb></lb>ctum P. </s>
          <s id="N12E5A">Erit <lb></lb>igitur maior li<lb></lb>nea GF quàm <lb></lb>ſit linea GH, &amp; <lb></lb>linea CD, quæ <lb></lb>eſt illi æqualis, <lb></lb>quod erat pro<lb></lb></s>
          <s id="N12E6A">bandum. </s>
        </p>
        <p id="N12E6D" type="main">
          <s id="N12E6F"><expan abbr="Itẽ">Item</expan> hinc manifeſtè apparet falſum <expan abbr="quoq;">quoque</expan> eſſe, manubrium <lb></lb>remi ad proram, vel puppim exiſtentis, æquale ſpatium per<lb></lb>tranſire, ac manubrium alterius remi in nauis medio conſti<lb></lb>tuti, palmulis vtriuſque remi in eodem ſitu, ſeu puncto ma<lb></lb>nentibus, vt à Baldo aſſumebatur ad probandam ſuam con<lb></lb>cluſionem. </s>
          <s id="N12E83">Quod ita facilè oſtenditur ex huiuſque demon<lb></lb>ſtratis. </s>
          <s id="N12E88">Nam ſi eo tempore quo ſcalmus D fertur in G, <lb></lb>ſcalmus C fertur in H ad æqualem diſtantiam, vt proba<lb></lb>tum eſt; vtique manubrium ipſius remi ad proram conſti<lb></lb>tuti, non erit in E, ſed in I, vbi deſinit recta ducta à <lb></lb>centro B, per punctum H ad arcum AE. </s>
          <s id="N12E94">Cumque AI <lb></lb>differat ab AE tanquam pars à toto, &amp; vterque arcus AE <lb></lb>ſit alter alteri æqualis ex conſtructione, palam fit, maius <lb></lb>ſpatium percurrere manubrium A remi ADB in medio <lb></lb>nauis conſtituti, dum fertur vſque ad E, quàm manubrium <lb></lb>alterius remi, quo d fertur vſque ad I. </s>
        </p>
        <pb pagenum="97" xlink:href="005/01/105.jpg"></pb>
        <p id="N12EA6" type="main">
          <s id="N12EA8">Præterea contra experientiam ſupponitur à Baldo, remi <lb></lb>palmulam ceu centrum manere immotam in ipſa remiga<lb></lb>tione, qua nauis fertur antrorſum. </s>
          <s id="N12EAF">Nam licet in vno caſu, vt <lb></lb>quando remi manubrium motu proprio circa ſcalmum na<lb></lb>uigium per impulſum acceptum in anteriora progrediens <lb></lb>æqualia ſpatia pertranſierint, id verè poſſit contingere, vt <lb></lb>optimè demonſtrat Petrus Nonius propoſit. </s>
          <s id="N12EBA">2. in ſequen. <lb></lb></s>
          <s id="N12EBE">problem. </s>
          <s id="N12EC1">Ariſtotelis; nullo tamen modo poteſt veriſicari <lb></lb>virtute eiuſdem tantum remigationis, de qua eſt nobis ſer<lb></lb>mo; ſed virtute alterius etiam commotionis, aut impulſus, <lb></lb>vt ſequenti quæſtione patebit. </s>
          <s id="N12ECA">Quare nihil ex eo colligi po<lb></lb>teſt in propoſito contra Ariſtotelem. </s>
        </p>
        <p id="N12ED0" type="main">
          <s id="N12ED2">Demum nec minus contra experientiam eſt, per appul<lb></lb>ſum palmulæ in B ad dexteram ſcilicet nauigij, ſcalmum <lb></lb>D ferri in G, &amp; ſcalmum C in F declinando totum <lb></lb>ipſum nauigium dextrorſum per ipſos arcus DG, &amp; CF. <lb></lb></s>
          <s id="N12EDC">Siquidem oppoſitum de facto contingit, etiam ſi palmula <lb></lb>vbi B in ſcopulum appellat, vel immoto alteri corpori ad<lb></lb>hæreat. </s>
          <s id="N12EE3">Videmus enim per impulſum remigum incuſſum <lb></lb>in parte dextera ſcalmum, ac nauigium moueri ad ſiniſtram. <lb></lb></s>
          <s id="N12EE9">Et ratio ipſa ſuadet, quia cum nauis ita ſupernatet in aqua, <lb></lb>vt quoquo uerſum dimoueri valeat, quando nouam poſitio<lb></lb>nem acquirit, per impulſum in vno tantum latere acceptum <lb></lb>neceſſariò intelligitur conuerti circa centrum ſuæ grauita<lb></lb>tis. </s>
          <s id="N12EF4">Illiſa igitur palmula in aquam in parte dextera, ab <expan abbr="eaq.">eaque</expan> <lb></lb>ob reſiſtentiam repulſa, non ſecus ac ſemidiametri extre<lb></lb>mum, nauim tanquam circulum ad ſiniſtram mouebit. <lb></lb></s>
          <s id="N12F00">Idem enim efficit aqua remigationi obſiſtens, ac ſi quis pal<lb></lb>mulam repelleret in contrariam partem. </s>
          <s id="N12F05">Cumque talis <lb></lb>remigatio fiat per modum circuli circa ſcalmum proceden<lb></lb>do dextrorſum, ſequitur repulſum accipi, ac fieri per op<lb></lb>poſitum procedendo ſiniſtrorſum. </s>
          <s id="N12F0E">Quamobrem ad hoc, <lb></lb>vt nauigium rectà antrorſum procedat, ex vtraque parte <lb></lb>ſimul remiges conantur impellere, vt ex vtroque motu cir<lb></lb>culari, &amp; contrario, reſultet vnus rectus, ac mixtus. </s>
          <s id="N12F17">Vt cer<lb></lb>nere eſt in hac figura, in qua ſit remus AB, cuius manu<pb pagenum="98" xlink:href="005/01/106.jpg"></pb>brium A; palmula B, ſcalmus verò C; ac ſpatium, <lb></lb>quod percurrit pal<lb></lb><figure id="id.005.01.106.1.jpg" xlink:href="005/01/106/1.jpg"></figure><lb></lb>mula per motum <lb></lb>proprium ipſius re<lb></lb>mi circa ſcalmum <lb></lb><expan abbr="tanquã">tanquam</expan> circa cen<lb></lb>trum ſit arcus BD. <lb></lb></s>
          <s id="N12F38">Dico igitur per im<lb></lb>pulſum incuſſum in <lb></lb>arcu BD palmu<lb></lb>lam neceſſariò re<lb></lb>pelli in oppoſitum per arcum BE, ac per conſequens vir<lb></lb>tute huiuſmodi remigationis, ſcalmum C, non ferri in <lb></lb>F, ſed in G; ita vt arcus. </s>
          <s id="N12F47">CG reſpondeat ipſi BE: Alio<lb></lb>quin repulſus non opponeretur impulſui. </s>
          <s id="N12F4C">Iam ergo per im<lb></lb>pulſum incuſſum ex parte dextera, ſcalmus C, &amp; vnà cum <lb></lb>illo nauigium mouebitur ad ſiniſtram. </s>
          <s id="N12F53">Quod cum ſimiliter <lb></lb>verificetur è contra, vt per impetum incuſſum ex parte ſi<lb></lb>niſtra, nauigium moueatur ad dexteram: hinc ſit, vt ex <lb></lb>contrarijs motionibus vtrinque procedentibus. </s>
          <s id="N12F5C">compona<lb></lb>tur vnus motus rectus, quo nauigium fertur antrorſum, vt <lb></lb>per lineam mediam, ac rectam CH. </s>
          <s id="N12F63">Quod valde diuer<lb></lb>ſum eſt ab eo, quod aſſumebatur à Baldo. </s>
        </p>
        <p id="N12F68" type="head">
          <s id="N12F6A">Quæſtio Quinta.</s>
        </p>
        <p id="N12F6D" type="main">
          <s id="N12F6F">C<emph type="italics"></emph>vr paruum exiſtens gubernaculum, &amp; in <lb></lb>extremo nauigio tantas habet vires, vt ab <lb></lb>exiguo temone: &amp; ab hominis vnius viri<lb></lb>bus alioqui modicè vtentis, magnæ nauigio<lb></lb>rum moueantur moles? </s>
          <s id="N12F7D">An quoniam guber<lb></lb>naculum vectis eſt, onus autem mare, guber<lb></lb>nator verò mouens eſt? </s>
          <s id="N12F84">Non autem ſecundum latitudinem, <lb></lb>veluti remus, mare accipit gubernaculum: non enim in ante <lb></lb>nauigium mouet, ſed ipſum commotum mare accipiens incli-<emph.end type="italics"></emph.end><pb pagenum="99" xlink:href="005/01/107.jpg"></pb><emph type="italics"></emph>nat obliquè. </s>
          <s id="N12F94">Quoniam enim pondus eſt mare, contrario inni<lb></lb>xum modo nauem inclinat. </s>
          <s id="N12F99">Hypomochlion enim in contra<lb></lb>rium verſatur: mare verò anteriùs, &amp; illud exteriùs: illud <lb></lb>autem ſequitur nauis, quoniam illi eſt alligata. </s>
          <s id="N12FA0">Et remus <lb></lb>quidem ſecundum latitudinem onus propellens, &amp; ab eodem <lb></lb>repulſus, in rectum propellit: gubernaculum autem vt obli<lb></lb>quum iacet, hinc inde in obliquum motionem facit. </s>
          <s id="N12FA9">In ex<lb></lb>tremo autem, &amp; non in medio iacet, quoniam mouenti facilli<lb></lb>mum eſt ab extremo motum mouere. </s>
          <s id="N12FB0">Prima enim pars celer<lb></lb>rimè fertur, &amp; quoniam quemadmodum in ijs, quæ ferun<lb></lb>tur, in fine deficit latio, ſic ipſius continui, in fine imbecilliſ<lb></lb>ſima eſt latio. </s>
          <s id="N12FB9">Imbecilliſsima autem ad expellendum eſt fa<lb></lb>cilis. </s>
          <s id="N12FBE">Propter hæc igitur in puppi gubernaculum ponitur: <lb></lb>nec minus, quoniam parua ibi motione facta, multò maius <lb></lb>interuallum fit in vltimo. </s>
          <s id="N12FC5">Quia æqualis angulus ſemper <lb></lb>maiorem ſpectat, <expan abbr="tantòq.">tantòque</expan> magis, quantò maiores fuerint il<lb></lb>læ, quæ continent. </s>
          <s id="N12FD0">Ex ijs etiam manifeſtum eſt, quam ob <lb></lb>cauſam magis in contrarium procedit nauigium, quàm re<lb></lb>mi ipſius palmula: eadem magnitudo ijſdem mota viribus, <lb></lb>in aere plus, quàm in aqua progreditur. </s>
          <s id="N12FD9">Sit enim AB remus, <lb></lb>C verò ſcalmus. </s>
          <s id="N12FDE">A autem in nauigio ſit remi principium, B <lb></lb>verò in mari palmula. </s>
          <s id="N12FE3">Si igitur A vbi D <expan abbr="tranſtatũ">tranſtatum</expan> eſt, <expan abbr="nõ">non</expan> erit <lb></lb>B vbi E; æqualis enim BE ipſi AD; æquale igitur tranſtatum <lb></lb>erit, ſed erat minus. </s>
          <s id="N12FF2">Erit igitur vbi eſt F, minor enim BF <lb></lb>ipſa AD, quare ipſa GF, ipſa DG. </s>
          <s id="N12FF8">Similes enim ſunt trian<lb></lb>guli. </s>
          <s id="N12FFD">Stans autem erit medium, vbi eſt C. </s>
          <s id="N13001">In contrarium <lb></lb>enim ipſi quod in mari eſt, extremo videlicet B procedit, vbi <lb></lb>extremum in nauigio eſt A. </s>
          <s id="N13009">Non procederet autem vbi eſt <lb></lb>D, niſi commoueretur nauigium, &amp; ab eo transferretur, vbi <lb></lb>remi eſt principium. </s>
          <s id="N13010">Id ipſum etiam facit gubernaculum, ni<lb></lb>ſi quod (vt dictum eſt retrò) nihil nauigio ad id, quod in ante <lb></lb>eſt, confert, ſed ſolùm puppim in obliquum pellit, vbicumque <lb></lb>fuerit: in contrarium enim &amp; modo vergit prora. </s>
          <s id="N13019">Vbi igitur <lb></lb>applicatum eſt gubernaculum, id oportet rei motæ ceu quoddam <lb></lb>intelligere medium, &amp; quemadmodum ſcalmus remo. </s>
          <s id="N13020">Me<lb></lb>dium autem procedit ſecundum quod gubernaculum tranſ-<emph.end type="italics"></emph.end><pb pagenum="100" xlink:href="005/01/108.jpg"></pb><emph type="italics"></emph>fertur. </s>
          <s id="N1302E">Siquidem introrſus agit, &amp; puppis eò transfertur, <lb></lb>prora verò ad contrarium vergit. </s>
          <s id="N13033">In eodem enim exiſtente <lb></lb>prora, totum transfertur nauigium.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1303A" type="head">
          <s id="N1303C">COMMENTARIVS.</s>
        </p>
        <p id="N13040" type="main">
          <s id="N13042">Celebris eſt hæc quæſtio tum propter communem <lb></lb>admirationem ortam ex paruitate gubernaculi, ac <lb></lb>temonis reſpectu magnæ molis nauigij, quæ illius <lb></lb>beneficio circumfertur: tum propter difficultatem, quæ <lb></lb>circa ſolutionem eiuſdem quæſtionis, ac doctrinam Philo<lb></lb>ſophi hic ſeſe offert. </s>
          <s id="N1304F">Quare vt luculentius in expoſitione <lb></lb>procedamus, diſtinguendum prius nobis erit inter ipſum <lb></lb>remonem, ſeu clauum, &amp; gubernaculum, quamuis ambo ad <lb></lb>vnicum pertineant inſtrumentum, ac ſæpe vnum pro alio <lb></lb>vſurpetur. </s>
          <s id="N1305A">Temonem itaque in præſenti vocamus cum <lb></lb>Ariſtotele alam illam ligneam, ſeu tabulam ad alæ veluti <lb></lb>similitudinem efformatam, quæ duplici cardine liberè in <lb></lb>dorſo puppis affigitur, <expan abbr="mariq.">marique</expan> ex parte immergitur, &amp; pro <lb></lb>opportunitate huc atque illuc ad directionem nauis con<lb></lb>uertitur. </s>
          <s id="N1306B">Gubernaculum verò appellamus anſam, qua te<lb></lb>mo ipſe manu cietur; cuius videlicet alterum extremum <lb></lb>lato foramine excipit caput temonis; alterum intra nauim <lb></lb>ſe extendit tanquam manubrium ad vſum Gubernatoris. </s>
        </p>
        <p id="N13074" type="main">
          <s id="N13076">Deinde duplex conſideranda erit motio nauis mediante <lb></lb>huiuſcemodi inſtrumento, quod ex gubernaculo, ac temo<lb></lb>ne conſtruitur. </s>
          <s id="N1307D">Vna eſt, quæ à gubernatore procedit per <lb></lb>motum ipſius gubernaculi, ac temonis, ſiue nauis aliunde <lb></lb>etiam moueatur ſiue quieſcat. </s>
          <s id="N13084">Quandoquidem dum temo, <lb></lb>qui rectà manebat mouetur in tranſuerſum pura ad dexte<lb></lb>ram, vel ſiniſtram, neceſſariò, maris <expan abbr="portionẽ">portionem</expan> propellit ver<lb></lb>ſus eam partem, in quam inclinatur, <expan abbr="neceſſarioq:">neceſſarioque</expan> ab ea pro<lb></lb>pter reſiſtentiam repellitur in contrarium: &amp; ſic temo cum <lb></lb>puppi, cui eſt affixus, repulſo accepto in dextera, mouebi<lb></lb>tur ad ſiniſtram, vel è conuerſo. </s>
          <s id="N13097">Non enim aliter ſe habet <lb></lb>gubernaculum ſimul cum temone in hac motione, quàm <lb></lb>remus conſtitutus in cuſpide puppis per longum iuxta re-<pb pagenum="101" xlink:href="005/01/109.jpg"></pb>ctitudinem carinæ, ita vt ſcalmus ſit in ipſa cuſpide, manu<lb></lb>brium intra puppim, &amp; palmula foris mari immerſa. </s>
          <s id="N130A5">Quia <lb></lb>nimirum eodem pacto ſi remi palmula mare propellerer ad <lb></lb>dexteram, ab eo vtique per reſiſtentiam repulſa, ſimul cum <lb></lb>toto remo, ſcalmo, ac puppi pergeret ad ſiniſtram prora <lb></lb>manente immota, vel quaſi immota. </s>
          <s id="N130B0">Et hoc pacto magna <lb></lb>nauigia abſque remis ſolo temone conuerti ſolent in <lb></lb>portu. </s>
        </p>
        <p id="N130B7" type="main">
          <s id="N130B9">Altera verò motio nauis, quæ ſit mediante gubernaculo, <lb></lb>ac temone, eſt illa, quæ non procedit ab ipſo gubernatore <lb></lb>tanquam à mouente, ſed tanquam à ſuſtinente temonem <lb></lb>in obliqua poſitione ad excipiendum impetum maris oc<lb></lb>currentis, quo nauis ipſa aliquantulum inclinatur. </s>
          <s id="N130C4">Obliquè <lb></lb>namque conſtituto temone, <expan abbr="nauigioq.">nauigioque</expan> ad anteriora progre<lb></lb>diente, neceſſariò mare obuians temonem in ea parte, qua <lb></lb>tranſuerſum eſt, offendit, <expan abbr="ipſumq.">ipſumque</expan> repellit. </s>
          <s id="N130D5">Per quem repul<lb></lb>ſum temo ipſe cum recta in contrarium ferri non poſſit, vi<lb></lb>delicet retrorſum, eo quod puppi ſit affixus procedenti an<lb></lb>trorſum, obliquè ſaltem ab itinere dimouetur, &amp; cum eo <lb></lb>tota nauis à latere aliquantulum circumuertitur, vt mox in<lb></lb>fra latius explicabitur. </s>
          <s id="N130E2">Illud interim adnotando, eandem <lb></lb>eſſe rationem de aqua in contrarium fluente, temonemque <lb></lb>cum naui ſtantem feriente, ac de aqua ſtante, inquam temo <lb></lb>obliquè conſtitutus dum fertur cum naui offendat. </s>
          <s id="N130EB">Non <lb></lb>minus enim vim patitur ſolidum manens à fluido currente, <lb></lb>quod excipit, vt velum à vento, quàm ſolidum currens à <lb></lb>fluido manente; vt verticilla ex papiro, quæ dum geſtantur <lb></lb>à pueris currentibus, circumaguntur ab aere quieſcente, vel <lb></lb>tenuiter obuiante. </s>
        </p>
        <p id="N130F8" type="main">
          <s id="N130FA">His ergo prænotatis facilè vim ſolutionis Ariſtotelis in <lb></lb>hac quæſtione percipiemus. </s>
          <s id="N130FF">Ait enim ex eo gubernaculum, <lb></lb>ac temonem tantas vires habere in motione nauis, quod <lb></lb>vtrunque ſe habeat tanquam vectis, mare autem tanquam <lb></lb>onus, &amp; gubernator, tanquam potentia. </s>
          <s id="N13108">Et enim ſi loqua<lb></lb>mur de prima motione ſupra explicata, non minus in illa <lb></lb>habet rationem vectis gubernaculum cum temone, quàm <pb pagenum="102" xlink:href="005/01/110.jpg"></pb>remus; Nec minus conſtituitur mouens gubernator, quàm <lb></lb>remiger, vt per ſe patet. </s>
          <s id="N13116">Si verò loquamur de ſecunda mo<lb></lb>tione, adhuc idem inſtrumentum in illa conſtituitur vectis <lb></lb>ad ſuſtinendum impetum maris; innixum ſcilicet fulcimen<lb></lb>to, ſeu cardini, quo puppi coniungitur: Non ſecus, ac quod<lb></lb>libet lignum alteri quomodolibet innixum ad ſuſtinendum <lb></lb>onus impoſitum. </s>
          <s id="N13123">Gubernator autem conſtituitur potentia, <lb></lb>nam adhibendo gubernaculum, temonem ipſum ſuſtentat <lb></lb>obliquum contra fluctus maris, veluti qui vecte pondus <lb></lb>quod cumque ſuſtinet, etiam ſi non moueatur. </s>
          <s id="N1312C">Mare deni<lb></lb>que in vtraque motione conſtituitur onus; quoniam vel eſt <lb></lb>id quod propellitur, vel id quod ſuſtinetur per temonem <lb></lb>tranſuerſum ne directè in oppoſitum fluat. </s>
        </p>
        <p id="N13135" type="main">
          <s id="N13137">Quamobrem immeritò nonnulli Ariſtotelem <expan abbr="redarguũt">redarguunt</expan>, <lb></lb>dicentes, mare habere potius rationem potentiæ mouentis <lb></lb>totam puppim cum temone; Nam ſicut ſaxum, vectem cui <lb></lb>imponitur ſemper premit appetendo deſcenſum ad ima, <lb></lb>&amp; tamen eſt onus reſpectu potentiæ, quæ vectem ſuſtinet in <lb></lb>illo ſitu, ita mare, licet ſucceſſiuè temonem impellat, ratio<lb></lb>nem habet oneris reſpectu potentiæ manu tenentis temo<lb></lb>nem in illo ſitu contra ictus eiuſdem maris. </s>
          <s id="N1314C">Quod ſi ipſe <lb></lb>temo cum puppi, cui adhæret verè ſimul moueatur à mare, <lb></lb>per accidens eſt, <expan abbr="proceditq.">proceditque</expan> à fluxibilitate aquæ, in qua diu <lb></lb>permanere non poteſt puppis omnino immota ad ſuſtinen<lb></lb>dum in ſuo cardine ipſum temonem. </s>
          <s id="N1315B">Motus enim fulcimen<lb></lb>ti per accidens ſe habet ad motum, vel operationem pro<lb></lb>priam vectis; vt motus ſcalmi cum naui, cui eſt affixus ad <lb></lb>motionem remi, qui tanquam vectis fulcitur in illo; vel mo<lb></lb>tus cuiuslibet fulcimenti, quod aſportatur cum curru, ad <lb></lb>motionem vectis eidem innixi. </s>
          <s id="N13168">Vnde potentia reſpectu ve<lb></lb>ctis dicitur illa, quæ vectem adhibet, onus mouendo, vel ſu<lb></lb>ſtentando, non autem illa, quæ mouet fulcimentum. </s>
          <s id="N1316F">Quare <lb></lb>tunc rectè mare diceretur potentia, cum mediante impetu <lb></lb>incuſſo in temonem, ipſo tanquam vecte adhibito, moueret <lb></lb><expan abbr="manũ">manum</expan> gubernatoris. </s>
          <s id="N1317B"><expan abbr="Cũ">Cum</expan> igitur contra accidat, nempe, vt po<lb></lb>tius gubernator adhibito temone mare ad latus depellat, <pb pagenum="103" xlink:href="005/01/111.jpg"></pb>vel <expan abbr="ſaltẽ">ſaltem</expan> excipiat reſiſtendo, iure &amp; <expan abbr="quidẽ">quidem</expan> optimo guberna<lb></lb>tor ab Ariſtotele conſtituitur potentia, mare autem onus. </s>
        </p>
        <p id="N13192" type="main">
          <s id="N13194">Sic autem explicato principio, ac inſtrumento vtriuſque <lb></lb>motionis, explicat Ariſtoteles modum, quo procedit ſecun<lb></lb>da motio à nobis propoſita, quæ potiſſima eſt, &amp; maioris <lb></lb>longè momenti quam prima: <expan abbr="aitq.">aitque</expan> temonem (quem cum <lb></lb>gubernaculo ſæpè confundit) non accipere mare ſecundum <lb></lb>latitudinem nauis, ſeu quod ad latera nauis eſt, eo modo <lb></lb>quo accipit remus, depellendo illud retrorſum, vt per repul<lb></lb>ſum inde acceptum, nauigium feratur antrorſum, quia nihil <lb></lb>temo nauigio confert, quo ad motum antrorſum, vt in fine <lb></lb>etiam quæſtionis idem Philoſophus animaduertit: Sed ac<lb></lb>cipere mare commotum, quod illi obuiat ſecundum longi<lb></lb>tudinem nauis à prora in puppim. </s>
          <s id="N131B1">Nam qua parte temo <lb></lb>vergit foris, <expan abbr="matiq.">matique</expan> eius ala obuertitur ad alterum latus na<lb></lb>uigij, mare ſecundum longitudinem nauis ei obuians exci<lb></lb>pit intra <expan abbr="angulũ">angulum</expan>, quem cum naui conſtituit. </s>
          <s id="N131C2">Excipiendo au<lb></lb>tem illud vim patitur in <expan abbr="contrariũ">contrarium</expan>, <expan abbr="tollereturq">tollereturque</expan> niſi fulciretur <lb></lb>in cardine. </s>
          <s id="N131CD">Cum igitur nec auferri poſſit à puppi, nec retro<lb></lb>cedere in <expan abbr="directũ">directum</expan> <expan abbr="cõtra">contra</expan> curſum nauigij, hinc fit, vt cedendo <lb></lb><expan abbr="ſaltẽ">ſaltem</expan> in parte quoad poſitionem, <expan abbr="quã">quam</expan> prius habebat, nauem <lb></lb><expan abbr="ipsã">ipsam</expan> inclinet obliquè; ſiqui<lb></lb><figure id="id.005.01.111.1.jpg" xlink:href="005/01/111/1.jpg"></figure><lb></lb>dem dimoto vno latere an<lb></lb>guli à ſua poſitione, <expan abbr="alterũ">alterum</expan> <lb></lb>dimoueri neceſſe eſt, cuſpi<lb></lb>de manente in eodem ſitu. <lb></lb></s>
          <s id="N131FB">Quod ſic poteſt amplius <lb></lb>explicari. </s>
          <s id="N13200">Eſto nauis AB; <lb></lb>cuius puppis A, prora B, te<lb></lb>mo verò AC obliquè con<lb></lb>ſtitutus ad ſiniſtram, ac ſuf<lb></lb>fultus in A, vbi eius cardo <lb></lb>ad puppim poſitus eſt, &amp; <lb></lb>vbi <expan abbr="angulũ">angulum</expan> efficiat <expan abbr="cũ">cum</expan> <expan abbr="lõgi-tudine">longi<lb></lb>tudine</expan> nauis, qui ſit BAC. <lb></lb></s>
          <s id="N1321E">Deinde mare obuians incidat in ipſam AC. </s>
          <s id="N13222">Tunc dicimus <pb pagenum="104" xlink:href="005/01/112.jpg"></pb>punctum C fore, vt transferatur verſus D; punctum verò <lb></lb>B, quod proram deſignat, verſus E, cardine manente <lb></lb>immoto vbi A. </s>
          <s id="N1322F">Etenim cum mare ſolum impellat temo<lb></lb>nem inquantum obliquè conſtituitur, &amp; à nauis rectitudine <lb></lb>deuiat, efficacius impellit extremum vbi C, quod magis <lb></lb>elongatur ab ea, quàm reliquas partes, quæ minus, ac mi<lb></lb>nus diſtant. </s>
          <s id="N1323A"><expan abbr="Proindeq">Proindeque</expan> remiſſius, ac remiſſius agit in illas <lb></lb>vniformiter difformiter vſque ad punctum A, vbi ſicut ter<lb></lb>minatur diſtantia, ac diuitatio, ita etiam deficit impulſus. </s>
          <s id="N13241">Ex <lb></lb>quo ſequitur punctum A, perſe non moueri ad talem im<lb></lb>pulſum, ſed tantum lineam AC circa illud tanquam ſemi<lb></lb>diametrum circa centrum conuerti, ac declinare verſus D. <lb></lb></s>
          <s id="N1324C">Cumque longitudo nauis angulum cum ipſa latitudine te<lb></lb>monis efficiat, ſequitur vlterius, vt tranſlato ipſo latere <lb></lb>AC, in AD, ſimul transferatur AB in AE, quod eſt na<lb></lb>uem declinare à ſua rectitudine, ad obliquam poſitionem <lb></lb>temonis mare intra angulum excipientis. </s>
          <s id="N13257">Diximus punctum <lb></lb>A per ſe non moueri ob talem impulſum, nam per acci<lb></lb>dens, nempe propter maris inconſtantiam, ac fluxibilitatem <lb></lb>etiam ipſum puppis extremum aliquantulum dimouetur <lb></lb>cum cardine, quo temo fulcitur, ſicut quodlibet fulcimen<lb></lb>tum ad motum vectis ob inconſtantiam ſoli. </s>
        </p>
        <p id="N13264" type="main">
          <s id="N13266">Contrario autem modo temonem innixum, ait Ariſtote<lb></lb>les nauem inclinare, quoniam temo rationem habet vectis, <lb></lb>vt dictum eſt cardini innixi tanquam fulcimento, mare au<lb></lb>tem ſe habet, vt onus: At omnis vectis mediat inter fulci<lb></lb>mentum, &amp; onus, nec aliter quam fulcimento tanquam cen<lb></lb>tro inhærendo, onus per modum circuli in contrarium mo<lb></lb>uet, aut certè ſuſtinet in tali poſitione; Ergo dum temo ſu<lb></lb>ſtinet mare cardini innixus tamquam fulcimento, &amp; angu<lb></lb>lum cum naui efficit ad excipiendum mare interius, cardo <lb></lb>manebit exterius tanquam ex alia parte ipſius vectis illi <lb></lb>contraria, ad quam facit nauem inclinari. </s>
        </p>
        <p id="N1327D" type="main">
          <s id="N1327F">Ad hæc Ariſtoteles rationem quandam affert cur in ex<lb></lb>tremo nauigij, &amp; non in medio temo, ſeu clauus locetur, <lb></lb><expan abbr="aitq.">aitque</expan> eam eſſe, quoniam id quod fertur, facilius ab incepto <pb pagenum="105" xlink:href="005/01/113.jpg"></pb>itinere, ſeu à rectitudine ſui motus declinat, cum in poſtre<lb></lb>ma eius parte ex latere diuerſum aliquem impulſum acce<lb></lb>pit, quàm ſi accipiat in alia parte anteriori. </s>
          <s id="N13292">Prima enim. <lb></lb></s>
          <s id="N13296">ſeu anterior pars lati <expan abbr="cõtinui">continui</expan>, intenſiori impetu fertur, quàm <lb></lb>partes ſubſequentes, <expan abbr="validiuſq.">validiuſque</expan> propterea in ſuo motu perſi<lb></lb>ſtit, <expan abbr="contrarijsq.">contrarijsque</expan> omnibus obſiſtit. </s>
          <s id="N132A9">E contra verò vltima. <lb></lb></s>
          <s id="N132AD">pars, tanquam remiſſiorem vim conſecuta, imbecillius mo<lb></lb>uetur, ac facilius cædit. </s>
          <s id="N132B2">Id quod maximè in proiectis ob<lb></lb>ſeruare licebit. </s>
          <s id="N132B7">Impetus namque in ea à proijciente im<lb></lb>preſſus, ſemper maior eſt in eorum parte anteriori, quàm in <lb></lb>ſequentibus: ſeu illa pars eorum conſtituitur anterior, cæ<lb></lb><expan abbr="terasq">terasque</expan> in latione præcedit, in qua maior impetus fuerit <lb></lb>impreſſus. </s>
          <s id="N132C2">Vnde cum denſitas materiæ, aut grauitas ſubie<lb></lb>cti, intenſioris impetus capax redat ipſum proiectum, hinc <lb></lb>fit, vt etiam ſi in principio motus pars grauior, vel denſior <lb></lb>fuerit poſterior in progreſſu euadat anterior. </s>
          <s id="N132CB">Quod apertè <lb></lb>in proiectione baculi experimur quando anteponitur extre<lb></lb>mum leuius, &amp; poſponitur grauius; nam ex ſe ipſa extrema <lb></lb>permutantur in aere, <expan abbr="priusq.">priusque</expan> grauius quàm leuius quo ten<lb></lb>debant pertingit. </s>
          <s id="N132DA">Certum ergo relinquitur, vt quo ante<lb></lb>riores fuerint partes ipſis lati continui, eo validius ferantur <lb></lb>tanquam maiorem adeptæ, aut ſortitæ impetum, quo verò <lb></lb>poſteriores, eo imbecillius, vnde etiam facilius vincantur. <lb></lb></s>
          <s id="N132E6">Hoc ipſum itaque applicando in latione nauis, ait Ariſtote<lb></lb>les, quod cum nauis rectà fertur antrorſum, facilius eſt illam <lb></lb>à curſu deflectere puppim à latere impellendo, quàm aliam <lb></lb>eiuſdem nauis partem mediam, aut proram. </s>
          <s id="N132EF">Siquidem in <lb></lb>puppi tanquam in poſtrema lati corporis parte imbecilliſſi<lb></lb>ma virtus eſt impetus impreſſi, in <expan abbr="eaq.">eaque</expan> terminatur, ac deficit <lb></lb>latio. </s>
          <s id="N132FC">Quare appoſitè clauus in puppi locatur ad excipien<lb></lb>dos ibi maris impulſus, vt facilius à rectitudine itineris na<lb></lb>uis ipſa deflectat. </s>
        </p>
        <p id="N13303" type="main">
          <s id="N13305">Quæ profectò Ariſtotelis doctrina, <expan abbr="eiusq">eiusque</expan> applicatio, ſa<lb></lb>no modo intelligenda eſt. </s>
          <s id="N1330A">Nam licet quando nauigia vni<lb></lb>co velo in prora locato feruntur, præcipuus impetus per <lb></lb>malum circa ipſam proram incutiatur; nihilominus quando <pb pagenum="106" xlink:href="005/01/114.jpg"></pb>remis, vel pluribus velis nauigare contingit, <expan abbr="puppisq.">puppisque</expan> pari<lb></lb>ter obtinet ſuum; res aliter ſe habet, cum pari, aut maiori <lb></lb>impetu, tunc puppis quàm prora feratur, quippe quæ illum <lb></lb>refundere etiam valeat vlterius in ipſam proram. </s>
          <s id="N13320">Id quod <lb></lb>patet cum ex maiori velocitate, qua mouetur nauigium, ac <lb></lb>ipſa prora adhibitis etiam velis, aut remis in puppi, ſeu pro<lb></lb>pe illam; tum ex maiori conatu, quem adhibent remiges, <lb></lb>quò magis prope puppim remigauerint; vt hinc in triremi<lb></lb>bus ad priores ſingulos remos promouendos conſtituantur <lb></lb>remiges quini, aut ſeni, ad reliquos verò, proram verſus pro<lb></lb>cedendo, quaterni, ac tandem terni. </s>
          <s id="N13331">Vbi autem maior co<lb></lb>natus adhibetur, ibi maior imprimitur impetus. </s>
          <s id="N13336">Rurſumque <lb></lb>obſeruandum eſt impetum, quo per velificationem feruntur <lb></lb>nauigia, non imprimi in ſola parte, quam antrorſum promo<lb></lb>uet malus, ſed in ijs quoque partibus vbi funes quibus vela <lb></lb>retrouerſum tenduntur alligari ſolent. </s>
          <s id="N13341">Etenim magna eſt <lb></lb>vis, qua per funes, qui dicuntur opiferi, partes nauis vbi pro<lb></lb>pe puppim illi colligantur ab antennæ cornibus trahuntur. <lb></lb></s>
          <s id="N13349">Vrgent enim antrorſum ipſa cornua non minus, ac ſæpè ma<lb></lb>gis quàm malus; nec alibi eorum impetus recipi poteſt, <lb></lb>quàm vbi ipſi funes opiferi alligantur. </s>
          <s id="N13350"><expan abbr="Similiaq.">Similiaque</expan> dici poſ<lb></lb>ſunt de funibus, qui dicuntur propedes, quique veli inferio<lb></lb>ra retrouerſum pariter tendentes in poſteriori parte nauis <lb></lb>ita colligantur, vt repentino <expan abbr="ſuperueniẽte">ſuperueniente</expan> turbine, vel quan<lb></lb>do opus fuerit relaxari protinus poſſint: Nam per hos quo<lb></lb>que funes maximè partes ipſæ poſteriores nauis trahuntur. <lb></lb></s>
          <s id="N13365">Ex quibus apparet non minus in puppi, quàm in prora im<lb></lb>petum iugiter imprimi ad procedendum antrorſum. </s>
          <s id="N1336A">Quare <lb></lb>Ariſtotelis doctrina de ijs, quæ feruntur, &amp; in fine imbecil<lb></lb>lam obtinent lationem, non ſemper applicari poteſt in la<lb></lb>tione nauis, vt ex ipſo retulimus. </s>
        </p>
        <p id="N13373" type="main">
          <s id="N13375">Aliam deinde, ac ſolidiorem rationem eiuſdem ſituatio<lb></lb>nis temonis Ariſtoteles ſubnectit. </s>
          <s id="N1337A">Quia nimirum parua mo<lb></lb>tione per temonem facta in eo ſitu, multo maius interual<lb></lb>lum prora obliquè declinando percurrit, vt patere poteſt <lb></lb>ex præcedenti figura <expan abbr="tantoq.">tantoque</expan> magis, quanto longior fuerit <pb pagenum="107" xlink:href="005/01/115.jpg"></pb>ipſa nauis. </s>
          <s id="N1338C">Etenim idem, vel æqualis angulus, quo in<lb></lb>ter longiores lineas continetur, eo maiorem baſim ſubten<lb></lb>dit, ſeu ſpectat, vt conſtare etiam poteſt per quartam propo<lb></lb>ſitionem ſexti Euclidis. </s>
          <s id="N13396">Cum igitur longitudo nauis conſi<lb></lb>derata in priori ſitu, deinde in poſteriori poſt <expan abbr="motionẽ">motionem</expan> <expan abbr="cir-cularẽ">cir<lb></lb>cularem</expan>, immota ferè manente cuſpide puppis, <expan abbr="angulũ">angulum</expan> quen<lb></lb>dam efficiat, vt BAE, cuius baſis EB: tanto maiorem ipſa <lb></lb>prora veluti baſim tranſmittet ad motionem temonis quan<lb></lb>to longior fuerit ipſa nauis. </s>
          <s id="N133AF">Quod quippe non contingeret <lb></lb>ſi alibi temo conſtitutus <lb></lb>fuiſſet, <expan abbr="indeq">indeque</expan> talis motio <lb></lb><figure id="id.005.01.115.1.jpg" xlink:href="005/01/115/1.jpg"></figure><lb></lb>initium ſumeret. </s>
          <s id="N133BE">Quam<lb></lb>obrem conſentanea idem <lb></lb>Ariſtoteles protulit lib.

de <lb></lb>motu animal. </s>
          <s id="N133C8">cap.

5. cum <lb></lb>ad explicandum quomo<lb></lb>do parua permutatio, quæ <lb></lb>fit in principio, magnas, &amp; <lb></lb>multas efficiat differentias <lb></lb>procul; exemplum adhi<lb></lb>bens ait, vt temone pau<lb></lb>lulum quid tranſpoſito, <lb></lb>multa proræ fit tranſpo<lb></lb>ſitio. </s>
        </p>
        <p id="N133DD" type="main">
          <s id="N133DF">Ex ijs autem ad aliam quæſtionem valde implexam. <lb></lb></s>
          <s id="N133E3">Ariſtoteles pertranſit, cuius ſolutionem hic inſerit, vt po<lb></lb>ſtea ex ea melius præfata confirmet. </s>
          <s id="N133E8">Ait igitur ex ijs etiam <lb></lb>manifeſtum eſſe, quam ob cauſam magis procedat naui<lb></lb>gium antrorſum, quàm ipſius remi palmula mare reijciens <lb></lb>cædat retrorſum. </s>
          <s id="N133F1">Eadem enim (inquit) magnitudo, ijſ<lb></lb>dem mota viribus, plus in aere progreditur, quàm in aqua; <lb></lb>eo ſcilicet, quod minorem in aere inueniat reſiſtentiam. <lb></lb></s>
          <s id="N133F9">Quod ipſe quamuis obſcurè propter defectum quorundam <lb></lb>verborum, ac falſitatem characterum, quibus figuram pro<lb></lb>ponit, ſic ferè explicat in propoſito. </s>
          <s id="N13400">Sit remus AB, ſcal-<pb pagenum="108" xlink:href="005/01/116.jpg"></pb><figure id="id.005.01.116.1.jpg" xlink:href="005/01/116/1.jpg"></figure><lb></lb>mus verò C, remi manubrium A, palmula in mari B. <lb></lb></s>
          <s id="N1340F">Si igitur manubrium A per aerem transferatur in D; vti<lb></lb>que palmula B transferri non poterit per aquam in E. <lb></lb></s>
          <s id="N13416">Quandoquidem non poſſet cum maiori reſiſtentia æquale <lb></lb>ſpatium pertranſire, quemadmodum eſt ſpatium BE ipſi <lb></lb>AD. </s>
          <s id="N1341E">Quare palmula B retrocedet tantum vſque ad F, <lb></lb><expan abbr="eritq.">eritque</expan> remus in DF, vbi ſpatium retroceſſionis palmulæ <lb></lb>conſtituitur minus. </s>
          <s id="N13428">Nam ſi conſiderentur duo trianguli, <lb></lb>AGD, &amp; BGF; erunt ſimiles ex quarta propoſitione <lb></lb>ſexti, ac propterea latera vnius, lateribus alterius erunt <lb></lb>proportionalia: Cumque latus GF minus ſi latere GD, <lb></lb>etiam latus BF, minus erit latere AD. </s>
        </p>
        <p id="N13434" type="main">
          <s id="N13436">Addit præterea Ariſtoteles, quod inter iſtos duos motus <lb></lb>contrarios id quod ſtabit, ſeu manebit, erit medium pun<lb></lb>ctum vbi C, nempe vbi conſtituitur ſcalmus circa quem <lb></lb>remus conuertitur. </s>
          <s id="N1343F">Siquidem verè reſpectu manubrij, ac <lb></lb>palmulæ, tanquam extremorum diametri circulariter du<lb></lb>ctæ, ſcalmus ipſe tanquam <expan abbr="cẽtrum">centrum</expan> manebit. </s>
          <s id="N1344C">Quare ſcalmus <lb></lb>C nunquam procederet ad partes D, nempe antrorſum, <lb></lb>niſi commoueretur nauigium, cui eſt affixus, &amp; eo transfer<lb></lb>retur, vbi remi eſt principium, cum ſemper nauigium per <lb></lb>impulſum in ipſa remigatione acceptum, ſequatur motum. <lb></lb></s>
          <s id="N13458">principij mouentis nempe manubrij à quo fertur antror<lb></lb>ſum, &amp; ſic impoſito per motum manubrij ab A vſque ad <lb></lb>D, ſcalmus, qui erat in C, conſtituetur in H, palmula re<lb></lb>trocedente à B vſque ad F. </s>
        </p>
        <p id="N13462" type="main">
          <s id="N13464">Hæc paucis mutatis, vel adiunctis Ariſtoteles profert, <lb></lb>quæ ſanè licet probent maius eſſe ſpatium AD, quod ma-<pb pagenum="109" xlink:href="005/01/117.jpg"></pb>nubrium conficit antrorſum; quam ſpatium BF, quod pal<lb></lb>mula tranſmittit retrorſum; non tamen probant prout opus <lb></lb>erat, ſpatium quoque CH, quod à ſcalmo cum naui per<lb></lb>curritur, maius eſſe, quàm ſpatium, quod in contrarium prę<lb></lb>terit palmula, vt BF, vel aliud ſimile. </s>
          <s id="N13476">Quare occaſionem <lb></lb>nobis tribuunt explicandi, num ſemper hoc accidat, vt ma<lb></lb>gis in anteriora progrediatur nauigium, quàm ipſius remi <lb></lb>palmula retrocedat, an verò quandoque tantum, &amp; qua. <lb></lb></s>
          <s id="N13480">ratione fiat. </s>
        </p>
        <p id="N13483" type="main">
          <s id="N13485">Dicendum ergo eſt, <expan abbr="aliquãdo">aliquando</expan> <expan abbr="nauigiũ">nauigium</expan> in <expan abbr="anterĩora">anterinora</expan> moue<lb></lb>ri abſque eo, quod palmula retrocedat, aliquando verò tan<lb></lb>tum prouehi nauigium, quantum palmula retroceſſerit; ſed <lb></lb>vt plurimum, magis procedi nauigium, quàm palmula in. <lb></lb></s>
          <s id="N1349C">contrarium cædat. </s>
        </p>
        <p id="N1349F" type="main">
          <s id="N134A1">Prima pars huius aſſertionis in duobus caſibus verifica<lb></lb>tur. </s>
          <s id="N134A6">Prior eſt, cum æquale ſpatium pertranſierit nauigium, <lb></lb>ac remi manubrium motu proprio, quo ſcilicet circa ſcal<lb></lb>mum conuertitur: tunc eorum palmula manet immota. <lb></lb></s>
          <s id="N134AE">Nam ſi exempli gratia nauigium pertranſeat palmum ſpa<lb></lb>tij, manubrium verò ſimul ſuo motu proprio alterum, iam, <lb></lb>in fine ipſius remigationis ipſum manubrium per duos pal<lb></lb>mos diſtabit à loco priori vnde diſceſſerat. </s>
          <s id="N134B7">At palmula cum <lb></lb>per motum quidem nauigij anterius tranſlata eſſet ad ſpa<lb></lb>tium vnius palmi, per motum verò manubrij ſimul retro<lb></lb>ceſſiſſet ad alium palmum (siquidem tantum retrocedit pal<lb></lb>mula quantum antecedit manubrium motu proprio, ſuppo<lb></lb>ſito, quod æquè diſtent à ſcalmo) ſequitur verè ac ſimplici<lb></lb>ter ipſam palmulam dimotam non fuiſſe. </s>
          <s id="N134C6">Sicut homo qui <lb></lb>pari paſſa graditur contra curſum nauigij à prora in pup<lb></lb>pim, ſimpliciter non mouetur, quia ſemper eandem ſeruat <lb></lb>diſtantiam à punctis fixis, vt a terra, vel cælo. </s>
        </p>
        <p id="N134CF" type="main">
          <s id="N134D1">Notandum tamen eſt in caſu deſcripto, nauigium non. <lb></lb></s>
          <s id="N134D7">moueri ſola virtute eiuſdem remigationis. </s>
          <s id="N134DA">Nam ſpatium, <lb></lb>quod percurrit virtute illius, nec computari poſſet vltra il<lb></lb>lud, quod ſimul percurrit manubrium motu proprio; nec <lb></lb>vnquam eſſet illi equale. </s>
          <s id="N134E3">Semper enim plus mouetur ma-<pb pagenum="110" xlink:href="005/01/118.jpg"></pb>nubrium, quam ſcalmus eodem tempore ad impulsum il<lb></lb>lius; nauis autem mouetur ad motum ſcalmi. </s>
          <s id="N134ED">Quod clarius <lb></lb>patebit in ſubiecta figura; in qua ſit remus AB, cuius ma<lb></lb>nubrium A, pal<lb></lb><figure id="id.005.01.118.1.jpg" xlink:href="005/01/118/1.jpg"></figure><lb></lb>mula B, ſcalmus <lb></lb>verò ſit in pun<lb></lb>cto medio vbi C. <lb></lb></s>
          <s id="N13502">Deinde promo-<lb></lb>ueatur manubrium <lb></lb>A motu proprio <lb></lb>vſque ad D, palmula manente in B. </s>
          <s id="N1350B">Scalmus verò C, <lb></lb>eodem tempore pertranſeat ſpatium CE, quod ſit æquale <lb></lb>ipſi AD; <expan abbr="ſubtendanturq.">ſubtendanturque</expan> æquales rectæ ipſis arcubus AD, <lb></lb>&amp; CE, &amp; conſtituatur paralellogrammum DECA, ſu<lb></lb>per ipſum AB. </s>
          <s id="N1351B">Tunc dico ſcalmum C vnà cum nauigio <lb></lb>tranſlatum non fuiſſe vſque ad E virtute ſola eiuſdem re<lb></lb>migationis, ſeu proprij motus manubrij ab A vſque ad D, <lb></lb>palmula manente in B. </s>
          <s id="N13524">Siquidem hoc ſolo motu remus <lb></lb>AB conſtitueretur in recta DB, cuius punctum medium <lb></lb>vbi ſcalmus poſitus eſt eſſet in F, non autem in E, qua <lb></lb>pertranſire non poteſt recta DB. </s>
          <s id="N1352D">Coincideret enim cum <lb></lb>linea DE paralella ipſi AC; <expan abbr="proindeq.">proindeque</expan> per 35. definitio<lb></lb>nem primi nunquam concurreret cum illa in punctum B, <lb></lb>vbi ſupponitur palmula. </s>
          <s id="N1353A">Cum autem linea CF minor ſit, <lb></lb>quàm CE, vel AD, quæſunt æquales: (Nam reſpectu <lb></lb>vnius ſe habet tanquam pars ad totum, reſpectu verò alte<lb></lb>rius, conſtituitur baſis anguli B, quæ per quartam propo<lb></lb>ſitionem ſexti minor eſt quam baſis AD, quæ longioribus <lb></lb>lineis continentibus ſubtenditur eidem angulo B) ſequitur <lb></lb>per motum, quo manubrium ab A transfertur in D, ſcal<lb></lb>mum cum naui pertranſire non poſſe ad æquale ſpatium <lb></lb>vſque ad E. </s>
          <s id="N1354E">Quod ſi illuc uſque pertingat, id certè contin<lb></lb>gere debet virtute alterius impulſus aliunde incuſſi in <expan abbr="ipsũ">ipsum</expan> <lb></lb>nauigium. </s>
          <s id="N13559">Qua virtute <expan abbr="eodẽ">eodem</expan> tempore ſimul ac manubrium <lb></lb>motu proprio perueniſſet vſque ad D, reperiatur in G; &amp; <lb></lb>ſcalmus qui eſſet in F, pertingat vſque ad E; quod eſt <pb pagenum="111" xlink:href="005/01/119.jpg"></pb>vtrumque, duplum ſpatium percurrere reſpectu illius, quod <lb></lb>virtute ſolius prædictæ remigationis percurriſſet. </s>
        </p>
        <p id="N1356B" type="main">
          <s id="N1356D">Poſterior verò caſus, in quo verificatur palmulam ad mo<lb></lb>tum antrorſum nauigij <expan abbr="nõ">non</expan> retrocedere, eſt cum celerius fer<lb></lb>tur nauigium, quàm remi manubrium. </s>
          <s id="N13578"><expan abbr="Siquidẽ">Siquidem</expan> cum in tan<lb></lb>tum palmula poſſit retrocedere, in quantum manubrium <lb></lb>motu proprio in anteriora amplius progreditur quàm naui<lb></lb>gium, ſi celerius feratur nauigium quàm manubrium, ma<lb></lb>iuſque proinde ſpatium percurrat, palmula nullo modo po<lb></lb>terit retrocedere. </s>
          <s id="N13588">Etenim poſito, quod manubrium motu <lb></lb>proprio decurrat ſpatium bipalmare, per totidem palmos <lb></lb>palmula retrocederet, ſi nauigium maneret immotum: At <lb></lb>ſi ſimul nauigium percurrat ſpatium quadripalmare, nihil <lb></lb>palmula retrocedet. </s>
          <s id="N13593">Nam quo tempore retrocederet <expan abbr="vnũ">vnum</expan>, <lb></lb>duplum progrederetur in contrarium. </s>
        </p>
        <p id="N1359C" type="main">
          <s id="N1359E">Secunda verò pars concluſionis, videlicet tantum <expan abbr="quan-doq.">quan<lb></lb>doque</expan> palmulam retrocedere, <expan abbr="quãtum">quantum</expan> prouehitur nauigium; <lb></lb>ex eo probatur. </s>
          <s id="N135AD">Nam ſi remi manubrium motu proprio, du<lb></lb>plum confecerit ſpatium, quam nauigium; vt verbi gratia <lb></lb>quadripalmare reſpectu bipalmaris, palmula quidem per <lb></lb>totidem ſpatij palmos retroceſſiſſet, niſi obſtaret motus na<lb></lb>uigij in contrarium: At non obſtat, niſi per dimidium, nem<lb></lb>pe ſecun dum ſpatium bipalmare, quod certè nauigium ſimul <lb></lb>cum toto remo in anteriora percurrit: ergo per æquale ſpa<lb></lb>tium bipalmare palmula retrocedet. </s>
        </p>
        <p id="N135BE" type="main">
          <s id="N135C0">Tertia denique aſſertionis pars, nempe magis, vt pluri<lb></lb>mum prògredi nauigium, quàm palmulam in contrarium, <lb></lb>ex dictis ferè oſtenditur apertiſsimè. </s>
          <s id="N135C7">Quia licet maius ſpa<lb></lb>tium decurrat remi manubrium, quàm nauigium, quando <lb></lb>ipſum nauigium mouetur ſolùm in virtute eiuſdem remiga<lb></lb>tionis, vt frequentius accidit: rarò tamen exceſſus ad dimi<lb></lb>dium videtur pertingere, ita vt manubrium motu proprio <lb></lb>duplum conficiat ſpatium, quàm nauigium. </s>
          <s id="N135D4">Cum autem <lb></lb>huiuſmodi exceſſus ad dimidium non pertingit, neque pal<lb></lb>mula per æquale ſpatium retrocedet, ſed minus. </s>
          <s id="N135DB">Vnde ſi <lb></lb>manubrium progrediatur vt tria; nauigium vero vt duo, pal-<pb pagenum="112" xlink:href="005/01/120.jpg"></pb>mula retrocedet vt vnum: tantum ſcilicet quantum eſt <lb></lb>ſpatium, quo excedit illud, quod conficitur per motum <lb></lb>contrarium. </s>
        </p>
        <p id="N135E9" type="main">
          <s id="N135EB">Quæ omnia Geometricè at que exactius conſtare poſſunt <lb></lb>ex his, quæ Petrus Nonius acutiſſimè demonſtrat in ſua <lb></lb>Annotatione ſuper hunc ipſum locum Ariſtotelis. </s>
          <s id="N135F3">Quam<lb></lb>uis non rectè videatur ſupponere, ipſum Philoſophum, vni<lb></lb>uerſaliter aſſumpſiſſe tantum ſpatium conficere nauigium, <lb></lb>quantum remi manubrium. </s>
          <s id="N135FC">Fortaſſe propter illa verba <lb></lb>ipſius Philoſophi: Non procederet autem vbi ex D, niſi <lb></lb>commoueretur nauigium, &amp; eò transferretur, vbi remi eſt <lb></lb>principium. </s>
          <s id="N13605">Quæ tamen verba in diuerſum, ac veriorem <lb></lb>prolata ſunt ſenſum, vt ſupra expoſuimus. </s>
          <s id="N1360A">Solum enim per <lb></lb>ea intendit Philoſophus, quod non præcederet ſcalmus an<lb></lb>trorſum ad partes D, quo tantum peruenit manubrium A; <lb></lb>niſi commoueretur nauigium verſus eandem partem, ſe<lb></lb>quendo remi principium, à quo trahitur, vel à quo illuc fuit <lb></lb>impulſum. </s>
        </p>
        <p id="N13617" type="main">
          <s id="N13619">His tandem ita conſtitutis de motione remi, applican<lb></lb>do Ariſtoteles eandem obſeruationem, non abſimile eſſe <lb></lb>docet, quod contingit in motione gubernaculi, ac temonis, <lb></lb>vt ſcilicet ſicut ſcalmus, qui conſtituitur medium inter ex<lb></lb>trema ipſius remi, quæ mouentur in contrarium, illuc tranſ<lb></lb>fertur vbi remi eſt principium, nempe antrorſum, quo remi <lb></lb>manubrium pergit, ac nauem propellit: ita locus vbi ap<lb></lb>plicatur gubernaculum, ac primo attingit temonem (qui <lb></lb>certè locus eſt in linea cadenti, qua temo puppi adhæret in <lb></lb>cuſpide, &amp; vbi conſtituitur etiam cardo) cum ſe habeat <lb></lb>tanquam medium inter duo extrema, quæ mouentur in <lb></lb>contrarium, videlicet manubrium gubernaculi, &amp; alam te<lb></lb>monis, qua mare propellitur, illuc intelligetur transferri, <lb></lb>quo ipſum gubernaculi manubrium erat. </s>
          <s id="N13636">Quemadmodum <lb></lb>enim ſcalmus, temo, ait Ariſtoteles, nempe ſecundum præ<lb></lb>dictam lineam circa quam quaſi immotam, conuertitur la<lb></lb>titudo ipſius temonis ex vna parte, &amp; guberna culi manu<lb></lb>brium ex alia, vt patet in hac prima figura; in qua cadens <pb pagenum="113" xlink:href="005/01/121.jpg"></pb>AB, <expan abbr="lineã">lineam</expan> oſtendit <lb></lb><figure id="id.005.01.121.1.jpg" xlink:href="005/01/121/1.jpg"></figure><lb></lb>circa cuius prin<lb></lb>cipium guberna-<lb></lb>culum applicatur, <lb></lb>ac primo attingit <lb></lb>temonem, quæ li<lb></lb>nea in motione <lb></lb>gubernaculi ma-<lb></lb>net immota, ſicut <lb></lb>ſcalmus in motio<lb></lb>ne remi. </s>
          <s id="N13664">Pars ve<lb></lb>rò AC ſignat fa<lb></lb>ciem dexteram <lb></lb>temonis; &amp; AD <lb></lb>manubrium gu-<lb></lb>bernaculi. </s>
          <s id="N13671">Quod <lb></lb>ſi extremum ma<lb></lb>nubrij D, intelli<lb></lb>gatur transferri in <lb></lb>E, vt cernere eſt <lb></lb>in ſecunda figura: <lb></lb>tunc ait Ariſtote<lb></lb>les, illuc transferri <lb></lb>etiam centrum A. <lb></lb></s>
          <s id="N13686">Nam D tranſlato in E, ſimul C transferretur in F; <lb></lb>ac per impulſum acceptum in latitudine AF neceſſariò <lb></lb>A transferri deberet ad partes G. </s>
          <s id="N1368E">Cumque ſimul naui<lb></lb>gium, cui temo eſt alligatus, procedat antrorſum, ipſum <lb></lb>A non conſtitueretur in G, ſed in E, vbi prius erat ma<lb></lb>nubrium gubernaculi. </s>
          <s id="N13697">Quare gubernaculum nihil naui<lb></lb>gio ad id, quod in ante progredi eſt, conferre ait Ariſto<lb></lb>teles, ſed ſolum puppim in obliquum pellere, aliquantu<lb></lb>lum ſcilicet ad latus, qua parua motione puppis, pro<lb></lb>ra in contrarium vergit, nempe ad latus oppoſitum, vt <lb></lb>ipſemet Philoſophus docet, &amp; conſiderare licebit in hac <pb pagenum="114" xlink:href="005/01/122.jpg"></pb><figure id="id.005.01.122.1.jpg" xlink:href="005/01/122/1.jpg"></figure><lb></lb>figura nauiculæ, cuius <lb></lb>puppis A, prora D, <lb></lb><expan abbr="gubernaculũ">gubernaculum</expan> verò EF <lb></lb>obliquè conſtitutum; <lb></lb>Nam certè ad impul<lb></lb>ſum aquæ in alam ob<lb></lb>uerſam FA, ipſa pup<lb></lb>pis A cum retrocede<lb></lb>re non poſſit ob <expan abbr="pro-greſsũ">pro<lb></lb>greſsum</expan> nauiculæ (dum<lb></lb>modo aliquantulum cedere debeat impulſui) declinabit in <lb></lb>E, vbi erat gubernaculi manubrium, qua parua motione <lb></lb>puppis, ob rationes in principio poſitas, prora ad contra<lb></lb>rium verget, inquit Ariſtoteles, ſcilicet ad latus oppoſitum, <lb></lb><expan abbr="proindeq.">proindeque</expan> conſtituetur in H, niſi validum aliquod ventum <lb></lb>inde ſpirans <expan abbr="paruaq.">paruaque</expan> conuerſio temonis non obſtet. </s>
        </p>
        <p id="N136DB" type="main">
          <s id="N136DD">Quo ex principio intelligi poteſt cur ex tranſuerſo per<lb></lb>flante admodum vento, ac directè nihilominus nauigia <lb></lb>procedendo, tandem non pertingant, quo præcisè tende<lb></lb>bant, ſed inferius multo, ſeu ad partem vento magis oppo<lb></lb>ſitam. </s>
          <s id="N136E8">Porro cum aliquantulum à latere vento perflante, <lb></lb>alam temonis illi ſatis obuerſam nautæ conſtituere tenean<lb></lb>tur, validiſsimè ipſam ſimul cum puppi fluctus repellunt, <lb></lb>quo ſanè repulſo circumagerent totam nauim, niſi ſimul in <lb></lb>latus verſus proram inciderent, nam hinc inde coadæquato <lb></lb>repulſu, ac gubernaculo moderante, dum nauis pergit an<lb></lb>trorſum ſemper eandem, quam prius in ſe poſitionem, ac <lb></lb><expan abbr="directionẽ">directionem</expan> ſeruat. </s>
          <s id="N136FC">Cum <expan abbr="itaq;">itaque</expan> fluctus ipſi nauem circumage<lb></lb>re nequeant, <expan abbr="nauisq.">nauisque</expan> aliquid pati debeat ex ipſo repulſu, to<lb></lb>ta ſimul cogitur ſenſim declinare ad latus <expan abbr="vẽto">vento</expan> oppoſitum; <lb></lb>Vt exempli gratia data poſitione, quam modo tenet deſcri<lb></lb>pta nauicula in AD, ac perflante vento ex tranſuerſo, vt <lb></lb>ex H, certè ad motum ipſius puppis ex A in E, prora <lb></lb>non conuerteretur à D in H, (niſi ob maiorem conuer<lb></lb>ſionem temonis, ſed potius non nihil cedendo ſicut puppis, <pb pagenum="115" xlink:href="005/01/123.jpg"></pb>declinaret in I; Quare nauis à ſitu AD conſtituta in EI, <lb></lb>eandem quippe ſeruaret poſitionem, ac directionem, tranſ<lb></lb>lata tamen eſſet inferius verſus partem vento oppoſitam, <lb></lb>ſicque vlterius incedendo quamuis ab initio deſtinatum ſi<lb></lb>bi locum per proram inſpiceret, illuc tamen peruenire ne<lb></lb>quiret, niſi altius, ſeu magis ad partem vnde ventus validè <lb></lb>ſpirat, proram direxerit, vt ſpatium, quod coacta declinatio<lb></lb>ne deperdit, compenſetur anticipata ſitus poſitione, ac di<lb></lb>rectione. </s>
        </p>
        <p id="N1372E" type="main">
          <s id="N13730">Demum illud, quod Ariſtoteles vltimo loco adiecit. </s>
          <s id="N13733">In <lb></lb>codem exiſtente prora, totum transferri nauigium, (niſi li<lb></lb>brariorum error irrepſerit, vt potius conſequenter ad ſupe<lb></lb>rius dicta legendum ſit, in eodem exiſtente puppi, eo quod <lb></lb>parua eius dimotio pro nihilo reputetur) ne cum doctrina <lb></lb>eiuſdem Philoſophi hactenus tradita pugnet, intelligendum <lb></lb>eſt, tum ſi quando per motum ſolius temonis tanquam remi <lb></lb>in cuſpide puppis, tota nauis conuerteretur, vt explicuimus <lb></lb>in principio: tum etiam quando idipſum contingit ad obli<lb></lb>quam tantum modo poſitionem temonis contra fluctus ad<lb></lb>uenientes, poſito ſcilicet quod nauigium, nec velis, nec re<lb></lb>mis, nec alio pacto feratur. </s>
          <s id="N1374C">Etenim ſi temo per ſui con<lb></lb>uerſionem, vel obliquam poſitionem fluctus maris à dex<lb></lb>tris excipiat, abſque dubio puppis ad ſiniſtram declinabit, <lb></lb>prora manente ferè immota, eo quod impetus obliquè ſit <lb></lb>impreſſus, &amp; illuc vſque pertingere nequeat, vel ob ſuam <lb></lb>imbecillitatem ibi tandem langueſcat. </s>
          <s id="N13759">Quod facilè con<lb></lb>templari eſt in ſubiecta, quam delineauimus nauicula, cuius <lb></lb>linea AB refert gubernaculum cum temone affixo in ipſa <lb></lb>cuſpide puppis vbi C, ac prora conſtituitur in G. </s>
          <s id="N13763">Nam <lb></lb>dato quod extremum temonis B, mare dextrorſum exci<lb></lb>piens, aut propellens transferatur in D per motum guber<lb></lb>naculi ab A in E, vtique cuſpis puppis, quæ eſt in C <lb></lb>transferetur ſiniſtrorſum vnà cum tota nauicula verſus F, <lb></lb>prora ipſa in eodem puncto manente, vel parum inde di<lb></lb>mota, vt vſque ad punctum H; ita vt nauicula, quæ erat <pb pagenum="116" xlink:href="005/01/124.jpg"></pb><figure id="id.005.01.124.1.jpg" xlink:href="005/01/124/1.jpg"></figure><lb></lb>in CG, conſtituatur in FG, vel in <lb></lb>FH. </s>
          <s id="N1377F">Licet hoc non ſemper veri<lb></lb>ficetur cum ſæpius impetus per <lb></lb>remonem incuſſus à mare in hu<lb></lb>iuſmodi caſu ſuperare, ac tranſ<lb></lb>ferre nequeat centrum grauitatis <lb></lb>totius nauis, quod eſt circa me<lb></lb>dium illius, <expan abbr="proindeq.">proindeque</expan> tota longi<lb></lb>tudo nauis conuerti non poſſit <lb></lb>tanquam ſemidiameter circa ter<lb></lb>minum prorae, tanquam circa cen<lb></lb>trum, ſed potius centrum huius <lb></lb>conuerſionis conſtituatur in ipſo centro grauitatis totius <lb></lb>nauis, vel in alio puncto lineæ per ipſum ad centrum mundi <lb></lb>cadentis. </s>
        </p>
        <p id="N137A0" type="main">
          <s id="N137A2">In prædictis ergo caſibus, &amp; cum explicata limitatione <lb></lb>loquendo de nauigio, quod nullo pacto fertur antrorſum <lb></lb>intelligitur verificari, quod docuit Ariſtoteles. </s>
          <s id="N137AA">In eodem <lb></lb>exiſtente prora, totum transferri nauigium; Alioquin ſi ſer<lb></lb>mo fuiſſet de nauigio, quod plenis velis, aut remis mare <lb></lb>tranſmittit, verificari certè non poſſet; cum talis ac tanta <lb></lb>ſit vis eiuſdem curſus, quo recta in anteriora citiſsimè fer<lb></lb>tur, vt non ſinat ipſam puppim per occurſum maris, quod <lb></lb>incidit in temonem à ſuo recto tramite admodum ſaltem <lb></lb>diuerti, ſicut à puncto ſuæ quietis facilè ipſa dimouetur cum <lb></lb>nauis quieſcit. </s>
          <s id="N137BD">Licet enim promoto ſemel antrorſum naui<lb></lb>gio, temo per obliquam ſui conſtitutionem, &amp; immediatum <lb></lb>repulſum quem patitur, omnino reſiſtere nequeat occur<lb></lb>rentibus fluctibus, <expan abbr="cogaturq.">cogaturque</expan> moueri, velut in gyrum circa <lb></lb>ipſius puppis extremum; vim tamen quam patitur transfun<lb></lb>dit in longitudinem nauis, tanquam in alterum latus, cum <lb></lb>quo efficit angulum, vt in principio cum ſua figura expreſsi<lb></lb>mus: Vnde cum non ſolum ad motum vnius lateris in an<lb></lb>gulo, moueatur alterum, ſed facilius ſit, vtrumque latus cir<lb></lb>culariter moueri, cuſpide anguli tanquam centro manente <pb pagenum="117" xlink:href="005/01/125.jpg"></pb>immota ob aliquod <expan abbr="limpedimentũ">impedimentum</expan>, quàm <expan abbr="totũ">totum</expan> <expan abbr="angulũ">angulum</expan> ſimul <lb></lb>transferri; hinc eſt, vt reſiſtentia nouis orta ex impetu indi<lb></lb>rectum tendente, ſufficiat vt cuſpis prædicti anguli, quæ in <lb></lb>propoſito eſt vbi puppis extremum; minimè dimoueatur à <lb></lb>tramite ſuper <expan abbr="quẽ">quem</expan> fertur, <expan abbr="nõ">non</expan> <expan abbr="autẽ">autem</expan> ſufficiat quin prora <expan abbr="tanquã">tanquam</expan> <lb></lb>extremum alterius lateris moueatur ad motum lateris, quod <lb></lb>conſtituitur à temone, ita vt temone ad leuam repulſo lon<lb></lb>gitudo nauis cum prora ad dexteram vergat. </s>
          <s id="N13805">Prouenit au<lb></lb>tem maior hæc facilitas motus lateris vtriuſque, circa pro<lb></lb>priam cuſpidem, tum ex facilitate motus circularis in vni<lb></lb>uerſum, tum ex ipſa reſiſtentia, qua cuſpis anguli, quem effi<lb></lb>ciunt detinetur ab impulſo in directum nè moueatur obli<lb></lb>què in tranſuerſum. </s>
          <s id="N13812">Innititur enim ei tanquam fulcimento, <lb></lb>ipſaque latera induunt rationem vectis cuiuſdam anguloſi <lb></lb>in medio fulti, qui ſanè facilius conuertitur circa fulcimen<lb></lb>tum ad motum alterius extremi, quàm ſimul ſecundum ſe <lb></lb>totum aliò transferatur. </s>
          <s id="N1381D">Antrorſum ergo naui promota, <lb></lb>ipſe impetus promotionis, ſeu curſus impedit ne puppis ex<lb></lb>tremum in tranſuerſum dimoueatur, non autem obſtat quin <lb></lb>ad motionem obliquam temonis, conuertatur ſecum &amp; <lb></lb>prora, cum propter vim illatam, quæ vrgentibus fluctibus, in <lb></lb>illam transfunditur; tum propter facilitatem conuerſionis <lb></lb>explicatam, conſentaneè ad doctrinam ſupra traditam, <expan abbr="men-temq.">men<lb></lb>temque</expan> Ariſtotelis aientis. </s>
          <s id="N13832">parua motione facta per temonem <lb></lb>in puppi, multo maius interuallum fieri in vltimo: Et alibi, <lb></lb>temone paululum quid tranſpoſito, multam fieri tranſpoſi<lb></lb>tionem proræ, vt ibidem commonuimus. </s>
        </p>
        <p id="N1383D" type="main">
          <s id="N1383F">Sed prætermiſſa Ariſtotelis doctrina, totius effectus quem <lb></lb>per vſum temonis experimur in naui, cauſam ſatis, ac bre<lb></lb>uius explicari poſſe videtur ſi ad libram potius quàm ad ve<lb></lb>ctem eam reuocauerimus. </s>
          <s id="N13848">Etenim nauis mari obuiando, <lb></lb>eiuſque impulſum æquabiliter à dextris, &amp; à ſiniſtris reci<lb></lb>piendo, non aliter ſe habet, quàm libra in æquilibrio conſti<lb></lb>tuta, in cuius brachijs æqualia pondera ſuſtinentur. </s>
          <s id="N13851">Idem <lb></lb>enim eſt vtrinque æqualia pondera ſuſtinere, ac impetus <lb></lb>pariter æquales. </s>
          <s id="N13858">Cum autem à dextris, vel à ſiniſtris ex na<pb pagenum="118" xlink:href="005/01/126.jpg"></pb>ui lignum aliquod, vt temo, vel aliud non abſimile promi<lb></lb>nuerit, cui mare obuians, maiorem impetum incutiat, iam <lb></lb>non eſt amplius æqualis impetus vtrinque incuſſus. </s>
          <s id="N13864">Ac ſicut <lb></lb>libram cum ipſa maius pondus altero brachio ſuſtinet incli<lb></lb>nari neceſſe eſt, ac cedere ſecundum illud brachium ex quo <lb></lb>maius pondus propendet: ita nauim inclinari oportet ſe<lb></lb>cundum illam partem, in qua maiorem impetum excipit, <lb></lb>quod ſit per circumuerſionem totius longitudinis nauis ad <lb></lb>latus ipſum vnde magis percutitur, prout paulò ante deſcri<lb></lb>pſimus. </s>
          <s id="N13875">Licet hic dicendi modus, <expan abbr="ipſumq,">ipſumque</expan> fundamentum, <lb></lb>quo nititur verificari poſſit, tum ſi centrum motionis circu<lb></lb>laris, quam experimur in naui conſtituatur in cuſpide pup<lb></lb>pis, tum ſi conſtituatur in prora, vt per ſe patet. </s>
          <s id="N1387E">Sed fortaſ<lb></lb>ſe multo melius ſi conſtituatur in medio, ſeu in centro gra<lb></lb>uitatis totius nauis, circa quod facilius eſt intelligere ipſam <lb></lb>nauis conuerſionem, ſiue inquiete, ſiue in motu. </s>
          <s id="N13887">Quomo<lb></lb>docunque enim temo obliquè conſtitutus vim patiatur ab <lb></lb>aqua; Nimirum ſiue excipiendo illam fluentem, &amp; obuian<lb></lb>tem; ſiue impingendo in illam quieſcentem, ſemper dimo<lb></lb>tio illa circularis intelligetur pertingere vſque ad cen<lb></lb>trum grauitatis totius nauis, cum qua temo vnum corpus <lb></lb>efficitur. </s>
          <s id="N13896">At in re tam occulta, quæ etiam dum ante ocu<lb></lb>los verſatur, adhuc imaginationem comprehenſionemque <lb></lb>obſeruantis fugit, conſultius erit ab Ariſtotelis doctrina non <lb></lb>diſcedere. </s>
        </p>
        <p id="N1389F" type="head">
          <s id="N138A1">Quæſtio Sexta.</s>
        </p>
        <p id="N138A4" type="main">
          <s id="N138A6">C<emph type="italics"></emph>vr quanto antenna ſublimior fuerit, ijſdem <lb></lb>velis, &amp; vento eodem cæle, iùs feruntur na<lb></lb>uigia? </s>
          <s id="N138B0">An quia malus quidem fit vectis, hy<lb></lb>pomochlion verò mali ſedes, in qua colloca<lb></lb>tur: pondus autem quod moueri debet, ipſum <lb></lb>nauigium; mouens verò is, qui vela tendit, <lb></lb>ſpiritus? </s>
          <s id="N138BB">Si igitur quando remotius fuerit hypomochlion,<emph.end type="italics"></emph.end><pb pagenum="119" xlink:href="005/01/127.jpg"></pb><emph type="italics"></emph>facilius eadem potentia, &amp; citius idem mouet pondus, altius <lb></lb>sertè ſublata antenna velum à mali ſede, quæ hypomochlion <lb></lb>eſt, remotius faciens, id efficiet.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N138CF" type="head">
          <s id="N138D1">COMMENTARIVS.</s>
        </p>
        <p id="N138D5" type="main">
          <s id="N138D7">Qværit hic Ariſtoteles cur <expan abbr="ijſdẽ">ijſdem</expan> prorſus velis, <expan abbr="eodẽq.">eodenque</expan> <lb></lb>vento perflante, celerius nauigia ferantur quando al<lb></lb>tius ſublimatur antenna. </s>
          <s id="N138E6"><expan abbr="Statimq.">Statimque</expan> reſpondet, ex eo <lb></lb>id prouenire, quod malus in ventorum impulſionibus conſti<lb></lb>tuitur vectis, cuius hypomochlion, ſeu fulcimentum eſt ipſa <lb></lb>mali ſedes in qua locatur; pondus autem quod moueri de<lb></lb>bet, ipſum nauigium, ac mouens ventum impellens. </s>
          <s id="N138F4">Etenim <lb></lb>cum huiuſmodi impulſus velis quidem exceptus verè totus <lb></lb>refundatur in eam mali partem vbi alligatur antenna; quan<lb></lb>tò ſublimius illa fuerit alligata, tantò remotius à fulcimento <lb></lb>vis mouentis incutietur in malum, ſeu vectem. </s>
          <s id="N138FF">At virtus <lb></lb>mouentis beneficio vectis, eo magis augetur, quo remotius <lb></lb>ab eius fulcimento imprimitur: ergo cum ſublimior fuerit <lb></lb>antenna, maior fiet virtus à ventis incuſſa, <expan abbr="validiusq.">validiusque</expan> proinde <lb></lb>mouebit nauigia. </s>
          <s id="N1390E">Diximus autem impetum velis exceptum <lb></lb>ferè totum, non abſolutè totum refundi in eam mali partem <lb></lb>vbi alligatur antenna; quia adhuc antennæ cornua, ac veli <lb></lb>pedes ex eodem impetu participant, dum per funes opife<lb></lb>ros <expan abbr="propedesq.">propedesque</expan> nauim ſecum trahunt atque proripiunt. </s>
        </p>
        <p id="N1391D" type="main">
          <s id="N1391F">Sed vt firmius doctrina Ariſtotelis teneatur, ac difficulta<lb></lb>tes omnes oppoſitæ ſoluantur, notandum eſt duplicem in <lb></lb>malo conſiderari poſſe rationem vectis cum nauis per veli<lb></lb>ficationem fertur antrorſum; vnam quæ illi competit abſo<lb></lb>lutè prout <expan abbr="cõdiſtinguitur">condiſtinguitur</expan> à reliquis partibus nauis; Alteram <lb></lb>verò quæ coniunctim ei conuenit ſimul cum nauis carina, <lb></lb>ſecundum cam partem, qua carina verſus puppim extendi<lb></lb>tur. </s>
          <s id="N13934">Porrò malus abſolutè conſideratus in latione nauis, <lb></lb>virtute ventorum, fulcimentum obtinet circa profundam <lb></lb>ſedem vbi locatur in nauis carina, <expan abbr="eiq.">eique</expan> innititur per ſui ex<lb></lb>tremum infimum, qua parte, ſeu facie vergit ad puppim. <lb></lb></s>
          <s id="N13942">Onus autem ſeu nauem promouet per partem ipſius altio<pb pagenum="120" xlink:href="005/01/128.jpg"></pb>rem ex ijs, quæ intra foramen continentur, vnde ipſe malus <lb></lb>foris prodit in altum, tanquam arbor è terra; <expan abbr="vrgetq.">vrgetque</expan> ſecun<lb></lb>dum eam ipſius partis faciem, quæ ad proram reſpicit vbi <lb></lb>vltimo foramen deſinit. </s>
          <s id="N13954">Siquidem ibi tota ferè vis incuti<lb></lb>tur naui ad progrediendum antrorſum, vt videre eſt in hac <lb></lb>figura, in qua extremum mali fundo innixum ſit A, cuius <lb></lb>facies puppim <lb></lb>reſpiciens B; <lb></lb><figure id="id.005.01.128.1.jpg" xlink:href="005/01/128/1.jpg"></figure><lb></lb>pars verò ip<lb></lb>ſius mali, quæ <lb></lb><expan abbr="flãtibus">flantibus</expan> ventis <lb></lb>à tergo naui<lb></lb>gium præmit, <lb></lb>vel vrget in an<lb></lb>te, vbi C, è <expan abbr="cõ-ſpectu">con<lb></lb>ſpectu</expan> prorę; &amp; <lb></lb>locus antennæ <lb></lb>in ipſo malo, ſit <lb></lb>D; vbi tota pe<lb></lb>nè virtus im<lb></lb>pellentis ſpiri<lb></lb>tus refunditur, <lb></lb>vt diximus ra<lb></lb>tione veli <expan abbr="illũ">illum</expan> <lb></lb>excipientis. </s>
          <s id="N13992"><expan abbr="Iã">Iam</expan> <lb></lb>igitur <expan abbr="cõſtat">conſtat</expan> ex <lb></lb>hoc, malum <lb></lb>per ſe ſumptum propriè vectem conſtitui in ipſa ventorum <lb></lb>impulſione, cum fulcimentum habeat in parte diſtincta ab <lb></lb>ea, qua nauem promouet, &amp; ab ea, qua mouetur à vento, vt <lb></lb>in ſimili commune eſt omnibus vectibus; vnde quo altius <lb></lb>conſtituetur antenna, vt verbi gratia ſi eleuaretur vſque ad <lb></lb>E, eo celerius moueretur nauigium, quia virtutem impellen<lb></lb>tem reciperet in parte à centro vectis diſtantiori. </s>
        </p>
        <p id="N139AE" type="main">
          <s id="N139B0">Altera verò vectis ratio, quæ conſideratur in malo con<lb></lb>iunctim cum nauis carina, eſt huiuſmodi. </s>
          <s id="N139B5">Quoniam vt rectè <pb pagenum="121" xlink:href="005/01/129.jpg"></pb>prænotat Baldus, eſt quædam vectium ſpecies, cuius bra<lb></lb>chia in angulum deſinunt, <expan abbr="ipſiusq.">ipſiusque</expan> anguli cuſpis in operatio<lb></lb>ne conſtituitur centrum, ac fulcimentum circa quod bra<lb></lb>chia conuertuntur. </s>
          <s id="N139C7">Ad quam ſpeciem reducitur ferreus <lb></lb>malleus prout eam partem continet, qua clauos reuellit. <lb></lb></s>
          <s id="N139CD">Etenim vt obſeruari poteſt in hac figura, mallei manubrium <lb></lb>conſtituit vnum brachium AB; alterum verò pars qua cla<lb></lb>uos reuellit, nempe BC. </s>
          <s id="N139D5">Et ex vtriſque fit angulus ABC, <lb></lb>ipſo malleo in extractione clauorum <lb></lb>cuſpidi innixo vbi B. </s>
        </p>
        <figure id="id.005.01.129.1.jpg" xlink:href="005/01/129/1.jpg"></figure>
        <p id="N139E1" type="main">
          <s id="N139E3">Similiter ergo malus in naui conſi<lb></lb>derari poteſt tanquam brachium ve<lb></lb>ctis, quod alteri coniungatur, nempe <lb></lb>illi parti carinę, quę vergit ad puppim, <lb></lb>&amp; cum qua conſtituit <expan abbr="angulũ">angulum</expan> in pun<lb></lb>cto vbi deſinit altitudo ipſius mali. </s>
          <s id="N139F4"><expan abbr="Nã">Nam</expan> <lb></lb>impetu in <expan abbr="alterũ">alterum</expan> extremum ipſius ma<lb></lb>li incuſſo, nempe circa locum vbi vr<lb></lb>get antenna velo agitata à ventis, ipſa <lb></lb>ſummitas mali declinaret ſi poſſet ad <lb></lb>proram, tanquam per conuerſionem <lb></lb>circa punctum explicatum, in quo conſtituitur angulus, <expan abbr="ſi-mulq.">ſi<lb></lb>mulque</expan> eleuaretur ſi poſſet carina ex parte puppis. </s>
          <s id="N13A10">Quemad<lb></lb><figure id="id.005.01.129.2.jpg" xlink:href="005/01/129/2.jpg"></figure><lb></lb>modum in propoſito an<lb></lb>gulo ABC; ſi latus AB <lb></lb>declinaret in BD per <lb></lb>impulſum acceptum in <lb></lb>A; latus etiam BC ele<lb></lb>uaretur in BE. </s>
          <s id="N13A26">Quoniam <lb></lb>verò declinare non po<lb></lb>teſt malus, nec pars illa <lb></lb>carinæ per conſequens <lb></lb>eleuari abſque immer<lb></lb>ſione proræ, totus impe<lb></lb>tus incuſſus refunditur <lb></lb>in lationem antrorſum, eo quod mare cum ſit fluidum non <pb pagenum="122" xlink:href="005/01/130.jpg"></pb>reſiſtat lationi, ſicut ipſius proræ immerſioni, quæ contra <lb></lb>naturam ligni ſequeretur ex declinatione mali. </s>
          <s id="N13A3E">Accedit <lb></lb>quia neque pars carinæ, quæ eſt à malo ad puppim poſſet <lb></lb>eleuari; tum propter grauitatem puppis, quæ ſe habet tan<lb></lb>quam onus in extremo vectis, <expan abbr="ibiq.">ibique</expan> maximè præponderat <lb></lb>impulſui contrario; tum propter naturalem reſiſtentiam ca<lb></lb>rinæ <expan abbr="totiusq.">totiusque</expan> fundi ne ſeparetur ab aqua, cui connaturalius <lb></lb>ligna præſertim plana adhærent; vt patet ex difficultate, <lb></lb>qua ſupernatantes tabulæ extrahuntur ex aqua. </s>
        </p>
        <p id="N13A57" type="main">
          <s id="N13A59">Secundum vtramque igitur vectis rationem, quam malus <lb></lb>participat, nauem promouet in anteriora, abſque eo, quod <lb></lb>verſus proram inclinetur, ſed tantum præmat, eo pacto, quo <lb></lb>diximus, in ſitu vnde è foramine exit. </s>
          <s id="N13A62">Quare non rectè Bal<lb></lb>dus ſecundam vectis rationem in malo admittens, primam <lb></lb>ab Ariſtotele allatam impugnat. </s>
          <s id="N13A69">Ex eo quod ſi malus talis <lb></lb>vectis vim haberet, vento validè impellente, aut ſequeretur <lb></lb>fractio ipſius mali ad ſedem, aut inclinatio verſus proram <lb></lb>cum immerſione ipſius proræ, &amp; eleuatione puppis: Siqui<lb></lb>dem nec probat ſequelam, nec id ipſum, quod damnat de<lb></lb>uitat iuxta ſecundam vectis rationem quam approbat, vt <lb></lb>per ſe patet. </s>
          <s id="N13A78"><expan abbr="Immeritoq.">Immeritoque</expan> proinde ſimul recurrit ad maio<lb></lb>rem infeſtationem ventorum, quam experimur in locis ſubli<lb></lb>mioribus, vt cauſam afferat propter quam, cum ſublimior <lb></lb>fuerit antenna, citius <expan abbr="nauigiũ">nauigium</expan> ſpiritu flante moueatur. </s>
          <s id="N13A88">Nam <lb></lb>&amp; cauſam quam Ariſtoteles tradit manifeſtam habemus; &amp; <lb></lb>non ſemper verum eſt, quod ipſe de vento aſſumit, maximè <lb></lb>in tam parua diſtantia, &amp; loco non minus expoſito. </s>
        </p>
        <p id="N13A91" type="main">
          <s id="N13A93">Denique ex his expediri etiam poteſt alia quæſtio, cur <lb></lb>nimirum fluctuante aliquantulum mare, ac minimè velis <lb></lb>munito, aut progrediente nauigio, quo altius ſublimatur an<lb></lb>tenna, minus ipſum commoueatur; vt in ſtatione nauium at<lb></lb>que triremium extra portum ſolet contingere. </s>
          <s id="N13A9E">Etenim <lb></lb>iuxta prædicta facilè reſpondetur, tunc quoque malum, ve<lb></lb>ctis rationem habere, altero in extremo ſuffulti prope na<lb></lb>uis carinam: antennam verò oneris vicem ſubire, ac mare <lb></lb>fluctuans, potentiæ mouentis, cuius virtus mediante naui-<pb pagenum="123" xlink:href="005/01/131.jpg"></pb>gio applicatur vecti inter fulcimentum, &amp; onus; nempe vbi <lb></lb>malus ipſe vltimo intra corpus nauigij continetur, vt paulo <lb></lb>ante deſcripſimus. </s>
          <s id="N13AB3">Dum enim iactatur ſimul cum nauigio <lb></lb>malus, ac propterea cogitur inclinari, obſtat quantum po<lb></lb>teſt antenna in ſuperiori eius parte alligata tanquam onus <lb></lb>incumbens, quod perpendiculariter ad mundi centrum gra<lb></lb>uitans, reſiſtit inclinationi, ne contra propriam rectitudinem, <lb></lb>ac naturalem propenſionem à perpendiculo deuians, obli<lb></lb>què ad latera vergat. </s>
        </p>
        <p id="N13AC2" type="main">
          <s id="N13AC4">Magis autem, aut minus valet reſiſtere, iuxta maiorem, <lb></lb>aut minorem diſtantiam, quam habet à ſede mali, vbi con<lb></lb>ſtituitur centrum ipſius motus circularis, quem ad commo<lb></lb>tionem nauigij per varios arcus conficit malus. </s>
          <s id="N13ACF">Quo enim <lb></lb>plus à centro, ſeu fulcimento diſceſſerit onus, eo difficilius <lb></lb>dimouetur: diſtabit autem tanto magis à ſede mali, ac fun<lb></lb>do nauis antenna, quantò altius ſublimatur. </s>
          <s id="N13AD8">Accedit quia <lb></lb>ſimul magis diſtabit à parte vbi vis incutitur malo in ſum<lb></lb>mo foramine nauis hinc inde illum impellentis: potentia <lb></lb>verò remotius ab onere applicata, quàm à fulcimento ve<lb></lb>ctis, minus illud mouere poteſt quando fulcimentum con<lb></lb>ſtituitur in altero vectis extremo: Vt ſi quiſpiam extremo <lb></lb>ſariſſæ alicubi obfirmato, ac manu prope ipſum extremum <lb></lb>illi admota, aliquod pondus altero extremo dimouere co<lb></lb>netur. </s>
          <s id="N13AEB">Antenna ergo remotiſſimè à loco vbi virtus impul<lb></lb>ſiua in malo refunditur collocata, difficillimè commouetur, <lb></lb><expan abbr="proindeq">proindeque</expan> ſimul cum illa totum nauigium cuius commotio<lb></lb>ni magis valebit obſtare. </s>
        </p>
        <p id="N13AF4" type="main">
          <s id="N13AF6">Quod ſanè verificatur in mediocri, vel modica fluctuum <lb></lb>eleuatione, vt conſultò innuimus; alioquin nimis extuante <lb></lb>mare, <expan abbr="nimisq.">nimisque</expan> obtumeſcentibus vndis, dum validè iactatur <lb></lb>nauigium, oppoſitum experimur. </s>
          <s id="N13B03">Tunc enim ſi antenna in <lb></lb>illo <expan abbr="diſtãtiori">diſtantiori</expan> ſitu conſtituatur, ac ſemel cum nauigio admo<lb></lb>dum inclinetur malus, ad totalem potius euerſionem con<lb></lb>duceret. </s>
          <s id="N13B10">Quandoquidem linea perpendicularis, qua onus <lb></lb>antennæ mundi centrum petit ob talem inclinationem, non <lb></lb>caderet intra nauigium, ſed foris à latere, quò propenſius <pb pagenum="124" xlink:href="005/01/132.jpg"></pb>tendendo antenna ipſa non modo amplius inclinationi ni<lb></lb>hil obſtaret, ſed vicem ſubiret potentiæ inclinantis eundem <lb></lb>malum tanquam vectem, &amp; cum illo totum nauigium cui <lb></lb>malus affigitur, eleuando ſcilicet alterum latus tanquam <lb></lb>onus impoſitum, alterum comprimendo veluti hypomo<lb></lb>chlion cui innititur, ex quo ſequeretur euerſio, atque ſum<lb></lb>merſio. </s>
        </p>
        <p id="N13B28" type="head">
          <s id="N13B2A">Quæſtio Septima.</s>
        </p>
        <p id="N13B2D" type="main">
          <s id="N13B2F">C<emph type="italics"></emph>vr quando ex puppi nauigare volue<lb></lb>rint, non flante ex puppi vento, veli qui<lb></lb>dem partem, quæ ad gubernatorem vergit, <lb></lb>conſtringunt: illam verò quæ proram verſus <lb></lb>eſt, pedem facientes relaxant? </s>
          <s id="N13B3F">An quia re<lb></lb>trahere quidem multò exiſtente vento guber<lb></lb>na culum non potest: pauco autem poteſt, quem conſtringunt? <lb></lb></s>
          <s id="N13B47">Propellit quidem igitur ipſe ventus: in puppim verò illum <lb></lb>constituit gubernaculum retrahens, &amp; mare compellens: ſi<lb></lb>mul &amp; nautæ ipſi cum vento contendunt: in contrarium enim <lb></lb>ſe reclinant partem.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N13B52" type="head">
          <s id="N13B54">COMMENTARIVS.</s>
        </p>
        <p id="N13B58" type="main">
          <s id="N13B5A">Cauſam hic inquirit Ariſtoteles cur nautæ ex puppi <lb></lb>antrorſum velo nauigare cupientes non flante ex <lb></lb>puppi vento, ſed puta ex latere, ſeu ex tranſuerſo, <lb></lb>velo quidem in altero atque oppoſito nauis latere conſtitu<lb></lb>to, partem eius, quæ ad puppim vergit vbi gubernator ad <lb></lb>clauum moderandum aſſiſtit, quantum fieri poteſt exten<lb></lb>dunt, ac fune reducto eius extrema conſtringunt: illam ve<lb></lb>rò quæ proram verſus eſt, ac tanquam inferiorem, pedem <lb></lb>ipſius veli conſtituunt, altero fune producto relaxant, ſeu <lb></lb>laxiorem eſſe ſinunt. </s>
          <s id="N13B6F"><expan abbr="Docetq.">Docetque</expan> ex eo id fieri, nam ſuppoſito <lb></lb>quod gubernaculum cum temone, multum impellente ven-<pb pagenum="125" xlink:href="005/01/133.jpg"></pb>to inclinare non poſſit nauigium quaſi in contrarium, ſicut cum <lb></lb>parum vel minus impellit; velo ſic conſtituto vt diximus, totus <lb></lb>penè impetus venti in eius partem, quæ ad puppim extenditur <lb></lb><expan abbr="tanquã">tanquam</expan> in ſinu excipitur atque colligitur, vbi propellit quidem <lb></lb>ex tranſuerſo, ſed cum magis appropinquetur temoni, quo ob<lb></lb>uiantibus fluctibus maris, nauis retrahitur in contrarium, minus <lb></lb>præualet, quàm ſi imprimeretur verſus proram, vel in totum ip<lb></lb>ſum velum vniformiter tenſum. </s>
          <s id="N13B8D"><expan abbr="Dumq.">Dumque</expan> nautæ mediante gu<lb></lb>bernaculo, ac temone, cum vento contendunt, in contrariam <lb></lb>partem proram reclinando, medium iter tenet nauigium, <expan abbr="per-gitq.">per<lb></lb>gitque</expan> antrorſum, quo ipſemet deſtinauerint nautæ. </s>
        </p>
        <p id="N13B9D" type="main">
          <s id="N13B9F">Hæc ex Ariſtotele, quæ vt clarius dilucidentur, ſit nauis AB, <lb></lb>cuius puppis A, prora verò B, gubernaculum obliquè conſti<lb></lb>tutum AC; temo ſimili<lb></lb><figure id="id.005.01.133.1.jpg" xlink:href="005/01/133/1.jpg"></figure><lb></lb>ter AD, malus E, ac ve<lb></lb>lum ſecundum <expan abbr="infimã">infimam</expan> ſui <lb></lb>oram, ſit curua linea FG, <lb></lb>lateraliter ventum exci<lb></lb>piens ex parte dextera <lb></lb>vbi H. </s>
          <s id="N13BBD">Tunc quaſi pugna <lb></lb><expan abbr="quædã">quædam</expan> <expan abbr="cõſideretur">conſideretur</expan> inter <lb></lb><expan abbr="ventũ">ventum</expan>, ac temonem. </s>
          <s id="N13BCE"><expan abbr="Nã">Nam</expan> <lb></lb>flante vento ex H, <expan abbr="naui-giũ">naui<lb></lb>gium</expan> transferri deberet in <lb></lb>oppoſitum, hoc eſt ſini<lb></lb>ſtrorſum verſus I per li<lb></lb>neam HLI. </s>
          <s id="N13BE3">Incidentibus <lb></lb>autem fluctibus maris in <lb></lb>alam temonis AD, prora <lb></lb>ex B conuerti deberet in H, circa ipſum <expan abbr="punctũ">punctum</expan> A <expan abbr="tanquã">tanquam</expan> cen<lb></lb>trum talis motionis obliquæ, vt probatum eſt. </s>
          <s id="N13BF6">Quoniam verò <lb></lb>neutrum præualet, nauis, medium curſum tenens, transfertur <lb></lb>antrorſum verſus K quo pergere, ac velificare cupiunt nautæ, <lb></lb>qui iccirco in tali poſitione nauim cum velo conſtituunt. </s>
        </p>
        <p id="N13BFF" type="main">
          <s id="N13C01">Cauſa verò cur neutrum præualeat hæc eſt: Nam ex vno ca<lb></lb>pite, licet temo, nauis <expan abbr="poſitionẽ">poſitionem</expan> immutet, ac inclinare eam va-<pb pagenum="126" xlink:href="005/01/134.jpg"></pb>leat obliquè, promouere tamen eam ipſam nequit, quo proram <lb></lb>reſpicientem conſtituit, <expan abbr="multoq.">multoque</expan> minus dum ventus inde validè <lb></lb>ſpirat. </s>
          <s id="N13C17">Quare in caſu propoſito, hoc tantum præſtat ala illa ob<lb></lb>uerſa temonis, quod eſt, eandem nauis <expan abbr="poſitionẽ">poſitionem</expan> obliquam ſer<lb></lb>uare contra impetum ſpiritus, quo certè prora <expan abbr="nõ">non</expan> minus quàm <lb></lb>puppis ad latus retrocedere cogeretur, <expan abbr="pariterq.">pariterque</expan> in oppoſitam <lb></lb><expan abbr="partẽ">partem</expan> abire. </s>
          <s id="N13C31">Ex alio verò capite licet ventus æquè incidat in to<lb></lb>tum <expan abbr="velũ">velum</expan>, ac vehementer pellat ex tranſuerſo: nihilo minus pro<lb></lb>pter explicatam veli poſitionem totum ferè ſe confert in par<lb></lb>tem ad puppim <expan abbr="vergentẽ">vergentem</expan>, quæ ſublimior, ac latior eſt, <expan abbr="ſinumq.">ſinumque</expan> <lb></lb>maiorem efficit, ex quo impetus quaſi retortus refunditur in <lb></lb>latus verſus proram, vt in LB, quo proinde latere nauis fertur <lb></lb>antrorſum ſuper lineam E K. </s>
        </p>
        <figure id="id.005.01.134.1.jpg" xlink:href="005/01/134/1.jpg"></figure>
        <p id="N13C52" type="main">
          <s id="N13C54">Retorqueri autem im<lb></lb>pulſum prędictum ex eo <lb></lb>contingit, quia <expan abbr="tã">tam</expan> infima <lb></lb>veli ora ab E <expan abbr="vſq;">vſque</expan> ad G, <lb></lb>quàm <expan abbr="antẽna">antenna</expan> à loco vbi <lb></lb>malo alligatur vſque ad <lb></lb><expan abbr="ceruchũ">ceruchum</expan>, ſeu cornu eius, <lb></lb>quod in <expan abbr="altũ">altum</expan> extollitur, <lb></lb>ſemper patitur magis à <lb></lb>vento perflante, quàm <lb></lb>pars tam veli; quàm an<lb></lb>tennæ, quæ eſt ab E in F <lb></lb>verſus <expan abbr="prorã">proram</expan>: nam inde <lb></lb>potius fugit <expan abbr="atq;">atque</expan> elabitur <lb></lb>ventus ob maiorem di<lb></lb>rectionem, quam ſeruat <lb></lb>erga ipſum ventum, quem non ita in faciem excipit, ſicut pars <lb></lb>concaua, quæ ad puppim vergit. </s>
          <s id="N13C94">Dum autem patitur, ac percu<lb></lb>titur magis cum velo, antennæ pars, quæ eſt à malo ad cornu, <lb></lb>verbi gratia in ſiniſtra, tanquam ſi moueretur circa ipſum <expan abbr="malũ">malum</expan> <lb></lb>veluti ſemidiameter circa centrum, vertere nititur nauigium in <lb></lb><expan abbr="contrariũ">contrarium</expan>, hoc eſt dextrorſum, quia vim accipit à ſiniſtra. </s>
          <s id="N13CA6">Vnde <lb></lb>impulſus quaſi retortus aliquantulum in gyrum, nauem ipſam <pb pagenum="127" xlink:href="005/01/135.jpg"></pb>non quidem ſiniſtrorſum, ſed antrorſum præualet commouere. <lb></lb></s>
          <s id="N13CB1">Id quod clariùs hic licebit inſpicere in delineata figura eiſdem <lb></lb>fermè litteris, quibus ſuperior conſignata. </s>
        </p>
        <figure id="id.005.01.135.1.jpg" xlink:href="005/01/135/1.jpg"></figure>
        <p id="N13CBB" type="main">
          <s id="N13CBD">Cæterum ex his <lb></lb>patet, quàm rectè <lb></lb>Ariſtoteles docuerit <lb></lb>ex eo nautas veli <lb></lb>partem verſus <expan abbr="prorã">proram</expan> <lb></lb>pedem facere, ac re<lb></lb>laxare, hoc eſt ex eo <lb></lb>partem veli inferio<lb></lb>rem <expan abbr="tanquã">tanquam</expan> pedem <lb></lb>verſus <expan abbr="prorã">proram</expan> collo<lb></lb>care, ac funibus mi<lb></lb>nus adducere; ſupe<lb></lb>riorem verò quæ <expan abbr="lõ-gè">lon<lb></lb>gè</expan> maior eſt verſus <lb></lb>puppim retrahere, &amp; <lb></lb>alligare, quia ſi vtramque partem veli ęquatameſſe paterentur, <lb></lb>malus vtrinque propulſus æquè etiam propelleretur. </s>
          <s id="N13CF0">Cumque <lb></lb>propulſus totus eſſet in directum à latere dextro, vel ſiniſtro, <lb></lb>nauis per illam pergere non poſſet antrorſum. </s>
          <s id="N13CF7">Accedit quia <lb></lb>ſi æqualis, vel maior impetus incuteretur in proram, non tam <lb></lb>facilè temo illam poſſet retrahere in contrarium. </s>
          <s id="N13CFE">Siquidem <lb></lb>magis diſtaret à fulcimento, ac centro, quod conſtituitur in <lb></lb>cuſpide puppis. </s>
          <s id="N13D05">Vnde quo magis velum appropinquatur pup<lb></lb>pi, eo magis temo præualet contra impulſum ventorum ad <lb></lb>conuertendam nauim obliquè. </s>
        </p>
        <p id="N13D0C" type="main">
          <s id="N13D0E">Quod autem ait Piccolomineus, in hac motione nauis cari<lb></lb>nam vectis vicem obtinere, quæ centro grauitatis ipſius nauis <lb></lb>tanquam fulcimento innixa mare mouente, ac impellente te<lb></lb>monem, ventum in prora ſuſtineat tanquam onus, valde ambi<lb></lb>guum eſt. </s>
          <s id="N13D1A">Tum quia non minus ventus per velum, quàm ma<lb></lb>re per temonem poteſt habere rationem potentiæ mouentis. <lb></lb></s>
          <s id="N13D20">Tum etiam quia ventus præcipuè non ſuſtinetur in prora, ſed <lb></lb>potius in parte veli, quæ vergit ad puppim, vt dictum eſt. </s>
        </p>
        <pb pagenum="128" xlink:href="005/01/136.jpg"></pb>
        <p id="N13D29" type="main">
          <s id="N13D2B">Ex dictis etiam licebit duas alias veluti affines quæſtiones <lb></lb>diluere. </s>
          <s id="N13D30">Vna eſt, cur flante ex latere vento, <expan abbr="veloq.">veloque</expan> cum malo <lb></lb>ad latus oppoſitum inclinante, non ſequatur nauis ſubmerſio? <lb></lb></s>
          <s id="N13D3A">Quamuis enim nautæ cum cæteris nauigantibus ideo in latus <lb></lb>nauis, quod verſus ventum eſt, ſe conferant, vt proprio onere <lb></lb>compenſetur impetus veli, ac pondus mali in oppoſitum incli<lb></lb>nantis: Nihilominus hoc non videtur ſufficere, attenta vehe<lb></lb>mentia ſpiritus impellentis, <expan abbr="magnaq.">magnaque</expan> vi quam exhibet malus <lb></lb>dum ſe conuertit, tanquam vectis ad latus illud quod deprimit. <lb></lb></s>
          <s id="N13D4C">Reſpondetur tamen iuxta prædicta, quod malus licet incline<lb></lb>tur ad latus præſcriptum, non vrget ſecundum ipſam inclina<lb></lb>tionem verſus idem latus directè, ſed verſus proram, vel oram <lb></lb>lli propinquam, propter rationem adductam; eo ſcilicet, quod <lb></lb>ſinu veli obliquato non minus ex parte eiuſdem lateris ventus <lb></lb>ibi collectus impellat, <expan abbr="modereturq.">modereturque</expan> proinde impetus in pedem <lb></lb>eiuſdem antennæ ex alia parte, ne ad latus oppoſitum malus <lb></lb>ipſe omnino cogatur nauem inflectere. </s>
        </p>
        <p id="N13D61" type="main">
          <s id="N13D63">Altera verò quæſtio eſt, cur nauis hunc prout deſcripſimus <lb></lb>curſum ſeruando, ſecurius incedat, <expan abbr="minusq.">minusque</expan> ſubmerſioni ſit ob<lb></lb>noxia, quàm cum ex puppi flante <expan abbr="vẽto">vento</expan> recta procedit? </s>
          <s id="N13D72">Id quod <lb></lb>inexpertis <expan abbr="mirũ">mirum</expan> videri ſolet, <expan abbr="cũ">cum</expan> quippe talis inclinatio, qua ſæ<lb></lb>pè <expan abbr="etiã">etiam</expan> mare intus excipitur, <expan abbr="ſubmerſionẽ">ſubmerſionem</expan> potius minetur, <expan abbr="quã">quam</expan> <lb></lb><expan abbr="ſecuritatẽ">ſecuritatem</expan> polliceatur. </s>
          <s id="N13D92">Contrà verò ſecundis ventis <expan abbr="æquatisq.">æquatisque</expan> <lb></lb>velis <expan abbr="abſq.">abſque</expan> vlla nauis inclinatione <expan abbr="progrediẽdo">progrediendo</expan>, nullus appareat <lb></lb>caſus pertimeſcendus. </s>
          <s id="N13DA5">Sed facilis eſt reſponſio; <expan abbr="nã">nam</expan> velo ad pro<lb></lb>ram laxato, <expan abbr="ventisq.">ventisque</expan> ſecundis <expan abbr="obtumeſcẽti">obtumeſcenti</expan>, plus <expan abbr="quandoq.">quandoque</expan> <expan abbr="cõ-tingit">con<lb></lb>tingit</expan> ſe ad vnum, quam ad <expan abbr="alterũ">alterum</expan> latus inflectere, eo quod ne<lb></lb>queat tam antenna, quàm velum exactè in duas partes ęquales <lb></lb>vtrinque ad malum diſtribui. </s>
          <s id="N13DC8">Cumque in hac latione qua nauis <lb></lb>recta è puppi mouetur in proram, temo ſcindat quidem mare <lb></lb>obuium eodem pacto in <expan abbr="directũ">directum</expan>, ſed illud non excipiat ad dex<lb></lb>teram, aut ſiniſtram, nec ideo vim alienam inferat naui circa <lb></lb>curſus <expan abbr="moderationẽ">moderationem</expan> per proræ <expan abbr="conuerſionẽ">conuerſionem</expan>: hinc fit, vt repen<lb></lb>tino ſuperueniente impetu vehementi, atque in vnam magis <lb></lb>quàm in alteram veli partem incuſſo, ob aptiorem poſitionem <lb></lb>illius, aut magnitudinem maiorem; facilè totum nauigium à re-<pb pagenum="129" xlink:href="005/01/137.jpg"></pb>ctitudine viæ deuiet, <expan abbr="moxq.">moxque</expan> ſe vnà cum malo ad latus, ad <lb></lb>quod pars illa maior vergerit, omnino declinando demer<lb></lb>gat; niſi protinus obſtauerit gubernator per conuerſionem <lb></lb>temonis, compellendo proram, ac reclinando illam ver<lb></lb>ſus eandem partem, in qua ſequeretur ſubmerſio, ac vn<lb></lb>de deflexerat, vt ventus à tergo ſpirans, ex æquo velum fe<lb></lb>riat in prora, <expan abbr="propellatq.">propellatque</expan> recta nauigium ſicut prius. </s>
        </p>
        <p id="N13DFE" type="head">
          <s id="N13E00">Quæſtio Octaua.</s>
        </p>
        <p id="N13E03" type="main">
          <s id="N13E05">C<emph type="italics"></emph>vr ex figurarum genere quæcunque rotun<lb></lb>dæ ſunt, &amp; circinatæ, facilius mouentur? <lb></lb></s>
          <s id="N13E0E">Trifariam autem circulum rotari contingit. <lb></lb></s>
          <s id="N13E12">Aut enim ſecundum abſidem centro ſimul mo<lb></lb>to, quemadmodum plauſtri vertitur rota: aut <lb></lb>circa manens centrum, veluti trochleæ ſtante <lb></lb>centro, aut in pauimento manente centro, ſicut figuli rota con<lb></lb>vertitur: an celerrima quidem huiuſmodi ſunt, quoniam par<lb></lb>ia ſui parte planum contingunt, veluti circulus ſecundum <lb></lb>punctum, &amp; quoniam non offenſant. </s>
          <s id="N13E21">A terra enim ſemotus eſt <lb></lb>angulus. </s>
          <s id="N13E26">Præterea etiam cui obuiam fiunt corpori, id rurſum <lb></lb>ſecundum puſillum tangunt. </s>
          <s id="N13E2B">Si autem rectilineum eſſet, re<lb></lb>ctitudine ſua multum plani contingeret. </s>
          <s id="N13E30">Ad hæc quo nutat <lb></lb>pondus, eò motor mouet. </s>
          <s id="N13E35">Cùm igitur ad rectum ſuper plano <lb></lb>circuli fuerit diameter, planum ſecundum punctum contin<lb></lb>gente circulo æquale vtrinque pondus diſterminat diameter. <lb></lb></s>
          <s id="N13E3D">Cùm autem mouetur plus illico, ad quod mouetur, ceri inde nu<lb></lb>tans, ab impellente facilius in ante mouetur. </s>
          <s id="N13E42">Quo enim vnum<lb></lb>quodque vergit, mouetur ex facili. </s>
          <s id="N13E47">Siquidem difficulter ad <lb></lb>contrarium nutus ſui mouetur motum. </s>
          <s id="N13E4C">Praeterea nonnulli <lb></lb>autumant, quod circule linea in perpeti verſatur motu, quem<lb></lb>admodum manentia propter contrarium nixum manent: ſicut <lb></lb>maioribus contingit circulis ad minores. </s>
          <s id="N13E55">Celeriùs enim ab <lb></lb>æquali mouentur potentia maiores circuli, <expan abbr="mouentq.">mouentque</expan> onera, <lb></lb>quoniam circuli maioris angulus ad minoris angulum, circu<lb></lb>li nutum habet quendam: &amp; ſicut diameter ad diametrum, <lb></lb>ita maior circulus ad minorem. </s>
          <s id="N13E64">Infiniti autem ſunt minores. <lb></lb></s>
          <s id="N13E68">Si autem ad alterum nutum habet circulus, ſimiliter eſt benè <lb></lb>mobilis. </s>
          <s id="N13E6D">Et aliam ſanè habet inclinationem circulus, &amp; ea<emph.end type="italics"></emph.end><pb pagenum="130" xlink:href="005/01/138.jpg"></pb><emph type="italics"></emph>quæ à circulo mouentur, licet planitiem abſide non contingat, <lb></lb>ſed aut iuxta planitiem, aut ueluti trochleæ. </s>
          <s id="N13E7D">Etenim hoc ſe <lb></lb>habentes modo facillimè mouentur, &amp; onera commouent. </s>
          <s id="N13E82">An <lb></lb>quia parua ſui portione cùm tangit, tum offenſat circulus, ſed <lb></lb>aliam ob cauſam? </s>
          <s id="N13E89">ea autem eſt, quæ dicta est prius, quod circu<lb></lb>lus ſcilicet ex duabus effectus eſt lationibus: quamobrem il<lb></lb>larum alteram pro nutu ſemper habet, &amp; veluti continuò mo<lb></lb>tum illum moueat quicumque mouent, quando ſecundum cir<lb></lb>cumferentiam illum mouerint: latam enim ipſam mouent. <lb></lb></s>
          <s id="N13E95">Eam quidem igitur, quæ in obliquum eſt, motionem, ipſum <lb></lb>impellit mouens: ſecundum verò illam, quæ ſuper diametrum <lb></lb>est, ſe ipſum mouet circulus.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N13E9E" type="head">
          <s id="N13EA0">COMMENTARIVS.</s>
        </p>
        <p id="N13EA4" type="main">
          <s id="N13EA6">Vt quæſtioni reſpondeat Ariſtoteles cur corpora, <lb></lb>quæ rotundam, aut orbiculatam figuram obtinent, <lb></lb>ſecundum illam facilius moueantur, triplicem mo<lb></lb>dum diſtinguit, quo ipſa moueri rotando contingit. </s>
          <s id="N13EAF"><expan abbr="Pri-mumq.">Pri<lb></lb>mumque</expan> eſſe docet, quo ſecundum abſidem, ſeu extimam ip<lb></lb>sorum curuaturam cientur, moto ſimul etiam centro, vt <lb></lb>plauſtrorum rotæ, quæ ſimul cum axe feruntur. </s>
          <s id="N13EBB">Secundum <lb></lb>verò modum, ait eſſe illum, quo circularia ipſa corpora re<lb></lb>cta quidem ſtantia, ſeu rectè ad horizontem conſtituta mo<lb></lb>uentur circa centrum immotum; veluti ſtantes trochlea<lb></lb>rum rotulæ, quæ circa manentem axem, ſeu centrum ad di<lb></lb>uerſos vſus conuertuntur. </s>
          <s id="N13EC8">Tertium denique modum eſſe <lb></lb>inquit, quo circa immotum pariter centrum mouentur, non <lb></lb>tamen ſtando, ſed quaſi proſtrata iuxta planitiem ſoli, aut <lb></lb>pauimenti horizonti paralellam; ſicut rota figuli, quæ ad <lb></lb>impulſum pedis illius conuertitur, ac circumagitur ſupra <lb></lb>axim pauimento perpendiculariter affixum, ſeruando ſem<lb></lb>per eandem diſtantiam ab horizonte. </s>
        </p>
        <p id="N13ED7" type="main">
          <s id="N13ED9">Loquendo itaque de primo modo, pluribus ex cauſis, ait <lb></lb>Ariſtoteles præfata corpora celerius, ac facilius moueri <lb></lb>quàm illa, quæ rectilineas adepta ſunt figuras, ſeu rectilineis <lb></lb>figuris terminantur, vt triangulari, vel quadrangulari, pirami-<pb pagenum="131" xlink:href="005/01/139.jpg"></pb>des, &amp; cubi. </s>
          <s id="N13EE7">Prima eſt, quia minima ſui parte planum con<lb></lb>tingunt hoc eſt minori, quam cuiuſlibet alterius figuræ cor<lb></lb>pora, reſpectu, verbi gratia ſphæræ, quæ planum tangit in <lb></lb>puncto. </s>
          <s id="N13EF0">Secunda verò eſt, quia hoc pacto non offendunt, aut <lb></lb>impingunt niſi ſcilicet rarius, ac difficilius; A terra enim ſe<lb></lb>motus eſt angulus, inquit Ariſtoteles, nimirum angulum <lb></lb>contingentiæ, ſeu contactus, quia poſt punctum contingen<lb></lb>tiæ, totum latus curuilineum ipſorum corporum orbicula<lb></lb>rium, quod cum plano conſtituit huiuſmodi angulum, è ter<lb></lb>ra eleuatur; ac propterea minus impingunt in offendicula, <lb></lb>quàm alia corpora, quorum latera <expan abbr="nõ">non</expan> ſtatim poſt minimum <lb></lb>contactum eleuantur, ſed ipſi plano, ſeu terræ adhærent. <lb></lb></s>
          <s id="N13F08">Tertia cauſa eſt, nam huiuſmodi corpora cuicunque ob<lb></lb>uient offendiculo, illud pariter nonniſi ſecundum puſillam <lb></lb>ſui partem attingunt, eadem ratione, qua planum, ſeu ſolum <lb></lb>ſuper quod ipſa mouentur, ſecus, ac rectilineam figuram ha<lb></lb>bentia, quæ ſemper ſua rectitudine ſecundum magnam, vel <lb></lb>ſaltem maiorem partem contingunt. </s>
        </p>
        <p id="N13F15" type="main">
          <s id="N13F17">Ad hæc quartam cauſam addit Ariſtoteles. </s>
          <s id="N13F1B">Nam (inquit) <lb></lb>quò nutat pondus, eo motor mouet. </s>
          <s id="N13F20">Hoc eſt, quia motor <lb></lb>dum huiuſmodi corpora rotunda, vel ſphærica ſecundum <lb></lb>abſidem mouet, eo profectò impellit, quo ſtatim ipſorum <lb></lb>pondus propendit ſiue inclinat. </s>
          <s id="N13F29">Etenim ſi conſtituatur ſu<lb></lb>per planum AB horizonti <lb></lb><figure id="id.005.01.139.1.jpg" xlink:href="005/01/139/1.jpg"></figure><lb></lb>paralellum erecta aliqua <lb></lb>rota, vt CDEF tanquam <lb></lb>circulus, eius diameter à <lb></lb>contactu plani vbi C per<lb></lb>pendiculariter ad angulos <lb></lb>rectos per centrum ſupra <lb></lb>traſcendens ad D, totam <lb></lb>rotam eiuſque pondus in <lb></lb>duas partes æquales diſtri<lb></lb>buet, nempe in DFC, &amp; <lb></lb>DEC. <expan abbr="Eritq.">Eritque</expan> ipſa rota in <pb pagenum="132" xlink:href="005/01/140.jpg"></pb>æquilibrio, quia non magis vna quam altera pars vtrinque <lb></lb>à perpendiculo DC grauitare poteſt. </s>
          <s id="N13F55">Quod ſi impulſus <lb></lb>quamuis perexiguus in ipſam rotam à motore incutiatur, <lb></lb>vt ex parte E verſus F, ſtatim pars vbi F nutabit ac pro<lb></lb>pendet verſus B; <expan abbr="ſuoq.">ſuoque</expan> nutu, totam rotam ſecum trahet il<lb></lb>luc. </s>
          <s id="N13F64">Nam quælibet vis poteſt æquiponderantia ab æquili<lb></lb>brio dimouere. </s>
          <s id="N13F69">Semel autem mota ipſa rota, niſi impe<lb></lb>diatur deinceps nutabit ad partem verſus quàm primò fuit <lb></lb>incitata; ideoque facilè vlterius atque vlterius mouebitur. <lb></lb></s>
          <s id="N13F71">Quo enim vnumquodque vergit, mouetur ex facili, ſubdit <lb></lb>ipſe Philoſophus, ſicut vice verſa difficulter in contrarium; <lb></lb>vt fuſius conſtabit quæſt. </s>
          <s id="N13F78">31. </s>
        </p>
        <p id="N13F7B" type="main">
          <s id="N13F7D">Atque hæc dicta intelliguntur de motu rotæ, aut ſphæræ <lb></lb>ſuper planum horizonti paralellum. </s>
          <s id="N13F82">Nam ſuper planum <lb></lb>quodlibet decliue, euidentius idem conſtabit. </s>
          <s id="N13F87">Siquidem <lb></lb>demiſſa tantum rota, vel ſphæra ſuper illud, ſuo ſemper nu<lb></lb>tu celerrimè deorſum rotando ſe conferet, imò in præceps <lb></lb>quandoque decurret. </s>
          <s id="N13F90">Cum enim huiuſcemodi corpora per <lb></lb>eam lineam maximè grauitent, quæ perpendiculariter ab <lb></lb>eorum centro tendit ad centrum mundi, ſi ſuper decliue <lb></lb>planum conſtituantur, nequibunt ſecundum eandem li<lb></lb>neam fulciri, ac ſuſtineri ab ipſo plano. </s>
          <s id="N13F9B">Nam punctum cir<lb></lb>cumferentiæ per quod ipſa linea cadit ad centrum mundi, <lb></lb>&amp; cui totum ferè onus incumbit, ſemper manebit ſuſpen<lb></lb>ſum ſupra planum ex parte inferiori ipſius, nec vnquam <lb></lb>planum ipſum decliue continget. </s>
          <s id="N13FA6">Circulus enim vel glo<lb></lb>bus non tangit planum, niſi in puncto in quod eius diame<lb></lb>ter incidit ad angulos rectos; quo ſanè pacto cadere non <lb></lb>poteſt perpendicularis tendens ad mundi centrum in pla<lb></lb>num, quod non eſt horizonti paralellum. </s>
          <s id="N13FB1">Cumque præ<lb></lb>dictum punctum, cui potiſſimum onus incumbit, ſuſtineri <lb></lb>non poſſit ab eo, quod non contingit; hinc fit, vt ſemper <lb></lb>verſus inferiores partes decliues propendat, ac nutet, de<lb></lb>feratque propterea ipſa orbiculata corpora quouſque ab <lb></lb>alio fulciatur. </s>
          <s id="N13FBE">Vt perſpicuè apparebit in propoſita ſphæra <pb pagenum="133" xlink:href="005/01/141.jpg"></pb>vel rota ABC, ſi decliue <lb></lb><figure id="id.005.01.141.1.jpg" xlink:href="005/01/141/1.jpg"></figure><lb></lb>planum DE contingat in <lb></lb>C ad angulos rectos ipſius <lb></lb>diametri BC: linea verò <lb></lb>cadens per centrum ipſius <lb></lb>ſphæræ ad centrum mundi, <lb></lb>ſit AF. </s>
          <s id="N13FD9">Nam ſic totum fe<lb></lb>rè onus incumberet in pun<lb></lb>cto G, quod cum fulciri <lb></lb><expan abbr="nõ">non</expan> poſſit in ipſa DE, quam <lb></lb>nullo modo tangit, neceſſa<lb></lb>riò <expan abbr="propẽdet">propendet</expan> in F, <expan abbr="rapietq.">rapietque</expan> <lb></lb>ſecum ad partes E totum <lb></lb>globum, qui deinceps rur<lb></lb>ſus eadem ratione nutabit per aliud ſimile punctum, <expan abbr="infe-tiusq.">infe<lb></lb>riusque</expan> citiſſimo curſu deſcendet ſuccedentibus ſibi ad inui<lb></lb>cem punctis, ac partibus. </s>
        </p>
        <p id="N13FFF" type="main">
          <s id="N14001">Ex hac autem maxima aptitudine, quam rotæ, vel ſimilia <lb></lb>orbiculata corpora habent ad motum, occaſionem ſumpſiſ<lb></lb>ſe videntur nonnulli arbitrandi, circuli periferiam nunquam <lb></lb>quieſcere, ſed perpetuo motu cieri, vt hic ſubiungit Ariſto<lb></lb>teles. </s>
          <s id="N1400E">Quia ſcilicet circulus contrarium nixum non habet, <lb></lb>quo reſiſtat motui, aut motori ſicut corpora manentia, quæ <lb></lb>ex eo quieſcunt, vel manent, quia habent, in quo contra ni<lb></lb>tantur, &amp; quo obſiſtant motui, ac mouenti. </s>
          <s id="N14017">Vbi addendum <lb></lb>quippe fuiſſet ab Ariſtotele, falsò eos ita putare; nam licet <lb></lb>circuli periferia nixum non habeat, quo retardetur, aut im<lb></lb>pediatur à proprio motu; non tamen ſemper habet in ſe <lb></lb>principium proximum, ac formale ſui motus, quod certè <lb></lb>cum ſit qualitas impetus impreſſi, hæc paulatim ex ſe re<lb></lb>mittitur, ac tandem deficit, vt patet in proiectis, quæ iccirco <lb></lb>deſiſtunt à motu. </s>
        </p>
        <p id="N14028" type="main">
          <s id="N1402A">Præterea Philoſophus doctrinam de mobilitate prædi<lb></lb>ctorum corporum proſequendo, docet maiores circulos, <lb></lb>mobiliores eſſe minoribus. </s>
          <s id="N14031">Celerius enim (inquit) ab æqua<lb></lb>li mouentur potentia, <expan abbr="mouentq.">mouentque</expan> onera. </s>
          <s id="N1403A"><expan abbr="Cauſamq.">Cauſamque</expan> eam eſſe <pb pagenum="134" xlink:href="005/01/142.jpg"></pb>ſubnectit; quoniam ſemper angulus circuli maioris, nutum <lb></lb>quendam habet ad angulum circuli minoris (in eo ſcilicet <lb></lb>contenti circa idem centrum.) Et ſicut diameter ad diame<lb></lb>trum, ita maior circulus, ſeu potius circumferentia ad mino<lb></lb>rem: In quolibet autem circulo maiori, infiniti circuli mi<lb></lb>nores continentur. </s>
          <s id="N1404F">Quo igitur maiores fuerint ipſi circuli, <lb></lb><expan abbr="maioremq.">maioremque</expan> proinde nutum, ſeu inclinationem ad minores <lb></lb>contentos habuerint, eo facilius, ac celerius mouebuntur. </s>
        </p>
        <p id="N14059" type="main">
          <s id="N1405B">Sed vt clarius hic Philoſophi diſcurſus innoteſcat, obſer<lb></lb>uandum eſt, per angulum circuli ſiue maioris, ſiue minoris, <lb></lb>non rectè intelligi ſectorem, vt cum Piccolomineo inter<lb></lb>pretatur Baldus. </s>
          <s id="N14065">Nam ſector circuli maioris eundem an<lb></lb>gulum conſtituit cum ſectore circuli minoris in eo conten<lb></lb>ti; Ariſtoteles autem loquitur de angulo circuli maioris, ac <lb></lb>de angulo circuli minoris tanquam de diuerſis, dum ait <expan abbr="vnũ">vnum</expan> <lb></lb>habere nutum ad alterum; alioquin perperam comparaſſet <lb></lb>idem ad idem formaliter. </s>
          <s id="N14076">Quod ſi aliunde ſectores ipſi dif<lb></lb>ferant inter ſe, vt reuera differunt in linearum longitudine, <lb></lb>ac ſpatio intercepto, ſecundum illam <expan abbr="rationẽ">rationem</expan> qua differunt, <lb></lb>&amp; non ſecundum angulum, in quo conueniunt Ariſtoteles <lb></lb>loquutus fuiſſet ad probandam differentiam motus circuli <lb></lb>maioris reſpectu minoris. </s>
          <s id="N14087">Nec per angulum circuli inter<lb></lb>pretari poſſumus <expan abbr="cũ">cum</expan> Blancano ipſius ſectoris arcum eo quod <lb></lb>opponatur angulo, qui eſt in centro circuli. </s>
          <s id="N14092">Siquidem fru<lb></lb>ſtra ſignificaretur oppoſitum per <expan abbr="nomẽ">nomen</expan> eius, cui opponitur, <lb></lb>cum vtrum que habeat ſuum vocabulum. </s>
          <s id="N1409D">Et eadem ratione <lb></lb>per angulum trianguli, poſſet intelligi latus illi oppoſitum, <lb></lb>quod eſſet inuertere omnem proprietatem terminorum de <lb></lb>mente Ariſtotelis. </s>
        </p>
        <p id="N140A7" type="main">
          <s id="N140A9">Potius ergo per angulum circuli, de quo hic loquitur Ari<lb></lb>ſtoteles, intelligi videtur angulus, qui ex diametro, vel ſe<lb></lb>midiametro, ac portione circumferentiæ efficitur, quem an<lb></lb>gulum Euclides vocat etiam angulum ſemicirculi in 16. <lb></lb>prop.

tertij. </s>
          <s id="N140B4">Etenim iuxta hanc acceptionem angulus cir<lb></lb>culi maioris non eſt idem cum angulo circuli minoris, opti<lb></lb>mèque intelligitur; &amp; explicatur nutus, quem Philoſophus <pb pagenum="135" xlink:href="005/01/143.jpg"></pb>docet habere iſtum ad illum. </s>
          <s id="N140C0">Hoc eſt propenſio, quam an<lb></lb>gulus circuli maioris habet ſupra angulum circuli minoris <lb></lb>circa idem centrum deſcripti, vt celerius, ac facilius cum. <lb></lb></s>
          <s id="N140C8">illo, ac toto circulo ſecundùm abſidem moueatur. </s>
        </p>
        <p id="N140CB" type="main">
          <s id="N140CD">Eſto enim circulus maior ABCD, minor verò EFGH, <lb></lb>circa idem centrum I ſupra planum KL. </s>
          <s id="N140D3">Diameter au<lb></lb>tem maioris circuli ſit AC, minoris EG. </s>
          <s id="N140D8">Angulus item <lb></lb>maioris ACD; minoris ve<lb></lb><figure id="id.005.01.143.1.jpg" xlink:href="005/01/143/1.jpg"></figure><lb></lb>rò EGH. </s>
          <s id="N140E6">Dicimus ergo an<lb></lb>gulum ACD habere nu<lb></lb>tum quendam, &amp; inclina<lb></lb>tionem ſupra angulum <lb></lb>EGH, qua, &amp; ſe ipſum, &amp; <lb></lb>illum procliuiorem reddit <lb></lb>ad motum ſecundum abſi<lb></lb>dem ſuper planum KL, ſi <lb></lb>circulus ipſe maior per im<lb></lb>pulſum motoris verſus L <lb></lb>moueatur. </s>
          <s id="N140FD">Porrò angulus <lb></lb>ACD, tam ex parte diametri, vel ſemidiametri, quàm ex <lb></lb>parte portionis circumferentiæ, ex quibus tanquam ex duo<lb></lb>bus lateribus conſtat, velocius, ac facilius poteſt moueri, <lb></lb>quàm angulus EGH. </s>
          <s id="N14109">Ex parte quidem ſemidiametri, ſeu <lb></lb>lateris recti; quia extremum C magis elongatur à centro <lb></lb>I quàm G. </s>
          <s id="N14111">Ex parte verò portionis circunferentiæ, ſeu la<lb></lb>teris curui; quia CD magis etiam diſtat ab eodem centro, <lb></lb>ac minus curuatur, quàm GH; <expan abbr="minusq.">minusque</expan> proinde retrahitur <lb></lb>nè moueatur motu naturali, ad rectum ſcilicet magis ap<lb></lb>propinquanti ideoque velocius ac facilius. </s>
          <s id="N14120">Sed angulus C <lb></lb>inclinari non poteſt verſus L quin ſecum rapiat angulum <lb></lb>G, quem intra ſe continet. </s>
          <s id="N14127">Igitur angulus ipſe C, nutum, <lb></lb>&amp; propenſionem habet ad angulum G, vt ſimul ac facilius <lb></lb>moueantur modo quo diximus ad quemlibet impulſum <lb></lb>motoris. </s>
          <s id="N14130">Cumque infiniti ſint huiuſmodi anguli in explica<lb></lb>tis circulis, hinc ſit, vt rectè ex illis concludat Ariſtoteles, <lb></lb>mobiliores eſſe circulos maiores, ac celerius moueri ab ea<pb pagenum="136" xlink:href="005/01/144.jpg"></pb>dem, vel æquali potentia; ſicut celerius mouentur maiores <lb></lb>libræ, quàm minores ab eodem, vel æquali pondere. </s>
          <s id="N1413E">Non <lb></lb>enim aliter ſe habet circulus ſtans ſuper planum, quàm libra <lb></lb>ſupra fulcimentum in æquilibrio conſtituta. </s>
        </p>
        <p id="N14145" type="main">
          <s id="N14147">At Ariſtotelem per angulos circuli intelligere angulos <lb></lb>à nobis explicatos, illud confirmat, quod cum dixiſſet an<lb></lb>gulum circuli maioris habere nutum ad angulum circuli <lb></lb>minoris, quaſi id probans ait: Et ſicut diameter ad diame<lb></lb>trum, ita circumferentia ad circumferentiam. </s>
          <s id="N14153">In quibus <lb></lb>verbis vtrumque ipſorum angulorum latus comprehendit <lb></lb>nempe rectum, &amp; <expan abbr="curuũ">curuum</expan>. </s>
          <s id="N1415E"><expan abbr="Idemq.">Idemque</expan> eſt, ac dicere, quia <expan abbr="cũ">cum</expan> præ<lb></lb>dicti anguli conſtent ex huiuſmodi lateribus, ſicut latera ma<lb></lb>iora, eo quod magis diſtent à centro, velocius mouentur; ita <lb></lb>pariter angulus ex illis conſtitutus, velocius mouebitur; ma<lb></lb>gis enim diſtat à centro extremum diametri maioris, quàm <lb></lb>minoris, ſimiliter que portio maioris circumferentiæ ab illo <lb></lb>deſcriptæ, quàm minoris, vt per ſe patet. </s>
        </p>
        <p id="N14174" type="main">
          <s id="N14176">Quod autem Baldus obijcit Ariſtoteli, prædictum nu<lb></lb>tum, quem ipſe gratis explicat per angulos sectores, nul<lb></lb>lam arguere maiorem mobilitatem circuli maioris, eo quod <lb></lb>quantum vnus ſector adiuuat deſcenſum ex vna parte, tan<lb></lb>tum alter oppoſitus retardet aſcenſum ex alia, nihil con<lb></lb>uincit. </s>
          <s id="N14183">Nam idem dici poſſet de extremitate diametri lon<lb></lb>gius à centro diſtante, vt nihil conferat ad maiorem veloci<lb></lb>tatem, eo quod altera extremitas tantundem debeat retar<lb></lb>dare; Quod ſanè falſum eſt, quoniam tam in illo, quàm in <lb></lb>iſto motu ſupponitur impetus aliquis impreſſus, virtute cu<lb></lb>ius motus ipſe exerceatur, ac vna pars circuli, vel diametri <lb></lb>ſuperet aliam æqualem. </s>
          <s id="N14192">Alioquin ſicut ſola maior diſtan<lb></lb>tia extremitatis diametri non ſufficit ad motum illius; ita <lb></lb>nec maior nutus circuli maioris. </s>
          <s id="N14199">Vtrumque tamen confert <lb></lb>ad velocitatem ſuppoſito motu. </s>
          <s id="N1419E">Nam virtus illa impreſſa <lb></lb>nutu proprio ipſius circuli adiuta, efficacius operatur in ea <lb></lb>parte vbi imprimitur, vel in quam prius impreſſa fuerit à <lb></lb>motore. </s>
        </p>
        <p id="N141A8" type="main">
          <s id="N141AA">Quod verò adducit ad probandum potius minores circu-<pb pagenum="137" xlink:href="005/01/145.jpg"></pb>los videri ad motum faciliores, eo quod maior eſt angulus <lb></lb>contingentiæ ad planum, circumferentiæ minoris, quàm <lb></lb>maioris circuli, vt in ſubiecta figura maior eſt angulus ABC, <lb></lb>quàm DBC: probat quidem mi<lb></lb><figure id="id.005.01.145.1.jpg" xlink:href="005/01/145/1.jpg"></figure><lb></lb>nores circulos minus offenſare <lb></lb>propter maiorem eleuationem <lb></lb>ipſius anguli à terra, vt ſupra ex<lb></lb>plicuimus; ſed non probat per ſe <lb></lb>facilius moueri; imò oppoſitum. <lb></lb></s>
          <s id="N141C9">Nam quo curuior eſt linea, eo re<lb></lb>motior à motu recto, ac naturali, <lb></lb><expan abbr="ideoq.">ideoque</expan> tardius mouetur, vt cum <lb></lb>Ariſtotele pariter probauimus in <lb></lb>principio. </s>
          <s id="N141D7">Nec recurrere fas eſt ad rotam materialem, quæ <lb></lb>ſi maior fit, maiore ſui parte tangit planum, cum idipſum <lb></lb>deſtruat eius aſſumptum, quod fundatur in eleuatione an<lb></lb>guli contactus ſupra punctum B ſupponendo contactum <lb></lb>fieri in puncto ipſo B, &amp; non in parte diuiſibili. </s>
          <s id="N141E2">Quod ſi di<lb></lb>catur reuera fieri in parte diuiſibili tanto maiore, quanto <lb></lb>maior fuerit circumferentia, tunc variatur ſuppoſitio ante<lb></lb>cedentis in conſequenti, <expan abbr="nihilq.">nihilque</expan> propterea verè concluditur. </s>
        </p>
        <p id="N141EF" type="main">
          <s id="N141F1">Iam verò lo quendo Ariſtoteles de duobus reliquis mo<lb></lb>dis, quibus dixerat rotunda, vel orbiculata corpora circula<lb></lb>riter moueri abſque eo, quod agitentur ſecundum abſidem, <lb></lb>ſeu abſide planum contingant, ait, his etiam modis iam ex<lb></lb>plicatis facillimè ipſa corpora moueri, ac alia ipſis adiuncta <lb></lb>veluti onera commouere. </s>
          <s id="N141FE">Non quidem ex eo, quod parua <lb></lb>ſui portione planum attingant, vel offenſent, vt dicebamus <lb></lb>de primo modo: ſed alia ex cauſa, quam initio huius operis <lb></lb>textu ſexto expoſuimus. </s>
          <s id="N14207">Nimirum quia circulus cum ex <lb></lb>duabus efficiatur lationibus, vel cum ſi moueatur ſecundum <lb></lb>circumferentiam, duabus feratur motionibus: altera obli<lb></lb>qua, ac præter naturam; altera verò recta, ac ſecundum na<lb></lb>turam: ad hanc ſemper habet nutum, ſeu propenſionem. </s>
          <s id="N14212">Si<lb></lb>cut verbi gratia quodlibet graue ad <expan abbr="motũ">motum</expan> deorſum. </s>
          <s id="N1421B">Quam<lb></lb>obrem qui mouent ipſum circulum ſecundum circumferen-<pb pagenum="138" xlink:href="005/01/146.jpg"></pb>tiam, parum aut nihil conantur reſpectu huius lationis ſe<lb></lb>cundum naturam; ſed mouent ipſum, veluti motum ab in<lb></lb>trinſeco propter explicatam propenſionem, quam habet <lb></lb>ad eandem lationem. </s>
          <s id="N1422B">Non ſecus ac ſi mouerent onus deor<lb></lb>ſum, quo ex ſe illud naturaliter tendit. </s>
          <s id="N14230">Solùm igitur impel<lb></lb>lentes circulum conantur, ac mouent illum ſecundum la<lb></lb>tionem obliquam, quæ eſt præter naturam, &amp; ad quam ipſe <lb></lb>circulus non habet nutum ſiue inclinationem. </s>
          <s id="N14239">Quod eſt fa<lb></lb>cillimè circularia ipſa corpora à mouentibus moueri. </s>
          <s id="N1423E">Nam <lb></lb>ſimpliciter loquendo de motione miſta, quæ ex ijs duabus <lb></lb>lationibus reſultat, mouentur quaſi à ſe ipſis. </s>
        </p>
        <p id="N14245" type="main">
          <s id="N14247">Vtitur autem Ariſtoteles illis verbis: ſecundum verò il<lb></lb>lam (ſcilicet motionem) quæ ſupra diametrum eſt, ſe ipſum <lb></lb>mouet circulus: ad connotandam ipſam motionem miſtam, <lb></lb>ac circularem reſultantem ex duabus lationibus explicatis. <lb></lb></s>
          <s id="N14251">Quam quidem ſuper diametrum quadrilateri exemplifica<lb></lb>uerat in principio, non ſeruata tamen eadem proportione <lb></lb>Quod non abs re fuerit in hac figura palam exprimere. </s>
        </p>
        <p id="N14258" type="main">
          <s id="N1425A">Sit enim circulus ABCD <lb></lb><figure id="id.005.01.146.1.jpg" xlink:href="005/01/146/1.jpg"></figure><lb></lb>circa centrum E, cuius ſemi<lb></lb>diameter EC. </s>
          <s id="N14267">A qua excite<lb></lb>tur quadratum ECFD. <expan abbr="Sitq.">Sitque</expan> <lb></lb>diameter quadrati recta CD. <lb></lb></s>
          <s id="N14274">Dico igitur quod ſi punctum <lb></lb>C, quod eſt extremum ſemi<lb></lb>diametri, moueri debeat <expan abbr="vſq;">vſque</expan> <lb></lb>ad D, circa immotum <expan abbr="centrũ">centrum</expan> <lb></lb>E, nullo ferè conatu mouen<lb></lb>tis mouebitur per arcum, cui <lb></lb>ſubtenditur recta CD. <expan abbr="Eo-demq.">Eo<lb></lb>demque</expan> tempore ipſum D transferetur in A; ſicut etiam <lb></lb>A in B, &amp; B vbi nunc eſt punctum C: quod eſt, totum <lb></lb>circulum nullo, aut paruo negotio, à mouente circulariter <lb></lb>moueri. </s>
          <s id="N14297">Cum enim punctum C per lationem ſecundum <lb></lb>naturam, ad quam ex ſe habet nutum, &amp; propenſio<lb></lb>nem, qualibet exigua vi moueatur verſus F; per latio-<pb pagenum="139" xlink:href="005/01/147.jpg"></pb>nem verò præter naturam retrahatur verſus centrum E; im<lb></lb>pellente ſcilicet ipſo mouente; vtique ſi pari proportione <lb></lb>ipſorum laterum CF, &amp; CE deduceretur, ipſis duabus <lb></lb>lationibus proculdubio moueretur per diametrum CD, vt <lb></lb>cum Ariſtotele demonſtrauimus in principio. </s>
          <s id="N142AB">At cum non <lb></lb>ſeruetur eadem proportio inter lationem ſecundum natu<lb></lb>ram, ac præter naturam, vt ibi etiam explicuimus; hinc fit, vt <lb></lb>punctum C moueatur per arcum CD, cui diameter qua<lb></lb>drati ſubtenditur, &amp; in quo nulla eſt pars, ſuper quam diſce<lb></lb>dendo à puncto C, non moueatur vtraque latione, nunc <lb></lb>magis; nunc minus ſe appropinquando puncto F, ac ſeruan<lb></lb>do ſemper eandem diſtantiam à centro E. </s>
          <s id="N142BD">Mouetur it a que <lb></lb>punctum C vſque ad D, motione reſultante ex duabus <lb></lb>lationibus explicatis: at que adeo nulla alia adhibita vi, aut <lb></lb>impulſu, qui correſpondeat ei ſicut illis, vt dictum eſt. </s>
          <s id="N142C6">Et <lb></lb>ſic verificatur, quod ait Ariſtoteles: ſecundum hanc motio<lb></lb>nem, quæ fit ſuper diametrum; (nempe per arcum, cui illa <lb></lb>ſubtenditur) ſe ipſum mouere circulum. </s>
        </p>
        <p id="N142CF" type="head">
          <s id="N142D1">Quæſtio Nona.</s>
        </p>
        <p id="N142D4" type="main">
          <s id="N142D6">C<emph type="italics"></emph>vr ea, quæ per maiores circulos tolluntur, &amp; <lb></lb>trahuntur, facilius &amp; citius moueri contin<lb></lb>git, veluti maioribus trochleis, quàm mino<lb></lb>ribus, &amp; ſcytalis ſimiliter? </s>
          <s id="N142E2">An quoniam <lb></lb>quantò maior fuerit illa, quæ à centro eſt, in <lb></lb>æquali tempore maius mouetur ſpatium? <lb></lb></s>
          <s id="N142EA">Quamobrem æquali inexiſtente onere, idem faciet: quemad<lb></lb>modum diximus, maiores libras minoribus exactiores eſſe. <lb></lb></s>
          <s id="N142F0">Spartum enim in illis centrum eſt: libræ autem vtrin que par<lb></lb>tes, quæ ex centro ſunt, exiſtunt.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N142F7" type="head">
          <s id="N142F9">COMMENTARIVS.</s>
        </p>
        <p id="N142FD" type="main">
          <s id="N142FF">Maior eſt difficultas, &amp; controuerſia circa experien<lb></lb>tiam hic <expan abbr="ſuppoſitã">ſuppoſitam</expan> ab Ariſtotele, dum quæſtionem <lb></lb>proponit, quam circa cauſam ipſius adductam in <pb pagenum="140" xlink:href="005/01/148.jpg"></pb>ſolutione. </s>
          <s id="N1430F">Scribit enim facilius ac celerius tolli, ac trahi <lb></lb>pondera per maiores circulos, quàm per minores. </s>
          <s id="N14314">Conſti<lb></lb>tuitque exemplum de trochleis, ac ſcytalis, quæ ſi maiores <lb></lb>ſint, aptius onera mouent. </s>
          <s id="N1431B">Quod falſum omnino eſſe cona<lb></lb>tur oſtendere Blancanus ex Guido Vbaldo. </s>
          <s id="N14320">Nam ſimplex <lb></lb>trochlea per rotulam cui funis ſupernè inditur nullas addit <lb></lb>vires potentiæ mouenti, eo quod reducatur ad vectem, cu<lb></lb>ius fultura eſt in medio ipſius. </s>
          <s id="N14329">Vnde ſiue rotula illa magna <lb></lb>fuerit ſiue parua, ſemper eadem ratione nullam augere po<lb></lb>teſt facilitatem, aut velocitatem in hac motione. </s>
          <s id="N14330">Subdit que <lb></lb>Blancanus, experientia quoque conſtare eodem labore <lb></lb>aquam hauriri, ſiue rotula illa magna fuerit ſiue parua. </s>
        </p>
        <p id="N14337" type="main">
          <s id="N14339">Verum ſi hoc vniuerſaliter demonſtraret experientia, fru<lb></lb>ſtra paſſim adhiberentur trochleæ ad leuanda, ac trahenda <lb></lb>pondera; nec eſſet cur iuxta maiorem ponderum grauita<lb></lb>tem, maioribus rotis, ac trochleis <expan abbr="vterẽtur">vterentur</expan> Architecti quan<lb></lb>do minoribus vti poſſent. </s>
          <s id="N14348">Quamuis igitur ſimplex trochlea <lb></lb>ſupernè appenſa nullam addat vim potentiæ motrici, ſicut <lb></lb>nec vectis, cuius fulcimentum non ſit propinquius oneri; <lb></lb>multam tamen affert commoditatem. </s>
          <s id="N14351">Vnde eadem quip<lb></lb>pè vi, ſed; non eodem labore eleuatur onus beneficio tro<lb></lb>chleæ, aut vectis prædicti, quàm ſine illis. </s>
          <s id="N14358">Commoditas enim <lb></lb>minuit laborem, ac ſi non auget potentiam, confert tamen <lb></lb>ad applicationem, &amp; exercitium illius: id quod eſt augere <lb></lb>facilitatem. </s>
          <s id="N14361">Rurſus quæcumque ſit facilitas, qua rotis, vel <lb></lb>trochleis pondera leuantur, certum eſt velocius ea leuari <lb></lb>maioribus, quàm minoribus rotis; ſed hoc ipſum eſt faci<lb></lb>lius mouere, quia licet non omnis facilitas includat veloci<lb></lb>tatem, vt pater in pluribus machinis tractorijs, quæ facilius, <lb></lb>ſed tardius mouent; nihilominus velocitas ſemper inuoluit <lb></lb>facilitatem; Ergo nihil contra experientiam aſſumpſit Ari<lb></lb>ſtoteles, vt Blancanus contendit. </s>
        </p>
        <p id="N14372" type="main">
          <s id="N14374">Baldus item ait non eſſe ſimpliciter verum idipſum, quod <lb></lb>Philoſophus aſſerit, vt ſcilicet quo maiores fuerint trochleæ, <lb></lb>eò facilius moueant. </s>
          <s id="N1437B">Quia tam maior, quàm minor trochlea <lb></lb>per eius centrum grauitatis diuiditur à perpendiculari ea-<pb pagenum="141" xlink:href="005/01/149.jpg"></pb>dente ad centrum mundi in duas partes æquales, &amp; æquè <lb></lb>ponderantes, ac proinde ſemper eſt eadem illarum pro<lb></lb>portio inter ſe, &amp; eadem ponderum ratio, ex qua prouenit <lb></lb>motus. </s>
          <s id="N1438B">Fatetur tamen hoc tantum procedere abſtractè lo<lb></lb>quendo cum alioquin in trochleis, ac rotis materialibus ne<lb></lb>gare non poſſit experientiam quam ſupponit Ariſtoteles. <lb></lb></s>
          <s id="N14394">Quare totam maiorem facilitatem, quam experimur in ipſis <lb></lb>trochleis, ac rotis maioribus, ipſe ad maiorem proportio<lb></lb>nem, quam vt plurimum rota maior habet cum proprio axe <lb></lb>reducit. </s>
        </p>
        <p id="N1439D" type="main">
          <s id="N1439F">Sed quidquid ſit de facilitate, aut difficultate ſimul <expan abbr="pro-ueniẽte">pro<lb></lb>ueniente</expan> ex hoc capite, quam certè admittimus, ac infra <expan abbr="etiã">etiam</expan> <lb></lb>explicabimus: ſiſtendo in ſola ratione maioris, aut minoris <lb></lb>ambitus rotæ prout hic ſupponit Ariſtoteles, cæteris ſcilicet <lb></lb>paribus; exploratiſſimum eſt, ac negari minimè poteſt, quam <lb></lb>facilius adhuc ſeruata eadem proportione axis, ſeu craſſitiei <lb></lb>illius ad ambitum rotæ, ferantur <expan abbr="põdera">pondera</expan>, ſi maioribus aſpor<lb></lb>tentur, eleuentur; aut trahantur rotis; ſicut etiam ſcytalis, de <lb></lb>quibus hic eadem eſt ratio. </s>
          <s id="N143BE">Loquitur autem Ariſtoteles <lb></lb>de illo genere <expan abbr="ſeytalarũ">ſcytalarum</expan>, quæ ſimiliter circa axim <expan abbr="coniunctũ">coniunctum</expan> <lb></lb>ad eleuanda pondera conuertuntur, appoſito in altera ex<lb></lb>tremitate <expan abbr="illarũ">illarum</expan> ferreo quoddam manubrio, vt in ſpecie eſt <lb></lb>in ſubiecta figura. </s>
          <s id="N143D5">Scytala enim de ſe <expan abbr="tantũ">tantum</expan> ſignificat lignum <lb></lb>quoddam <expan abbr="oblongũ">oblongum</expan>, ac teres <expan abbr="tanquã">tanquam</expan> <expan abbr="cylindrũ">cylindrum</expan>, cui <expan abbr="quandoq.">quandoque</expan> <lb></lb>alijs adiunctis diuerſæ machinæ, ac inſtrumenta vectoria, ſi<lb></lb>ue tractoria efficiuntur, quorum nonnulla adhuc ſcytalæ <lb></lb>vocantur, vt hæc de qua loquimur, &amp; alia de qua infra quæ<lb></lb>ſtione 11. </s>
        </p>
        <figure id="id.005.01.149.1.jpg" xlink:href="005/01/149/1.jpg"></figure>
        <p id="N143FB" type="main">
          <s id="N143FD">His itaque ſic ſe habentibus breuiter ac perſpicuè quæ<lb></lb>ſtionem diluit Ariſtoteles, inquiens, maiorem hanc facilita<lb></lb>tem, ac velocitatem motus procedere à maiori diſtantia, <pb pagenum="142" xlink:href="005/01/150.jpg"></pb>quam à centro habet extremum diametri amplioris circu<lb></lb>li, aut rotæ reſpectu minoris, ob principium illud ſæpè re<lb></lb>petitum, &amp; à nobis pluries explicatum, quod iterum in libra <lb></lb>hic exemplificat. </s>
          <s id="N1440F">Quoniam (inquit) ſicut exactiores ſunt <lb></lb>maiores libræ, quam minores, <expan abbr="magisq.">magisque</expan> aut facilius mouen<lb></lb>tur; ita maiores circuli, vel rotæ, æquali exiſtente onere, <lb></lb><expan abbr="cæterisq.">cæterisque</expan> paribus, vt dictum eſt: Cum rotæ ex totidem li<lb></lb>bris, ſeu brachijs libræ videantur compactæ, quot ſunt dia<lb></lb>metri ex quibus conſtant. </s>
        </p>
        <p id="N14423" type="main">
          <s id="N14425">Diximus autem cæteris paribus; nam vt rectè Baldus ad<lb></lb>monuit, ſi rota maior corpulentiorem proportionaliter ha<lb></lb>beat axem, quàm minor, non mouetur velocius. </s>
          <s id="N1442C">Siquidem <lb></lb>quo maior fuerit diameter rotæ reſpectu diametri ſui axis, <lb></lb>eò facilius mouebitur: quo verò minor, eò difficilius. </s>
          <s id="N14433">Magis <lb></lb>enim retardat, ac impedit axis craſſior, quam ſubtilior. </s>
          <s id="N14438">Quod <lb></lb>adhuc (aliter tamen quàm ille) poſſumus probare; Nimirum <lb></lb>quia ambitus ſubtilioris axis per minorem ſui partem attin<lb></lb>git rotam, quàm ambitus craſſioris: &amp; ſic minus impedit <lb></lb>circumuolutionem. </s>
          <s id="N14443">Itemque poſt punctum, quod eſt in <lb></lb>ſummitate circumferentiæ, &amp; cui potiſſimum onus rotæ in<lb></lb>cumbit, partes vtrinque circulariter declinantes, decliuio<lb></lb>res ſunt in axe ſubtiliori; eo quod minor circumferentia <lb></lb>magis curuetur; ſicut è contra quæ amplior eſt, rectius pro<lb></lb>cedat, ſiue magis rectæ appropinquetur. </s>
          <s id="N14450">Cumque partes <lb></lb>decliuiores, minus valeant onus ſuſtinere nè dilabatur, <lb></lb>quàm partes, quæ minus declinant; hinc fit, vt ſubtilior <lb></lb>axis ex decliuioribus conſtitutus, minus retardet, aut impe<lb></lb>diat rotæ circumuolutionem. </s>
        </p>
        <p id="N1445B" type="main">
          <s id="N1445D">Cæterum data axium paritate, præter cauſam ab Ariſto<lb></lb>tele aſſignatam adhuc duplici ex capite reperiemus, maio<lb></lb>res rotas citiùs, ac faciliùs quàm minores conuolui. </s>
          <s id="N14464">Primò <lb></lb>nimirum quia per maiores diametros tanquam per longio<lb></lb>res vectes aptius ſuperatur impedimentum, quod experimur <lb></lb>tam ex parte axis, quàm ex parte foraminis rotæ vbi inditur <lb></lb>ipſe axis, ad expeditum motum circumuolutionis illius, <lb></lb>dum propter vtriuſque corporis aſperitatem adinuicem co-<pb pagenum="143" xlink:href="005/01/151.jpg"></pb>guntur fricari, vnde non parum circumuolutio retardatur. <lb></lb></s>
          <s id="N14477">Secundo quia quæ minor eſt rota, ſicut pluries, quàm ma<lb></lb>ior debet conuolui ad eleuandum, vel trahendum aliquod <lb></lb>pondus, ita pluries eſt illi ſuperanda huiuſmodi reſiſtentia, <lb></lb>ſeu impedimentum fricationis; <expan abbr="proindeq.">proindeque</expan> difficilius id præ<lb></lb>ſtabit: ſicut è contra facilius, quæ maior eſt, <expan abbr="paucioribusq.">paucioribusque</expan> <lb></lb>circumuolutionibus indiget. </s>
          <s id="N1448C">Quo fit, vt ex quatuor rotis <lb></lb>curruum, duæ anteriores, vt quæ minores ſint, ac ſæpius cir<lb></lb>cumuoluantur, ſæpius etiam indigeant vnctione, ac facilius <lb></lb>conterantur; vt Aurigis ſatis eſt notum. </s>
          <s id="N14495">Cum enim ſimul <lb></lb>eodem tempore æquale ſpatium percurrere debeant, ac ro<lb></lb>tæ maiores, quod ipſis deeſt extentionis ad <expan abbr="coadæquandũ">coadæquandum</expan> <lb></lb>ſe eidem ſpatio, compenſatur per multiplicationem, ac re<lb></lb>petitionem circumuolutionis earum; non ſecus ac qui bre<lb></lb>uiori, ſed frequentiori paſſu ſimul gradiuntur cum ijs, qui <lb></lb>longiori, ac tardiori. </s>
          <s id="N144A8">Vt dicitur de Iulo cum Aenea patre <lb></lb>apud Maronem. </s>
          <s id="N144AD">Dextræ ſe paruus Iulus implicuit, <expan abbr="ſequi-turq.">ſequi<lb></lb>turque</expan> patrem non p aſſibus æquis. </s>
        </p>
        <p id="N144B6" type="head">
          <s id="N144B8">Quæſtio Decima.</s>
        </p>
        <p id="N144BB" type="main">
          <s id="N144BD">C<emph type="italics"></emph>vr facilius quando ſine pondere eſt, moue<lb></lb>tur libra, quàm cùm pondus habet? </s>
          <s id="N144C5"><expan abbr="ſimiliq.">ſimilique</expan> <lb></lb>modo rota, &amp; huiuſmodi quippiam, quod gra<lb></lb>uius quidem eſt, maius autem minore, &amp; le<lb></lb>uiore? </s>
          <s id="N144D1">An quia non ſolum in contrarium, <lb></lb>quod graue eſt, ſed in obliquum etiam diffi<lb></lb>culter mouetur? </s>
          <s id="N144D8">In contrarium enim ei, ad quod vergit onus, <lb></lb>mouere difficile eſt: quo autem vergit, eſt facilè: in obliquum <lb></lb>autem haud quaquam vergit.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N144E1" type="head">
          <s id="N144E3">COMMENTARIVS.</s>
        </p>
        <p id="N144E7" type="main">
          <s id="N144E9">Dvo in vnum collecta quærit hic Ariſtoteles, nempe <lb></lb>cur facilius moueatur tàm libra ponderibus vacua <lb></lb>reſpectu ſui ipſius cum pondera ſuſtinet; quàm ro-<pb pagenum="144" xlink:href="005/01/152.jpg"></pb>ta leuior reſpectu grauioris, non ſolum æqualis magnitudi<lb></lb>nis, ſed etiam maioris, quam aliàs quæſtione præcedenti di<lb></lb>xerat moueri facilius, ac velocius minore cæteris paribus. <lb></lb></s>
          <s id="N144FA"><expan abbr="Cauſamq.">Cauſamque</expan> ſciſcitandi eam eſſe videtur, quoniam libra in <lb></lb>æquilibrio conſtituta, ſicut etiam rota ſtans perpendicula<lb></lb>riter ſuper planum, aut in axe ſuffulta, quæ ſimilem habet <lb></lb>rationem, cuiuſcunque grauitatis fuerit, ſtatim atque ex ali<lb></lb>qua parte impingatur, vel onus aliquod alteri eius extremo <lb></lb>ſuperaddatur; amplius manere non poteſt in illo ſitu, aut <lb></lb>poſitione, eo quod neceſſariò æquilibrium auferatur per <lb></lb>additionem ponderis, vel impetum incuſſum in alteram eius <lb></lb>extremitatem; <expan abbr="proindeq.">proindeque</expan> ſiue ipſa libra ſit ferrea, ſiue li<lb></lb>gnea grauior, aut leuior, æquè facilè deberet moueri: idem<lb></lb>que verificari de rota. </s>
        </p>
        <p id="N14518" type="main">
          <s id="N1451A">Quæſtioni tamen reſpondet Ariſtoteles, grauiora corpo<lb></lb>ra difficilius moueri non modo directè contra proprium <lb></lb>nutum, quo tendunt deorſum, vt cum rurſum eleuantur; ſed <lb></lb>etiam obliquè cum feruntur ad latera in tranſuerſum, quo <lb></lb>certè natura ſua pondus non vergit. </s>
          <s id="N14525">Quamobrem hoc ip<lb></lb>ſo, quod libra, vel rota dimoueri non poſſit ab æqui<lb></lb>librio, quin obliquè circumferatur per motum miſtum, ac <lb></lb>præter naturalem circa proprium fulcimentum, vel axim; <lb></lb>quo grauior fuerit, eo difficilius mouebitur, <expan abbr="magisq.">magisque</expan> huic <lb></lb>motui repugnabit, grauior autem eſt libra ponderibus onu<lb></lb>ſta, quàm vacua. </s>
          <s id="N14538"><expan abbr="Similiterq.">Similiterque</expan> rota ferrea, quàm lignea, vel <lb></lb>ferrea, aut lignea quadripalmaris diametri, quàm alia eiuſ<lb></lb>dem materiæ, ſed bipalmaris. </s>
        </p>
        <p id="N14542" type="main">
          <s id="N14544">Nec retorqueri poteſt hoc argumentum contra Ariſtote<lb></lb>lem, vt Baldus contendit ex eo, quod cum grauius pondus <lb></lb>violentius deſcendat, maiori niſu deorſum ferri deberet <lb></lb>pars illa rotæ, vel libræ per additionem ponderis, vel impul<lb></lb>ſu aliquo mota. </s>
          <s id="N1454F">Nam licet grauius pondus ſi deorſum fe<lb></lb>ratur, violentius quidem deſcendet, non tamen per hoc fa<lb></lb>cilius à loco ſuo, vel quiete dimouetur. </s>
          <s id="N14556">Deinde quia ſicut <lb></lb>maius pondus auget procliuitatem ad motum perpendicu<lb></lb>larem verſus mundi centrum; ita difficultatem auget re-<pb pagenum="145" xlink:href="005/01/153.jpg"></pb>ſpectu motus contrarij, vel obliqui, vt eſt motus circularis <lb></lb>libræ, vel rotæ. </s>
        </p>
        <p id="N14564" type="main">
          <s id="N14566">Rurſumque nec ſubſiſtit contradictio, quam Blancanus <lb></lb>Philoſopho attribuit, quaſi in præcedenti quæſtione di<lb></lb>xerit, maiores trochleas, ac ſcytalas, minoribus facilius <lb></lb>moueri; hic autem aſſerat, maiorem rotam difficilius mo<lb></lb>ueri, quam minorem. </s>
          <s id="N14571">Quandoquidem Ariſtoteles apertè <lb></lb>per minorem intelligit etiam leuiorem. </s>
          <s id="N14576">Ait enim, maius <lb></lb>autem minore, &amp; leuiore. </s>
          <s id="N1457B">Quare ſenſus eſt, quod licet <lb></lb>rotæ maiores ratione magnitudinis, ſint mobiliores; ni<lb></lb>hilominus quando grauiores ſunt minoribus, difficilius <lb></lb>commouentur. </s>
        </p>
        <p id="N14584" type="main">
          <s id="N14586">Ex quibus patere etiam poteſt ſolutio ad rationem <expan abbr="dubi-tãdi">dubi<lb></lb>tandi</expan> in principio <expan abbr="poſitã">poſitam</expan>. </s>
          <s id="N14593">Nam eſtò quolibet perexiguo pon<lb></lb>dera in <expan abbr="alterã">alteram</expan> <expan abbr="partẽ">partem</expan> adiuncto, vel modico impetu in <expan abbr="illã">illam</expan> in<lb></lb>cuſſo, re vera tollatur <expan abbr="æquilibriũ">æquilibrium</expan> tam leuioris, quàm grauio<lb></lb>ris libra, aut rotæ conſideratæ in abſtracto, vt Guidus Vbal<lb></lb>dus demonſtrat ex principijs Archimedis: id tamen ſenſibi<lb></lb>liter non apparet in facto, nec propterea libra ipſa, vel rota <lb></lb>mouetur, niſi exceſſus ponderis, vel impulſus proportionem <lb></lb>quandam habeat cum grauitate partis oppoſitæ, quam ex<lb></lb>cedit; ita ut, quo grauior eſt libra, vel rota ſecundum vtran<lb></lb>que partem in æquilibrio conſtitutam, eo maior ſit ipſe ex<lb></lb>ceſſus ſuperadditus in altera parte ad alteram ſuperandam. <lb></lb></s>
          <s id="N145BB">Quod totum procedit ex eo; nam hoc ipſo, quod grauiora <lb></lb>corpora ægrius præter, vel contra proprium nutum feran<lb></lb>tur, maior pariter virtus requiritur ad ea circumferenda <lb></lb>motu præternaturali, ac miſto, prout eſt motus circularis. <lb></lb></s>
          <s id="N145C5">Sed ad concilianda principia Archimedis cum principijs <lb></lb>Ariſtotelis in propoſito diſcurſu explicandum ſuper eſt, cur <lb></lb>quando libra, vel rota conſideratur ſuſpenſa per centrum <lb></lb>ſuæ grauitatis indiuiſibiliter, non requiratur eadem propor<lb></lb>tio inter exceſſum partis præponderantis, &amp; grauitatem ma<lb></lb>iorem, aut minorem alterius, ſed ſufficiat quilibet exceſſus. <lb></lb></s>
          <s id="N145D3">Siquidem etiam in iſto caſu abſtracto maior grauitas partis <pb pagenum="146" xlink:href="005/01/154.jpg"></pb>eleuandæ, maiorem exceſſum ponderis, aut virtutis videre<lb></lb>tur requirere in parte eleuante. </s>
        </p>
        <p id="N145DD" type="main">
          <s id="N145DF">Dicimus ergo huiuſmodi diſparitatem deſumendam eſſe <lb></lb>ex propria conditione materiæ. </s>
          <s id="N145E4">Nam axis materialis circa <lb></lb>quem vertitur, cum non ſit indiuiſibilis; neceſſariò ſecundum <lb></lb>plures ſui partes, ac puncta correſpondet partibus, ac pun<lb></lb>ctis incumbentibus ipſius rotæ, vel libræ, quam ſuſtinet. <lb></lb></s>
          <s id="N145EE">Quare ad eleuandam verbi gratia partem ſiniſtram libræ, <lb></lb>vel rotæ per depreſſionem dexteræ inter quas mediat cen<lb></lb>trum grauitatis, conſequenter obſtabit pars illa axis corre<lb></lb>ſpondens ipſi dexteræ incumbenti, ac deprimendæ, eritque <lb></lb>veluti fulcimentum vectis ad eleuandam non modo partem <lb></lb>ſiniſtram, ſed etiam punctum medium, quod eſt centrum <lb></lb>grauitatis tanquam præcipuum onus. </s>
          <s id="N145FD">Vnde licet propter <lb></lb>maximam approximationem <expan abbr="fulcimẽti">fulcimenti</expan> ad huiuſmodi onus, <lb></lb>facilè onus ipſum, ſeu centrum grauitatis aliquantulum ele<lb></lb>uetur; non per hoc tollitur, quin eo difficilius iſte motus <lb></lb>exerceatur, quo maius fuerit pondus incumbens per ipſum <lb></lb>centrum grauitatis; ac proinde maior virtus requiratur ad <lb></lb>ſuperandam ipſam reſiſtentiam, ac maiorem difficultatem <lb></lb>Quod non ita contingeret ſi libra, vel rota ſuſpenderetur per <lb></lb>axim indiuiſibilem, ac centrum ipſum grauitatis. </s>
          <s id="N14616">Nam hoc <lb></lb>æquè ſemper ſuſtineretur, ſiue in motu, ſiue inquietè ipſius <lb></lb>libræ, vel rotæ. </s>
          <s id="N1461D">Imo ſemper quieſceret, nec vlla eſſet reſi<lb></lb>ſtentia partium axis explicata, ſiue pondus incumbens eſſet <lb></lb>grauius, ſiue leuius. </s>
          <s id="N14624">Ideoque nullo negotio ad quem<lb></lb>libet exiguum impulſum, vel modicam additio<lb></lb>nem ponderis ſtatim ab æquilibrio, &amp; à <lb></lb>quiete dimoueretur omnis quan<lb></lb>tumuis ingens, &amp; grauiſſi<lb></lb>ma libra, vel <lb></lb>rota. </s>
        </p>
        <pb pagenum="147" xlink:href="005/01/155.jpg"></pb>
        <p id="N14637" type="head">
          <s id="N14639">Quæſtio Vndecima.</s>
        </p>
        <p id="N1463D" type="main">
          <s id="N1463F">C<emph type="italics"></emph>vr ſuper ſcytalas facilius portantur one<lb></lb>ra, quàm ſuper currus, cùm tamen ÿ ma<lb></lb>gnas habeant rotas, illæ verò puſillas? </s>
          <s id="N14649">An <lb></lb>quoniam in ſcytalis nulla eſt offenſatio, in <lb></lb>curribus autem axis est, ad quem offenſant. <lb></lb></s>
          <s id="N14651">Deſuper enim illum premunt, &amp; à lateri<lb></lb>bus. </s>
          <s id="N14656">Quod autem eſt in ſcytalis, ad iſthæc duo mouetur, &amp; <lb></lb>infernè ſubſtrato ſpatio, &amp; onere ſuperimpoſito. </s>
          <s id="N1465B">In viriſ<lb></lb>que enim ijs reuoluitur locis circulus, &amp; motus impellitur.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N14662" type="head">
          <s id="N14664">COMMENTARIVS.</s>
        </p>
        <p id="N14668" type="main">
          <s id="N1466A">Scytalæ, de quibus hic loquitur Ariſtoteles non ſunt <lb></lb>eiuſdem generis cum illis, quæ ſupra quæſtione no<lb></lb>na commemorauerat. </s>
          <s id="N14671">Nam vltra communem for<lb></lb>mam cylindricam, ſicut illæ axim, ac manubrium, ſic <lb></lb>iſtæ rotulas quaſdam habent ſingulas in ambis extremitati<lb></lb>bus ex eodem ligno compactas; prominentiores quidem, <lb></lb>ſeu maioris ambitus, quàm ſit reliquum corpus teres, <lb></lb>quod intermediat, quodque axis vicem gerere videtur, <lb></lb>ſed non ab eo ſeiunctas, quippe cum ad vnum, &amp; idem <lb></lb>corpus continuatum pertineant, ac ſimul cum eo in latio<lb></lb>ne ſuper planum circumuoluantur ſecus ac illæ, quæ à <lb></lb>proprio axe ſunt ſeiunctæ. </s>
          <s id="N14686">Maximo autem adiumento hu<lb></lb>iuſmodi ſcytalæ eſſe ſolent cum binæ, vel ternæ æquidi<lb></lb>ſtantes oneribus ſupponuntur, vt ea facilius moueantur, <lb></lb>præſertim ſuper ſolum ſatis conſiſtens, &amp; æquatum, à <lb></lb>quo nulla vnquam ſupereminentia, aut cauitate rotarum <lb></lb>paruitas abſorbeatur. </s>
          <s id="N14693">Licet non minus imò frequentius <lb></lb>vtamur ſcytalis ſimplicibus, ac non rotatis, quarum memi<pb pagenum="148" xlink:href="005/01/156.jpg"></pb>nit Pappus lib.

8. Vtrarumque autem figuram hic erit in<lb></lb>ſpicere delineatam. </s>
        </p>
        <figure id="id.005.01.156.1.jpg" xlink:href="005/01/156/1.jpg"></figure>
        <p id="N146A4" type="main">
          <s id="N146A6">Quærit igitur Ariſtoteles quid ſit in cauſa, vt huiuſmodi <lb></lb>ſcytalis, quæ minores valde rotas obtinent, quàm currus, <lb></lb>facilius quàm ipſis curribus onera aſportentur cum quæ<lb></lb>ſtione nona conſtiterit, maiores rotas facilius, ac celerius <lb></lb>onera mouere. </s>
          <s id="N146B1">Optimèque ſtatim reſpondet, id ex eo con<lb></lb>tingere, quòd cum ſcytalarum rotæ vnitum ſibi axem, non <lb></lb>autem ſeiunctum, vt plauſtrorum rotæ ſortiantur, nulla inter <lb></lb>ipſas, &amp; axem offenſatio intercedit, ſicut in curribus, aut <lb></lb>plauſtris. </s>
          <s id="N146BC">Axis enim currus duplici ex parte præmitur, <lb></lb>nempe deſuper ab oneribus incumbentibus, &amp; ex latere <lb></lb>dum ante, vel retro trahitur à mouentibus. </s>
          <s id="N146C3">Quare in dupli<lb></lb>ci etiam &amp; correſpondenti parte præmit rotas intra ipſarum <lb></lb>modiolum, vbi cum rotæ ſeiunctæ ab eo ſint, ac diſſimili mo<lb></lb>do moueantur, neceſſario ſeſe ad inuicem ſecundum vtram<lb></lb>que partem offenſant atque collidunt, eo quod diuerſo ſibi <pb pagenum="149" xlink:href="005/01/157.jpg"></pb>motu atque impulſu occurrant. </s>
          <s id="N146D3">Quod non ita ſe habet in <lb></lb>ſcytalis, in quibus cum non ſit axis diſtinctus, nec motus di<lb></lb>uerſus, &amp; ab eodem pondere, quod ſuſtinent ipſæ anterius <lb></lb>ſuper planum impellantur, nullus fit in rotatione occurſus <lb></lb>nullaque offenſatio, ſecluſo omni offendiculo extrinſeco, de <lb></lb>quo non loquimur. </s>
          <s id="N146E0">Pondus enim licet de ſe ſemper graui<lb></lb>tet, ac præmat per lineam perpendicularem cadentem ad <lb></lb>mundi centrum; nihilominus poſitum ſuper ſcytalas, tan<lb></lb>quam ſuper ſtantes circulos; dum antrorſum impingitur, <lb></lb>totam præſsionem, ac impulſum refundit in nutum, quem <lb></lb>auget in circulis ſubiectis, &amp; concitat, vt facilius mouean<lb></lb>tur. </s>
          <s id="N146EF">Tollit namque explicatum æquilibrium illorum per <lb></lb>magnam additionem ponderis, aut virtutis in eam partem, <lb></lb>quam ſucceſsiuè in illis deprimit, &amp; ad rotandum impellit. <lb></lb></s>
          <s id="N146F7">Et ſic corpus ipſum cylindricum, quod in ſcytalis axis vi<lb></lb>cem gerit, ac mediat inter duas vnitas ſibi rotulas inter <lb></lb>pondus, &amp; planum ſubſtratum reuoluitur tanquam circu<lb></lb>lus inter duas ſuperficies, mutando ſemper locum ex par<lb></lb>te vtriuſque. </s>
          <s id="N14702">Nam &amp; onus à motore impulſum per ſucce<lb></lb>dentes iugiter ſui partes impingit, &amp; ſubſtratum planum <lb></lb>per nouas etiam partes correſpondentes ſcytalas ipſas cum <lb></lb>onere ſuſtinet. </s>
        </p>
        <p id="N1470B" type="head">
          <s id="N1470D">Quæſtio Duodecima.</s>
        </p>
        <p id="N14710" type="main">
          <s id="N14712">C<emph type="italics"></emph>vr longiùs feruntur miſſilia funda, quàm <lb></lb>manu miſſa, cùm alioqui proiector manu <lb></lb>magis pondus comprehendat, quàm cùm il<lb></lb>lud ſuſpendit? </s>
          <s id="N1471E">Præterea ſic quidem duo mo<lb></lb>uet pondera, fundæ videlicet, &amp; miſsilis: illo <lb></lb>autem modo ſolum miſsile. </s>
          <s id="N14725">An quia in funda <lb></lb>quidem commotum miſsile funditor proijcit? </s>
          <s id="N1472A">Fundam enim <lb></lb>circulo, ſubinde rotans, id iaculatur: ex manu autem, à quie<lb></lb>te eſt initium: omnia autem cùm in motu ſunt, quàm cùm <lb></lb>quieſcunt, faciliùs mouentur. </s>
          <s id="N14733">An &amp; eam ob cauſam est, ſed <emph.end type="italics"></emph.end><pb pagenum="150" xlink:href="005/01/158.jpg"></pb><emph type="italics"></emph>nec minus etiam, quia in fundæ vſu manus quidem fit cen<lb></lb>trum: funda verò, quod à centro exit? </s>
          <s id="N14741">Quanto autem pro<lb></lb>ductius fuerit id, quod à centro eſt, tantò citiùs mouetur. <lb></lb></s>
          <s id="N14747">Tactus autem, qui manu fit, fundæ reſpectu breuis eſt.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1474C" type="head">
          <s id="N1474E">COMMENTARIVS.</s>
        </p>
        <p id="N14752" type="main">
          <s id="N14754">Dvas hic Aristoreles rationes dubitandi proponit, <lb></lb>vt explicet cauſam cur longius ferantur miſsilia <lb></lb>funda, quàm manu miſſa. </s>
          <s id="N1475B">Prima eſt, quia proie<lb></lb>ctor melius miſſilia ipſa manu comprehendit, quàm cum <lb></lb>funda ſuſpendit: Quod autem melius comprehenditur, va<lb></lb>lidius iacitur ac propterea longius mittitur: Potius itaque <lb></lb>manu miſſa, quàm funda proiecta miſsilia longius ferri de<lb></lb>berent. </s>
          <s id="N14768">Secunda verò ratio eſt, nam <expan abbr="cũ">cum</expan> funda quis proijcit; <lb></lb>duo ſimul mouet <expan abbr="põdera">pondera</expan>; fundá nempe <expan abbr="ipsã">ipsam</expan>, &amp; miſsile, quod <lb></lb>proijcit; <expan abbr="abſq;">abſque</expan> autem funda <expan abbr="nõ">non</expan> mouet niſi proiectum: At am<lb></lb>plius quilibet mouere valet quando <expan abbr="totã">totam</expan> eius vim applicat <lb></lb>in vnum, quàm cum diſtribuit in plura: Ergo magis ac remo<lb></lb>tius proiector manu mittet, ac proijciet, quàm funda. </s>
        </p>
        <p id="N1478D" type="main">
          <s id="N1478F">Duplicem deinde cauſam propoſiti <expan abbr="experimẽti">experimenti</expan> aſsignat, <lb></lb>vna eſt, quia per fundam agitatum atque commotum miſ<lb></lb>ſile mittitur. </s>
          <s id="N1479A">Siquidem priuſquam emittatur, ac è funda <lb></lb>elabatur, eadem funda circumagitur, ac rotatur; manu au<lb></lb>tem non niſi quieſcens proijcitur: ita vt ſtatim proiectio <lb></lb>poſt quietem ſequatur, <expan abbr="ſumatq.">ſumatque</expan> initium à loco vbi mane<lb></lb>bat, nempe ab ipſa manu. </s>
          <s id="N147A9">Omnia autem cum in motu ſunt, <lb></lb>facilius vlterius per nouum impulſum feruntur, quàm cum <lb></lb>quieſcunt, ac tunc primò moueri coguntur. </s>
        </p>
        <p id="N147B0" type="main">
          <s id="N147B2">Quocirca vt hæc doctrina iuxta rei veritatem clarius elu<lb></lb>ceſcat, obſeruandum eſt, proiecta in rigore loquendo non <lb></lb>ſtatim poſt quietem è manu iaculantis elabi; ſed aliquan<lb></lb>tulum ſaltem prius manu ipſa comitante moueri antequam <lb></lb>emittantur. </s>
          <s id="N147BD">Motus enim brachij iaculantis arcum quen<lb></lb>dam ſemper deſcribit, in cuius fine, non autem in principio <lb></lb>miſsilia proijciuntur; &amp; quò longius proijcienda ſunt eò <pb pagenum="151" xlink:href="005/01/159.jpg"></pb>maiorem arcum brachium ipſum efficit; magis nimirum <lb></lb>prius retrocedendo, magiſque poſtea antrorſum ſe exten<lb></lb>dendo, atque in fine extenſionis è manu miſsilia dimitten<lb></lb>do. </s>
          <s id="N147CF">Alioqui niſi manus imò etiam brachium ſimul cum il<lb></lb>lis antea moueretur, nec impetum inferre, nec proijcere <lb></lb>ipſa valeret. </s>
          <s id="N147D6">Quare cum ait Ariſtoteles, nullam antecede<lb></lb>re commotionem in proiectione, quæ fit ſola manu, intelli<lb></lb>gendus non eſt de commotione immediata coniuncta, &amp; <lb></lb>quaſi eſſentialiter pertinente ad eundem actum proiectio<lb></lb>nis: ſed de commotione diſpoſitiua accidentali, &amp; quaſi re<lb></lb>mota ad ipſum actum iaculandi, vt eſt præcedens illa irro<lb></lb>tatio, &amp; agitatio fundæ. </s>
          <s id="N147E5"><expan abbr="Congruuntq.">Congruuntque</expan> verba ipſius, nam <lb></lb>ad probandum, commotum miſsile proijci à funditore, ait: <lb></lb>funda enim circulo ſubinde rotans id iaculatur. </s>
        </p>
        <p id="N147EF" type="main">
          <s id="N147F1">Quod certè vim argumenti ipſius Ariſtotelis non labe<lb></lb>factat, tum quia etſi nunquam abſque comitante aliquo <lb></lb>motu proximo ipſius manus iaciantur proiecta, ſæpè tamen <lb></lb>iaciuntur abſque præuio motu remoto, quo nunquam ca<lb></lb>rent miſsilia, quæ funda mittuntur: tum etiam, quia eadem <lb></lb>ſaltem procedit ratio à minori ad maius, nimirum vt quo <lb></lb>magis in motu eſt aliquid, eò facilius adhuc vlterius alio ſu<lb></lb>peraddito impulſu procurrat. </s>
          <s id="N14802">Quare cum magis in motu <lb></lb>ſit miſsile, quod funda rotatur, quàm quod manu vnico, ac <lb></lb>breuiori arcu cietur, rectè concluditur longè facilius funda, <lb></lb>quàm manu vlterius mitti. </s>
          <s id="N1480B">Nec obſtat, funditores tardè po<lb></lb>tius quàm citò fundam irrotare, ac brachio circumferre; <lb></lb>Nam id faciunt, vt aptius erga deſtinatum ſitum ipſa irrota<lb></lb>tio dirigatur, aptiuſque brachium paulatim procedendo di<lb></lb>ſponatur, antequam miſsile ab eo totis viribus proijciatur. </s>
        </p>
        <p id="N14816" type="main">
          <s id="N14818">Altera verò cauſa propoſiti experimenti, quam Ariſtote<lb></lb>les aſsignat, eaque potior eſt, quia in fundæ vſu manus (ſeu <lb></lb>potius pars vbi brachium humero iungitur, vt optimè Bal<lb></lb>dus adnotauit) conſtituitur quaſi centrum circuli deſcripti <lb></lb>per eius motum, funda verò (ſcilicet ſimul cum brachio) <lb></lb>ſe habet tanquam linea, quæ à centro ad peripheriam ex<lb></lb>tenditur. </s>
          <s id="N14827">Quanto autem productior, ac longior eſt linea, <pb pagenum="152" xlink:href="005/01/160.jpg"></pb>quæ à centro ad periferiam tendit, vt illa, quæ ex brachio, &amp; <lb></lb>funda conſtituitur in rotatione; tanto velocius mouetur. <lb></lb></s>
          <s id="N14832">Cumque ex maiori velocitate iſtius motus, maior impetus <lb></lb>producatur; hinc fit, vt quod funda iacitur, tanquam per <lb></lb>velociorem iaculationem, maiorem impetum à funditore <lb></lb>recipiat, quàm ſi manu mittatur, longiuſque valde proinde <lb></lb>feratur. </s>
          <s id="N1483D">Iactus enim qui manu fit, inquit Ariſtoteles, breuis <lb></lb>eſt reſpectu ſcilicet eius, qui funda efficitur. </s>
        </p>
        <p id="N14842" type="main">
          <s id="N14844">Ad primam igitur rationem dubitandi reſponderi poteſt, <lb></lb>maiorem, aut minorem comprehenſionem proiecti, parum <lb></lb>aut nihil conferre ad vlteriorem eius emiſsionem, ſed po<lb></lb>tius modum comprehendendi diuerſum proportionatum, <lb></lb>in quantum ſcilicet ipſa comprehenſio ad commoditatem <lb></lb>pertinet iaculandi quaſi artificiosè. </s>
          <s id="N14851">Vt ſi quis teſtam, vel <lb></lb>complanatum lapillum eminus proijcere velit, inter pol<lb></lb>licem, &amp; indicem ſupra medium digitum collocat, vt ip<lb></lb>ſo indice incuſſo impetu in latus poſterius, ille per aera, ean<lb></lb>dem poſitionem ſeruando, feratur, qua cum facilius præeun<lb></lb>te acie aerem ſcindat, vlterius quoque pergere valeat. </s>
          <s id="N1485E">Alio<lb></lb>quin ad abſolutam proiecti emiſsionem, ſatis illud com<lb></lb>prehenditur funda, <expan abbr="ideoq.">ideoque</expan> nihil minor comprehenſio ob<lb></lb>ſtat, quominus funditor longius iaciat, cum hoc ſibi vendi<lb></lb>cet aliunde. </s>
        </p>
        <p id="N1486D" type="main">
          <s id="N1486F">Ad ſecundam reſpondetur, grauitatem inſtrumenti nul<lb></lb>lam, vt plurimum augere difficultatem in latione, aut <lb></lb>proiectione ponderis dummodo proportionem quandam <lb></lb>habeat cum potentia motrice, vt patere poteſt inductio<lb></lb>ne, tam in vectibus plurimis, ac rotis curruum, quàm in <lb></lb>in machinis bellicis, aut venatorijs, quibus miſsilia iaciuntur. <lb></lb></s>
          <s id="N1487D">Quare cum grauitas fundæ, vel nullius momenti in ſe ſit, <lb></lb>vel ad ſummum ſit grauitas inſtrumenti, nullam pariter ſu<lb></lb>pra pondus proiecti augere poteſt difficultatem, ad quam <lb></lb>ſuperandam maior conatus potentiæ requiratur, minuſque <lb></lb>propterea funda, quàm ſola manu, proiectum mittatur. </s>
        </p>
        <p id="N14888" type="main">
          <s id="N1488A">Vna tamen adhuc ſupereſt difficultas, quæ non mediocris <lb></lb>eſt momenti; nimirum quo pacto motus circularis, quo <pb pagenum="153" xlink:href="005/01/161.jpg"></pb>funda circumducitur miſsile, antequam proijciatur, ad mo<lb></lb>tum rectum proiectionis vim ac robur adijcere poſsit; ita vt <lb></lb>impetus in circumlatione acquiſitus, in impetum proie<lb></lb>ctionis refundatur. </s>
          <s id="N1489A">Siquidem quilibet ex ijs duobus im<lb></lb>pulſibus, natura ſua ad <expan abbr="motũ">motum</expan> valde <expan abbr="diuersũ">diuersum</expan> videtur ordinari. </s>
        </p>
        <p id="N148A7" type="main">
          <s id="N148A9">Sed pro ſolutione ſtabiliendum prius eſt, qualitatem im<lb></lb>petus corporibus impreſſam, varios quidem motus per ac<lb></lb>cidens in illis poſſe cauſare; per ſe tamen ac natura ſua non <lb></lb>niſi ad motum rectum ordinari. </s>
          <s id="N148B2">Id quod obſeruatione faci<lb></lb>lè comprobatur; Nam ſi attentè animaduertere quis velit, <lb></lb>nullum inueniet impetum per quem proiectum aliter quàm <lb></lb>recta tendat in terminum ſui motus: niſi fortaſſe aliqua ex <lb></lb>parte repercutiatur, aut impediatur. </s>
          <s id="N148BD">Vt cum proiecta pila <lb></lb>repercutiatur à loco in quem impulerit, ac reddere cogitur, <lb></lb>vel declinando à rectitudine propter impedimentum, obli<lb></lb>què vlterius pergit. </s>
          <s id="N148C6">Aut certè cum corpori fune ſuſpenſo, <lb></lb>&amp; alicubi alligato incutitur impulſus, <expan abbr="illudq.">illudque</expan> non rectà quò <lb></lb>mittitur, ſed in orbem mouetur, eo quod detineatur in cen<lb></lb>tro ex quo per funem propendet. </s>
          <s id="N148D3">Nam ſi in eadem circum<lb></lb>latione rumpatur funis, aut ſoluatur, videmus idem corpus <lb></lb>recta tendere, quò verſus per vltimum arcum ſuæ circum<lb></lb>uolutionis reſpiciebat. </s>
          <s id="N148DC">Quod ſanè apertum indicium eſt, <lb></lb>abſque impedimento per impulſum impreſſum corpora <lb></lb>nonniſi rectà moueri. </s>
        </p>
        <p id="N148E3" type="main">
          <s id="N148E5">Quod ſi ignes miſsiles ſulphureo puluere artificioſiſsimè <lb></lb>compactos videamus huc illuc variis <expan abbr="tortuoſisq.">tortuoſisque</expan> itineribus <lb></lb>diſcurrere; id ex eo fit, quia ſulphureus puluis, ita eſt intra <lb></lb>cartaceos eorum anfractus artificiosè diſpoſitus, vt accen<lb></lb>ſus, diuerſis ex lateribus vim inferat, ex quibus illi in oppo<lb></lb>ſita loca ferantur, ac veluti per obliquos calles ſerpendo <lb></lb>diſcurrere videantur. </s>
          <s id="N148F8">Quod quippe tantum arguit mixtio<lb></lb>nem ipſius motus procedentem à varia ſituatione pulueris, <lb></lb>ſeu cauſæ impellentis; cum alias etiam quilibet impetus ab <lb></lb>accenſo puluere productus directè tendat, ac moueat verſus <lb></lb>eam partem in quam ſeſe dilatando confert, &amp; qua eſt illi <lb></lb>additus, vt ex anguſtia elabatur, ac foris erumpat. </s>
        </p>
        <pb pagenum="154" xlink:href="005/01/162.jpg"></pb>
        <p id="N14909" type="main">
          <s id="N1490B">His ergo ſic ſtabilitis, facilè ſoluetur difficultas propoſi<lb></lb>ta, nam impetus miſſili incuſſus dum funda circumageretur <lb></lb>non corrumpitur, nec deſinit eſſe per aduentum noui impe<lb></lb>tus, quo recta illud proijcitur, cum neque natura ſua, neque <lb></lb>poſitione ei opponatur. </s>
          <s id="N14916">Siquidem in fine cuiuſdam rotatio<lb></lb>nis iacitur proiectum verſus eam partem in quam vltimò <lb></lb>vergebat, ſeu reſpiciebat vltimus arcus deſcriptus per cir<lb></lb>cumductionem illius; ita vt motus obliquus circuitionis ſen<lb></lb>ſim rectus euadat. </s>
          <s id="N14921">Quamobrem ipſe impetus quo circum<lb></lb>ducebatur facilè tranſit in impetum, quo rectà illud rapitur, <lb></lb>vel addit ſe ei, qui de nouo illi per actum proiectionis incu<lb></lb>titur. </s>
        </p>
        <p id="N1492A" type="head">
          <s id="N1492C">Quæſtio Decimatertia.</s>
        </p>
        <p id="N1492F" type="main">
          <s id="N14931">C<emph type="italics"></emph>vr circa idem iugum maiores collopes faci<lb></lb>liùs, quàm minores mouentur: &amp; item ſucu<lb></lb>læ, quæ graciliores ſunt, ab eadem vi, quàm <lb></lb>craſsiores? </s>
          <s id="N1493D">An quia ſucula quidem &amp; iu<lb></lb>gum, centrum est: prominentes autem longi<lb></lb>tudines, eæ quæ ſunt à centro? </s>
          <s id="N14944">Celerius au<lb></lb>tem &amp; plus mouentur, quæ maiorum ſunt circulorum, ab ea<lb></lb>dem vi, quàm quæ minorum. </s>
          <s id="N1494B">Ab eadem enim vi plus tranſ<lb></lb>fertur id extremum, quod longius à centro distat. </s>
          <s id="N14950">Quamob<lb></lb>rem ad iugum quidem inſtrumenta faciunt collopas, quibus <lb></lb>facilius verſant: in gracilibus autem ſuculis plus fit id, quod <lb></lb>extra lignum est. </s>
          <s id="N14959">Hoc autem id efficitur, quod à centro exit.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1495E" type="head">
          <s id="N14960">COMMENTARIVS.</s>
        </p>
        <p id="N14964" type="main">
          <s id="N14966">Cvm plura iugum de ſe poſſit ſignificare, hoc loco ſu<lb></lb>mitur ab Ariſtotele pro <expan abbr="inſtrumẽto">inſtrumento</expan> quodam ligneo, <lb></lb>quo textores in machina textoria. </s>
          <s id="N14971">vtuntur, vt ſta<lb></lb>men <expan abbr="telasq.">telasque</expan> conuoluant. </s>
          <s id="N1497A">Oblongum itaque ac teres quod<lb></lb>dam lignum eſt ſuper tranſuerſa ipſius textrinæ locatum, <pb pagenum="155" xlink:href="005/01/163.jpg"></pb>bina circa <lb></lb><figure id="id.005.01.163.1.jpg" xlink:href="005/01/163/1.jpg"></figure><lb></lb><expan abbr="vtramq.">vtramque</expan> ex<lb></lb>tremitatem <lb></lb><expan abbr="habẽs">habens</expan> fora<lb></lb>mina, qui<lb></lb>bus toti<lb></lb>dem collo<lb></lb>pes, ſeu fu<lb></lb>ſtes infigun<lb></lb>tur, vt faci<lb></lb>liùs iugum ipſum eorum beneficio cum opus fuerit conuer<lb></lb>tatur, vt præ ſefert ſubſtrata figura. &lt;</s>
        </p>
        <p id="N149A6" type="main">
          <s id="N149A8">Sucula item quamuis alia poſſit ſignificare, hic tamen <lb></lb>machinam ſignificat tractorij generis, quæ ex tereti ligno, <lb></lb>aut lignorum compagine conſtat, adiuncto axe ſuffulta <lb></lb>æquidiſtante à plano horizontis, duobus, vel pluribus col<lb></lb>lopibus pari longitudine vtrinque immobiliter adſtantibus <lb></lb>tanquam rotæ radijs circa modiolum, quibus admota ma<lb></lb>nu, ſucula ipſa circa proprium axem obuoluitur, <expan abbr="funeq.">funeque</expan> cir<lb></lb>cumducto, pondera ſubleuat, vt præ oculis hic eſt videre <lb></lb>in eius figura. </s>
        </p>
        <p id="N149BF" type="main">
          <s id="N149C1">Quærit igitur Ari<lb></lb><figure id="id.005.01.163.2.jpg" xlink:href="005/01/163/2.jpg"></figure><lb></lb>ſtoteles cur ſi lon<lb></lb>giores fuerint collo<lb></lb>pes facilius iugum <lb></lb>circumagatur, quam <lb></lb>ſi minores, ac bre<lb></lb>uiores extiterint. <lb></lb></s>
          <s id="N149D7"><expan abbr="Itemq.">Itemque</expan> cur gracilio<lb></lb>res ſucculæ facilius <lb></lb>pariter ab <expan abbr="eadẽ">eadem</expan> po<lb></lb>tentia circumuoluantur, quàm craſſiores. </s>
          <s id="N149E7">Vtriuſque ſubin<lb></lb>de cauſam eſſe inquit, quod in vtraque machina quilibet <lb></lb>collops tanquam vectis ſe habet, cuius <expan abbr="centrũ">centrum</expan>, ac fulcimen<lb></lb>tum eſt in medio iugi, vel ſuculæ, ſiue in intimo axe coniun<lb></lb>cto, aut ſaltem in ipſis concepto: potentia verò in extremi-<pb pagenum="156" xlink:href="005/01/164.jpg"></pb>tate, quæ extra ipſum iugum, vel ſuculam prominet, vbi <lb></lb>manus communiter adhibetur: ac onus conſtituitur in exti<lb></lb>ma ipſa vtriuſque corporis ſuperficie, quam fortiter præ<lb></lb>mendo vbi è foramine prodit, ſecum conuoluit, ac verſat. <lb></lb></s>
          <s id="N14A02">Cuius quippe vectis ſimilitudinem, &amp; operationem hacte<lb></lb>nus etiam in malo expreſsimus loquendo de motione nauis <lb></lb>vento agitatæ. </s>
          <s id="N14A09">Cum itaque plus atque celerius transfera<lb></lb>tur ab eadem potentia extremum ſemidiametri, quod ma<lb></lb>gis à centro diſtat in deſcriptione circuli, nec non plus, ac <lb></lb>facilius mouere valeat extremum vectis, quod longius à <lb></lb>fulcimento reſpectu oneris leuandi protenditur, quò lon<lb></lb>giores fuerint collopes, ſemidiametri, ac vectis rationem <lb></lb>adepti, <expan abbr="magisq.">magisque</expan> eorum extrema à fulcimento, ſeu centro <lb></lb>in ſuperficie conuoluenda diſtauerint, eò faciliùs iugum, aut <lb></lb>ſuculam contorquendo verſabunt. </s>
          <s id="N14A20">Quoniam verò in omni <lb></lb>vecte maior, aut minor diſtantia, quàm à centro, vel fulci<lb></lb>mento habet extremum, in quo applicatur potentia, atten<lb></lb>ditur ſolummodo reſpectu diſtantiæ, quam ſimul habet onus <lb></lb>ab eodem centro, vel fulcimento; hinc fit, vt in graciliori<lb></lb>bus ſuculis, minore exiſtente diſtantia à centro ad circum<lb></lb>ferentiam, ſeu extimam ſuperficiem conuexam vbi conſti<lb></lb>tuitur onus, &amp; vbi fit collopis præſsio, maior diſtantia relin<lb></lb>quatur vſque ad alterum extremum eiuſdem collopis, quod <lb></lb>eſt extra; ac iuxta maiorem hanc proportionem, magis pa<lb></lb>riter collops ipſe mouere ſuculam valeat. </s>
        </p>
        <p id="N14A37" type="main">
          <s id="N14A39">Quod ſi contra hanc expoſitionem obijciatur, quòd Ari<lb></lb>ſtoteles palàm &amp; abſolutè docuerit, tàm ſuculam, quàm iu<lb></lb>gum <expan abbr="cõſtitui">conſtitui</expan> centrum in collopum motione; ex quo aſſum<lb></lb>pto minus concluderentur, quæ de ipſius mente relata ſunt; <lb></lb>Occurrendum eſt, id ſano modo eſſe intelligendum. </s>
          <s id="N14A48">Nam <lb></lb>eodem pacto præcedenti quæſtione apud ipſum Philoſo<lb></lb>phum legimus, manum, non iuncturam brachij habere <lb></lb>rationem centri in motu circulari, quo circumuertitur fun<lb></lb>da. </s>
          <s id="N14A53">Et tamen ibi vt vidimus ſicut hic omnino diuerſus eſt <lb></lb>ſenſus, qui ſanè potius ex contextu aliorum omniumque <lb></lb>verborum, quàm ex vno tantum verbo fortè mendoſo eli-<pb pagenum="157" xlink:href="005/01/165.jpg"></pb>ciendus eſt. </s>
          <s id="N14A5F">Cum igitur vtrobique iuxta ſenſum explica<lb></lb>tum conſonent reliqua verba, viſque argumenti non aliter <lb></lb>appareat, quàm quo expoſuimus modo, ſecluſo omni con<lb></lb>tentionis pruritu, nullus ambigendi locus relinquitur de <lb></lb>mente Ariſtotelis in his, quæ illum interpretando retuli<lb></lb>mus. </s>
        </p>
        <p id="N14A6C" type="head">
          <s id="N14A6E">Quæſtio Decimaquarta.</s>
        </p>
        <p id="N14A71" type="main">
          <s id="N14A73">C<emph type="italics"></emph>vr eiuſdem magnitudinis lignum faciliùs <lb></lb>genu. </s>
          <s id="N14A7B">frangitur, ſi quiſpiam æquè deductis <lb></lb>manibus extrema comprehendens fregerit, <lb></lb>quàm ſi iuxta genu: &amp; ſi terræ illud appli<lb></lb>cans pelle ſuperimpoſito, manu longè didu<lb></lb>cta confregerit, quàm propè? </s>
          <s id="N14A86">An quia ibi <lb></lb>quidem genu centrum eſt, bìs verò ipſe pes. </s>
          <s id="N14A8D">Quantò autem <lb></lb>remotiùs à centro fuerit, faciliùs mouetur quodcunque. </s>
          <s id="N14A92">Mo<lb></lb>ueri autem quod frangitur, neceſſe est.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N14A99" type="head">
          <s id="N14A9B">COMMENTARIVS.</s>
        </p>
        <p id="N14A9F" type="main">
          <s id="N14AA1">Qvoniam fracturus quiſpiam manibus, ac ſimul ge<lb></lb>nu, aut pede aliquod lignum, dupliciter poteſt ad <lb></lb>hoc præſtandum ſe gerere; nempe vel æquè dedu<lb></lb>ctis manibus extrema ligni comprehendens, <expan abbr="genuq.">genuque</expan> aut pe<lb></lb>de circa medium tanquam fulcimento adhibito, illa ad ſe <lb></lb>retrahendo: vel manibus non niſi iuxta genu àc prope me<lb></lb>dium vtrinque admotis, vtrunque ipſius ligni dimidium in<lb></lb>clinando: Quærit hic Ariſtoteles, cur facilius priori, quàm <lb></lb>poſteriori modo ſequatur præruptio, etiam ſi eiuſdem ma<lb></lb>gnitudinis ſit lignum, <expan abbr="eademq.">eademque</expan> virtus in fractione adhibea<lb></lb>tur. </s>
          <s id="N14AC0"><expan abbr="Idemq.">Idemque</expan> contingat ſi humi lignum ipſum ſubſternatur <lb></lb><expan abbr="pedeq.">pedeque</expan> circa medium ſuperimpoſito, manus ad tollendum <lb></lb><expan abbr="ſurſumq.">ſurſumque</expan> curuandum alterum, vel vtrumque eius extremum <lb></lb>admoueatur, vt ſcilicet quò longius à pede lignum com-<pb pagenum="158" xlink:href="005/01/166.jpg"></pb>prehenderit, eo facilius tollat atque confringat. </s>
        </p>
        <p id="N14AD7" type="main">
          <s id="N14AD9">Huius igitur cauſam eam eſſe, inquit Ariſtoteles. </s>
          <s id="N14ADD">Nam <lb></lb>explicatus motus, qui fit in fractione ligni, eſt motus circu<lb></lb>laris, cuius centrum conſtituitur genu vel pes, ſeu punctum <lb></lb>ligni medium, quod ſuffultum illis quieſcit. </s>
          <s id="N14AE6">Dimidia verò <lb></lb>ipſius ligni confringendi dum inclinantur ſe <expan abbr="habẽt">habent</expan> tanquam <lb></lb>duo ſemidiametri circulariter ducti angulum efficientes in <lb></lb>ipſo centro circuli quem deſcribunt. </s>
          <s id="N14AF3">Quanto autem remo<lb></lb>tius à centro fuerit quodcumque circulariter moueri de<lb></lb>bet, tanto facilius mouetur. </s>
          <s id="N14AFA">Facilius ergo manus dictum <lb></lb>motum perficient ſi longius, quàm ſi propius genu, vel <expan abbr="pe-dẽ">pe<lb></lb>dem</expan>, lignum apprehenderint. </s>
          <s id="N14B05"><expan abbr="Cumq.">Cumque</expan> ex hac motione, &amp; <lb></lb>inclinatione vtriuſque dimidij procedat ipſa fractio ligni, ſe<lb></lb>quitur etiam facilius longè quàm propè diductis manibus <lb></lb>ipſum lignum confringi. </s>
        </p>
        <p id="N14B11" type="main">
          <s id="N14B13">Cur autem non obſtante prædicta diſparitate in modo, <lb></lb>quo frangitur lignum, cæteris paribus difficilius <expan abbr="fuãgatur">frangatur</expan> <lb></lb>ſi craſsius ipſum ſit, quàm ſi gracilius, non docet Ariſtote<lb></lb>les. </s>
          <s id="N14B23">Ex ipſa <expan abbr="tamẽ">tamen</expan> rei natura quiſque ſtatim intelliget abſque <lb></lb>eo, quod recurrat cum Baldo ad rationem illam angulati <lb></lb>vectis, quam dicit habere <expan abbr="vtrumq.">vtrumque</expan> dimidium ligni prærupti. <lb></lb></s>
          <s id="N14B33">Siquidem cum tota difficultas, quæ reperitur in fractione <lb></lb>ligni oriatur ex reſiſtentia partium ſeparandarum, eo quod <lb></lb>hæ inter ſe naturali nexu coniunctæ, neceſſariò obſtent ſe<lb></lb>parationi ab inuicem: quo plures fuerint ipſæ partes, eo ma<lb></lb>gis obſtabunt, <expan abbr="difficiliusq.">difficiliusque</expan> proinde per earum diuiſionem <lb></lb>lignum quodlibet ex ipſis compoſitum confringetur. </s>
        </p>
        <p id="N14B44" type="main">
          <s id="N14B46">Illud etiam hic quæri poſſet, quod Ariſtoteles prætermi<lb></lb>ſit, cur prius ex parte ſuperiori, ac extra angulum, quem effi<lb></lb>ciunt dimidia ligni inclinata, quàm ex parte inferiori in cu<lb></lb>ſpide ipſius anguli vbi <expan abbr="cẽtrum">centrum</expan> motionis conſtituitur, fractio <lb></lb>ipſa ligni ſequatur. </s>
          <s id="N14B55">Facilisque erit reſponſio ſi dicamus id <lb></lb>fieri, quia illæ partes continui in fractione prius ab inuicem <lb></lb>ſeparantur, quæ &amp; citius &amp; longius coguntur diſcedere: In <lb></lb>fractione autem ligni per inclinationem, &amp; complicationem <lb></lb>vtriuſque dimidij, ex partibus craſsitiei, quæ ab inuicem di-<pb pagenum="159" xlink:href="005/01/167.jpg"></pb>uelluntur, illæ citius ac longius ab inuicem coguntur diſce<lb></lb>dere, quæ magis diſtant à puncto, quod conſtituitur cen<lb></lb>trum in hac motione; quia nimirum illæ diſcedendo, maio<lb></lb>rem ſemper arcum deſcribunt eodem tempore, quam quæ <lb></lb>propinquiores ſunt centro. </s>
          <s id="N14B6D">Illæ igitur ipſæ partes craſſitiei <lb></lb>diſtantiores a centro prius, ac citius ab inuicem ſeparantur, <lb></lb>ac proinde fractio non ab ipſo centro, vel parte inferiori vbi <lb></lb>fulcitur, ſed à parte ſuperiori, ac remotiori ab illo, initium <lb></lb>ſumere debet. </s>
        </p>
        <p id="N14B78" type="main">
          <s id="N14B7A">Quod vt planius conſtet, eſto lignum, quod frangitur AB. <lb></lb></s>
          <s id="N14B7F">Centrum vbi fulcitur C, <expan abbr="ſintq.">ſintque</expan> fracta, vel frangenda dimi<lb></lb>dia AD, &amp; EB ſemicirculum deſcribentia AFB circa <lb></lb><figure id="id.005.01.167.1.jpg" xlink:href="005/01/167/1.jpg"></figure><lb></lb>ipſum C. </s>
          <s id="N14B91">Partes <lb></lb>verò quæ ab in<lb></lb>uicem ſeparan<lb></lb>tur ſint illæ, quæ <lb></lb>exiſtunt in lineis <lb></lb>DC, &amp; EC re<lb></lb>pręſentantes la<lb></lb>titudinem, vel <lb></lb>craſsitiem ligni. <lb></lb></s>
          <s id="N14BA5">Dicimus ergo ex <lb></lb>huiuſmodi par<lb></lb>tibus, quæ ſunt in ipſis lineis DC, &amp; EC, illas quæ magis <lb></lb>diſtant à puncto C citius moueri, ac per maius interuallum <lb></lb>ab inuicem ſeparari: quod eſt prius confringi, quàm quæ <lb></lb>propinquiores ſunt puncto C. </s>
          <s id="N14BB3">Siquidem ipſum C non <lb></lb>modo conſtituitur centrum in hac motione reſpectu ſemi<lb></lb>circuli AFB; ſed etiam reſpectu ſemicirculi GDEH, qui <lb></lb>efficitur à punctis DE, vt tandem DA poſt abſolutam <lb></lb>complicationem ligni reperiatur in GI; &amp; EB in HK. </s>
          <s id="N14BBE">Qua<lb></lb>propter lineæ DC, &amp; EC conſtituuntur tanquam duo ſe<lb></lb>midiametri, cuius partes quo remotiores fuerint à centro <lb></lb>C, eo velocius ab eadem potentia mouentur, <expan abbr="maiusq">maiusque</expan> ſpa<lb></lb>tium in æquali tempore percurrunt, vt ſępius probatum eſt. </s>
        </p>
        <p id="N14BC9" type="main">
          <s id="N14BCB">Diximus autem prius ſeparari partes diſtantiores à pun-<pb pagenum="160" xlink:href="005/01/168.jpg"></pb>cto C in ipſis lineis DC, &amp; EC, loquendo de illis prout <lb></lb>repræſentant materialem craſsitiem ligni, quæ non ſtatim <lb></lb>ac tota ſimul diſrumpitur. </s>
          <s id="N14BD7">Nam abſtractè loquendo de ip<lb></lb>ſis lineis, quæ ante diuiſionem coincidebant in vnam, non <lb></lb>poſſet intelligi, prius ſeparari vnam partem illarum, quàm <lb></lb>aliam cum ſimul omnes, magis aut minus diſtando diſiungi <lb></lb>deberent conſtituendo angulum DCE. </s>
          <s id="N14BE2">Alioquin non eſ<lb></lb>ſent rectæ, vt per ſe patet. </s>
        </p>
        <p id="N14BE7" type="head">
          <s id="N14BE9">Quæſtio Decimaquinta.</s>
        </p>
        <p id="N14BEC" type="main">
          <s id="N14BEE">C<emph type="italics"></emph>vr ea, quæ circa littora appellantur, crocæ, <lb></lb>rotunda ſunt figura, cùm alioqui à principio <lb></lb>ex magnis ſint lapidibus, ostreisvè? </s>
          <s id="N14BF8">An <lb></lb>quia, ea, quæ plus recedunt à medio in motio<lb></lb>nibus: feruntur celeriùs? </s>
          <s id="N14BFF">Medium enim <lb></lb>fit centrum: interuallum verò ea, quæ à cen<lb></lb>tro. </s>
          <s id="N14C06">Semper autem maior ab ęquali motione maiorem deſcri<lb></lb>bit circulum. </s>
          <s id="N14C0B">Quod autem maius in ęquali pertranſit tem<lb></lb>pore, celeriùs fertur. </s>
          <s id="N14C10">Quę autem celeriùs ex ęquali feruntur <lb></lb>ſpatio, vebementius impetunt. </s>
          <s id="N14C15">Quę autem magis impetunt, <lb></lb>impetuntur &amp; magis: quamobrem ea, quę plus à medio di<lb></lb>ſtant, confringi neceſſe eſt: id autem cùm patiantur, rotunda <lb></lb>fieri eſt neceſſarium. </s>
          <s id="N14C1E">Crocis autem propter maris motum, <lb></lb>quoniam ſimul cum illo agitantur, in perpeti e&lt;32&gt;e accidit mo<lb></lb>tione, <expan abbr="eòq.">eòque</expan> verſatas modo ſemper offenſare. </s>
          <s id="N14C29">Id autem ipſis <lb></lb>maximè extremis contingere partibus eſt neceſſe.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N14C30" type="head">
          <s id="N14C32">COMMENTARIVS.</s>
        </p>
        <p id="N14C36" type="main">
          <s id="N14C38">Crocæ apud Græco sidem ſignificant, ac apud Lati<lb></lb>nos vmbilici, quorum meminit Cicero 2. de Orato<lb></lb>re; <expan abbr="ſuntq.">ſuntque</expan> expoliti illi calculi, qui in littoribus repe<lb></lb>riuntur continua maris agitatione attriti, ac in orbicularem, <lb></lb>vel rotundam figuram redacti, vt qui in glarea arenis viſun-<pb pagenum="161" xlink:href="005/01/169.jpg"></pb>tur admiſti. </s>
          <s id="N14C4C">De ijs igitur hic loquens Ariſtoteles, quærit, <lb></lb>qua de cauſa rotundam potius quam aliam figuram per at<lb></lb>tritionem ac perpetuam illam agitationem adipiſcantur, <lb></lb>cum frequentius ex lapidibus, ac fragmentis alterius figuræ <lb></lb>efficiantur. </s>
          <s id="N14C57">Quod enim ſecundum omnes ſui partes paula<lb></lb>tim conteritur, ac minuitur, vniformiter difformiter contun<lb></lb>di debet, ac ſenſim attenuari, eadem partium proportione <lb></lb>ſeruata, <expan abbr="eademq.">eademque</expan> proinde figura. </s>
          <s id="N14C64">Non igitur ſatis apparet <lb></lb>cur ex tot tanquam ex diuerſis figuris teſtarum oſtreorum <lb></lb><expan abbr="concarumq.">concarumque</expan> ac lapidum angularium non niſi rotundam, &amp; <lb></lb>orbicularem formam eorum reliquiæ videantur ſeruare, <lb></lb><expan abbr="eiuſdemq.">eiuſdemque</expan> figuræ penè omnes euadant cuius non erant. </s>
        </p>
        <p id="N14C75" type="main">
          <s id="N14C77">Huic autem quæſtioni Ariſtoteles reſpondet, partes, quæ <lb></lb>magis à centro, ſeu puncto medio circumlati corporis rece<lb></lb>dunt, cum celerius in eius circumuolutione ferantur (maius <lb></lb>videlicet in æquali tempore ſpatium in rotatione conficien<lb></lb>do) vehementius impetere, <expan abbr="vicinaq.">vicinaque</expan> corpora rotando per<lb></lb>cutere, quàm partes centro propinquiores; velocitas enim <lb></lb>auget impulſum: Quæ autem partes <expan abbr="vehemẽtius">vehementius</expan> impetunt, <lb></lb>atque impingunt, ſi fragiles in ſe ſint, facilius etiam refran<lb></lb>guntur. </s>
          <s id="N14C92">Cum igitur prominentiores partes crocearum ſint <lb></lb>huiuſmodi, vt celerius in ſuos orbes ruant, vehementiuſque <lb></lb>propterea illidant, ſequitur facilius ipſas contundi, <expan abbr="ſolumq.">ſolumque</expan> <lb></lb>propterea relinqui partes à centro æquidiſtantes, ex quibus <lb></lb>reſultat orbicularis, ac rotunda figura, quam in ipſis croceis <lb></lb>communiter cernimus. </s>
        </p>
        <p id="N14CA3" type="main">
          <s id="N14CA5">Quod ſi ex hoc Ariſtotelis diſcurſu ſequatur maiores <lb></lb>croceas rotundiores fieri, quàm minores propter maiorem <lb></lb>à centro diſtantiam, qua in rotatione prominentes partes <lb></lb>facilius contunduntur; id certè ab experientia non eſt om<lb></lb>nino alienum, vt Baldus arbitratur; ſicut nec ipſas croceas <lb></lb>circa centrum conuerti, quamuis alijs, ac diuerſis etiam mo<lb></lb>tionibus agitentur. </s>
          <s id="N14CB4">Si enim in pluribus littoribus attentius <lb></lb>obſeruaſſet, vidiſſet vtique fluctuum iactatione fluxu, ac re<lb></lb>fluxu, non modo glareas, paruoſque lapillos circa centrum <lb></lb>omnino conuolui, ſed etiam maiores vmbilicos, &amp; non me<pb pagenum="162" xlink:href="005/01/170.jpg"></pb>diocria ſaxa ſimiliter in orbem ruere, <expan abbr="ſeſeq.">ſeſeque</expan> collidere, quæ <lb></lb>niſi magna valde ſint, vt rotari minus commodè poſsint, <lb></lb>mutua ipſorum colliſione, orbiculata euadunt, vel ad orbi<lb></lb>cularem figuram accedunt magis quàm minores lapilli, vel <lb></lb>teſtæ. </s>
          <s id="N14CCE">Vnde latiſsimæ plagæ viſuntur his tantum rotundis <lb></lb>lapidibus ſtratæ, nulla ferè admiſta arena, parua teſta, vel <lb></lb>glarea. </s>
          <s id="N14CD5">Quod verò non omnes lapides leuigatos, ac rotun<lb></lb>dos tanquam torno fabrefactos ſe videantur oſtendere; id <lb></lb>potius materiæ varietati tribuendum eſt, qua non omnes <lb></lb>partes æquè fragiles conſtituuntur, vt pariter poſsint ſua <lb></lb>volubilitate contundi. </s>
          <s id="N14CE0">Imò minores vmbilicos, vt plurimùm <lb></lb>fragiliorem adeptos eſſe materiam argumento eſſe poteſt <lb></lb>ipſa eorum paruitas. </s>
          <s id="N14CE7">Non enim ex magnis parui facti eſſent, <lb></lb>niſi materia, ex qua conſtant facilè cederet, ac cedendo vni<lb></lb>formiter attenuaretur, ex quo prouenit leuitas. </s>
        </p>
        <p id="N14CEE" type="main">
          <s id="N14CF0">Denique ratio, vel cauſa ab Ariſtotele adducta non tollit <lb></lb>quin ex alia ſimul concauſa idipſum dicamus procedere, <lb></lb>quam tetigit Piccolomineus ac Baldus. </s>
          <s id="N14CF8">Quia nimirum vni<lb></lb>uerſaliter loquendo omnes eminentiæ, <expan abbr="omnesq.">omnesque</expan> anguli in <lb></lb>corporibus, natura ſua infirmiores ſunt reliquis partibus in<lb></lb>timioribus, quæ æquè diſtant à centro. </s>
          <s id="N14D05">Minus enim cir<lb></lb>cumfulciuntur ab illis dum prominent, <expan abbr="magisq.">magisque</expan> extrinſecis <lb></lb>offenſionibus ſunt expoſiti atque obnoxij. </s>
          <s id="N14D10">Vnde faciliùs <lb></lb>læduntur, ac retunduntur. </s>
          <s id="N14D15">Sicut nares, ac digiti manuſque <lb></lb>vel pedes in marmoreis ſtatuis, quæ propterea ſæpius mu<lb></lb>tilatæ reperiuntur effoſſæ. </s>
          <s id="N14D1C">Cum igitur reliquiæ lapidum, <lb></lb>ac oſtrearum aſsidua maris agitatione in littoribus vo<lb></lb>lutentur, atque inuicem illidantur, extremas <lb></lb><expan abbr="eminentesq.">eminentesque</expan> earum partes retundi neceſ<lb></lb>ſe eſt, ob idque eas in orbicularem <lb></lb>formam redigi, vel ad ip<lb></lb>ſam quantum fieri <lb></lb>poteſt acce<lb></lb>dere. </s>
        </p>
        <pb pagenum="163" xlink:href="005/01/171.jpg"></pb>
        <p id="N14D36" type="head">
          <s id="N14D38">Quæſtio Decimaſexta.</s>
        </p>
        <p id="N14D3B" type="main">
          <s id="N14D3D">C<emph type="italics"></emph>vr quantò longiora ſunt ligna, tantò imbe<lb></lb>cilliora fiunt: &amp; ſi tollantur, inflectuntur <lb></lb>magis, tametſi quod breue quidem eſt, ceu <lb></lb>cubitum, fuerit tenue: quòd verò cubitorum <lb></lb>centum, craſſum? </s>
          <s id="N14D4B">An quia &amp; vectis, &amp; onus, <lb></lb>&amp; hypomochlion, in leuando ipſa fit ligni <lb></lb>proceritas? </s>
          <s id="N14D52">Prior namque illius pars ceu hypomochlion fit: <lb></lb>quòd verò in extremo eſt, pondus. </s>
          <s id="N14D57">Quamobrem quantò ex<lb></lb>tenſius fuerit id, quod ab hypomochlio eſt, tantò inflecti ne<lb></lb>ceſſe eſt magis. </s>
          <s id="N14D5E">Quo enim plus ab hypomochlio diſtat, eò ma<lb></lb>gis incuruari neceſſe eſt. </s>
          <s id="N14D63">Neceſſariò igitur extrema vectis ele<lb></lb>uantur. </s>
          <s id="N14D68">Si igitur flexilis fuerit vectis, ipſum inflecti magis <lb></lb>cum extollitur, neceſſe eſt, quod longis accidit lignis: in bre<lb></lb>uibus autem quod vltimum eſt, quieſcenti hypomochlion de pro<lb></lb>pe fit.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N14D73" type="head">
          <s id="N14D75">COMMENTARIVS.</s>
        </p>
        <p id="N14D79" type="main">
          <s id="N14D7B">Dvo quærit hic Ariſtoteles, quorum vnum pendet ex <lb></lb>alio. </s>
          <s id="N14D80">Primum eſt cur quanto longiora ſunt ligna, <lb></lb>tanto imbecilliora fiant, etiam ſi ſint pariter craſſio<lb></lb>ra. </s>
          <s id="N14D87">Secundum verò eſt cur longiora ipſa ligna ſi ab aliquo <lb></lb>extremo tollantur, magis inflectantur quàm breuiora, atque <lb></lb>etiam ſimul graciliora, vt haſtæ, vel ſariſſæ dum manu ab al<lb></lb>tero extremo apprehenduntur, atque à terra eleuantur ad <lb></lb>lineam horizonti parallelam: Nam quo longiores extite<lb></lb>rint, eò magis inclinantur, <expan abbr="minusq.">minusque</expan> rectitudinem, quam in <lb></lb>ſolo iacendo, vel ſtantes habebant, ſeruare queunt in aere <lb></lb>ita ſuſpenſæ. </s>
        </p>
        <p id="N14D9C" type="main">
          <s id="N14D9E">Ex ijs autem duobus quæſitis, ſecundo tantum <expan abbr="reſpõdet">reſpondet</expan> <lb></lb>Ariſtoteles, cum ex eius ſolutione facilè patere poſsit ſolu<lb></lb>tio primi. </s>
          <s id="N14DA9">Ait igitur ex hoc procedere maiorem inflexio<pb pagenum="164" xlink:href="005/01/172.jpg"></pb>nem ligni procerioris, quod cum lignum ita ſuſpenſum, ſi<lb></lb>mul conſtituatur vectis, &amp; onus, fulcimentum habens prope <lb></lb>alterum extremum in manu à qua eleuatur; quanto exten<lb></lb>ſius fuerit id quod à fulcimento eſt verſus alteram extremi<lb></lb>tatem, quæ conſtituitur pondus; tanto magis ipſum inflecti <lb></lb>neceſſe eſt, ſuppoſito quod vectis ipſa ſeu lignum, ex ſe fle<lb></lb>ctile ſit; id quod non contingit in breuibus lignis, aut vecti<lb></lb>bus etiam ſi eadem ſeruetur proportio: Porrò extremum, <lb></lb>quod grauitat parum ſemper diſtat à fulcimento. </s>
          <s id="N14DC1">Sit enim <lb></lb>ſariſſa decem cubitorum longitudinis aliquantulum incli<lb></lb><figure id="id.005.01.172.1.jpg" xlink:href="005/01/172/1.jpg"></figure><lb></lb>nata ipſa AB, cuius manubrium A, cuſpis B, ſuffulta di<lb></lb>gitis vbi C, pollice præ mente in A tanquam potentia <lb></lb>eleuante. </s>
          <s id="N14DD2"><expan abbr="Eodemq">Eodemque</expan> pacto conſtituatur gracilior ſurculus <lb></lb>bicubitus DE fultus in F. </s>
          <s id="N14DD9">Dico igitur ſariſſam magis in<lb></lb>clinari quàm ſurculum, eo quod licet vtrumque habeat ra<lb></lb>tionem vectis ſimul &amp; oneris; pondus tamen conſtitutus in <lb></lb>B magis diſtat à fulcimento C, quàm quod <expan abbr="cõſtituitur">conſtituitur</expan> in E <lb></lb>ab ipſo F; <expan abbr="magisq.">magisque</expan> propterea grauitat, &amp; inclinat deorſum, <lb></lb>paulatim recedendo à rectitudine, quam ſtans, vel in ſolo <lb></lb>iacens habebat. </s>
        </p>
        <p id="N14DF0" type="main">
          <s id="N14DF2">Quod non abs re fuerit aliundè etiam confirmare, ac vl<lb></lb>terius declarare, notando prius ad inflexionem <expan abbr="cõtinui">continui</expan> duo <lb></lb>neceſſario requiri. </s>
          <s id="N14DFD">Vnum eſt determinata, ac proportiona<lb></lb>ta quædam virtus ſiue ponderis, ſiue motricis potentiæ, ita <lb></lb>vt ab alia minori nulla cauſari poſſit talis inflexio. </s>
          <s id="N14E04"><expan abbr="Quõd">Quod</expan> <lb></lb>certè <expan abbr="cõmune">commune</expan> eſt omnibus cauſis naturalibus reſpectu pro<lb></lb>priorum effectuum, ad quos ordinantur. </s>
          <s id="N14E12">Alterum verò eſt <pb pagenum="165" xlink:href="005/01/173.jpg"></pb>conſtipatio quædam aliquarum partium, aliarumque laxa<lb></lb>tio in corporibus flexibilibus tanquam condenſatio, ac ra<lb></lb>refactio. </s>
          <s id="N14E1E">Non enim poſſet continuum inflecti niſi partes il<lb></lb>lius, quæ concauam ſuperficiem conſtituunt viciſſim conſti<lb></lb>parentur; illæ verò quæ conuexam, laxarentur; ſeu quo fie<lb></lb>ri poteſt extenderentur. </s>
          <s id="N14E27">Cumque ſenſim natura ab vno ad <lb></lb>aliud in omnibus gradum faciat; hinc eſt, vt non in qualibet <lb></lb>longitudine ſiue diſtantia æquè fieri poſſit inflexio, ſed lon<lb></lb>gè facilius in ea, in qua paulatim procedendo, ita partes va<lb></lb>lent curuari, vt ſingulæ à rectitudine non videantur recede<lb></lb>re. </s>
          <s id="N14E34">Vt obſeruare eſt in portione, vel arcu alicuius magnæ <lb></lb>circumferentiæ, qui videtur à linea recta differre. </s>
        </p>
        <p id="N14E39" type="main">
          <s id="N14E3B">His poſitis duplici etiam ex capite dicemus contingere, <lb></lb>ligna quo longiora fuerint facilius inflecti. </s>
          <s id="N14E40">Primò namque <lb></lb>hoc ipſo, quod longiora ſunt magis grauitant, <expan abbr="maiorq.">maiorque</expan> con<lb></lb>ſtituitur vis à quo procedit inflexio. </s>
          <s id="N14E4B">E contra verò quo bre<lb></lb>uiora extiterint, eo minor eſt virtus huiuſmodi; quæ tandem <lb></lb>ſi minor ſit minima, quæ ſufficere poſsit ad motionem, nullo <lb></lb>pacto valet inflectere, vt patet in ſurculis calamis ac paleis, <lb></lb>quæ cum leuitate materiæ, tùm breuitate corporis, graui<lb></lb>tare non poſſunt quantum ſufficiat ad motum inflexionis. <lb></lb></s>
          <s id="N14E59">Quod ſi breuitas ligni compenſetur magna craſſitiei, obſta<lb></lb>bit ex alio capite ipſamet eadem craſsities propter maio<lb></lb>rem multitudinem partium, quarum aliæ conſtipari, aliæ au<lb></lb>tem laxari debent cum fit ipſa inflexio. </s>
          <s id="N14E62">Secundo verò nam <lb></lb>quanto maior eſt longitudo ipſius flexilis, tanto minor con<lb></lb>ſtituitur laxatio, &amp; conſtipatio ſingularum partium, quæ ar<lb></lb>cum inflexionis efficiunt, meliuſque valent ſenſim inflecti. <lb></lb></s>
          <s id="N14E6C">Vice autem verſa, quò breuior eſt longitudo illius, eò magis <lb></lb>ſingulæ partes curuari debent, vt totius continui fiat infle<lb></lb>xio. </s>
          <s id="N14E73"><expan abbr="Ideoq.">Ideoque</expan> difficilius curuantur, &amp; inflectuntur etiam ſi gra<lb></lb>cile ſit ipſum lignum, quod debet inflecti. </s>
        </p>
        <p id="N14E7B" type="main">
          <s id="N14E7D">Vtrum verò ſeruata eadem proportione craſsitiei ad lon<lb></lb>gitudinem, æquè facilè inclinetur magnum, ac paruum, ſeu <lb></lb>longum, ac breue, non ſatis videtur conſtare. </s>
          <s id="N14E84">Probabiliter <lb></lb>tamen dici poteſt, ſpectandum primò eſſe qualitatem, ac di<pb pagenum="166" xlink:href="005/01/174.jpg"></pb>ſpoſitionem materiæ, vt ſi grauior, aut leuior; denſior, aut <lb></lb>rarior; fortior, aut imbecillior in ſe ſit. </s>
          <s id="N14E90">Nam frequenter ex <lb></lb>ijs pendet, vt nonnulla corpora plus facilitatis ad ſe incli<lb></lb>nandum acquirant ex maiori longitudine, quàm difficulta<lb></lb>tis ex maiori craſſitie: Alia verò contra. </s>
          <s id="N14E99">Deinde ſpectan<lb></lb>dam eſſe ipſam eandem proportionem craſſitiei ad longitu<lb></lb>dinem conſiderando quænam illa ſit. </s>
          <s id="N14EA0">Etenim quamuis con<lb></lb>ſtituatur eadem proportio, in vno atque in altero, non ta<lb></lb>men omnis proportio eundem effectum in illis producit. <lb></lb></s>
          <s id="N14EA8">Eadem namque eſt proportio craſſitiei vnius digiti ad lon<lb></lb>gitudinem vnius cubiti atque quinquaginta digitorum ad <lb></lb>quinquaginta cubitorum: &amp; tamen virga ferrea, aut lignea <lb></lb>ſi digitalis craſſitiei fuerit <expan abbr="longitudinisq.">longitudinisque</expan> vnius cubiti, non <lb></lb>tam facilè ſuo pondere flectetur, ac lignum, vel ferrum <lb></lb>quinquaginta digitorum craſsitiei, <expan abbr="totidemq.">totidemque</expan> cubitorum <lb></lb>longitudinis. </s>
          <s id="N14EBF">Quod ſi vnius palmæ fuerit craſsitudo, longi<lb></lb>tudo verò vnius cubiti nihil difficilius videretur inflecti, <lb></lb>quam ſi duarum palmarum conſtitueretur craſsitudo in <lb></lb>longitudine bicubita. </s>
          <s id="N14EC8">Ad hæc proportio, quæ auget facili<lb></lb>tatem, aut difficultatem inflexionis in vna ſpecie ligni, non <lb></lb>auget in alia ſicut non æquè in ligno, ac ferro plumbo, aut <lb></lb>calibe. </s>
          <s id="N14ED1">Quare nihil determinari poteſt quo ad hoc niſi per<lb></lb>ſpecta, vt diximus diſpoſitione materiæ, <expan abbr="variaq.">variaque</expan> proportio<lb></lb>ne, quæ diuerſimodè iuxta maiorem, aut minorem corpo<lb></lb>rum magnitudinem operatur. </s>
        </p>
        <p id="N14EDE" type="main">
          <s id="N14EE0">Denique vt dictum eſt de eleuatione, ac ſuſpenſione li<lb></lb>gni, vel alterius corporis oblongi ſumpti ab altera tantum <lb></lb>extremitate, vt exemplificauimus in ſariſſa, idem dicendum <lb></lb>eſt de eleuatione, ac ſuſpenſione, quæ fit, vel ex ambabus <lb></lb>extremitatibus; vel ex medio inter illas: Nam ſi vtrinque ab <lb></lb>extremitatibus ſuſpendatur aliquod lignum ad paralellum <lb></lb>horizonti, duo quidem in illo vectes fient in ipſis extremita<lb></lb>tibus fulti, <expan abbr="ponderaq">ponderaque</expan> in communi puncto intermedio gra<lb></lb>uitabunt tanquam in remotiſsimo ſitu ab vtriuſque fultura. <lb></lb></s>
          <s id="N14EF4">Quapropter ibidem fiet vtriuſque vectis, ſeu totius ligni in<lb></lb>flexio, ſuppoſita vt diximus flexibilitate materiæ, <expan abbr="ipſaq.">ipſaque</expan> ce-<pb pagenum="167" xlink:href="005/01/175.jpg"></pb>dente ſuomet ponderi. </s>
          <s id="N14F02">Alioquin lignum ipſum, aut non <lb></lb>recederet à ſua rectitudine, aut frangeretur. </s>
          <s id="N14F07">Quod ſi ſu<lb></lb>ſpendatur ex medio, in ipſo medio fulcietur vtrumque di<lb></lb>midium, ceu duplex vectis vtrinque applicatus, extremita<lb></lb>tibus vtrinque pariter grauitantibus, ac propendentibus <lb></lb>tanquam in remotiſſimo loco à communi centro ſiue fùlci<lb></lb>mento. </s>
          <s id="N14F14">In quibus omnibus ſemper valet eadem ratio ſu<lb></lb>pra explicata. </s>
        </p>
        <p id="N14F19" type="head">
          <s id="N14F1B">Quæſtio Decimaſeptima.</s>
        </p>
        <p id="N14F1E" type="main">
          <s id="N14F20">C<emph type="italics"></emph>vr à paruo existente cuneo magna ſcindun<lb></lb>tur pondera, &amp; corporum moles, <expan abbr="validaq.">validaque</expan> fit <lb></lb>impreſsio? </s>
          <s id="N14F2E">An quia cuneus duo ſunt vectes, <lb></lb>ſibi inuicem contrarii? </s>
          <s id="N14F33">vterque autem &amp; <lb></lb>pondus habet, &amp; hypomochlion; quod diuellit, <lb></lb>&amp; comprimit. </s>
          <s id="N14F3A">Plagæ quin etiam ipſius latio <lb></lb>pondus, quod percutit, &amp; mouet, magnum facit, &amp; quoniam <lb></lb>motum mouet, ipſa celeritate valentius fit. </s>
          <s id="N14F41">Paruo autem exi<lb></lb>stente vectæ, magnæ illum conſequuntur vires: quamobrem <lb></lb>vltra magnitudinis decentiam latet mouens. </s>
          <s id="N14F48">Sit cuneus vbi <lb></lb>ABC, quod verò cuneo ſcinditur DEFG. </s>
          <s id="N14F4E">Vectis igitur fit <lb></lb>ipſa AB, pondus verò ipſius B inferior pars, hypomochlion <lb></lb>autem DG huic autem contrarius vectis BC. </s>
          <s id="N14F56">Percuſſa igi<lb></lb>tur AC, vtroque illorum vtitur vecte ſcindit enim ipſum B.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N14F5D" type="head">
          <s id="N14F5F">COMMENTARIVS.</s>
        </p>
        <p id="N14F63" type="main">
          <s id="N14F65">Celebrem non minus ac agitatam quæſtionem tam <lb></lb>parua in re hic inſtituit Ariſtoteles. </s>
          <s id="N14F6B">Quippe cum <lb></lb>eius ſolutioni aliàs præclaræ, &amp; ingenioſæ, non om<lb></lb>nes pręſertim recentiores prorſus velint, aut valeant acquie<lb></lb>ſcere. </s>
          <s id="N14F74">Quærit enim cur paruo exiſtente cuneo, tam valida <lb></lb>eius adminiculo fiat virtutis impreſsio, vt facilè magna ſcin<lb></lb>dantur corpora, quæ alijs <expan abbr="maioribusq.">maioribusque</expan> adhibitis inſtrumen<lb></lb>tis vix ſcindi aliquo modo poſſent. </s>
          <s id="N14F81"><expan abbr="Soluitq.">Soluitque</expan> ſtatim, quia in <pb pagenum="168" xlink:href="005/01/176.jpg"></pb>cuneo, duo ſunt vectes ſibi inuicem aduerſi, quorum vter<lb></lb>que &amp; pondus habet, &amp; fulcimentum, quod comprimens <lb></lb>diuellit; impulſu ſcilicet accepto ab ipſo motore, qui dum <lb></lb>cuneum malleo, vel alio corpore percutit, ſimul vtroque <lb></lb>vtitur vecte. </s>
          <s id="N14F94">Magna autem vis illi incutitur ex mallei per<lb></lb>cuſſione, eo quod malleus celerrimè motus moueat ſiue <lb></lb>percutiat. </s>
          <s id="N14F9B">Lationis enim celeritate validius ferit. </s>
          <s id="N14F9E">Ob vectis <lb></lb>igitur naturam, quam cuneus participat, &amp; qua vires augen<lb></lb>tur, validamque mallei percuſſionem, magnas contingit <lb></lb>ſcindi, aut ſaltem findi corporum moles, paruo adhibito <lb></lb>cuneo in rimula ipſius molis. </s>
          <s id="N14FA9">Quod adhuc ſchemate decla<lb></lb>rans, hæc ferè ſubnectit idem Ariſtoteles. </s>
        </p>
        <p id="N14FAF" type="main">
          <s id="N14FB1">Eſto cuneus ABC, cuius apex, ſeu vertex B ſit ìntra <lb></lb>corpus ſcindendum DEFG. </s>
          <s id="N14FB7">Vectis autem vna conſiderata <lb></lb>in ipſo cuneo ſit AB, cuius pondus infra verticem B, nem<lb></lb>pe ad partes ED, vt vbi H. </s>
          <s id="N14FBF">Fulcimentum verò I circa in<lb></lb>greſſum cunei, ſeu principium rimæ. </s>
          <s id="N14FC4">Huic autem vecti alius <lb></lb><figure id="id.005.01.176.1.jpg" xlink:href="005/01/176/1.jpg"></figure><lb></lb>oppoſitus vectis <lb></lb><expan abbr="cõſtituatur">conſtituatur</expan> BC, <lb></lb>cuius <expan abbr="põdus">pondus</expan> ſu<lb></lb>pra verticem B <lb></lb>ad partes FG <lb></lb>vbi K, fulcimen<lb></lb>tum verò in L. <lb></lb></s>
          <s id="N14FE4">Valde igitur per<lb></lb>cuſſo cuneo in <lb></lb>AC, vectis AB fulta in I ſimul fulcimentum præmens, mo<lb></lb>uebit verſus G; onus autem H verſus M. </s>
          <s id="N14FED">Vice autem ver<lb></lb>ſa vectis CB, fulcimentum L mouebit verſus D: Onus ve<lb></lb>rò K verſus N. </s>
          <s id="N14FF5">Quibus motibus dum partes molis ad <lb></lb>oppoſita impelluntur, molem ipſam ſcindi neceſſe eſt. </s>
        </p>
        <p id="N14FFA" type="main">
          <s id="N14FFC">Huic autem Ariſtotelis doctrinæ, ac ſolutioni duo obijcit <lb></lb>Baldus. </s>
          <s id="N15002">Primum eſt, quia ſi darentur explicati vectes in cu<lb></lb>neo, eorum extremitates inuicem contendentes in puncto <lb></lb>B altera alteri ne quidquam operarentur eſſet impedimen<lb></lb>to, vt late probat Guidus Vbaldus tractatu de cuneo. </s>
          <s id="N1500C">Se-<pb pagenum="169" xlink:href="005/01/177.jpg"></pb>cundum verò eſt, quia in ipſo ſciſſionis actu, facta aliqua di<lb></lb>ſtractione partium molis adhuc non in totum diſciſſæ, ver<lb></lb>tex cunei, quo pondera vtrinque diuelli, ac moueri debe<lb></lb>rent, nihil vt plurimum tangit in rimula dum ipſa vlterius <lb></lb>dilatatur. </s>
        </p>
        <p id="N1501C" type="main">
          <s id="N1501E">Ad primum tamen reſpondetur, ſi concipiamus in cuneo <lb></lb>vectes explicatos ex parte A vrgere verſus G, &amp; ex parte <lb></lb>C vrgere verſus D; verticem verò non tranſgredi punctum <lb></lb>B; ſed in eo quieſcere: tunc quidem ſequi, extrema ipſorum <lb></lb>vectium ſibi inuicem obſtare in puncto B, nè in contrarium <lb></lb>moueantur, moueantque adiacentia pondera modo deſcri<lb></lb>pto. </s>
          <s id="N1502D">At ſi concipiamus, vt re vera eſt apicem ipſum ſimul <lb></lb>pergere ad partes EF: tunc in ipſo motu optimè intellige<lb></lb>mus, concurrentiam extremorum vtriuſque vectis in vni<lb></lb>cum illud punctum terminatiuum verticis, nihil obſtare <lb></lb>quominus pars vectis, quæ ſequitur poſt illud vbi K, impel<lb></lb>lat aliam ſibi correſpondentem in mole ſcindenda verſus <lb></lb>N: &amp; pars vbi H, aliam ſimilem verſus M. </s>
          <s id="N1503C">Siquidem hoc <lb></lb>ipſo, quod vertex vlterius pergit, partes illum vtrinque con<lb></lb>ſequentes in proportionatum ſibi locum ſuccedere non poſ<lb></lb>ſent, niſi prius inde <expan abbr="expellerẽtur">expellerentur</expan> per ſciſſionem partes molis, <lb></lb>quæ eundem locum occupabant. </s>
          <s id="N1504B">Pars autem vbi K in <lb></lb>mole ſcindenda non expellitur inde virtute vectis AB; ſicut <lb></lb>nec H virtute vectis CB; cum nullam vim vtraque pati <lb></lb>poſſit à vecte niſi illa nitatur in contrariam partem. </s>
          <s id="N15054">Ergo ex<lb></lb>pulſio partis K fit virtute vectis CB, quæ contra nititur; &amp; <lb></lb>expulſio partis H, virtute vectis AB. </s>
          <s id="N1505C">Quod eſt ipſum ver<lb></lb>ticem, ſeu apicem fungi officio extremorum vtriuſque ve<lb></lb>ctis ad remouendas vtrinque partes corporis ſcindendi tan<lb></lb>quam ad leuanda pondera virtute impetus in contrarium <lb></lb>impreſsi in alterutro extremo, vt in AC vbi applicatur po<lb></lb>tentia mouentis, ſeu percutientis. </s>
          <s id="N15069">Non igitur res ita eſt con<lb></lb>cipienda quaſi vertex B tanquam extremum duorum ve<lb></lb>ctium contra nitentium ſimul moueretur ad oppoſita ad <lb></lb>partes M, &amp; N: Sed vt dum ipſe vertex B mouetur ſu<lb></lb>per lineam BO, partes cunei vtrinque ſequentes, ac paula-<pb pagenum="170" xlink:href="005/01/178.jpg"></pb>tim ſe dilatantes, &amp; ab inuicem recedentes, neceſſariò im<lb></lb>pingant in partes molis, quas ab eodem loco diſterminant, <lb></lb>vt ibidem ipſæ ſuccedant. </s>
          <s id="N1507D">Non enim abſque impulſu inde <lb></lb>poſſent eas expellere, nec abſque expulſione in earum lo<lb></lb>cum ſuccedere. </s>
          <s id="N15084">Cumque impulſus fiat virtute impetus in <lb></lb>alterum vectis extremum impreſſi vbi adhibetur motoris <lb></lb>potentia; ſequitur verè extremitates ipſas KH, partes mo<lb></lb>lis ſibi correſpondentes tanquam pondera ſcindendo diſtra<lb></lb>here, ac mouere, prout Ariſtoteles intendebat. </s>
        </p>
        <p id="N1508F" type="main">
          <s id="N15091">Ad ſecundum verò Baldi argumentum reſpondetur, con<lb></lb>cedendo ſæpè cuſpidem cunei, nihil in ſciſſura contingere; <lb></lb>negando tamen propterea nullam ibi vectis rationem inter<lb></lb>cedere. </s>
          <s id="N1509A">Porrò extremum quo vectis pondera mouet, vt <lb></lb>plurimum non eſt vltimum punctum terminatiuum illius, <lb></lb>ſed ſufficit, vt ſit circa illud, vel ſaltem poſt fulcimentum, <lb></lb>quod intermediat inter pondus, &amp; potentiam: Quare etiam <lb></lb>ſi vltimæ, &amp; extremæ partes cunei, quæ verticem conſe<lb></lb>quuntur quandoque molem ſcindendam ob rimæ latitudi<lb></lb>nem nullo pacto attingant: adhuc tamen explicata ratio du<lb></lb>plicis vectis in illo procedit applicando nimirum, quæ dicta <lb></lb>ſunt de vltimis partibus terminantibus in vertice, ad alias <lb></lb>partes ſequentes, vbi primo fit contactus inter molem, &amp; <lb></lb>cuneum. </s>
        </p>
        <p id="N150B1" type="main">
          <s id="N150B3">Cæterum ſi quis vrgeat ex Guido Vbaldo, potius verti<lb></lb>cem cunei eſſe commune <expan abbr="fulcimentũ">fulcimentum</expan> vtriuſque vectis pon<lb></lb>dera verò mediare inter fulcimentum, ac potentiam, ita vt <lb></lb>vectis AB fulta in ipſo B moueat molis partem vbi eſt I, <lb></lb>tanquam onus verſus G. <expan abbr="Similiterq.">Similiterque</expan> vectis CB ibidem <lb></lb>fulta, partem L verſus D. </s>
          <s id="N150C9">Occurrendum eſt, hoc cum alijs, <lb></lb>quæ Guidus Vbaldus fusè proſequitur, probare quidem <lb></lb>talem pariter vectis rationem competere ipſis AB &amp; <lb></lb>CB; prout conſtituuntur in cuneo: nihil tamen contra <lb></lb>Ariſtotelem concludere; cuius propterea diſcurſum refe<lb></lb>rens Guidus Vbaldus minimè improbat. </s>
          <s id="N150D6">Nihil enim prohi<lb></lb>bet, quominus idem numero vectis ſecundum diuerſas ra<lb></lb>tiones ad duas, ac diuerſas vectium ſpecies pertineat, vtriuſ-<pb pagenum="171" xlink:href="005/01/179.jpg"></pb>que ſcilicet vices gerendo atque exercendo: <expan abbr="idemq.">idemque</expan> cor<lb></lb>pus ſimul poſſit eſſe fulcimentum, &amp; onus quod mouetur <lb></lb>per vectem reſpectu diuerſorum, vt in ſimili ſupra explicui<lb></lb>mus quæſt. </s>
          <s id="N150EC">3. Optime igitur ſecundum vtranque vectis ra<lb></lb>tionem dicere poſſumus, cuneum virtutis incrementum ſu<lb></lb>mere à duplici vecte, quam continet, &amp; ab ictu percuſſionis, <lb></lb>qua validius omni alio impulſu ipſe adhibetur. </s>
        </p>
        <p id="N150F5" type="head">
          <s id="N150F7">Quæſtio Decimaoctaua.</s>
        </p>
        <p id="N150FA" type="main">
          <s id="N150FC">C<emph type="italics"></emph>vr ſi quiſpiam trochleas componens duas in <lb></lb>ſignis duobus ad ſe inuicem iunctis contrario <lb></lb>ad trochleas moto circulo funem circumdu<lb></lb>xerit, cuius alterum quidem caput ſignorum <lb></lb>appendatur alteri, alterum verò trochleis ſit <lb></lb>innixum, &amp; à funis initio trahere cœperit, <lb></lb>magna trahit pondera, licet imbecillium fuerit virium? </s>
          <s id="N1510E">An <lb></lb>quia idem pondus à minori potentia ſi mouetur, vecte medio <lb></lb>transfertur magis, quàm à manu? </s>
          <s id="N15115">Trochlea autem idem ve<lb></lb>cti facit. </s>
          <s id="N1511A">Quamobrem ſi vna facilius trahet, &amp; ab vnico <lb></lb>tractu multò grauius trahet, quàm facere poſsit manus, idip<lb></lb>sum duæ trochleæ plus quàm in dupla velocitate leuabunt. <lb></lb></s>
          <s id="N15123">Minus enim altera trahit, quàm ſi ipſa per ſe ipſam trahe<lb></lb>ret, quando circa alteram iniectus fuerit funis, illa namque <lb></lb>minus etiam pondus effecit. </s>
          <s id="N1512A"><expan abbr="Pariq.">Parique</expan> modo ſi ad plures iniectus <lb></lb>fuerit funis in paucis trochleis, multa fit differentia, quamob<lb></lb>rem à prima pondere quatuor minas trahente, ab vltima trahi <lb></lb>multò minus. </s>
          <s id="N15136">Et in re ędificatoria faciliter magna mouent <lb></lb>pondera, traducunt enim ab una trochlea ad aliam, &amp; rurſus <lb></lb>ab illa ad ſuculas, &amp; vectes. </s>
          <s id="N1513D">Hoc autem idem est, ac ſi mul<lb></lb>tas facerent trochleas.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N15144" type="head">
          <s id="N15146">COMMENTARIVS.</s>
        </p>
        <p id="N1514A" type="main">
          <s id="N1514C">Svppoſita deſcriptione trochleæ, <expan abbr="eiusq.">eiusque</expan> multiplici di<lb></lb>ſtinctione quam ſupra prima parte tex. 8. Additione <lb></lb>prima tradidimus, illud in præſenti primò notandum <pb pagenum="172" xlink:href="005/01/180.jpg"></pb>occurrit, <expan abbr="Ariſtotelẽ">Ariſtotelem</expan> hic non agere niſi de trochlea, quæ vni<lb></lb>cam, ac ſimplicem rotulam contineat, quam pariter eodem <lb></lb>nomine trochleam appellat, ac diſtinguit à tigno, ſeu ligno, <lb></lb>quod illam tanquam conceptaculum quoddam, aut capſu<lb></lb>la inſertam continet; cum re vera communi acceptione <lb></lb>trochlea, vt diximus vtrumque ſimul ſignificet, nempe, &amp; <lb></lb>rotulam inditam ſiue orbiculum, &amp; capſulam continentem. <lb></lb></s>
          <s id="N1516F">Nec audiendus eſt Piccolomineus dum ait tigna hic apud <lb></lb><expan abbr="Ariſtotelẽ">Ariſtotelem</expan>, non ſignificare ligna prædicta, ſeu thecas ligneas, <lb></lb>rotulas continentes, ſed trabes ad ſe inuicem iunctas, qui<lb></lb>bus trochleæ cum pondere ſuſtinentur. </s>
          <s id="N1517B">Quandoquidem ſi <lb></lb>hoc eſſet, Philoſophus <expan abbr="nõ">non</expan> dixiſſet, alterum extremum funis <lb></lb>ductarij, altero <expan abbr="tignorũ">tignorum</expan> appendi. </s>
          <s id="N1518A">Cum certum ſit, funem du<lb></lb>ctarium nullo modo ad trabem aliquam appendi, ſed ad ip<lb></lb>ſum extremum trochleæ ſuperioris, ſeu ligni, quod rotulam <lb></lb>tegit, ac per axiculum regit, vt ſtatim patebit. </s>
          <s id="N15193">Præterea vbi <lb></lb>leonicus vertit in tignis duobus ad ſe inuicem iunctis, Græ<lb></lb>cus textus habet <foreign lang="grc"><gap></gap>π̀ δυσὶ ξύλοις συμβάλλουσιν ἑαυτοῑς ἐναντίως</foreign>, <lb></lb>hoc eſt in duobus lignis concurrentibus ad inuicem ex op<lb></lb>poſito, quod propriè deſignat ipſam ſituationem capſula<lb></lb>rum rotulas continentium, ſeu trochlearum, quæ ex oppo<lb></lb>ſito ſe debent reſpicere, &amp; quaſi ad inuicem currere. </s>
        </p>
        <p id="N151A7" type="main">
          <s id="N151A9">His ergo præmiſſis ad <expan abbr="nominũ">nominum</expan> dilucidationem, quæritur <lb></lb>hic ab Ariſtotele, qua de cauſa <expan abbr="cõtingat">contingat</expan>, vt ſi quis duas tro<lb></lb>chleas ad <expan abbr="inuicẽ">inuicem</expan> ex oppoſito componat, &amp; fune ad <expan abbr="eorũ">eorum</expan> ro<lb></lb>tulas circumducto, alterum eius caput alteri trochleæ, ſeu <lb></lb>ligno rotulam continenti appendat, alterum verò manu tra<lb></lb>hat, magna eleuet pondera, quamuis imbecilla ſit virtus tra<lb></lb>hentis. </s>
          <s id="N151C8"><expan abbr="Cauſamq.">Cauſamque</expan> mox reddit; quia nimirum facilius vel po<lb></lb>tius vectis adiumento quàm ſola manu, mouentur pondera <lb></lb>à minori potentia; rotula verò in trochlea vectis vicem obti<lb></lb>net, ſeu vectis habet virtutem. </s>
          <s id="N151D4">Cumque in trochleis prædi<lb></lb>cto modo applicatis, non tantum vna, ſed duæ ſaltem rotu<lb></lb>læ tanquam totidem vectes adhibeantur, mirum non eſt ſi <lb></lb><expan abbr="earũ">earum</expan> beneficio, celerius, ac facilius, <expan abbr="maioraq.">maioraque</expan> leuentur pon<lb></lb>dera quàm ſit virtus <expan abbr="trahẽtis">trahentis</expan>. </s>
          <s id="N151EA">Imò ſi vnius rotulæ adiumen-<pb pagenum="173" xlink:href="005/01/181.jpg"></pb>to plus <expan abbr="faciliusq.">faciliusque</expan> leuatur quàm ſola manu, ſi duæ fuerint ro<lb></lb>tulæ, plus ac celerius leuabitur, quàm in dupla proportione, <lb></lb>&amp; ſic deinceps tanto magis, ſeu maius pondus, quantò plu<lb></lb>res extiterint rotulæ in ipſis duabus, vel pluribus trochleis <lb></lb>adhibitæ; ita vt ex multiplicatione <expan abbr="totularũ">rotularum</expan>, intelligatur au<lb></lb>geri virtutem trahentis, ac pondus imminui, cum certè plu<lb></lb>ribus impertiatur tanquam diuiſum. </s>
          <s id="N15208">Quare inquit Ariſtote<lb></lb>les in re ædificatoria, multiplicatis trochleis ſuculis, ac ve<lb></lb><figure id="id.005.01.181.1.jpg" xlink:href="005/01/181/1.jpg"></figure><lb></lb>ctibus magna <expan abbr="mouẽtur">mouentur</expan> <expan abbr="põde">ponde</expan><lb></lb>ra non ſecus ac multiplicatis <lb></lb>tantummodo trochleis, quę <lb></lb>vectis <expan abbr="vicẽ">vicem</expan> <expan abbr="gerũt">gerunt</expan> vt diximus. </s>
        </p>
        <p id="N1522B" type="main">
          <s id="N1522D">Sed vt prædicta ad oculos <lb></lb>etiam pateant, ſint duæ tro<lb></lb>chleæ ex oppoſito <expan abbr="cõſtitutæ">conſtitutæ</expan>, <lb></lb>vna ſupernè ac ſtabiliter ap<lb></lb>penſa vbi A; altera verò in<lb></lb>fernè locata vbi B, cui pon<lb></lb>dus C ſit <expan abbr="religatũ">religatum</expan>, <expan abbr="habeatq.">habeatque</expan> <lb></lb><expan abbr="vtraq;">vtraque</expan> trochlea <expan abbr="ſuũ">ſuum</expan> <expan abbr="orbiculũ">orbiculum</expan> <lb></lb>inditum, cui funis ductarius <lb></lb><expan abbr="circũducatur">circunducatur</expan>; <expan abbr="alligeturq.">alligeturque</expan> al<lb></lb>terum extremum ipſius funis <lb></lb>in parte inferiori ſuperioris <lb></lb>trochleæ vbi D. </s>
          <s id="N15267">Alterum ve<lb></lb>rò relinquatur <expan abbr="trahẽti">trahenti</expan> vbi E. <lb></lb></s>
          <s id="N15272">Tunc dicimus cum Ariſtote<lb></lb>le, quòd ſi quis manu trahat <lb></lb>funis caput vbi E, facilè au<lb></lb>xilio ipſarum trochlearum <lb></lb>eleuabit pondus C, eo quod <lb></lb>trochlearum orbiculi, vectis <lb></lb>vicem, ac virtutem ſubeant. </s>
        </p>
        <p id="N15281" type="main">
          <s id="N15283">Quod vt <expan abbr="palã">palam</expan> omnino fiat, <lb></lb><expan abbr="diſtinguendũ">diſtinguendum</expan> in primis eſt in<lb></lb>ter orbiculos ſuperioris, &amp; <pb pagenum="174" xlink:href="005/01/182.jpg"></pb>inferioris trochleæ, <expan abbr="quandoquidẽ">quandoquidem</expan> <expan abbr="nõ">non</expan> <expan abbr="vterq.">vterque</expan> idem genus ve<lb></lb>ctis exprimit, aut participat. </s>
          <s id="N152A4">Si igitur <expan abbr="orbiculũ">orbiculum</expan> trochleæ ſu<lb></lb>perioris, hoc eſt ſupernè appenſæ conſideremus, eam ratio<lb></lb>nem vèctis obtinere comperiemus, quam participat etiam <lb></lb>libra æqualium brachiorum, nempe, cuius fulcimentum in<lb></lb>ter pondus, &amp; potentiam collocatur. </s>
          <s id="N152B3">Porrò diameter or<lb></lb>biculi orizonti parallela FG longitudinem vectis refert, <lb></lb>axiculus verò qui in centro eſt vbi H, fulcimentum. </s>
          <s id="N152BA">Deinde <lb></lb>diametri extremum F à quo pondus cum inferiori trochlea <lb></lb>per funem propendet, vectis extremum exprimit, cui onus <lb></lb>eſt alligatum. </s>
          <s id="N152C3">Alterum verò diametri extremum G, vectis <lb></lb>extremum deſignat, cui virtus mouentis applicatur. </s>
        </p>
        <p id="N152C8" type="main">
          <s id="N152CA">At ſi orbiculum inferioris trochleæ conſiderare velimus, <lb></lb>aliam in eo vectis ratione deprehendemus; illam vtique <lb></lb>cuius fulcimentum conſtituitur in altero extremo, pondus <lb></lb>verò in medio, vt 1. par. </s>
          <s id="N152D3">tex. 8. Additione 1 explicuimus. <lb></lb></s>
          <s id="N152D9">Etenim ex duobus eius diametri extremis IK, alterum nem<lb></lb>pe K fulcitur à fune, cui veluti immobiliter innititur, eo <lb></lb>quod ipſa ſuſtineatur in D. </s>
          <s id="N152E1">Alterum verò extremum I ſur<lb></lb>ſum attollitur verſus F per motum eiuſdem funis ibi vim <lb></lb>præcipuam imprimentis. </s>
          <s id="N152E8">Pondus denique C propendet ex <lb></lb>medio vbi L, <expan abbr="ibiq.">ibique</expan> propterea grauitat inter fulcimentum, &amp; <lb></lb>potentiam attollentem. </s>
          <s id="N152F3">Ex quibus conſtat, <expan abbr="vtriuſq;">vtriuſque</expan> trochleæ <lb></lb>orbiculos vectis rationem habere, ſed non eandem. </s>
        </p>
        <p id="N152FC" type="main">
          <s id="N152FE">Quod ſi quæras quæ nam ex his duabus trochleis maius <lb></lb>potentiæ mouenti auxilium præſtet. </s>
          <s id="N15303">Reſpondetur, ſuperio<lb></lb>rem trochleam non tam auxilium, quàm commoditatem, <lb></lb>ac facilitatem ad trahendum illi præbere. </s>
          <s id="N1530A">Vt enim patet ex <lb></lb>Guido Vbaldo de trochlea propoſitione prima, beneficio <lb></lb>ipſius trochleæ ſuperioris ſupernè videlicet appenſæ quan<lb></lb>do potentia æqualis eſt ponderi inferius alligato, nullatenus <lb></lb>eleuare illud poterit, cum ita ſe habeat, ac ſi aliud eſſet ap<lb></lb>penſum pondus, æquale ponderi prædicto cum æquali di<lb></lb>ſtantia à centro, ſiue axiculo, circa quem diameter orbiculi <lb></lb>non ſecus ac libra conuertitur, vt clarius videre eſt in hac <lb></lb>figura, in qua linea AB diametrum referat orbiculi ABC <pb pagenum="175" xlink:href="005/01/183.jpg"></pb>deſcripta circa axiculum C, nam ſi funis ex vtroque dia<lb></lb>metri extremo à centro æquidiſtanti propendeat, &amp; hinc <lb></lb>pondus D, illinc potentia E æqualiter præmat, idem erit, ac <lb></lb><figure id="id.005.01.183.1.jpg" xlink:href="005/01/183/1.jpg"></figure><lb></lb>ſi in libra æqualibus prædita <lb></lb>brachijs æqualia pondera ap<lb></lb>pendantur, quorum vnum, alte<lb></lb>rum per proprium deſcenſum <lb></lb>eleuare non poſſet, cum actio <lb></lb>debeat eſſe ab inæquali propor<lb></lb>tione, vt docet idem Ariſt. </s>
        </p>
        <p id="N1533B" type="main">
          <s id="N1533D">Quare tota vis quæ adiungi<lb></lb>tur potentiæ, pondus aliquod <lb></lb>eleuanti prædictarum trochlea<lb></lb>rum beneficio, petenda eſt ex <lb></lb>trochlea inferiori. </s>
          <s id="N15348">Etenim cum <lb></lb>alterum <expan abbr="extremũ">extremum</expan> funis orbicu<lb></lb>lo huius trochleæ circumdu<lb></lb>cti, in ſuperiori ligno firmiter ſu<lb></lb>ſpenſo ſit religatum; alterum <lb></lb>verò à potentia ſuſtineatur, vel traha<lb></lb>tur, pondus quod ex ipſius trochlea <lb></lb>pendet, quaſi diuiſum, partim à ligno <lb></lb>ſuperiori, ac partim à potentia trahen<lb></lb>te ſuſtentatur, vt optimè demonſtrat <lb></lb>Guidus Vbaldus propoſit. </s>
          <s id="N15363">2. &amp; Baldus <lb></lb>in hac quæſt. </s>
          <s id="N15368"><expan abbr="videreq.">videreque</expan> eſt in ſequenti <lb></lb>figura. </s>
        </p>
        <p id="N15370" type="main">
          <s id="N15372">Quoniam ſi trochlea ABC ſuſpen<lb></lb>datur per funem eius orbiculo cir<lb></lb>cumductum, cuius vnum <expan abbr="extremũ">extremum</expan> ſit <lb></lb>in D ſtabiliter alligatum, alterum verò <lb></lb>à potentia in E conſtituta ſuſtineatur; <lb></lb>ac pondus F ab ipſa inferiori parte <lb></lb>trochleæ vbi B propendeat ſubliga<lb></lb>tum, pondus ipſum <expan abbr="totũ">totum</expan>, non quidem <lb></lb>à ſola potentia E, nec à ſolo ſuſten<pb pagenum="176" xlink:href="005/01/184.jpg"></pb>taculo D ſuſtineri intelligetur, ſed ſimul ab vtroque, ita <lb></lb>vt dimidium, alterutri reſpondeat virtuti. </s>
          <s id="N15395">Quo fit vt cum <lb></lb>potentia ad pondus attollendum, ipſa inferiori trochlea vti<lb></lb>tur tanquam vecte non paruam virtutem ab ipſa trochlea <lb></lb>mutuetur, <expan abbr="nõ">non</expan> ſecus ac à vecte, cuius alterum extremum fir<lb></lb>miter alicubi ſit innixum, ad eleuandum pondus, quod ex <lb></lb>eius medio pendeat, vt conſtare poteſt in deſcripto vecte <lb></lb><figure id="id.005.01.184.1.jpg" xlink:href="005/01/184/1.jpg"></figure><lb></lb>ABC, cuius extre<lb></lb>mum C fulciatur in <lb></lb>D, extremum verò <lb></lb>A ſit à <expan abbr="potẽtia">potentia</expan> ele<lb></lb>uandum, &amp; ex pun<lb></lb>cto medio B <expan abbr="propẽ-deat">propen<lb></lb>deat</expan> onus <expan abbr="alligatũ">alligatum</expan>, <lb></lb>quod ſit ipſum E. <lb></lb></s>
          <s id="N153CA">Nam &amp; ſi pondus <lb></lb>potentiæ vires excederet, <expan abbr="duplamq.">duplamque</expan> ferè proportionem ha<lb></lb>beret reſpectu earum, omnino tamen beneficio vectis tolle<lb></lb>retur, cum dimidium tantùm illius ipſi potentiæ reſponde<lb></lb>ret. </s>
          <s id="N153D9">Quod ſi plures orbiculi in ipſa inferiori trochlea con<lb></lb>tineantur, idem fiet, ac ſi totidem vectibus eiuſdem rationis <lb></lb>idem pondus ab eadem potentia moueatur. </s>
          <s id="N153E0">Nam cum ſin<lb></lb>gulis pariter onus leuandum impartiri debeat, quò plures <lb></lb>fuerint rotulæ ſicut vectes, eò minus potentiæ ad leuandum <lb></lb>propria virtute relinquitur, ac propterea minor, ac minor <lb></lb>virtus in trahente requiritur iuxta numerum rotularum. </s>
        </p>
        <p id="N153EB" type="main">
          <s id="N153ED">Cæterum in qua ſigillatim proportione ad multiplicatio<lb></lb>nem ipſarum rotularum in inferioribus trochleis, augeatur <lb></lb>virtus mouentis, vel pondus imminuatur, ſumendum eſt ex <lb></lb>codem Guido Vbaldo, &amp; alijs, qui hac de re ex profeſſo, ac <lb></lb>fuſiùs tractant; cum ad explicationem, &amp; confirmationem <lb></lb>doctrinæ Ariſtotelis, ſufficiat oſtendiſſe, qua ratione, &amp; via <lb></lb>id poſſit contingere. </s>
          <s id="N153FC">Et ſi quis multiplicatis trochleis, ſu<lb></lb>culis, ac vectibus, vt hic idem Philoſophus ait, magna vide<lb></lb>rit pondera eb exigua virtute moueri, aut eleuari, deſinat <lb></lb>admirari. </s>
          <s id="N15405">Nam &amp; ore tantum perflando vidi pondus tre-<pb pagenum="177" xlink:href="005/01/185.jpg"></pb>centorum quinquaginta axium, &amp; eius loco hominem ſtan<lb></lb>tem ſuper tabulam dimoueri, trochleis, ac ſcytalis, axeque <lb></lb>in paruo peritrochio adhibitis, quod idem vnciali pondere <lb></lb>præponderante contigerat, vt vtrumque cernere eſt in <lb></lb>ſubſtrata figura. </s>
        </p>
        <figure id="id.005.01.185.1.jpg" xlink:href="005/01/185/1.jpg"></figure>
        <p id="N1541A" type="head">
          <s id="N1541C">Quæſtio Decimanona.</s>
        </p>
        <p id="N1541F" type="main">
          <s id="N15421">C<emph type="italics"></emph>vr ſi quis ſuper lignum magnam imponat <lb></lb>ſecurim, <expan abbr="deſuperq.">deſuperque</expan> illi magnum adijciat pon<lb></lb>dus, ligni quippiam, quod curandum ſit, non <lb></lb>diuidit: ſi verò ſecurim extollens percutiat, <lb></lb>illud ſcindit, cùm alioqui multò minus ha<lb></lb>beat ponderis id, quod percutit, quàm id quod <lb></lb>ſuperiacet, &amp; premit? </s>
          <s id="N15437">An quia omnia cum motu fiunt, &amp; <lb></lb>graue ipſum, grauitatis magis aſſumit motum dum mouetur, <lb></lb>quàm dum quieſcit. </s>
          <s id="N1543E">Incumbens igitur connatam graui mo<lb></lb>tionem non mouetur, motum verò &amp; ſecundum hanc moue<lb></lb>tur, &amp; ſecundum eam, quæ est percutientis. </s>
          <s id="N15445">Præterea ſe-<emph.end type="italics"></emph.end><pb pagenum="178" xlink:href="005/01/186.jpg"></pb><emph type="italics"></emph>curis ipſa efficitur cuneus. </s>
          <s id="N15451">Paruus autem exiſtens cuneus <lb></lb>magna diuidit, cùm ex duobus ſit vectibus, contrario ad ſe in<lb></lb>uicem modo constitutis.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1545A" type="head">
          <s id="N1545C">COMMENTARIVS.</s>
        </p>
        <p id="N15460" type="main">
          <s id="N15462">Tam quæſtionis propoſitio quàm dubitandi ratio <lb></lb>per ſe eſt manifeſta, ex quo nimirum contingat, vt <lb></lb>ſi quis ſuper lignum magnam imponat ſecurim, <expan abbr="de-ſuperq.">de<lb></lb>ſuperque</expan> ingens illi adijciat pondus, nihil conſideratione di<lb></lb>gnum, aut alicuius momenti diuidat; ſi verò ſecurim ipſam <lb></lb>extollens percutiat, illud ſcindat, etiam ſi multo minus illa <lb></lb>habeat ponderis, quam id quod ſuperiacet, ac præmit. <lb></lb></s>
          <s id="N15476">Quod profecto ex eo euenire docet, quia cum omnia motu <lb></lb>fiant, &amp; graue ipſum maiorem grauitatem acquirat per mo<lb></lb>tum, magis etiam mouet dum mouetur, quàm dum quie<lb></lb>ſcit. </s>
          <s id="N1547F">Quare licet maior ſit grauitas innata totius incumben<lb></lb>tis oneris quod præmit, nempe ſecuris cum ſuperadiecto <lb></lb>pondere, quàm ſit ſolius motæ ſecuris; nihilominus dum <lb></lb>prius elata ſecuris deijcitur, non modò operatur per inna<lb></lb>tam ſibi grauitatem, ſed per eam, quam in ipſo motu acqui<lb></lb>rit, &amp; per impetum à percutiente impreſſum. </s>
          <s id="N1548C">Vnde mirum <lb></lb>non eſt, ſi tune efficacius percutiat, ac ita percutiendo <lb></lb>ſcindat lignum, quod percutit. </s>
          <s id="N15493">Præſſio namque oneris <lb></lb>ab vna tantum cauſa grauitante ſine locali motu proce<lb></lb>dit; percuſſio verò ſecuris à duplici, vel triplici cauſa im<lb></lb>pellente, à qua mixtus quidam, violentiſsimus efficitur <lb></lb>motus. </s>
        </p>
        <p id="N1549E" type="main">
          <s id="N154A0">Quod autem motus penderi addat pondus, ſeu grauitas <lb></lb>augeatur in motu, ac propterea efficacius operetur, explo<lb></lb>ratiſsimum eſt, non modo in ijs, quæ cadunt ex alto (nam <lb></lb>quò magis à principio motus diſceſſerint, eò velocius ipſa <lb></lb>deorſum ferri conſpicimus, <expan abbr="magisq.">magisque</expan> impellere non ſecus ac <lb></lb>corpora grauiora;) ſed in reliquis quoque motibus proie<lb></lb>ctorum, quorum pondus magis operatur in motu, quam in-<pb pagenum="179" xlink:href="005/01/187.jpg"></pb>quiete, <expan abbr="magisq.">magisque</expan> in velociori motu, quàm in tardiori. </s>
          <s id="N154BC">Quam<lb></lb>uis in rigore loquendo virtus illa grauium, quæ augetur in <lb></lb>motu, non ſit eadem propriè ipſa grauitas per maiorem in<lb></lb>tentionem ſui ipſius, ſeu acquiſitionem aliorum graduum <lb></lb>eiuſdem qualitatis in ſpecie, ſed potius ſit impetus ipſorum, <lb></lb>grauium, vel à proijciente impreſſus, vel per ipſam grauita<lb></lb>tem deſcendentis oneris in eodem onere productus dum <lb></lb>præceps fertur ad ima, ac ſucceſsiuè in ſe impetum au<lb></lb>get. </s>
          <s id="N154CF">Quamobrem in motu ſecuris tendentis deorſum ad <lb></lb>ſcindendum aliquod lignum, vterque impetus prædictus <lb></lb>concurrit, nempe &amp; ille, qui à ſcindente fuit impreſſus, &amp; <lb></lb>is qui ab ipſa grauitate in deſcenſu producitur, ac ſucceſ<lb></lb>ſiuè ſemper augetur. </s>
          <s id="N154DA">Quod tamen non ita ſe habet dum <lb></lb>ligna non ſcinduntur per motum deorſum, ſed ſurſum ad<lb></lb>mouendo, ac vibrando ipſam ſecurim, vt ad amputandum <lb></lb>ramum ex arbore; Nam tunc non intercedit niſi ſolus im<lb></lb>petus admouentis; &amp; iccirco diximus huiuſmodi motum <lb></lb>ſecuris à duplici, vel triplici cauſa procedere; cum gra<lb></lb>uitas innata ſemper ad ipſam percuſsionem, aut inciſio<lb></lb>nem concurrat ſicut impetus impreſſus ab incidente; im<lb></lb>petus verò à grauitate productus, vel auctus, tantum<lb></lb>modo in deſcenſu, hoc eſt cum ad ſcindendum tendit <lb></lb>deorſum. </s>
        </p>
        <p id="N154F1" type="main">
          <s id="N154F3">Omninò autem quilibet motus ſecuris, prout mos eſt <lb></lb>illam in ſcindendo adhibere, validiſsimus etiam conſtitui<lb></lb>tur ex ipſa circulatione quam efficit. </s>
          <s id="N154FA">Nam ex hac maior <lb></lb>velocitas, &amp; ex maiori velocitate efficacior ictus proce<lb></lb>dit. </s>
          <s id="N15501">Tanto enim fortius corpus quodlibet in aliud impin<lb></lb>git, quantò celerius fertur, ac magis eius moles agitatur. <lb></lb></s>
          <s id="N15507">Celerius autem fertur ſecuris per motum circularem, ma<lb></lb>giſque agitatur, quàm quolibet alio motu; Alioquin ſi <lb></lb>rectà, verbi gratia moueretur ſimul cum manu, tantùm <lb></lb>ſpacij percurreret eodem tempore, quantum ipſa manus; <lb></lb>vt ſi ſecuris ex loco A ſimul ac manus manubrio appli<lb></lb>cata ex loco B, rectà deſcenderent verſus lineam CD <pb pagenum="180" xlink:href="005/01/188.jpg"></pb><figure id="id.005.01.188.1.jpg" xlink:href="005/01/188/1.jpg"></figure><lb></lb>paralellam ipſi AB <lb></lb>ad <expan abbr="percutiẽdum">percutiendum</expan> li<lb></lb>gnum infra ipſam <lb></lb>lineam collocatum <lb></lb>in E. </s>
          <s id="N1552C">Mouerentur <lb></lb>enim per latera op<lb></lb>poſita <expan abbr="eiuſdẽ">eiuſdem</expan> <expan abbr="para-lellogrãmi">para<lb></lb>lellogrammi</expan> ABCD, <lb></lb>quæ ſunt æqualia. <lb></lb></s>
          <s id="N15540">At ſi ſecuris non <lb></lb>rectà, ſed circulari<lb></lb>ter moueatur, vt <lb></lb>mos eſt illam à <lb></lb>ſcindentibus agitari, multò maius ſpatium in eodem tem<lb></lb>pore percurret quàm manus, eo quod magis diſtaret à <lb></lb>centro, circa quod ambæ conuerterentur. </s>
          <s id="N1554F">Etenim ſiue <lb></lb>centrum huius motionis circularis conſtituatur in ver<lb></lb>tebra vbi manus, ſeu palma iungitur cubito, ſiue in iunctura, <lb></lb>qua cubitus iungitur brachio, aut qua brachium iungitur <lb></lb>humero; ſemper tantum ſecuris excedet diſtantiam manus <lb></lb>à centro, quanta fuerit longitudo manubrij, in cuius extre<lb></lb>mo ipſa ſecuris conſtituitur; <expan abbr="proindeq.">proindeque</expan> tantundem ſpatium, <lb></lb>quod percurrit ſecuris, excedet ſpatium eodem tempore <lb></lb>peragratum à manu. </s>
          <s id="N15566">Cum igitur quæ eadem vi commota <lb></lb>inæquali <expan abbr="tẽpore">tempore</expan> maius <expan abbr="percurrũt">percurrunt</expan> <expan abbr="ſpatiũ">ſpatium</expan>, velocius <expan abbr="moueãtur">moueantur</expan>, <lb></lb>apertè <expan abbr="cõſequitur">conſequitur</expan>, ſecurim <expan abbr="ipsã">ipsam</expan> velocius ferri motu circula<lb></lb>ri, quàm recto ab eadem vi percutientis <expan abbr="cõmotam">commotam</expan>: ac pro<lb></lb>pterea vltra <expan abbr="impetũ">impetum</expan> ipſi à percutiente impreſſum, magnam <lb></lb>ſibi ad ſcindendum ex tali velocitate efficaciam vendicare. </s>
        </p>
        <p id="N15593" type="main">
          <s id="N15595">Accedit, quia ipſemet impetus aptius imprimitur per <lb></lb>motum circularem, <expan abbr="magisq.">magisque</expan> conſeruatur in illo, vt obſerua<lb></lb>re licet in rotis, quæ facilius mouentur, ac diu circumuol<lb></lb>uuntur poſt impulſum acceptum; &amp; in pilis, quæ longius <lb></lb>rotando feruntur, quàm corpora, quæ non mouentur in gy<lb></lb>rum. </s>
          <s id="N155A6">Deinde aptius in particulari imprimitur impetus per <pb pagenum="181" xlink:href="005/01/189.jpg"></pb>circularem motum ſecuris, quia in tali motu eius manu<lb></lb>brium, vectis vicem ſubit, cuius alterum extremum, quod <lb></lb>latet in manu, fulcitur vbi complicantur digiti minores in <lb></lb>ipſiſmet digitis minoribus; alterum verò mouet ipſam ſe<lb></lb>curim tanquam pondus ei alligatum, &amp; pars quæ inter pol<lb></lb>licem, &amp; indicem continetur, ſuſcipit impulſum ab eodem <lb></lb>indice tanquam à potentia monente. </s>
          <s id="N155BA">Vt videre eſt in de<lb></lb>ſcripto manubrio AB, cuius alterum extremum fulcitur <lb></lb><figure id="id.005.01.189.1.jpg" xlink:href="005/01/189/1.jpg"></figure><lb></lb>in A quaſi tanquam in centro ſui motus; alterum verò pro<lb></lb>mouet ſecurim in B: &amp; pars vbi C, impulſum recipit à <lb></lb>potentia motrice tendentem in D. </s>
          <s id="N155CC">Quo fit vt ipſum manu<lb></lb>brium tanquam vectis, ac ſemidiameter circulariter mouea<lb></lb>tur, <expan abbr="efficiatq.">efficiatque</expan> arcum, ſeu lineam BE. </s>
          <s id="N155D8">Quamuis contingat <lb></lb>vltimum extremum A aliquantulum retrocedere verſus <lb></lb>F, eo quod fulcimentum non ſit omnino ſtabile, nec poſsit <lb></lb>ei tam exactè ipſum extremum manubrij applicari. </s>
          <s id="N155E1">Cum <lb></lb>itaque omnia, quæ vectis vicem obtinent, ac circulariter ſuo <lb></lb>innixa fulcimento cientur, aptiſsimè virtutem, ſeu impul<lb></lb>ſum à mouente recipiant, ſequitur vt hac etiam ratione ſe<lb></lb>curis ipſa per motum circularem magnam vim ad ſcinden<lb></lb>dum adipiſcatur. </s>
        </p>
        <pb pagenum="182" xlink:href="005/01/190.jpg"></pb>
        <p id="N155F2" type="main">
          <s id="N155F4">Rurſus accedit, quod intra latitudinem ſpatij, quo ma<lb></lb>nus mouere poteſt ſecurim, illud maximum erit ſpatium, <lb></lb>quod circumeundo ab ipſa vnà cum ſecuri complectitur. <lb></lb></s>
          <s id="N155FC">Cumque mobile quodlibet quanto maius ſpatium percur<lb></lb>rit, tanto maiorem ſibi vindicet efficaciam ſui motus, vt pro<lb></lb>batum eſt, dummodo impetus illi impreſſus non deſinat ne<lb></lb>que langueſcat; hinc fit, vt efficacius per motum circula<lb></lb>rem, quàm per alium ſecuris mota impingat atque per<lb></lb>cutiat. </s>
        </p>
        <p id="N15609" type="main">
          <s id="N1560B">Cæterum Ariſtoteles aliam ſubiungit cauſam ſciſsionis, <lb></lb>quæ fit per ſecurim. </s>
          <s id="N15610">Quia nimirum dum ſecuris lignum ſcin<lb></lb>dit, conſtituitur veluti cuneus, vt ex propria eius figura, &amp; <lb></lb>ex modo, quo intimè ſeſe inſinuando diuidit, poteſt com<lb></lb>prehendi. </s>
          <s id="N15619">Eſt enim ſecuris, vt ait Baldus, vel malleus cu<lb></lb>neatus, vel cuneus malleatus manubrio inſertus; <expan abbr="operaturq.">operaturque</expan> <lb></lb>ſicut cuneus cum manubrio motus. </s>
          <s id="N15624">Paruus autem exiſtens <lb></lb>cuneus magnam diuidit molem, cum ex duobus ſit vecti<lb></lb>bus compactus, contrario ad ſeſe inuicem modo conſtitu<lb></lb>tis, vt ſupra ſuo loco explicuimus quæſt. </s>
          <s id="N1562D">17. </s>
        </p>
        <p id="N15630" type="main">
          <s id="N15632">Quæ autem dicta ſunt de ſecuri, eadem accommodari <lb></lb>poſſunt ad malleum clauam enſem, bipennem runcam, <expan abbr="cæ-teraq.">cæ<lb></lb>teraque</expan> inſtrumenta, quæ impulſo accepto percutiunt, diui<lb></lb>dunt, ſcindunt, vel ſimilia munera obeunt. </s>
          <s id="N1563F">Maximè autem <lb></lb>omnium ad ſtipites loratos, qui communiter ad enuclean<lb></lb>dum triticum in area ab agriculis adhibentur. </s>
          <s id="N15646">Hi enim im<lb></lb>petu accepto per motum circularem incredibili vehemen<lb></lb>tia ac virtute percutiunt. </s>
          <s id="N1564D">Porrò cum alter ex alterius extre<lb></lb>mitate cui loris alligatur liberè pendeat, ac per ipſum tan<lb></lb>quam per manubrium ſatis procerum circulariter agitetur, <lb></lb>longè à centro, quod eſt in iunctura lacerti cum humero <lb></lb>percutientis, ſuum quaſi circulum perficit; <expan abbr="proindeq.">proindeque</expan> citiſ<lb></lb>ſimè fertur, vnde &amp; validiſsimè ferit, ac percutit. </s>
          <s id="N1565E">Iuxta <lb></lb>quam rationem colligitur, quod &amp; experientia comproba<lb></lb>tur prædicta omnia inſtrumenta maximam, ac præcipuam <lb></lb>virtutem ſortiri in extremo, quod magis diſtat à centro ſui <lb></lb>motus. </s>
        </p>
        <pb pagenum="183" xlink:href="005/01/191.jpg"></pb>
        <p id="N1566D" type="main">
          <s id="N1566F">Nec obſtat, quod Baldus adducit ad probandum ictum <lb></lb>ex enſe, efficaciorem eſſe à parte, quæ eſt circa medium, ex <lb></lb>eo quod ibi conſtituatur centrum grauitatis, ac propterea <lb></lb>cuſpis non niſi dimidium ponderis habeat reſpectu illius. <lb></lb></s>
          <s id="N15679">Nam licet pondus cuiuſlibet inſtrumenti multum conducat <lb></lb>ad validiorem percuſsionem, vt patet in malleo, &amp; in claua, <lb></lb>cuius caput propterea efficitur maius: Nihilominus præ<lb></lb>ſertim in enſe runca, &amp; alijs procerioribus inſtrumentis, non <lb></lb>tam attenditur pondus ipſius partis ferientis, quàm diſtan<lb></lb>tia à centro ſui motus, ex qua prouenit maior velocitas, &amp; <lb></lb>efficacitas ictus ipſius. </s>
          <s id="N15688">Et planè ſi quæramus centrum gra<lb></lb>uitatis in enſe, nec circa medium enſis illud reperire fas erit, <lb></lb>ſed potius prope capulum, vel manubrium, vt obſeruanti <lb></lb>patebit, ex qua parte euidentiſsimum eſt, non procedere <lb></lb>ictum validiorem. </s>
        </p>
        <p id="N15693" type="main">
          <s id="N15695">Quod ſi enſis ictus facilius euitetur, aut euadatur cum <lb></lb>quis enſi obuiet verſus cuſpidem, quàm cum in medio; hoc <lb></lb>prouenit ex eo quod pars illa cum magis diſtet à centro, ſi<lb></lb>cut facilius mouetur, ſic etiam facilius diuertatur, tanquam <lb></lb>vectis, cuius fulcimentum centrum conſtituitur in manu <lb></lb>gladiatoris. </s>
          <s id="N156A2">Deinde obſeruandum eſt, non cedere <expan abbr="ſecun-dũ">ſecun<lb></lb>dum</expan> propriam contrarietatem, ita vt facilè euitetur ictus de<lb></lb>ſcendens per ictum aſcendentem, aut reſiſtentiam illi ex di<lb></lb>recto oppoſitam; ſed ex latere, remouendo ad latus ipſam <lb></lb>cuſpidem deſcendentem, nempe dextrorſum, vel ſiniſtror<lb></lb>ſum. </s>
          <s id="N156B3">Quandoquidem impetus ita eſt determinatus ad vnam <lb></lb>poſitionem ex vi ſuæ impreſsionis, vt non ſuſcipiat contra<lb></lb>rietatem niſi ab oppoſita. </s>
          <s id="N156BA"><expan abbr="Proindeq.">Proindeque</expan> idem ferè eſt, moue<lb></lb>re dextrorſum, vel ſiniſtrorſum ipſam cuſpidem circumlati <lb></lb>enſis deſcendentem, &amp; ſtantem, vel quieſcentem, eo quod <lb></lb>tali dimotio non apponatur directè ipſi deſcenſui, ad quem <lb></lb>impetus natura ſua eſt determinatus. </s>
        </p>
        <pb pagenum="184" xlink:href="005/01/192.jpg"></pb>
        <p id="N156CC" type="head">
          <s id="N156CE">Quæſtio Vigeſima.</s>
        </p>
        <p id="N156D1" type="main">
          <s id="N156D3">C<emph type="italics"></emph>vr ſtatera qua carnes ponderantur, paruo ap<lb></lb>pendiculo magna trutinat onera cùm alioqui <lb></lb>tota dimidiata exiſtat libra? vbi enim onus im<lb></lb>ponitur ſolùm ſuſpenditur lanx: in altera <lb></lb>verò parte ſola est ſtatera. </s>
          <s id="N156E3">An quia ſimul li<lb></lb>bra &amp; vectem ipſam contingit eſſe ſtateram? <lb></lb></s>
          <s id="N156E9">libram quidem, vbi ſpartorum quodcumque ſtatera fit cen<lb></lb>trum: in altera enim parte lancem, in altera autem pro lance <lb></lb>æquipondij appendiculum habet, quod libræ incumbit, ceu ſi <lb></lb>quis alteram apponeret lancem, &amp; illi pondus imponeret. </s>
          <s id="N156F2">Ma<lb></lb>nifeſtum enim quod tantundem trahit ponderis ei, quod in al<lb></lb>tera iacet lance. </s>
          <s id="N156F9">Quemadmodum autem ſi vna libra multæ <lb></lb>ſint libræ, ſic talia inſunt ſparta multa in eiuſmodi libra, <lb></lb>quorum vniuſcuiusque quod intrinſecus eſt ad appendiculum, <lb></lb>ſtateræ eſt dimidium: &amp; omnino iſthuc libra eſt, vnam qui<lb></lb>dem habens lancem, in qua pondus appenditur: alteram ve<lb></lb>rò vbi id ſtatera æquipondium. </s>
          <s id="N15706">Quamobrem appendiculum <lb></lb>ad alteram ſui partem eſt ſtatera. </s>
          <s id="N1570B">Huiuſmodi autem exi<lb></lb>ſtens multæ ſunt libræ, totque quot fuerint ſparta. </s>
          <s id="N15710">Semper <lb></lb>autem quod lanci propinquius eſt ſpartum, <expan abbr="appensòq.">appensòque</expan> oneri, <lb></lb>maius trahit pondus, quoniam fit quidem omnis ſtatera in<lb></lb>uerſus vectis, hypornochlion namque vnumquodque ſpar<lb></lb>tum ſupernè exiſtens, pondus verò id quod lanci ineſt. </s>
          <s id="N15721">Quan<lb></lb>tò autem productior vectis fuerit longitudo ab ipſo hypomo<lb></lb>chlio, tantò ibi quidem facilius mouet, hic autem æquilibrium <lb></lb>facit, ponduſque ſtateræ trutinat, quod ad æquipondij vergit ap<lb></lb>pendiculam.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1572E" type="head">
          <s id="N15730">COMMENTARIVS.</s>
        </p>
        <p id="N15734" type="main">
          <s id="N15736">Cauſam hic inquirit Ariſtoteles, ob quam in ſtatera <lb></lb>paruo appendiculo magna leuentur, ac trutinentur <lb></lb>pondera; Cum quippe ſtatera nonniſi libra quæ<lb></lb>dam eſſe videatur, licet quaſi dimidiata, vtpotè quæ ex <lb></lb>altera tantum parte lancem pendentem habeat, ex altera <lb></lb>verò diſcurrens quoddam appendiculum æquipondij. </s>
          <s id="N15743">Vt <pb pagenum="185" xlink:href="005/01/193.jpg"></pb>videre eſt in deſcripta ſtatera AB ſuſpenſa in C ex cuius <lb></lb>extremo A pendet lanx D, &amp; ex B appendiculum E. <lb></lb></s>
          <s id="N1574F">Etenim ſicut libra æqualia duntaxat ponderibus onera le<lb></lb><figure id="id.005.01.193.1.jpg" xlink:href="005/01/193/1.jpg"></figure><lb></lb>uat, ac trutinat; ita ſimiliter ſtatera, cum libra quædam <lb></lb>ſit, æqualia tantùm appendiculo onera videtur poſſe leua<lb></lb>re; quod ſecus experimur contingere. </s>
          <s id="N1575E">Nam paruæ molis <lb></lb>appendiculo, magna videmus onera extolli, ac menſu<lb></lb>rari. </s>
        </p>
        <p id="N15765" type="main">
          <s id="N15767">Mox deinde cauſam ipſam in eo docet conſiſtere, quòd <lb></lb>ſtatera, libræ ſimul ac vectis rationem induat, ac vtriuſque <lb></lb>vicem obtineat. </s>
          <s id="N1576E">Libræ nimirum, quia reuera eſt veluti iu<lb></lb>gum tranſuerſum, ſeu haſta bilancis ex puncto quaſi medio <lb></lb>ſuſpenſa, atque vtrinque ponderibus pendentibus librata <lb></lb>circa ipſum punctum <expan abbr="intermediũ">intermedium</expan>. Quo ſuſpenditur tanquam <lb></lb>circa centrum, vel axem. </s>
          <s id="N1577F">Qamuis enim ſtatera conſtitua<lb></lb>tur ex inæqualibus brachijs, &amp; ex altero tantum lanx vna <lb></lb>propendeat; vel certè loco lancis vnci nonnulli demittan<lb></lb>tur, qui mercibus, aut rebus ponderandis compacti, eas non <lb></lb>minus commodè ſuſtinent, vt in ſubiecta figura. </s>
          <s id="N1578E">Ex altero <pb pagenum="186" xlink:href="005/01/194.jpg"></pb>verò nonniſi appendiculum æquipondij ſuſpenſum depen<lb></lb>deat: Semper tamen ipſa ſtatera libram refert, cum eius <lb></lb>axis, ac fulcimentum ſit inter onus, &amp; æquipondium, <expan abbr="ipſiusq.">ipſiusque</expan> <lb></lb><figure id="id.005.01.194.1.jpg" xlink:href="005/01/194/1.jpg"></figure><lb></lb>æquipondij appendiculum, alterius lancis, vel vnci cum <lb></lb>pondere vicem ſubeat; ſiue ipſum fulcimentum, aut ſpar<lb></lb>tum conſtituatur in puncto omnino medio, ſiue ſecus, vnde <lb></lb>prouenit inæqualitas brachiorum, cum hæc libræ naturam <lb></lb>non auferat, nec immutet, vt diximus ſuo loco. </s>
        </p>
        <p id="N157AE" type="main">
          <s id="N157B0"><expan abbr="Rurſumq.">Rurſumque</expan> vectis pariter naturam ſimul ſortitur ſtatera, <lb></lb>quia fulcimentum habet vbi incumbit in axe, ſeu ſparto, <lb></lb>quod idem eſt, ac punctum vnde ſuſpenditur, &amp; circa quod <lb></lb>ipſa conuertitur, <expan abbr="pondusq.">pondusque</expan> leuandum conſtituitur merces <lb></lb>in lancem inuecta, vel vncis infixa; &amp; potentia mouens, ip<lb></lb>ſum appendiculum æquipondij. </s>
          <s id="N157C4">Cum igitur ea ſit vectis, ac <lb></lb>libræ natura <expan abbr="propriaq.">propriaque</expan> conditio, vt cum alterum eius à ful<lb></lb>cimento brachium longius protenditur, vt in ſtatera contin<lb></lb>git, paruo in ipſius extremitate adhibito pondere, magnam <lb></lb>valeat molem ex altero breuiori brachio pendentem attol<lb></lb>lere, iuxta proportionem vtriuſque diſtantiæ à centro, vt <pb pagenum="187" xlink:href="005/01/195.jpg"></pb>alibi demonſtrauimus; planum profecto relinquitur, qua <lb></lb>ratione, paruo appendiculo in ſtatera, magna leuari poſſint <lb></lb>pondera, vt intendebat Philoſophus. </s>
        </p>
        <p id="N157E1" type="main">
          <s id="N157E3">Quoniam verò in præfato diſcurſu ſemel atque iterum <lb></lb>Ariſtoteles docuit, ſtateram eſſe veluti libram, in qua plures <lb></lb>ſint libræ, ac totidem quot fuerint ſparta, hinc Blancanus <lb></lb>conijcit, apud Priſcos, ſtateram ex multis trutinis, ſeu ſpar<lb></lb>tis compactam fuiſſe, paribus interuallis per totam longi<lb></lb>tudinem ipſius ſtateræ diſſeminatis; Ex quibus ſingulis <lb></lb>prout pondus poſtulabat, illa ſuſpenderetur, appendiculo <lb></lb>ſemper in extremitate ſui brachij immoto manente; It aut <lb></lb>tantum mercis lanci imponeretur, quantum appendiculo <lb></lb>æquiponderaret, iuxta <expan abbr="ſituationẽ">ſituationem</expan> cuiuſlibet trutinæ. </s>
          <s id="N157FC"><expan abbr="Proin-deq.">Proin<lb></lb>deque</expan> ſingulæ trutinæ ad aliquod determinatum mercium <lb></lb>pondus trutinandum fuerint conſtitutæ. </s>
          <s id="N15806">Atque de hac ve<lb></lb>teri ſtatera putat Ariſtotelem locutum fuiſſe, de eaque ſo<lb></lb>lum verificari, quod ſe habeat tanquam libra, quæ plures <lb></lb>contineat libras. </s>
          <s id="N1580F">Nam tot erunt libræ quot ſparta, quæ di<lb></lb>uerſas proportiones libræ conſtituunt, atque adeo veluti <lb></lb>diuerſas omnino libras. </s>
        </p>
        <p id="N15816" type="main">
          <s id="N15818">Verumenimuerò non ſatis id colligitur ex Ariſtotele, nec <lb></lb>videtur neceſſarium ad verificandum dictum illud eiuſdem <lb></lb>Philoſophi. </s>
          <s id="N1581F">Quandoquidem etiam ſtatera prout modò apud <lb></lb>noſtrates eſt in vſu, ex duplici ſaltem trutina ſolet conſtare, <lb></lb>vna quæ loco vnde lanx pendet eſt propior, altera verò <lb></lb>quæ aliquantulum eſt remotior, &amp; in oppoſito, ſeu inuerſo <lb></lb>ſtateræ latere locatur: Ac per propiorem vtique onera ma<lb></lb>iora, per remotiorem verò minora conſueuerunt librari; li<lb></lb>bero ſemper manente appendiculo, vt per reliquum ſtateræ <lb></lb>brachium iuxta exigentiam ponderis diſcurrere valeat. <lb></lb></s>
          <s id="N15831">Quamobrem hac quoque in ſtatera contineri videntur plu<lb></lb>res libræ, cum ſaltem duplex in ea trutina reperiatur, quæ <lb></lb>tanquam duplex libra deſeruit ad maiora, vel minora one<lb></lb>ra aptius ponderanda, &amp; vt eadem ſecundum maiores, vel <lb></lb>minores differentias ponderum quando opus fuerit innote<lb></lb>ſcant. </s>
          <s id="N15840">Et quidem cum Ariſtoteles ait: ac ſi vna libra multæ <pb pagenum="188" xlink:href="005/01/196.jpg"></pb>ſint libræ, eo quod in ea inſint ſparta multa: fortaſſe idem <lb></lb>intellexit per multa, vel multas, ac plura, vel plures; cum no<lb></lb>men Græcum <foreign lang="grc">πολλὸς</foreign> vtrumque ſignificet, &amp; à Cicerone <lb></lb><foreign lang="grc">ω̄ολλὰ</foreign> in Timæo Platonis vertatur plures. </s>
          <s id="N15855">Niſi etiam cum <lb></lb>Baldo rectè dixerimus, ſtateram tot libras conſtitui, quot <lb></lb>ſunt tranſlationes appendiculi de loco ad locum; quia toties <lb></lb>variatur proportio, <expan abbr="proindeq.">proindeque</expan> etiam libra. </s>
          <s id="N15862">Quare gratis ad <lb></lb>exponenda verba Ariſtotelis putat Blancanus ſtateræ ap<lb></lb>pendiculum apud veteres fuiſſe immobile, <expan abbr="ipſamq.">ipſamque</expan> ſtateram <lb></lb>ex tot ſpartis, ſeu trutinis conſtaſſe, quot erant metienda <lb></lb>pondera: Quamuis alioquin id non fuerit impoſſibile, ſed <lb></lb>laborioſum duntaxat, &amp; inutile. </s>
        </p>
        <p id="N15873" type="main">
          <s id="N15875">Diximus, non impoſſibile: Nam quolibet in lance onere <lb></lb>impoſito, eſt adinuenire centrum grauitatis totius ſtateræ <lb></lb>ſic conſtitutæ, ex quo ſi ipſa per trutinam ſuſpendatur, <lb></lb>ſtabit <expan abbr="æquiponderabitq.">æquiponderabitque</expan> appendiculum immobile ipſi one<lb></lb>ri in lance impoſito. </s>
          <s id="N15884">Vnde ſingula puncta longitudinis ſta<lb></lb>teræ conſtitui poſſunt centra grauitatis reſpectu diuerſorum <lb></lb>onerum imponibilium, ac in quolibet illorum poterit truti<lb></lb>na locari, quæ ad determinatum ſuum onus librandum de<lb></lb>ſeruiat. </s>
          <s id="N1588F">Diximus tamen hoc eſſe laborioſum, &amp; inutile, <lb></lb>tum quia difficilius eſt multiplicare trutinas, <expan abbr="ipſamq.">ipſamque</expan> totam <lb></lb>ſtateram diuerſis ex punctis ſuſpendere ad quamlibet oneris <lb></lb>differentiam dignoſcendam, cum ſola appendiculi mobili<lb></lb>tate, atque diſcurſu id conſequi poſſit: tum etiam quia ad <lb></lb>pauciora onera libranda, <expan abbr="paucioresq.">paucioresque</expan> admodum ponderum <lb></lb>differentias percipiendas deſeruire poſſet ipſa huiuſmodi <lb></lb>ſtatera. </s>
          <s id="N158A8">Cum certè multiplicari trutinæ non valeant ad nu<lb></lb>merum linearum, aut denticulorum, in quos modò diuer<lb></lb>ſum eſt brachium ſtateræ, &amp; in quos diſcurrens appendicu<lb></lb>lum pro opportunitate transfertur, vt ſingulis notis, ſeu li<lb></lb>neis, ſingula onera trutinentur, ac determinatè quodlibet <lb></lb>eorum pondus diſtinctiſſimè innoteſcat. </s>
        </p>
        <p id="N158B5" type="main">
          <s id="N158B7">Addit autem Ariſtoteles quòd quantò propinquius one<lb></lb>ri in lance, vel vncis appenſo ſpartum conſtituitur, tanto <lb></lb>magis onus ipſum, ſeu maius onus valet ſtatera leuare. </s>
          <s id="N158BE">Id <pb pagenum="189" xlink:href="005/01/197.jpg"></pb>quod experientia conſtat, &amp; ea ratione ab eodem Philoſo<lb></lb>pho probatur, quia cum <expan abbr="ſpartũ">ſpartum</expan> conſtituatur hypomochlion, <lb></lb>ſeu fulcimentum talis vectis, nempe ſtateræ; <expan abbr="tantoq.">tantoque</expan> faci<lb></lb>lius vectis beneficio onera leuentur, quantò productior fue<lb></lb>rit vectis longitudo à fulcimento; hinc fit, vt ſparto magis <lb></lb>ad <expan abbr="locũ">locum</expan> vnde onus dependet appropinquato, maior vectis <lb></lb><expan abbr="lõgitudo">longitudo</expan> relinquatur <expan abbr="vſq;">vſque</expan> ad <expan abbr="appendiculũ">appendiculum</expan>, <expan abbr="faciliusq.">faciliusque</expan> propte<lb></lb>rea ipſum <expan abbr="appendiculũ">appendiculum</expan> valeat in maiori diſtantia <expan abbr="æquipõde-rare">æquiponde<lb></lb>rare</expan>, <expan abbr="maioraq.">maioraque</expan> onera trutinare: permutata videlicet <expan abbr="ponderũ">ponderum</expan>, <lb></lb>ac <expan abbr="brachiorũ">brachiorum</expan> proportione, vt ex Archimede lib.

1. æquipon<lb></lb>derantium propoſit.6. &amp; ſequenti; necnon ex <expan abbr="eodẽ">eodem</expan> Ariſto<lb></lb>tele ſup. </s>
          <s id="N1590F">quæſt. </s>
          <s id="N15912">3. in vniuerſum agendo de vecte retulimus. </s>
        </p>
        <p id="N15915" type="head">
          <s id="N15917">Quæſtio Vigeſimaprima.</s>
        </p>
        <p id="N1591A" type="main">
          <s id="N1591C">C<emph type="italics"></emph>vr medici facilius dentes extrahunt denti<lb></lb>forcipis onere adiecto, quàm ſi ſola vtantur <lb></lb>manu? </s>
          <s id="N15926">An quia ex mana magis, quàm ex den<lb></lb>tiforcipe lubricus elabitur dens? </s>
          <s id="N1592B">An ferro id <lb></lb>potius accidit, quàm digitis, quoniam vndique <lb></lb>dentem non comprehendunt, quod mollis di<lb></lb>gitorum facit caro, adhæret enim &amp; complectitur magis. </s>
          <s id="N15934">An <lb></lb>quia dentiforcipes duo ſunt contrarij vectes, vnicum habentes <lb></lb>hypomochlion, eius ſcilicet inſtrumenti connexionem? </s>
          <s id="N1593B">Hoc <lb></lb>igitur ad extractionem vtuntur organo, vt facilius moueant. <lb></lb></s>
          <s id="N15941">Sit dentiforcipis alterum quidem extremum vbi eſt A; alterum <lb></lb>autem quod extrahit, B, vectis autem vbi A D F, alter verò <lb></lb>vectis vbi BCE, hypomochlion autem CGD, connexio verò <lb></lb>vbi G, dens autem pondus. </s>
          <s id="N1594A">Vtroque igitur B &amp; F ſimul com<lb></lb>prehendentes mouent: quomodo autem commotus fuerit, faci<lb></lb>lius manu trahitur, quàm instrumento.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N15953" type="head">
          <s id="N15955">COMMENTARIVS.</s>
        </p>
        <p id="N15959" type="main">
          <s id="N1595B">Qværitur in præſenti ab Ariſtotele, ex quo nam pro<lb></lb>ueniat, vt facilius dentes extrahantur dentiſorcipis <lb></lb>adhibito inſtrumento, quàm ſola manu, immediata <lb></lb>opera digitorum. </s>
          <s id="N15964">Ac primò ex eo, inquit videri poſſe, id or-<pb pagenum="190" xlink:href="005/01/198.jpg"></pb>tum habere, quòd cum dens lubricus in ſe ſit, magis for<lb></lb>ſan è manu quæ leuis, &amp; mollis eſt, quàm ex rudi, ac tenaci<lb></lb>forcipe elabatur. </s>
          <s id="N15970"><expan abbr="Statimq.">Statimque</expan> hanc ipſam rationem impugnat, <lb></lb>ac penitus euertit, inquiens, potius ferro, quàm digitis con<lb></lb>tingere, vt dens ab illis apprehenſus, propter ſui lubricita<lb></lb>tem aufugiat. </s>
          <s id="N1597C">Quandoquidem ferrum, ſeu ferrei dentiforci<lb></lb>pes, minus quàm digiti <expan abbr="vndiq.">vndique</expan> dentem valent comprehen<lb></lb>dere. </s>
          <s id="N15987">Mollis enim digitorum caro cedendo, ac flectendo <lb></lb>ſeſe, adhæret, &amp; complectitur magis quàm ferrum præ ſua <lb></lb>duritie, ac in flexibilitate. </s>
          <s id="N1598E">Vnde perperam huiuſmodi Ariſto<lb></lb>telis verba intelligunt cum ij, qui ea tanquam in confirma<lb></lb>tionem prioris rationis, aut ſolutionis dicta exponunt: tum <lb></lb>etiam qui ex oppoſito, ea ipſa propoſitam quęſtionis ſuppo<lb></lb>ſitionem arbitrantur deſtruere. </s>
          <s id="N15999">Etenim non ſuppoſitioni, &amp; <lb></lb>experientiæ aſſumptæ, ſed priori duntaxat opponuntur ſolu<lb></lb>tioni, vt vidimus, <expan abbr="rationemq.">rationemque</expan> dubitandi non mediocriter au<lb></lb>gent, vt magis ea, <expan abbr="quã">quam</expan> traditurus eſt vera ſolutio eluceſcat. </s>
        </p>
        <p id="N159AA" type="main">
          <s id="N159AC">Soluit igitur Ariſtoteles <expan abbr="quæſtionẽ">quæſtionem</expan> dicens, id ex eo con<lb></lb>tingere, quòd in dentiforcipe duo continentur vectes ſibi in<lb></lb>uicem contrarij, videlicet ipſa dentiforcipis brachia, quorum <lb></lb>vnicum eſt commune hypomochlion, nempe ipſa vtriuſque <lb></lb>connexio, parisque alterius ad <expan abbr="alterũ">alterum</expan> inflexio, qua <expan abbr="inuicẽ">inuicem</expan> ob<lb></lb>uiantur. </s>
          <s id="N159C7">Proindeq, <expan abbr="horũ">horum</expan> <expan abbr="vectiũ">vectium</expan> virtute arctius, ac validius, <lb></lb>quàm digitis <expan abbr="dentẽ">dentem</expan> perſtringi, <expan abbr="faciliusq.">faciliusque</expan> <expan abbr="cõſequenter">conſequenter</expan> auelli. </s>
        </p>
        <p id="N159E0" type="main">
          <s id="N159E2">Sit enim dentiforcipis inſtrumentum AB, quod dentem <lb></lb><expan abbr="quidẽ">quidem</expan> comprehen<lb></lb>dat, &amp; conſtringat <lb></lb><figure id="id.005.01.198.1.jpg" xlink:href="005/01/198/1.jpg"></figure><lb></lb>per ſui extremum <lb></lb>B. </s>
          <s id="N159F6">Vectis autem <lb></lb>vnus ſit brachium <lb></lb>BC. </s>
          <s id="N159FE">Alter verò <lb></lb>AD ſuffulti in con<lb></lb>nexione quaſi axe <lb></lb><expan abbr="vtriuſq;">vtriuſque</expan> vbi E. </s>
          <s id="N15A0B">Pon<lb></lb>duſque ſit ipſum <lb></lb>dens F. </s>
          <s id="N15A13">Vtroque <pb pagenum="191" xlink:href="005/01/199.jpg"></pb>igitur vecte ſimul admoto per extrema BD ipſum dentem <lb></lb>tanquam onus in contrarium repellendo, validiſſimè con<lb></lb>ſtringent adhibita, ſcilicet manu in AC, qua extremum <lb></lb>A compellatur verſus C, &amp; extremum C verſus A. </s>
          <s id="N15A22">Dens <lb></lb><expan abbr="autẽ">autem</expan> ita conſtrictus facilè dimouetur, ac dimotus extrahi<lb></lb>tur. </s>
        </p>
        <p id="N15A2C" type="main">
          <s id="N15A2E">Hæc ferè Ariſtoteles, quæ tamen vt rectè Baldus obſer<lb></lb>uat, conſtrictionem potius, quam dimotionem, &amp; abſtractio<lb></lb>nem dentis demonſtrant. </s>
          <s id="N15A35">Addendum ergo erit dentem <lb></lb>dentiforcipe conſtrictum, vnà cum ipſo inſtrumento alium <lb></lb>quendam conſtituere vectem, ac ſi eſſet vnum continuum, <lb></lb>cuius longitudo in præſenti erit ADF, vel CDF. </s>
          <s id="N15A3E">Si enim <lb></lb>attentè conſideretur, pręter conſtrictionem, non datur alius <lb></lb>motus dentiforcipis ad dentem, ſeu reſpectu dentis, ſed ſi<lb></lb>mul cum illo, nempe ambo tanquam vnicum corpus ad <lb></lb>modum vectis mouentur. </s>
          <s id="N15A49">Cuius fulcimentum eſt in parte <lb></lb>gingiuæ vbi dens primò ex illa emergit, &amp; in ſua conuerſio<lb></lb>ne innititur, vt in D. </s>
          <s id="N15A51">Pondus verò conſtituitur gingiuæ <lb></lb>pars reſiſtens ex oppoſito circa dentis radicem vbi B. </s>
          <s id="N15A56">Cum <lb></lb>igitur parua ſit diſtantia à fulcimento D ad extremum F; <lb></lb>magna verò ab eodem fulcimento D ad alterum eiuſdem <lb></lb>vectis extremum A, vel C: hinc fit, vt immoto manente <lb></lb>puncto D facilè ad motum circularem AC verſus G; ex<lb></lb>tremum F moueatur in oppoſitum etiam circulariter ver<lb></lb>ſus B. </s>
          <s id="N15A65">Et ſic dimota dentis radice ex proprio loco, dens <lb></lb>totus per dentiforcipem extrahatur. </s>
          <s id="N15A6A">Quod difficile eſſet <lb></lb>abſque illo ſola manu præſtari. </s>
          <s id="N15A6F">Quippe cum digiti nec tam <lb></lb>tenaciter dentem apprehendere, nec ita vnum veluti corpus <lb></lb>oblongum, ac tenſum cum eo poſſint componere; quod to<lb></lb>tum vnius vectis rationem ſubeat. </s>
        </p>
        <p id="N15A78" type="main">
          <s id="N15A7A">Quocirca admittenda non erunt, quæ Baldus aliter Phi<lb></lb>loſophus hac in re profert, quamuis acutè fuerint excogita<lb></lb>ta, cum ait, dentiforcipis partium, quibus dens apprehendi<lb></lb>tur, eam quæ longior eſt, potentiæ mouentis loco ſuccede<lb></lb>re, breuiorem verò fulcimentum conſtitui: Quandoquidem <lb></lb>in vſu dentiforcipis ad extrahendum dentem etiam prout <pb pagenum="192" xlink:href="005/01/200.jpg"></pb>ab ipſo explicatur, fulcimentum non poteſt conſtitui in ipſa <lb></lb>breuiori dentiforcipis parte, qua apprehenditur dens; tum <lb></lb>quia hæc ſimul cum altera parte mouetur, licet per mino<lb></lb>rem circulationem, quæ ſanè fit circa punctum illud gingi<lb></lb>uæ, cui in abſtractione conuertendo ſeſe innititur dens, &amp; à <lb></lb>quo ſemper dentiforcipis extremum aliquantulum diſtat, <lb></lb>eo quod nequeat ad illam vſque partem gingiuæ interio<lb></lb>rem, ac ſolidam vbi huiuſmodi fit nixus pertingere: tum, <lb></lb>etiam quia eſto pars ipſa breuior per ſui extremum non, <lb></lb>moueretur ad motum alterius, ſed quieſceret, non propte<lb></lb>rea ſequeretur conſtitui fulcimentum huius motionis. </s>
          <s id="N15AA0">Nam <lb></lb>punctum cuiuſlibet vectis correſpondens puncto fulcimen<lb></lb>ti cui innititur, penetratur cum illo, &amp; ſimul cum illo quie<lb></lb>ſcit in motione ipſiusmet vectis; &amp; tamen non poteſt con<lb></lb>ſtitui fulcimentum ſuæ propriæ motionis. </s>
          <s id="N15AAB">Nimirum quia, <lb></lb>nihil in ſeipſo poteſt fulciri, ſed ſemper inter fulcimentum, <lb></lb>&amp; ſuffultum ea debet eſſe diſtinctio, quæ eſt inter mobile, <lb></lb>&amp; immobile, vel commotum, &amp; immotum. </s>
          <s id="N15AB4">Quare cum, <lb></lb>conſtitutum ex dente, ac forcipe ſe habeat per <expan abbr="modũ">modum</expan> vnius <lb></lb>vectis, non ſecus ac ſi eſſet vnicum corpus continuum, <lb></lb>etiam ſi <expan abbr="ſecundũm">ſecundum</expan> punctum aliquod ſibi intrinſecum quie<lb></lb>ſceret, ac circa illud ſecundum reliquas ſui partes circulari<lb></lb>ter moueretur; Non propterea poſſet illi tanquam proprio <lb></lb>fulcimento in ſua ipſius motione inniti. </s>
          <s id="N15ACB">Potius igitur fulci<lb></lb>mentum conſtituendum eſt extrinſecum, in ea gingiuæ par<lb></lb>te, quam deſcripſimus vbi dens ipſe in auulſione fulcitur, ac <lb></lb>præmit, <expan abbr="doloremq.">doloremque</expan> infert non minus, quam vbi ex oppoſito <lb></lb>dimotæ eius radici reſiſtitur. </s>
        </p>
        <p id="N15ADA" type="main">
          <s id="N15ADC">In calce tandem huius quæſtionis Ariſtoteles ſubnectit, <lb></lb>dentem commotum facilius manu ſola quàm inſtrumento <lb></lb>ſimul auferri. </s>
          <s id="N15AE3">Quod ſanè intellexerim habita ratione ad <lb></lb>dolorem, quem in dentis abſtractione quiſque vitare, aut <lb></lb>ſaltem minuere intendit; ita vt facilitas ad commoditatem <lb></lb>patientis, non autem ad abſolutam effectus conſecutionem <lb></lb>referatur. </s>
          <s id="N15AEE">Quo ſenſu id ex eo videtur probari, quoniam ſi <lb></lb>ſemel dens fuerit commotus, &amp; à poſitione ſuæ ſedis dimo-<pb pagenum="193" xlink:href="005/01/201.jpg"></pb>tus, non modò ſolis digitis poterit ſimpliciter auelli, non, <lb></lb>minus ac ſimul adhibito inſtrumento; ſed etiam commo<lb></lb>dius, ac facilius, dolorem ſcilicet penitus, vel maiori ex par<lb></lb>te vitando, eo quod digiti ſentire ſecus, ac dentiforcipis <lb></lb>ferrum, &amp; ſuperare magis valeant pro opportunitate ali<lb></lb>qualem dentis reſiſtentiam. </s>
          <s id="N15B02">Alioquin abſolutè loquendo <lb></lb>nulla habita ratione ad dolorem, ipſum dentiforcipis inſtru<lb></lb>mentum, ſicut maiorem præualet ſuperare dentis reſiſten<lb></lb>tiam firmiter inhærentis; ita &amp; multo magis minorem, vt <lb></lb>cum iam ille à propria ſede dimotus debiliter tantum gin<lb></lb>giuæ inhæret. </s>
        </p>
        <p id="N15B0F" type="head">
          <s id="N15B11">Quæſtio Vigeſimaſecunda.</s>
        </p>
        <p id="N15B14" type="main">
          <s id="N15B16">C<emph type="italics"></emph>vr nuces abſque ictu facilè confringuntur in<lb></lb>strumentis, qua ad eum fiunt vſum. </s>
          <s id="N15B1E">Multum <lb></lb>enim aufertur virium, motionis ſcilicet &amp; vio<lb></lb>lentia. </s>
          <s id="N15B25">Praeterea duro &amp; graui comprimens in<lb></lb>ſtrumento citiùs confringet, quàm ligneo &amp; <lb></lb>leui. </s>
          <s id="N15B2C">An quia ſic vtrunque à duobus compri<lb></lb>mitur vectibus ipſa nux, à vecte autem facilè <lb></lb>diuelluntur onera? </s>
          <s id="N15B33">Id enim instrumentum ex duobus com<lb></lb>ponitur vectibus, idem habentibus hypomochlion, connexio<lb></lb>nem videlicet ipſam, vbi est A, quemadmodum igitur fue<lb></lb>ro diducta ſecundum extrema molis CD, ipſæ FE ſic à par<lb></lb>ua faciliter potentia conducuntur, quod igitur cum percuſsio<lb></lb>ne feciſſet pondus id valentiores illæ EC, &amp; FD vectes effi<lb></lb>ciunt. </s>
          <s id="N15B42">Eleuatione enim in contrarium elati, &amp; comprimentes <lb></lb>frangunt vbi eſt K. </s>
          <s id="N15B48">Hanc etiam ob cauſam quanto vicinius <lb></lb>fuerit K ipſum A, confringitur celerius. </s>
          <s id="N15B4D">Quantò enim ab hipo<lb></lb>mochlio plus diſtat vectis, facilius &amp; plus mouet ab codem <lb></lb>potentia. </s>
          <s id="N15B54">Eſt igitur A quidem hipomochlion: ipſa autem DAF <lb></lb>vectis, &amp; item ipſa CAE. </s>
          <s id="N15B59">Quantò igitur ipſum K vicinius <lb></lb>fuerit angulo ipſius A, tantò vicinius fit connexioni, vbi est <lb></lb>A, hoc autem hypomochlion, ab eadem igitur potentia appli<lb></lb>cante FE plus extolli neceſſe eſt. </s>
          <s id="N15B62">Quamobrem quoniam ex <lb></lb>contario eſt eleuatio, neceſſe eſt magis comprimi, quod autem <lb></lb>comprimitur magis, citius frangitur.<emph.end type="italics"></emph.end></s>
        </p>
        <pb pagenum="194" xlink:href="005/01/202.jpg"></pb>
        <p id="N15B6F" type="head">
          <s id="N15B71">COMMENTARIVS.</s>
        </p>
        <p id="N15B75" type="main">
          <s id="N15B77">Præſens quæſtio circa ſimile admodum inſtrumentum <lb></lb>verſatur, ac præcedens, quamuis ad diuerſum om<lb></lb>nino effectum natura ſua ordinatum. </s>
          <s id="N15B7E">Quærit enim <lb></lb>Philoſophus quo fiat, vt nuces abſque ictu, facilè inſtru<lb></lb>mento ad id opus fabrefacto, confringantur: quod ſanè in<lb></lb>ſtrumentum forcipi ſimillimum, &amp; ex ligneis regulis com<lb></lb>pactum ipſe videtur ſupponere. </s>
          <s id="N15B89">Eamque mox rationem <lb></lb>dubitandi affert; quia abſque ictu ac violenta aliqua per<lb></lb>cuſſione, remiſſius abſolutè quam cum illa corpus compri<lb></lb>mitur; impetus namque ictus aut percuſſionis vires maxi<lb></lb>mè auget in ipſamet motione, ad comprimendum acrius <lb></lb>quod percutitur, vt hactenus explicuimus. </s>
          <s id="N15B96">Quare non tam <lb></lb>facilè præfato <expan abbr="inſtrumẽto">inſtrumento</expan> abſque ictu nuces confringi poſſe <lb></lb>viderentur, ſicut cum malleo adacto impetu confringuntur. <lb></lb></s>
          <s id="N15BA2">Id quod præterea ex eo confirmat, quia graui ac duro in<lb></lb>ſtrumento, vt eſt ferreus malleus, citius, conſentaneum eſt, <lb></lb>fieri confractionem quàm ligneo ac leui, quale hoc de quo <lb></lb>agimus in præſenti ſupponitur. </s>
        </p>
        <p id="N15BAB" type="main">
          <s id="N15BAD">Attamen ipſe Philoſophus huiuſmodi difficultatem ac <lb></lb>dubitationem ex eodem principio, quo præcedentem quæ<lb></lb>ſtionem ſoluerat, aptiſſimè ac breuiſſimè diluit, inquiens, <lb></lb>explicatum inſtrumentum duobus brachijs tanquam duo<lb></lb>bus vectibus contrarijs, ad ſeſe inuicem conuerſis conſtare, <lb></lb>vnico fulcimento innixis, quod eſt vtriuſque connexio ac <lb></lb>veluti axis: duorum autem vectium compreſſione, vt potè <lb></lb>qui magnam vim habeant comprimendi, æquè facile nuces <lb></lb>amygdalas, vel id genus alia confringi, ac ictu vel percuſſio<lb></lb>ne cum impetu. </s>
          <s id="N15BC2">Quod vt ad oculos etiam pateat, conſti<lb></lb>tuatur primo inſtrumentum ABCD, cuius brachia ſint AD <lb></lb>&amp; CB ſuffulta in connexione vtriuſque vbi E. </s>
          <s id="N15BCA">Nux verò <lb></lb><expan abbr="confringẽda">confringenda</expan> locetur inter A &amp; C vbi F, nempe inter extre<lb></lb>ma brachiorum ea parte qua minus diſtant à fulcimento. <lb></lb></s>
          <s id="N15BD5">Potentia verò confringentis applicetur in extremis eorun<lb></lb>dem brachiorum ea parte, qua magis diſtant a fulcimento, <pb pagenum="195" xlink:href="005/01/203.jpg"></pb><figure id="id.005.01.203.1.jpg" xlink:href="005/01/203/1.jpg"></figure><lb></lb>tanquam in manubrijs, <expan abbr="nimirũ">nimirum</expan> in BD. </s>
          <s id="N15BEA">Conſideretur dein<lb></lb>de vtrum que brachium tanquam duplicem vectem moueri <lb></lb>circa immotum fulcimentum E; ita vt ad motum B verſus <lb></lb>D, alterum extremum nempe C appropinquetur ad A; &amp; è <lb></lb>conuerſo, ad motum D verſus B, ipſum A appropinquetur <lb></lb>ad C. </s>
          <s id="N15BF8">Tunc dicimus nucem, quę quidem tanquam pondus <lb></lb>ab vtroque extremo duplicis vectis AC pellitur ac repelli<lb></lb>tur, facilè comprimi, ac tandem nimia compreſſione con<lb></lb>fringi, ſiquidem dum magis ac magis ipſa extrema AC ad <lb></lb>inuicem appropinquantur, neceſſariò quæ inter ipſa interci<lb></lb>pitur, nucem comprimunt, &amp; comprimendo confringunt. </s>
        </p>
        <p id="N15C05" type="main">
          <s id="N15C07">Addit autem primò Ariſtoteles, quo <expan abbr="lõgiora">longiora</expan> fuerint bra<lb></lb>chia huius inſtrumenti à connexione ipſorum ſeu <expan abbr="fulcimẽto">fulcimento</expan> <lb></lb>ad extrema, quibus applicatur potentia: &amp; ex alia parte, quo <lb></lb>breuiora eadem brachia fuerint à conexione ſeu <expan abbr="fulcimẽto">fulcimento</expan> <lb></lb>ad nucem, eo facilius confractionem fieri; ac proinde à mi<lb></lb>nori potentia, ita vt id ipſum quod cum percuſſione feciſſet <lb></lb>pondus, præſtetur à binis explicatis vectibus in contrarium <lb></lb>ſeſe conantibus, &amp; comprimentibus ipſam nucem; cuius <lb></lb>reſiſtentia gerit vicem ponderis. </s>
        </p>
        <p id="N15C26" type="main">
          <s id="N15C28">Secundo verò addit Ariſtoteles, eò <expan abbr="maiorẽ">maiorem</expan> fieri vectium <lb></lb>ſeu brachiorum dilatationem, <expan abbr="quõ">quom</expan> propinquius fulcimento, <lb></lb>ſeu angulo connexionis eorum nux confringenda conſtitua<lb></lb>tur, quia nimirum vterque angulus ad verticem ab illis <expan abbr="cõ-ſtitutus">con<lb></lb>ſtitutus</expan>, per talem appropinquationem dilatatur (nempe <lb></lb>AEC. &amp; BED.) &amp; cum angulo ipſa quoque brachia, quæ <lb></lb>angulum conſtituunt, ita vt magis tunc diſtare oporteat in<lb></lb>ter ſe extrema AC, ſicut &amp; DB, <expan abbr="cũ">cum</expan> maius ſit latus, quod ſub <pb pagenum="196" xlink:href="005/01/204.jpg"></pb>maiori angulo ſubtenditur, vt conſtat ex 18. primi ele<lb></lb>ment. </s>
          <s id="N15C50">Dilatatur autem magis ipſe angulus AEC, &amp; con<lb></lb>ſequenter alius ad verticem BED; Nam quò propinquius <lb></lb>ei acceſſerit nucis magnitudo, cum qua conſtituit veluti <lb></lb><expan abbr="triangulũ">triangulum</expan> AEC, eò minora ſeu breuiora <expan abbr="euadũt">euadunt</expan> duo latera, <lb></lb>quibus ipſe angulus E continetur, prædictamque magnitu<lb></lb>dinem tanquam baſim ſubtendit. </s>
          <s id="N15C64">Duo autem latera ſuper <lb></lb>eandem baſim quanto minora ſunt, tanto <expan abbr="maiorẽ">maiorem</expan> angulum <lb></lb><expan abbr="cõſtituunt">conſtituunt</expan>, vt patet per vigeſimam <expan abbr="primã">primam</expan> primi. </s>
          <s id="N15C76">Magis ergo <lb></lb>dilatatis brachijs ſeu vectibus cum angulo <expan abbr="cõnexionis">connexionis</expan> <expan abbr="eorũ">eorum</expan>, <lb></lb>propter <expan abbr="maiorẽ">maiorem</expan> <expan abbr="approximationẽ">approximationem</expan> nucis ad ipſum validius, ac <lb></lb>facilius, vt docet Ariſtot. <expan abbr="potẽtia">potentia</expan> quę in extremis manubrijs <lb></lb>adhibetur, comprimere, atque adeò <expan abbr="cõfringere">confringere</expan> intelligetur. </s>
        </p>
        <p id="N15C9B" type="main">
          <s id="N15C9D">Quæ quidem conſequentia duplici ex capite poteſt pro<lb></lb>bari. </s>
          <s id="N15CA2">Primo quia dilatatis brachijs, diſtantioribuſque ex<lb></lb>tremis eorum ab inuicem conſtitutis, ob maiorem propin<lb></lb>quitatem nucis ad centrum, velocior poſtea conſequitur <lb></lb>motus compreſſionis eorum. </s>
          <s id="N15CAB">Siquidem maiorem arcum in <lb></lb>eodem tempore eadem potentia per talem <expan abbr="motũ">motum</expan> deſcribet. <lb></lb></s>
          <s id="N15CB5">Licet enim eadem ſit extenſio, quæ deperditur per com<lb></lb>preſſionem ex parte corporis compreſſi, aut confracti vbi<lb></lb>cunque fiat ipſa compreſſio, ſemper tamen quò propriùs <lb></lb>centro fit, &amp; amplius brachia dilatata ſupponit, eo maiorem <lb></lb>arcum extrema brachiorum, in quibus applicatur potentia <lb></lb>comprimendo percurrunt. </s>
        </p>
        <figure id="id.005.01.204.1.jpg" xlink:href="005/01/204/1.jpg"></figure>
        <p id="N15CC7" type="main">
          <s id="N15CC9">Sint <expan abbr="namq;">namque</expan> tanquam <lb></lb>brachia dilatata duæ <lb></lb>diametri AD, &amp; CB <lb></lb>in circulo ABCD ſeſe <lb></lb>inuicem <expan abbr="bifariã">bifariam</expan> inter<lb></lb>ſecantes, &amp; connecten<lb></lb>tes in <expan abbr="cẽtro">centro</expan> E. </s>
          <s id="N15CE5">Exten<lb></lb>ſio verò corporis con<lb></lb>fring<expan abbr="ẽdi">endi</expan>, quæ per <expan abbr="com-preſſionẽ">com<lb></lb>preſſionem</expan> deperditur, <lb></lb>ſit ſpatium AF, quod <pb pagenum="197" xlink:href="005/01/205.jpg"></pb>primò conſtituatur inter extrema AC eorundem brachio<lb></lb>rum. </s>
          <s id="N15CFF">Et à puncto F per centrum E ducatur recta FG, quæ <lb></lb>locum, vel ſitum deſignat, in quo conſtituendum eſt bra<lb></lb>chium AD poſt ipſam compreſſionem, ita vt extremum A <lb></lb>transferatur in F, &amp; extremum D transferatur in G. <lb></lb></s>
          <s id="N15D0A">Tunc certè ipſum extremum D per huiuſmodi tranſlatio<lb></lb>nem, æqualem arcum, aut lineam deſcriberet ipſi ſpatio <lb></lb>AF. </s>
          <s id="N15D12">Siquidem æquales anguli ad centrum circuli, æquali<lb></lb>bus arcubus inſiſtunt, vt patet per 26. tertij. </s>
          <s id="N15D17">Anguli autem <lb></lb>conſtituti ad centrum E per ipſas rectas AD, &amp; FG, nem<lb></lb>pe AEF, &amp; GED, ſunt æquales per 15. primi, eo quod <lb></lb>ſint ad verticem. </s>
          <s id="N15D20">Quando igitur corpus <expan abbr="confringendũ">confringendum</expan> col<lb></lb>locatur inter extrema <expan abbr="brachiorũ">brachiorum</expan> præfati inſtrumenti longiſ<lb></lb>ſime a centro, <expan abbr="tantũ">tantum</expan> ſpatium in fractione percurrunt ipſa ex<lb></lb>trema, <expan abbr="quantũ">quantum</expan> alia oppoſita in quibus applicatur potentia. </s>
        </p>
        <p id="N15D39" type="main">
          <s id="N15D3B">Quod fi corpus confringendum collocetur propinquius <lb></lb>centro, ſeu connexioni brachiorum E, ita vt extenſio eius <lb></lb>AF, quæ per confractionem deperditur, conſtituatur exem<lb></lb>pli gratia in HI, A tranſlato in H ſuper eandem lineam, <lb></lb>AD, &amp; F in I verſus lineam CB; &amp; per ipſum punctum <lb></lb>I, &amp; centrum E excitetur alia diagonalis KL, quæ pa<lb></lb>riter deſignet locum, ac situm quo transferri debet idem <lb></lb>brachium AD poſt confractionem: Tunc maiorem ar<lb></lb>cum inueniemus deſcribitura in ipſa compreſſione extrema <lb></lb>DA, quam ſit ſpatium HI, quod deperditur per illam. <lb></lb></s>
          <s id="N15D51">Quandoquidem A transferetur in K, &amp; D in L: Spatium <lb></lb>autem DL continet ſpatium DG, ſicut ſpatium AK con<lb></lb>tinet ſpatium AF æquale ipſi HI, quo propterea maius eſt <lb></lb>ipſum AK, &amp; DL, quæ per rationem ſupra factam ſunt <lb></lb>æqualia. </s>
          <s id="N15D5C">Rurſus verò ſi excitetur linea recta à puncto A <lb></lb>ad punctum K, &amp; conſiderentur iſta duo triangula, nempe <lb></lb>HEI, &amp; AEK, inuenientur habere latera proportionalia <lb></lb>circa eundem angulum E; baſesque ſimilis rationis per quar<lb></lb>tam propoſ. </s>
          <s id="N15D67">ſexti. </s>
          <s id="N15D6A">Cumque baſis AK longioribus lineis <lb></lb>ſubtendatur ipſi angulo E, maior erit, quàm baſis HI ei<lb></lb>dem angulo ſubtenſa breuioribus lineis EH, &amp; EI. </s>
        </p>
        <pb pagenum="198" xlink:href="005/01/206.jpg"></pb>
        <p id="N15D75" type="main">
          <s id="N15D77">Quod autem exempliſicauimus in brachio, ſeu vecte AD, <lb></lb>idem etiam procedit de brachio CB. </s>
          <s id="N15D7D">Et quod de brachijs <lb></lb>in medio ad inuicem connexis, ac bifariam ſeſe interſecan<lb></lb>tibus dictum eſt, accommodari poteſt in alijs non ita ſe ha<lb></lb>bentibus ſeu alibi connexis. </s>
          <s id="N15D86">Nam ſemper verificabitur ad <lb></lb>maiorem approximationem corporis confringendi ad cen<lb></lb>trum connexionis eorum, ſeu fulcimentum, magis ipſa bra<lb></lb>chia dilatari, maiuſque deinde ſpatium eodem tempore, <lb></lb>comprimendo percurrere, quod eſt velocius agere, vnde &amp; <lb></lb>validius colligitur frangere, vt dicebamus ex Ariſtotele. </s>
        </p>
        <p id="N15D94" type="main">
          <s id="N15D96">Alio verò ex capite eadem conſequentia probatur, quia <lb></lb>cum vectis beneficio eandem proportionem habeat po<lb></lb>tentia ad pondus leuandum, aut deprimendum, quam habet <lb></lb>eius diſtantia à fulcimento ad diſtantiam ponderis ab eo<lb></lb>dem fulcimento, vt quæſt. </s>
          <s id="N15DA1">3. ex Ariſtotele, &amp; Archimede <lb></lb>probauimus: quanto magis corpus confringendum ad pun<lb></lb>ctum connexionis, ſeu axem E, quo vterque vectis huius <lb></lb>inſtrumenti fulcitur, appropinquabitur; tanto maior erit ex<lb></lb>ceſſus diſtantiæ ipſius potentiæ motricis digitorum in ex<lb></lb>tremis BD applicatis, reſpectu diſtantiæ ipſius nucis, aut <lb></lb>alterius corporis confringendi ab eodem puncto E. <expan abbr="Proin-deq.">Proin<lb></lb>deque</expan> tanto maior pariter erit vis eiuſdem potentiæ ad de<lb></lb>primendum, vel confringendum in tali ſitus proportione <lb></lb>præſertim cum duo concurrant vectes duplicantes ſuas vi<lb></lb>res, quod erat Philoſophi intentum. </s>
        </p>
        <p id="N15DBC" type="head">
          <s id="N15DBE">Quæſtio Vigeſimatertia.</s>
        </p>
        <p id="N15DC1" type="main">
          <s id="N15DC3">C<emph type="italics"></emph>vr ſi duo extrema in rhombo puncta duabus <lb></lb>ferantur latonibus, haudquaquam æquale <lb></lb>vtrumque eorum pertranſit rectam, ſed multò <lb></lb>plus alterum? </s>
          <s id="N15DCF">Idem autem eſt ſermo, cur quod <lb></lb>ſuper latus fertur, minus pertranſit quam <lb></lb>ipſum latus? </s>
          <s id="N15DD6">Illud enim diametrum minorem <lb></lb>hoc vero maius latus. </s>
          <s id="N15DDB">Et hoc quidem vnica. </s>
          <s id="N15DDE">Il<lb></lb>lud verò duabus fertur lationibus. </s>
          <s id="N15DE3">Feratur enim ex ipſa AB, A <emph.end type="italics"></emph.end><pb pagenum="199" xlink:href="005/01/207.jpg"></pb><emph type="italics"></emph>quidem ad <expan abbr="ipsũ">ipsum</expan> B, B verò ad <expan abbr="ipsũ">ipsum</expan> D eadem celeritate. </s>
          <s id="N15DF7">Feratur <lb></lb><expan abbr="autẽ">autem</expan> &amp; ipſa AB in ipſi AC iuxta CD <expan abbr="eadẽ">eadem</expan> celeritate <expan abbr="cũ">cum</expan> illis. <lb></lb></s>
          <s id="N15E08">Neceſſe igitur eſt A quidem in ipſa AD diametro ferri, B verò <lb></lb>in ipſa BC, &amp; vtranque ſimul pertranſiſſe, &amp; ipſam AB <expan abbr="ipſũ">ipſum</expan> <lb></lb>latus AC: latum enim ſit ipſum A ipſam AE, AB autem ipſam <lb></lb>AF, &amp; proiecta ſit FG iuxta ipſum AB, &amp; ab ipſo E ſimiliter <lb></lb>repleatur. </s>
          <s id="N15E17">Similiter igitur fit quod <expan abbr="repletũ">repletum</expan> eſt, ipſi toti: æqualis <lb></lb>igitur AF ipſi AE. </s>
          <s id="N15E21">Ipſa autem AB ipſam AF lata erit: in dia<lb></lb>metro igitur erit ſecundum K, &amp; ſemper neceſſe eſt ipſum fer<lb></lb>ri ſecundum diametrum, &amp; ſimul AB latus pertranſit latus <lb></lb>AC, &amp; ipſum A diametrum pertranſit AD. </s>
          <s id="N15E2B">Similiter etiam <lb></lb>demonſtrabitur &amp; ipſum B in ipſa BC diametrum lato, æqua<lb></lb>lis enim eſt ipſa BE ipſi BG. </s>
          <s id="N15E33">Repleto igitur ab ipſo G quod in<lb></lb>tus eſt, toti eſt ſimile, &amp; ipſum B in ipſa diametro erit ſecun<lb></lb>dum laterum connexionem. </s>
          <s id="N15E3A">Et ſimul latus pertranſit latus, &amp; <lb></lb>B ipſum BC diametrum. </s>
          <s id="N15E3F">Simul igitur Amultò plus ipſa AB <lb></lb>pertranſit, &amp; ipſum latus minus latus eadem lata teleritate: <lb></lb>&amp; ipſum latus maiorem quàm B pertranſiuit vna <expan abbr="latũ">latum</expan> latio<lb></lb>ne. </s>
          <s id="N15E4C">Quantò enim acutior fuerit rhombus, diameter quidem <lb></lb>minor fit, AC autem maior; latus verò ipſius BC minus. </s>
          <s id="N15E51">Ab<lb></lb>ſurdum eſt enim (vt dictum eſt) id quod duabus fertur latio<lb></lb>nibus, aliquando ferri tardius illo, quo fertur vnica, &amp; vtriſ<lb></lb>que poſitis æquali velocitate punctis, alterum pertranſire ma<lb></lb>iorem Cauſa autem eſt quoniam ei, quod ab obtuſo fertur an<lb></lb>gulo, ambæ ferè contrariæ fiunt lationes, &amp; illa ſecundum <lb></lb>quam ipſum fertur, &amp; illa ſecundum quam ipſum à latere de<lb></lb>fertur. </s>
          <s id="N15E62">Ei autem quod ab acuto fertur, accidit vt ad idem fe<lb></lb>ratur. </s>
          <s id="N15E67">Coadiuuat enim quæ ipſius eſt lateris,, illam quæ eſt ſu<lb></lb>per diametrum. </s>
          <s id="N15E6C">Et quantò hunc quidem acutiorem feceris, <lb></lb>illum verò obtuſum magis: hæc quidem tardior erit, illa verò <lb></lb>celerior. </s>
          <s id="N15E73">Hæ quidem igitur magis contrariæ fiunt, quoniam <lb></lb>obtuſior fit angulus: illæ verò ad idem magis, quoniam lineæ <lb></lb>coarctantur. </s>
          <s id="N15E7A">Ipſum enim A ferè ad idem fertur ſecundum <lb></lb>ambas lationes. </s>
          <s id="N15E7F">Coadiuuatur igitur altera &amp; quantò ſanè <lb></lb>acutior fuerit angulus, tantò magis ipſum A ad contrarium, <lb></lb>ipſum enim ad B fertur, latus autem defert ipſum ad D. </s>
          <s id="N15E87">Et <lb></lb>quantò ſanè obtuſior fuerit angulus, magis contrariæ fiunt <lb></lb>lationes, rectior enim efficitur linea. </s>
          <s id="N15E8E">Si autem omnino recta <lb></lb>fieret penitus vtique eſsent contrariæ. </s>
          <s id="N15E93">Latus verò ſecundum <lb></lb>vnicam latam lationem à nullo præpeditur, rationabiliter igi<lb></lb>tur maiorem pertranſit.<emph.end type="italics"></emph.end></s>
        </p>
        <pb pagenum="200" xlink:href="005/01/208.jpg"></pb>
        <p id="N15EA0" type="head">
          <s id="N15EA2">COMMENTARIVS.</s>
        </p>
        <p id="N15EA6" type="main">
          <s id="N15EA8">Dvas hic peracutas difficultates proponit Ariſtote<lb></lb>les examinandas, <expan abbr="easq.">easque</expan> ingenioſiſſimas, quas accu<lb></lb>ratè admodum contemplari, ac diligentiſſimè pon<lb></lb>derare opere pretium eſt, cum non parum confert ad miſto<lb></lb>rum motuum naturam, <expan abbr="variamq.">variamque</expan> <expan abbr="proportionẽ">proportionem</expan> internoſcen<lb></lb>dam prout mechanicos maximè decet. </s>
        </p>
        <p id="N15EC1" type="main">
          <s id="N15EC3">Prima difficultas eſt, cur ſi duo puncta extrema vnius la<lb></lb>teris in rhombo duabus ſimul ferantur lationibus cum ea<lb></lb>dem velocitate, vnum maius, alterum minus ſpatium per<lb></lb>currit. </s>
          <s id="N15ECC">Ad cuius rei explicationem ſupponimus ex. </s>
          <s id="N15ECF">31. de<lb></lb>finitione primi Euclidis Rhombum eſſe figuram quadrila<lb></lb>teram quidem, &amp; æquilateram, ſed non rectangulam; quip<lb></lb>pe quæ duos angulos habet acutos, duos verò obtuſos. </s>
          <s id="N15ED8">Si <lb></lb><figure id="id.005.01.208.1.jpg" xlink:href="005/01/208/1.jpg"></figure><lb></lb>igitur in Rhombo ABCD, cuius <lb></lb>acuti anguli ſint A &amp; D, obtuſi <lb></lb>verò B &amp; C, duo extrema pun<lb></lb>cta lateris AB, nempe ipſum A, &amp; <lb></lb>ipſum B, æqua velocitate duabus <lb></lb>ferantur lationibus, vna qua pun<lb></lb>ctum A ſuper idem latus feratur <lb></lb>verſus B, &amp; B feratur verſus A: <lb></lb>altera verò qua <expan abbr="dũ">dum</expan> ipſa duo pun<lb></lb>cta ſibi obuiam procedunt, ſimul <lb></lb>cum toto latere AB, moueantur <lb></lb>verſus latus CD, ita vt ſemper la<lb></lb>tus, ſeu linea AB, ipſi CD ſit pa<lb></lb>ralella, deſcendatque per latera <lb></lb>AC, &amp; BD quouſque coincidat <lb></lb>cum eadem CD: Cum ex duabus lationibus, eadem ſem<lb></lb>per laterum proportione ſeruata, recta quædam linea pro<lb></lb>ducatur, vt ſupra demonſtratum eſt ex eodem Ariſtotele <lb></lb>1. par. </s>
          <s id="N15F0B">tex. 6. vtraque puncta prædicta eandem laterum ip<lb></lb>ſius rhombi proportionem in ſuo motu ſeruando, propriam <pb pagenum="201" xlink:href="005/01/209.jpg"></pb>rectam lineam deſcribent: A quidem lineam AD, B verò <lb></lb>BC: quæ nimirum erunt diametri eiuſdem rhombi. </s>
          <s id="N15F19"><expan abbr="Cumq.">Cumque</expan> <lb></lb>in rhombo diametri non ſint æquales, ſed quæ obtuſis an<lb></lb>gulis opponitur, vt AD maior ſit ea, quæ opponitur acutis, <lb></lb>vt BC: ſiquidem maius latus maiorem angulum ſubtendit <lb></lb>per 18. primi; hin c eſt, vt ex ipſis duobus punctis AB, dua<lb></lb>bus lationibus eodem tempore, <expan abbr="eademq.">eademque</expan> velocitate pro<lb></lb>motis, vnum quippe maius ſpatium, nempe maiorem dia<lb></lb>metrum, alterum verò minus, ſeu minorem diametrum per<lb></lb>currat. </s>
          <s id="N15F33">Quod mirum proculdubio omnibus cauſam igno<lb></lb>rantibus videri ſolet. </s>
        </p>
        <p id="N15F38" type="main">
          <s id="N15F3A">Verùm quod linea recta, quam deſcribere diximus pun<lb></lb>ctum A, ſit ipsa diameter AD; quam verò punctum B, <lb></lb>ſit diameter BC, facilè demonſtratur ex eo. </s>
          <s id="N15F41">Nam ſi pun<lb></lb>ctum A, proprio motu delatum fuerit exempli gratia vſque <lb></lb>ad punctum E medium ipſius lineæ AB, &amp; linea tota <lb></lb>AB eodem tempore, æquale ſpatium pertranſierit verſus <lb></lb>CD, ita vt alterum eius extremum peruenerit ad punctum <lb></lb>F, medium lateris AC; alterum verò ad punctum G, me<lb></lb>dium lateris BD: quoniam AF æqualis eſt ipſi AE, ſi com<lb></lb>pleatur figura ſimilis toti, productis lineis EH, &amp; FG per <lb></lb>punctum medium K, nempe rhombus AEKF, ſimilis <lb></lb>rhombo maiori ABCD per 24. ſexti elementorum; erit <lb></lb>recta FK æqualis oppoſitæ AE, &amp; AF ipſi EK; proin<lb></lb>deque punctum A cum duabus tranſlatum ſit lationibus <lb></lb>ſemper proportionalibus iuxta rationem æqualitatis; quam <lb></lb>latera rhomborum habent inter ſe, vtique tranſlatum erit <lb></lb>ſuper rectam AK in ipſum K, quod eſt punctum medium <lb></lb>diametri AD; Cuius reliquum dimidium conficiet, tum <lb></lb>ex motu ſuo ab E vſque ad B, tum ex alieno ab F vſque <lb></lb>ad C, ita vt tandem perueniat ad punctum D. </s>
        </p>
        <p id="N15F67" type="main">
          <s id="N15F69">Eodem pacto, quod dictum eſt de puncto A, applica<lb></lb>ri poteſt in puncto B. </s>
          <s id="N15F6E">Nam ſi hoc cum eadem velocitate <lb></lb>moueatur verſus A, ſicut linea AB verſus CD, quo tem<lb></lb>pore per proprium motum percurriſſet vſque ad E, alieno <lb></lb>motu perueniſſet vſque ad G; <expan abbr="æqualesq.">æqualesque</expan> forent lineæ BE, <pb pagenum="202" xlink:href="005/01/210.jpg"></pb>&amp; BG; productiſque lateribus, EH, &amp; GF, rhombus <lb></lb>EBGK per illa conſtitutus, ſimilis eſſet rhombo continen<lb></lb>ti ABCD: Ideoque GK æqualis oppoſitæ BE, &amp; BG <lb></lb>æqualis EK. </s>
          <s id="N15F86">Quare punctum B vtroque motum tranſla<lb></lb>tum cum eadem proportione æqualitatis, mouebitur motu <lb></lb>mixto ſuper diametrum ipſius rhombi, &amp; quo tempore <lb></lb>transferri deberet in E &amp; in G, transfertur in K, quod eſt <lb></lb>punctum medium diametri BC; cuius reliquum dimidium <lb></lb>conficiet per motum proprium ab E vſque ad A, &amp; alie<lb></lb>no à G vſque ad D; ita vt tandem reperiatur in C. </s>
          <s id="N15F98">Cum <lb></lb>igitur ſpatium BC, vt dicebamus, minus ſit quam ſpatium <lb></lb>AD eodem tempore peragratum à puncto A, difficile vi<lb></lb>detur qua ratione id poſſit contingere, poſtquam ita rem <lb></lb>ſe habere conſtiterit. </s>
        </p>
        <p id="N15FA3" type="main">
          <s id="N15FA5">Huius tamen euentus cauſam ſoluendo primam partem <lb></lb>quæſtionis, <expan abbr="primamq.">primamque</expan> difficultatem, eam eſſe inquit Ariſto<lb></lb>teles, quia cum in rhombo duo ſint obtuſi anguli, duo verò <lb></lb>acuti, lationes illæ, quibus fertur punctum, quod ab obtuſo <lb></lb>angulo diſcedit, vt in propoſita figura eſt punctum B, ſunt <lb></lb>inter ſe omnino ferè contrariæ, cum vna, verbi gratia ſur<lb></lb>ſum penè tendat verſus A, altera verò deorſum verſus D: <lb></lb>Quo fit vt mutuo præpediantur, ac retardentur. </s>
          <s id="N15FBA">Lationes <lb></lb>verò quibus fertur punctum, quod ab acuto angulo diſcedit <lb></lb>vt A; quamuis diuerſæ in ſe ſint, nullo tamen modo con<lb></lb>ſtituuntur contrariæ, cum ad eandem ferè partem pergere <lb></lb>teneantur, <expan abbr="parumq.">parumque</expan> aut minus ſemper diſtent inter ſe termi<lb></lb>ni ad quos tendunt. </s>
          <s id="N15FCB">Quare potius ipſæ ad inuicem iuuan<lb></lb>tur, quàm aliquo modo impediantur. </s>
          <s id="N15FD0">Rationi autem con<lb></lb>ſentaneum eſt, vt punctum contrarijs ferè lationibus ſeſe <lb></lb>impedientibus latum, minori interuallo in eodem tempore <lb></lb>feratur, quàm punctum, quod duabus lationibus ſeſe mutuo <lb></lb>adiuuantibus aſportatur; mirumque propterea non eſſe ſi <lb></lb>hoc maiorem diametrum, illud verò minorem eodem tem<lb></lb>pore percurrat. </s>
          <s id="N15FDF">Vnde etiam ſequitur, vt quò acutiores <lb></lb>conſtituantur anguli A, &amp; D, <expan abbr="proindeq.">proindeque</expan> obtuſiores B, <lb></lb>&amp; C; tardius ac minori interuallo feratur ipſum B; cele-<pb pagenum="203" xlink:href="005/01/211.jpg"></pb>rius verò ac maiori ſpatio ipſum A. </s>
          <s id="N15FF0">Quandoquidem ex ma<lb></lb>iori anguſtia angulorum magis. </s>
          <s id="N15FF5">vniuntur latera, magis <expan abbr="q.">que</expan> ad <lb></lb>vnum, &amp; idem terminum appropinquantur. </s>
        </p>
        <p id="N15FFE" type="main">
          <s id="N16000">Quam Ariſtotelis ſolutionem pluribus euerrere conatur <lb></lb>Baldus, quæ ſummatim in hoc tantum redigi poſſunt, quòd <lb></lb>ex ea ſequeretur, idem ſimiliter dicendum eſſe de duo<lb></lb>bus punctis vnius lateris in quadrato, ſi duabus ſimul latio<lb></lb>nibus mouerentur eo pacto quo in rhombo Philoſophus <lb></lb>deſcripſit; vt ſcilicet punctum, quod duabus lationibus fer<lb></lb>tur, ambabus deorſum tendentibus ſuper deſcendentem <lb></lb>diametrum ipſius quadrati, velocius feratur, quàm punctum, <lb></lb>quod duabus lationibus fertur, vna deorſum tendente, alte<lb></lb>ra verò ſurſum ſuper diametrum tranſuerſam. </s>
          <s id="N16017">Id quod per <lb></lb>ſe falſum eſſe conſtat; cum æquali tempore; æquale ſpatium <lb></lb>vtrumque punctum conficeret Siquidem in quadrato vtra<lb></lb>que diameter alteri ad inuicem ſemper eſt æqualis. </s>
          <s id="N16020"><expan abbr="Idemq.">Idemque</expan> <lb></lb>confirmat: in rhombo inuerſo. </s>
          <s id="N16028">Nam ſequeretur, punctum <lb></lb>duabus lationibus latum deorſum per minorem diametrum, <lb></lb>citius ferri, quàm punctum, quod duabus lationibus, vna <lb></lb>ſurſum: altera deorſum tendente: pertranſiret diametrum <lb></lb>tranſuerſam, nempe maiorem, Quod quippe abſurdum eſ<lb></lb>ſe liquet. </s>
        </p>
        <p id="N16035" type="main">
          <s id="N16037">Verumenimuerò Baldus in his propriam potius appre<lb></lb>henſionem, quam Ariſtotelis ſolutionem euertit. </s>
          <s id="N1603C">Porrò <lb></lb>hæc non fundatur in eo, quod eſt ſurſum, aut deorſum pun<lb></lb>cta ipſa duabus lationibus ferri, vt ipſe ſupponit, quamuis ad <lb></lb>explicationem præ dicti motus, <expan abbr="doctrinæq.">doctrinæque</expan> Ariſtotelis, om<lb></lb>nes vtamur exemplo diuerſarum poſitionum, vt ſurſum, aut <lb></lb>deorſum: ſed abſtrahendo à quacumque poſitione, tota <lb></lb>ſolutionis ratio ab Ariſtotele conſtituitur in maiori vnione, <lb></lb>ſeu propinquitate laterum acuti anguli, &amp; in maiori ſepara<lb></lb>tione, ſeu diſtantia laterum anguli obtuſi. </s>
          <s id="N16053">Nam per ipſa <lb></lb>latera anguli obtuſi; punctum in diuerſas longè partes ra<lb></lb>pitur, quaſi omnino contrario motu: per latera verò anguli <lb></lb>acuti, in vnam ferè partem, quaſi per eundem motum, qui <lb></lb>propterea velocior conſtituitur, vt dictum eſt. </s>
        </p>
        <pb pagenum="204" xlink:href="005/01/212.jpg"></pb>
        <p id="N16062" type="main">
          <s id="N16064">Deinde propria Baldi ſolutio, quam ex proprijs cauſis <lb></lb>ipſe ait eſſe deſumptam, nullam cauſam affert propoſiti effe<lb></lb>ctus ad diluendam difficultatem, ſeu rationem dubitandi, <lb></lb>ſed rurſus noua duntaxat via idipſum demonſtrat, quod Ari<lb></lb>ſtotelis argumento demonſtratum eſt de veritate ipſius ef<lb></lb>fectus, nempe punctum A per longiorem diametrum AD, <lb></lb>illis duabus lationibus ferri eodem tempore, quo punctum <lb></lb>B fertur ſuper minorem diametrum BC; quod eſt citius <lb></lb>moueri: nihil attingens de cauſa cur id contingat, ſeu ob <lb></lb>quam punctum A, eodem tempore maiorem valeat li<lb></lb>neam pertranſire, <expan abbr="proindeq.">proindeque</expan> velocius moueri; id quod opti<lb></lb>mè fecit Ariſtoteles vt vidimus. </s>
        </p>
        <p id="N16081" type="main">
          <s id="N16083">Secunda autem difficultas, quam Philoſophus hac in <lb></lb>quæſtione proponit, eſt, cur in eodem rhombo punctum B, <lb></lb>quod vt diximus ſua ſponte fertur ſuper latus BA, <expan abbr="totamq.">totamque</expan> <lb></lb>eius longitudinem percurrit; minus quippe pertranſeat ſpa<lb></lb>tium, quàm totum ipſummet latus BA, in quo fertur verſus <lb></lb>CD; imò quàm ſit ipſummet latus BA, quod percurrit. <lb></lb></s>
          <s id="N16095">Quandoquidem punctum B non conficit niſi ſpatium BC: <lb></lb>totum autem latus BA conficit ſpatium BD, ſeu AC, <lb></lb>quod maius eſt quàm BC. </s>
          <s id="N1609D">Sicut ipſum latus BA maius <lb></lb>conſtituitur, quàm diameter BC in rhombo propoſito. <lb></lb></s>
          <s id="N160A3"><expan abbr="Totaq.">Totaque</expan> ratio difficultatis in eo ſita eſt, quoniam punctum <lb></lb>B, duplici fertur latione, latus verò AB, vnica, &amp; <lb></lb>vtrunque pari velocitate: Quamobrem potius punctum <lb></lb>B, quàm latus BA, ſequeretur maius ſpatium pertranſi<lb></lb>re. </s>
          <s id="N160B1">Accedit quia punctum B verè totum latus BA, in <lb></lb>quo fertur percurrit eodem tempore, quo vehitur cum ip<lb></lb>ſomet latere verſus CD; ideoque ſatis arduum videtur, <lb></lb>minus ipſum B ſpatium pertranſire quàm ſit latus BA, in <lb></lb>quo fertur. </s>
        </p>
        <p id="N160BE" type="main">
          <s id="N160C0">Sed vnde hæc dubitandi ratio deſumpta eſt, inde pariter <lb></lb>adeſt ratio difficultatem ſoluendi. </s>
          <s id="N160C5">Etenim hoc ipſo, quod <lb></lb>punctum B feratur duplici latione explicata ſuper diame<lb></lb>trum BC, latus verò BA vnica vel ſimplici motione <lb></lb>vehatur verſus CD, hoc quidem à nullo motu contrario <pb pagenum="205" xlink:href="005/01/213.jpg"></pb>præpeditur, illud verò contrarijs ferè lationibus detinetur <lb></lb>ne velocius eodem tempore moueatur, maiuſque proin<lb></lb>de ſpatium valeat peragrare. </s>
          <s id="N160D7">Quod perſpicuè ex dictis <lb></lb>iam poteſt patere. </s>
        </p>
        <p id="N160DC" type="head">
          <s id="N160DE">Quæſtio Vigeſimaquarta.</s>
        </p>
        <p id="N160E1" type="main">
          <s id="N160E3">D<emph type="italics"></emph>vbitatvr, quam ob cauſam maior cir<lb></lb>culus æqualem minori circulo conuoluitur li<lb></lb>neam, quando circa idem centrum fuerint po<lb></lb>ſiti: Seorſum autem reuoluti, quemadmodum <lb></lb>alterius magnitudo ad magnitudinem ſe. </s>
          <s id="N160F1">ha<lb></lb>bet alterius, ſic &amp; illorum ad ſe inuicem fiunt <lb></lb>lineæ. </s>
          <s id="N160F8">Præterea vno etiam &amp; eodem vtriſque <lb></lb>existente centro, aliquando quidem tanta fit linea, quam con<lb></lb>uoluuntur, quantum minor per ſe conuoluitur circulus, <expan abbr="quan-doq.">quan<lb></lb>doque</expan> verò quantam maior. </s>
          <s id="N16105">Quod quidem igitur maiorem con<lb></lb>uoluitur maior, manifestum est, angulus enim ſenſu videtur <lb></lb>eſse cuiuſque circum ferentia propriæ diametri, maioris circuli <lb></lb>maior, minoris minor, quamobrem eandem habebunt proportio<lb></lb>nem ſecundum ſenſum ad ſe lineæ, ſecundum quas fuerint <lb></lb>conuoluti. </s>
          <s id="N16112">Verumenimuerò quod etiam æqualem conuoluun<lb></lb>tur, quando circa idem fuerint poſiti centrum, manifeſtum <lb></lb>eſt, &amp; ſic fiunt aliquando quidem æquales lineæ, ſecundum <lb></lb>quam maior conuoluitur circulus, aliquando verò ſecundum <lb></lb>quam minor. </s>
          <s id="N1611D">Sit enim circulus maior quidem, vbi DFC, mi<lb></lb>nor verò vbi EGB, vtriaſque autem centrum A. </s>
          <s id="N16123">Et quam qui<lb></lb>dem magnus per ſe conuoluitur, ſit vbi FI, quam verò per ſe <lb></lb>minor, vbi GK, æqualis AF. </s>
          <s id="N1612B">Si igitur minorem mouero, idem <lb></lb>mouens centrum vbi A, maior autem ſit annexus: quando <lb></lb>igitur AB fuerit recta ad ipſam GK, ſimul &amp; AC fit recta <lb></lb>ad ipſam FI: quamobrem æqualem ſemper translata erit, ip<lb></lb>ſam quidem GK, vbi eſt GB circumferentia, ipſam verò <lb></lb>FL, quæ est vbi FC. </s>
          <s id="N16138">Si autem quarta pars æqualem conuol<lb></lb>uitur, manifeſtum eſt, quod totus circulus toti circulo æqualem <lb></lb>conuoluetur. </s>
          <s id="N1613F">Quare quando BG linea ad ipſum peruenerit <lb></lb>K, &amp; ipſa FC circumferentia erit in ipſa CL &amp; vniuerſus <lb></lb>erit conuolutus circulus. </s>
          <s id="N16146"><expan abbr="Similiq.">Similique</expan> modo ſi magnum mouero, <lb></lb>illi paruum annectens, eodem existente centro, ſimul cum AC <lb></lb>ipſa AB perpendiculum &amp; recta erit: hac quidem ad ipſam <emph.end type="italics"></emph.end><pb pagenum="206" xlink:href="005/01/214.jpg"></pb><emph type="italics"></emph>FI, illæ verò ad GM. </s>
          <s id="N16159">Quamobrem quando hæc quidam <lb></lb>ipſi GM pertranſiuerit, illa verò ipſi FI, &amp; rurſum facta <lb></lb>fuerit recta ipſa FA ad ipſam FL, &amp; ipſa AG rurſum re<lb></lb>cta, velut à principio erant in ipſis MI. </s>
          <s id="N16162">Hoc autem neque <lb></lb>alia intercedente mora maioris ad minorem, vbi ſcilicet per <lb></lb>aliquod temporis ſpatium ſtaret in eodem puncto, neque tranſi<lb></lb>liente minore aliquod punctum, maiorem quidem æqualem mi<lb></lb>nori pertranſire, hunc autem maiori, abſurdum eſt. </s>
          <s id="N1616F">Præterea <lb></lb>vnica etiam ſemper existente motione, centrorum motum inter<lb></lb>dum quidem magnam, nonnunquam verò minorem conuerti, <lb></lb>admirandum est. </s>
          <s id="N16178">I dem enim celeritate eadem latum æqualem <lb></lb>natum hoc eſt pertranſire: eadem autem celeritate vtroque <lb></lb>modo æqualem licet mouere. </s>
          <s id="N1617F">Principium autem ſumendum <lb></lb>est circa iſtorum cauſam, quod eadem potentia, &amp; æqualis <lb></lb>hanc quidem tardius mouet magnitudinem, illam verò cele<lb></lb>rius. </s>
          <s id="N1618A">Si enim fuerit quippiam, quod à ſeipſo moueri, natum <lb></lb>non ſit, ſi ſimul &amp; illud mouerit, quod natum eſt moueri, tar<lb></lb>dius mouebitur, quàm ſi ipſum per ſe moueretur. </s>
          <s id="N16192">Et ſiquidem <lb></lb>natum fuerit moueri, non ſimul autem moueatur, ſimiliter <lb></lb>ſe habebit. </s>
          <s id="N1619A">Et impoſſibile certè eſt, plus moueri quàm mouem, <lb></lb>non enim ſuam ipſius mouetur motionem. </s>
          <s id="N161A0">Sit igitur e reu&#039;us <lb></lb>maior vbi A, minor autem vbi B, ſi minor maiorem impel<lb></lb>let non reuolutum ex ſe, manifeſtum eſt, quod tantum ipſius <lb></lb>rectæ maior pertranſit, quantum eſt impulſus. </s>
          <s id="N161A9">Tantum autem <lb></lb>eſt impulſus, quantum paruus est motus æqualem igitur ipſius <lb></lb>rectæ pertranſiuerunt. </s>
          <s id="N161B0">Neceſſe igitur eſt ſi reuolutus minor <lb></lb>maiorem impellet, reuoluti ſimul cum impulſione; tantum <lb></lb>autem, quantum minor reuolutus eſt, ſi nihil ipſe ſui ipſius <lb></lb>motione mouetur. </s>
          <s id="N161B9">Quomodo enim &amp; quantum mouit, tantum <lb></lb>motum eſſe neceſſe eſt, quod mouetur ab illo. </s>
          <s id="N161BE">Sed profectò par<lb></lb>uus circulus tantum ſeipſum circulariter mouit, quantum est <lb></lb>pedalis quantitas (tantum enim ſit id, quod motus eſt) &amp; ma<lb></lb>gnus igitur tantum motus erit. </s>
          <s id="N161C7"><expan abbr="Similiq.">Similique</expan> modo ſi magnus par<lb></lb>uum mouebit, motus erit paruus quemadmodum maior. </s>
          <s id="N161CF">Per <lb></lb>ſe autem motus illorum vtrumlibet, ſiue celeriter, ſeu tardè <lb></lb>eadem velocitate, statim quando maior natus eſt circumferri <lb></lb>lineam, quod difficultatem facit, quod non ſimiliter faciunt <lb></lb>quando fuerint connexi. </s>
          <s id="N161DA">Hoc autem eſt, ſi alter ab altero mo<lb></lb>ueatur, non quam natus eſt, neque peculiarem motionem: nihil <lb></lb>enim refert circumponere, &amp; annectere, aut <expan abbr="eõiungere">coniungere</expan> vtrum<lb></lb>libet alteri. </s>
          <s id="N161E7">Similiter enim quando hic quidem mouet, ille ve<lb></lb>rò mouetur ab isto, quantum vtique mouerit, alter, tantum <emph.end type="italics"></emph.end><pb pagenum="207" xlink:href="005/01/215.jpg"></pb><emph type="italics"></emph>alter mouebitur. </s>
          <s id="N161F7">Quandoquidem igitur adiacens mouerit, aut <lb></lb>propenſus, non ſemper conuoluitur, quando verò circa idem <lb></lb>poſiti fuerint centrum, alterum ab illo ſemper conuolui neceſ<lb></lb>ſe est. </s>
          <s id="N16200">Sed nihil e minus non ſuam ipſius motionem mouetur al<lb></lb>ter, ſed velut nullam haberet motionem: &amp; ſi habuerit, illa <lb></lb>autem non vtatur, tantundem accidit. </s>
          <s id="N16207">Quandoquidem igitur <lb></lb>magnus mouerit ſibi <expan abbr="alligatũ">alligatum</expan> paruum, paruus mouetur quan<lb></lb>tum ille: quando autem paruus, rurſus magnus quantum iſte, <lb></lb>ſeparatus autem vterque ſeipſum mouet. </s>
          <s id="N16214">Quod autem eodem <lb></lb>exiſtente centro, &amp; mouente eadem velocitate, accidit inæqua<lb></lb>lem illos pertranſire lineam, paralogiſmo ſophiſticè vtitur is, <lb></lb>qui dubitat: idem enim ambobus eſt centrum, verùm per acci<lb></lb>dens, veluti muſicum, &amp; album. </s>
          <s id="N1621F">Eſſe enim vtriuſque circuli <lb></lb>centro non eodem vtitur. </s>
          <s id="N16224">Quandoquidem igitur mouens fue<lb></lb>rit paruus, vt illius centrum, &amp; principium: quando verò <lb></lb>magnus, vt illius. </s>
          <s id="N1622B">Non igitur idem ſimpliciter mouet, ſed eſt <lb></lb>quo modo.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N16232" type="head">
          <s id="N16234">COMMENTARIVS.</s>
        </p>
        <p id="N16238" type="main">
          <s id="N1623A">Qvæſtio hæc admirabilem complectitur difficulta<lb></lb>tem, vtpotè inſtituta circa rem, quæ vix credi poſſet, <lb></lb>niſi ante oculos obſeruaretur: Vnde inter cæteras <lb></lb>præcipua ac omnium difficillima exiſtimatur, <expan abbr="multumq.">multumque</expan> pa<lb></lb>riter ſicut præcedens ad mixti motus naturam exploran<lb></lb>dam conducit. </s>
          <s id="N1624B">Cauſam igitur ſciſcitatur Ariſtoteles, cur <lb></lb>duo circuli alter altero maior circa idem centrum ſimul an<lb></lb>nexi, &amp; coaptati, ſi ſecundùm abſidem volutentur (vt plau<lb></lb>ſtrorum progredientium rotæ) ambo æquale pertranſeant <lb></lb>ſpatium: ſeorſum verò ſeparati, ſi eodem pacto circum<lb></lb>uoluantur, non ita ſed maior circulus maiorem lineam, mi<lb></lb>nor verò minorem percurrat iuxta proportionem circumfe<lb></lb>rentiæ vnius ad circumferentiam alterius? </s>
          <s id="N1625C">Quod vt diſtin<lb></lb>ctius obſeruetur addit Ariſtoteles, circulos ipſos circa idem <lb></lb>centrum coniunctos, <expan abbr="quandoq.">quandoque</expan> in circumuolutione tantam <lb></lb>lineam ſpatij pertranſire, quantam ſeorſum pertranſiret cir<lb></lb>culus minor: quandoque verò quantam eodem pacto per<lb></lb>curreret circulus maior. </s>
          <s id="N1626D">Etenim, vt quiſque experiri po-<pb pagenum="208" xlink:href="005/01/216.jpg"></pb>teſt, ſi ex ipſis duobus circulis ſimul circa idem centrum <lb></lb>coniunctis volutetur minor ſecundum abſidem ſuam ſuper <lb></lb>aliquod planum, ad motum ipſius conuoluetur ſimul &amp; ma<lb></lb>ior ſuper aliud planum; ſed vtraque linea ab ipſis deſcripta, <lb></lb>æqualis erit ei quam deſcriberet ipſemet circulus minor ſi <lb></lb>ſolus per ſe ac ſeorſum volutaretur. </s>
          <s id="N1627F">E contra verò ſi ſuper <lb></lb>planum eodem pacto volutetur ſecundum abſidem ſuam <lb></lb>circulus maior, &amp; ad motum ipſius circumuoluatur etiam <lb></lb>circulus minor, vtraque linea recta ab ipſis deſcripta æqua<lb></lb>lis erit ei quam per ſe volutatus deſcriberet idemmet circu<lb></lb>lus maior. </s>
        </p>
        <p id="N1628C" type="main">
          <s id="N1628E">Manifeſtum autem eſſe, ait Ariſtoteles, circulum maio<lb></lb>rem ſeorſum reuolutum, maius <expan abbr="ſpaciũ">ſpacium</expan>, ſeu maiorem lineam <lb></lb>pertranſire, quàm pertranſeat circulus minor. </s>
          <s id="N16299">Idque ex eo, <lb></lb>nam ſicut ſenſu conſtat, ambitum cuiuſque circuli eſſe, at<lb></lb>que conſtitui per ipſam circumferentiam, ſeu circumuolu<lb></lb>tionem propriæ diametri eiuſdem circuli, maioris quidem <lb></lb>maiorem, minoris verò minorem: ita ſenſu pariter dignoſci<lb></lb>tur eandem inter ſe proportionem habere lineas, quæ per <lb></lb>circumuolutionem ipſorum circulorum deſcribuntur in <lb></lb>plano; vt ſcilicet linea deſcripta à maiori circumferentia <lb></lb>ſit maior, quæ verò à minori deſcribitur, ſit minor. </s>
          <s id="N162AC">Vbi <lb></lb>autem vſi ſumus nomine (ambitus) textus habet (angulus) <lb></lb>cuius propria ſignificatio difficile cohæret cum ſenſu ipſius <lb></lb>orationis, <expan abbr="proindeq.">proindeque</expan> non paruam ſuſpicionem præbuit er<lb></lb>roris librariorum, qui fortaſſe angulum pro ambitu ſcripſe<lb></lb>runt: Cum alioquin vox ambitus contextui planè cohęreat, <lb></lb><expan abbr="explicetq.">explicetque</expan> magis ac breuius quod auctor intendit. </s>
        </p>
        <p id="N162C2" type="main">
          <s id="N162C4">Veruntamen ſi ſenſum eiuſdem textus prout ſonat ipſa <lb></lb>vox (angulus) explicare velimus, non incongrue ad hoc to<lb></lb>tus Ariſtotelis diſcurſus poteſt reduci, vt dicat, ſenſu conſta<lb></lb>re, angulum cuiuſque circuli (conſtitutum ſcilicet ex cir<lb></lb>cumferentia propriæ diametri, &amp; ex ipſa diametro) eſſe <lb></lb>quidem maiorem ſi circulus ſit maior, minorem verò ſi cir<lb></lb>culus ſit minor. </s>
          <s id="N162D3">Atque ex hoc fieri, vt ipſa circumferentia, <lb></lb>ſeu ambitus circuli maioris ſit pariter maior, minoris verò, <pb pagenum="209" xlink:href="005/01/217.jpg"></pb>ſit minor, iuxta maiorem, vel minorem remotionem ipſius <lb></lb>ab altero latere nempe diametro, cum qua conſtituit an<lb></lb>gulum. </s>
          <s id="N162E1">Ac propterea in circumuolutione ipſorum circu<lb></lb>lorum, etiam ad ſenſum conſtare, eandem inter ſe propor<lb></lb>tionem habere lineas, quas ipſi circuli ſuper planum deſcri<lb></lb>bunt, vt ſcilicet linea deſcripta à maiori iuxta maiorem cir<lb></lb>cumferentiam ſit maior, quæ verò à minori deſcribitur iux<lb></lb>ta propriam circumferentiam ſit minor. </s>
          <s id="N162EE">Sumpſimus autem <lb></lb>angulum circuli de mente Ariſtotelis ſecundum præfatam <lb></lb>acceptionem, quam latius explicuimus quæſt. </s>
          <s id="N162F5">8. nè maxi<lb></lb>ma ei tribuatur improprietas locutionis explicando angu<lb></lb>lum pro Sectore, vt Baldus, vel pro arcu qui ſubtenditur <lb></lb>angulo, vt Blancanus: Cum vnumquodque iſtorum, pro<lb></lb>prium habeat vocabulum, quod Ariſtoteles non ignorabat, <lb></lb><expan abbr="eoq.">eoque</expan> vſus fuiſſet, ſi idipſum per illud ſignificare voluiſſet </s>
        </p>
        <p id="N16305" type="main">
          <s id="N16307">Vlterius verò quod prædicti circuli quando ſunt ſimul <lb></lb>coniuncti circa idem centrum, æquale ambo pertranſeant <lb></lb>ſpatium, ſiue maius illud ſit, vt rotando ſecundum abſidem <lb></lb>circuli maioris, ſiue minus ſecundum abſidem minoris, hoc <lb></lb>ferè pacto probat Philoſophus. </s>
        </p>
        <figure id="id.005.01.217.1.jpg" xlink:href="005/01/217/1.jpg"></figure>
        <p id="N16318" type="main">
          <s id="N1631A">Sint circa <lb></lb>idem <expan abbr="pũctum">punctum</expan> <lb></lb>A ipſi duo cir<lb></lb>culi <expan abbr="coniũcti">coniuncti</expan>, <lb></lb>maior <expan abbr="quidẽ">quidem</expan> <lb></lb>BCDE, minor <lb></lb>verò FGHI. <lb></lb></s>
          <s id="N16336">Sintque dia<lb></lb>metri maioris <lb></lb>BD, &amp; EC; <lb></lb>minoris verò <lb></lb>FH, &amp; IG ſeſe <lb></lb>inuicem interſecantes ad angulos rectos in centro A. </s>
          <s id="N16344">Ideo<lb></lb>que quadrans circuli maioris ſit CD, minoris verò GH. <lb></lb></s>
          <s id="N1634A">Deinde conſtituamus vtrunque circulum ad dexteram ſi<lb></lb>mul moueri cum ſuo communi centro, rotando alterum <pb pagenum="210" xlink:href="005/01/218.jpg"></pb>quidem per ſe ſuper rectam lineam DK, alterum verò ad <lb></lb>motum illius, deſcribendo aliam rectam huic parallelam, <lb></lb>quæ ſit HL. </s>
          <s id="N16358">Rurſus conſtituamus, maiorem circulum per <lb></lb>ſe moueri ſecundum abſidem quadrantis CD ſuper lineam <lb></lb>DK, ita vt aliquando punctum C perueniat in M, percur<lb></lb>rendo ſpatium DM æquale ipſi CD. </s>
          <s id="N16362">Tunc ſemidiame<lb></lb>ter AC conſtitueretur perpendicularis ipſi DK, <expan abbr="eſſetq.">eſſetque</expan> <lb></lb>vbi NM, puncto C tranſlato in M, &amp; puncto A tranſ<lb></lb>lato in N. </s>
          <s id="N16370">Cumque punctum G circuli minoris, ſit in <lb></lb>linea AC, neceſſariò poſt huiuſmodi quadrantis rotatio<lb></lb>nem conſtitueretur in loco vbi O, ita vt ſemidiameter AG <lb></lb>circuli minoris transferatur in NO. </s>
          <s id="N16379">Ad reuolutionem igi<lb></lb>tur vtriuſque circuli ſecundum abſidem maioris, quadrans <lb></lb>ipſius maioris circuli conficiet ſpatium DM; quadrans ve<lb></lb>rò minoris circuli, quod ſimul cogitur conuolui, percurret <lb></lb>ſpatium HO, quod æquale eſt ipſi DM per 34. primi ele<lb></lb>ment. </s>
          <s id="N16386">Idemque quod de quadrantibus dictum eſt verificari <lb></lb>poterit de totis ipſis eorum circulis. </s>
          <s id="N1638B">Conſtat ergo mino<lb></lb>rem circulum eodem tempore ad motum maioris circa <lb></lb>idem centrum conuolutum, æqualem lineam peragrare ipſi <lb></lb>rectæ quam maior circulus per ſe motus pertranſit. </s>
        </p>
        <p id="N16394" type="main">
          <s id="N16396">Sed nec minus conſtabit è contra ad <expan abbr="rotationẽ">rotationem</expan> propriam <lb></lb>minoris circuli ſecundum abſidem, maiorem circulum ei <lb></lb>annexum, æquale pariter ſpatium, &amp; non amplius percurre<lb></lb>re. </s>
          <s id="N163A3">Rotetur enim motu proprio minoris circuli quadrans <lb></lb>GH ſuper rectam HL, ita vt punctum G aliquando per<lb></lb>ueniat in P, percurrendo ſpatium HP, æquale ipſi GH; <lb></lb>&amp; centrum A conſequenter conſtituatur in Q, exiſten<lb></lb>te ſpatio A Q æquale ipſi HP. </s>
          <s id="N163AE">Tum excitetur linea <lb></lb>QPR, perpendicularis ipſis planis HL, &amp; DK; <expan abbr="eritq.">eritque</expan> <lb></lb>punctum C in R, ſicut punctum G in P, &amp; punctum <lb></lb>A in <expan abbr="q.">que</expan> Siquidem hæc tria puncta ſunt in eadem recta, <lb></lb>vel ſemidiametro circuli maioris. </s>
          <s id="N163C1">Iam igitur poſt huiuſmo<lb></lb>di rotationem, quo tempore quadrans minoris circuli con<lb></lb>fecit ſpatium HP; quadrans maioris circuli conuoluti ad <lb></lb>motum illius, confecit ſpatium. </s>
          <s id="N163CA">DR, quod æquale eſt ipſi <pb pagenum="211" xlink:href="005/01/219.jpg"></pb>HP. per eandem 34 primi. </s>
          <s id="N163D2">Quod &amp; de tota circumferen<lb></lb>tia vtriuſque circuli demonſtrari poteſt, non abſque magna <lb></lb>omnium admiratione, quibus fortaſſe videretur, maiorem <lb></lb>circulum, ſemper maiorem lineam deſcribere, quàm circu<lb></lb>lus minor in ipſa rotatione. </s>
        </p>
        <p id="N163DD" type="main">
          <s id="N163DF">Admirationis autem ratio ex eo maximè augetur apud <lb></lb>ipſum Philoſophum, quòd cum circulus maior minorem <lb></lb>lineam pertranſit, quàm ſit eius peripheria, nulla vel mini<lb></lb>ma intercedit mora, in qua ipſe quieſcat. </s>
          <s id="N163E8">Ac vice verſa <lb></lb>cum circulus minor maiorem lineam deſcribit, nullam tran<lb></lb>ſiliat, vel modicam partem, quam percurrendo non attin<lb></lb>gat. </s>
          <s id="N163F1">Præterea quòd vnica exiſtente motione vtriuſque cir<lb></lb>culi connexi, centrum commune commotum, interdum <lb></lb>quidem maiorem, interdum verò minorem lineam percur<lb></lb>rat iuxta abſidem, ſcilicet maioris, aut minoris circuli ſe<lb></lb>cundum quam mouetur: cum tamen idem eadem celerita<lb></lb>te latum, æqualem lineam regulariter debeat pertranſire. </s>
        </p>
        <p id="N163FE" type="main">
          <s id="N16400">Pro ſolutione igitur quæſtionis ad explicandam cauſam <lb></lb>tam mirifici effectus, duo ſupponit Ariſtoteles fundamenta. <lb></lb></s>
          <s id="N16406">Vnum eſt eandem, vel æqualem potentiam, tardius quidem <lb></lb>mouere vnam magnitudinem, quàm aliam. </s>
          <s id="N1640B">Licet enim illæ <lb></lb>æquè ex ſe mobiles ſint, ſi tamen vna ſimul cum alia ad <lb></lb>motum inepta vel difficili reperiatur coniuncta, tardius mo<lb></lb>uebitur, quàm illa, quæ reperitur ſoluta, vel quam ipſamet <lb></lb>ſeorſum moueretur ab eadem potentia. </s>
          <s id="N16416">Quod ſi magni<lb></lb>tudo, quæ moueri debet ad motum alterius, cui reperi<lb></lb>tur connexa, mobilis quidem facilè ex ſe ſit, nihil tamen <lb></lb>ex ſe moueatur, vel ad motum alterius conferat, perin<lb></lb>de eſt, ac ſi minimè apta eſſet ad motum: vnde &amp; altera, <lb></lb>quæ ſimul cum ipſa moueri debet, tardius non minus mo<lb></lb>uebitur. </s>
        </p>
        <p id="N16425" type="main">
          <s id="N16427">Alterum verò fundamentum à Philoſopho ſuppoſitum <lb></lb>illud eſt, quòd impoſſibile profectò exiſtimandum ſit aliquid <lb></lb>plus moueri, quàm mouens à quo mouetur; Siquidem non <lb></lb>ſua, ſed illius motione cietur, <expan abbr="nullaq.">nullaque</expan> propria vtitur mobili<lb></lb>tate intrinſeca, &amp; actiua, qua motus poſſit augeri. </s>
        </p>
        <pb pagenum="212" xlink:href="005/01/220.jpg"></pb>
        <p id="N1643A" type="main">
          <s id="N1643C">Quibus poſitis Ariſtoteles quæſtionem ſoluendo prædi<lb></lb>ctum effectum ex eo inquit contingere. </s>
          <s id="N16441">Nam ſi circulus ma<lb></lb>ior non moueatur niſi ad motum minoris cui eſt annexus, <lb></lb>tantum ſpatium poterit pertranſire, quantum delatus fuerit <lb></lb>ex impulſu illius: tantum autem deferri poterit quantum <lb></lb>minor ipſe circulus ex ſe motus impulerit, &amp; non amplius. <lb></lb></s>
          <s id="N1644D">Quomodo enim &amp; quantum ex ſe motus fuerit mouens, <lb></lb>tantundem neceſſe eſt moueri, qui mouetur ab illo. </s>
          <s id="N16452">Aequa<lb></lb>lem igitur viam vterque circulus rotando conficiet dum <lb></lb>maior mouetur ad motum minoris. </s>
          <s id="N16459"><expan abbr="Idemq.">Idemque</expan> infert contin<lb></lb>gere ſi minor circulus moueatur ad motum maioris ſibi an<lb></lb>nexi, &amp; eodem pacto ſecundum abſidem lati. </s>
          <s id="N16463">Nam tantum <lb></lb>ipſe minor circulus, &amp; non minus moueri poterit, quantum <lb></lb>à maiori deportabitur. </s>
          <s id="N1646A">Rapitur enim iugiter ab illo in ſua <lb></lb>rotatione vſque ad vltimum terminum, <expan abbr="æqualemq.">æqualemque</expan> propte<lb></lb>rea lineam rectam <expan abbr="cũ">cum</expan> illo deſcribet, quamuis minorem pe<lb></lb>ripheriam obtineat. </s>
          <s id="N1647B">Quod ſi vtrumlibet ipſorum circulo<lb></lb>rum ſeorſum ex ſe ſecundum propriam abſidem eadem ve<lb></lb>locitate moueatur, tunc maior circulus maiorem rectam, <lb></lb>minor verò minorem ſua volutatione conficiet iuxta men<lb></lb>ſuram ſecundum quam natus eſt circumferri. </s>
        </p>
        <p id="N16486" type="main">
          <s id="N16488">Cæterum eam, ac profectò <expan abbr="arduã">arduam</expan> difficultatem ſibi obij<lb></lb>cit Philoſophus. </s>
          <s id="N16492">Nam quæ dicta ſunt, rectè ac facilè intel<lb></lb>ligerentur procedere, ſi circulus qui mouetur ad motum al<lb></lb>terius, non eſſet cum illo concentricus, ſed alio modo com<lb></lb>pactus, <expan abbr="eiq.">eique</expan> connexus. </s>
          <s id="N1649F">Siquidem moueri non poſſet circa <lb></lb>proprium centrum, nec proinde peculiarem, ac proportio<lb></lb>natam ſibi motionem vendicare, ſed tantum circa alienum <lb></lb>centrum ipſius circuli deferentis conuerti: Non ſecus ac <lb></lb>quælibet alia magnitudo adiacens eidem circulo deferenti, <lb></lb>vel ei extra centrum quoquo modo appenſa; tantum ſcili<lb></lb>cet ſpatium tranſmittendo, quantum ipſe circulus, ad cuius <lb></lb>motum defertur, pertranſierit. </s>
          <s id="N164B0">Verùm cum hic ſermo ſit <lb></lb>de duobus circulis concentricis, qui nimirum circa idem <lb></lb>commune <expan abbr="centrũ">centrum</expan> ſimul conuertuntur, non videntur præfa<lb></lb>ta, &amp; ab ipſo Philoſopho adducta rectè procedere, aut con-<pb pagenum="213" xlink:href="005/01/221.jpg"></pb>cludere. </s>
          <s id="N164C2">Quoniam ſicut circulus delatus, non minus ac de<lb></lb>ferens conuoluitur circa proprium centrum, ac ſimul cum <lb></lb>illo progreditur modo ſibi connaturali; ita nec minus pro<lb></lb>portionatum ſibi interuallum rotando videtur poſſe tranſ<lb></lb>mittere, deſcribendo lineam rectam æqualem ſuæ periphe<lb></lb>riæ ſeu abſidi ſecundum quam conuoluitur. </s>
        </p>
        <p id="N164CF" type="main">
          <s id="N164D1">Huic tamen difficultati occurrit Philoſophus reſponden<lb></lb>do, quòd licet ipſi circuli ſupponantur concentrici, vtpotè <lb></lb>circa idem pariter centrum coniuncti, ac reuoluti, non pro<lb></lb>pterea ſequitur, quod ambo debeant connaturali modo ſua <lb></lb>propria motione moueri. </s>
          <s id="N164DC">Nam qui ab altero fertur, moue<lb></lb>tur ad motionem illius, non ſecus ac ſi nullam ad talem mo<lb></lb>tum, ſeu rotationem circa idem centrum propriam aptitu<lb></lb>dinem obtineret quemadmodum reuera obtinet; quippe <lb></lb>cum illa non vtatur: Vnde tantum poterit moueri, quan<lb></lb>tum mouebitur is, à quo fertur, &amp; cui eſt alligatus. </s>
          <s id="N164E9"><expan abbr="Ideoq.">Ideoque</expan> <lb></lb>inquit rectè concludi, inæquales circulos circa idem cen<lb></lb>trum connexos æquale ſpatium in ſua rotatione tranſmitte<lb></lb>re, ſi vnus moueatur ad motum alterius. </s>
        </p>
        <p id="N164F5" type="main">
          <s id="N164F7">Poſtremò illud hic adnotat Ariſtoteles, quòdlicet vter<lb></lb>que circulus circa idem centrum reuoluatur, non tamen <lb></lb>ſimpliciter idem eſt vtriuſque circuli centrum; ſed vnius <lb></lb>quidem per ſe, nempe deferentis, alterius verò per accidens, <lb></lb>nempe delati. </s>
          <s id="N16502">Quandoquidem deferens ex ſe vtitur pro<lb></lb>prio centro dum circa illud mouetur, <expan abbr="ipſumq.">ipſumque</expan> ſecum rapit <lb></lb>dum ad vlteriora ſuper planum rectà progreditur: delatus <lb></lb>verò per accidens circa illud conuertitur; ſicut per accidens <lb></lb>etiam progreditur ad motum deferentis. </s>
          <s id="N16511">Quamobrem ſo<lb></lb>phiſticè ac deceptiua ratiocinatione inquit argumentari <lb></lb>eos, qui abſolutè, idem ambobus circulis eſſe centrum do<lb></lb>cent, eo quod ambo circa idem reuoluantur, ac inde infe<lb></lb>runt, vtrumlibet proportionato, &amp; connaturali motu cir<lb></lb>cumferri debere: Quod eſt vnumquemque illorum æqua<lb></lb>lem rectam ſuæ peripheriæ rotando deſcribere; nempe ma<lb></lb>iorem circulum rectam maiorem, minorem verò minorem, <lb></lb>ſecus quàm de facto accidit propter cauſas explicatas. </s>
        </p>
        <pb pagenum="214" xlink:href="005/01/222.jpg"></pb>
        <p id="N16528" type="main">
          <s id="N1652A">Huiuſque ex mente, ac doctrina Ariſtotelis, qui tamen <lb></lb>multorum iudicio non videtur obiectam ſibi difficultatem <lb></lb>ſatis infringere, vt quæ adhuc magna ex parte maneat in ſuo <lb></lb>robore. </s>
          <s id="N16535">Nam hoc quod eſt proprio, vel alieno motu cieri, <lb></lb><expan abbr="centrumq.">centrumque</expan> circuli deferentis per accidens eſſe etiam cen<lb></lb>trum circuli delati, non tollit, vtrunque circulum ſecun<lb></lb>dum abſidem codem pacto rotari, ac propriam lineam <lb></lb>rectam in ſuo plano deſcribere: vnde videtur inferri eodem <lb></lb>etiam pacto vtramque lineam deſcriptam propriæ periphe<lb></lb>riæ à qua deſcribitur debere commenſurari. </s>
          <s id="N16547">Parum enim <lb></lb>refert, circulum per ſe rotari circa proprium centrum ad <lb></lb>impulſum axis immediatè, vel per accidens mediante alio <lb></lb>circulo, dummodo eodem pacto per circumuolutionem ſuę <lb></lb>abſidis circa idem centrum lineam deſcribat, cui illa debeat <lb></lb>commenſurari. </s>
          <s id="N16554">Sphæra namque ſuper planum rotando ſi<lb></lb>ue proprio nutu, ſiue alieno impulſu, tardius, aut velocius, <lb></lb>ſicut omnes plani partes, per quas tranſit debet attingere; <lb></lb>ita per totidem partes ſuas illis debet correſpondere, &amp; ad <lb></lb>æqualitatem in tranſitu adaptari. </s>
          <s id="N1655F">Ratio verò vtriuſque eſſe <lb></lb>poteſt, quia non datur inſtans, in quo abſis ipſa, vel periphe<lb></lb>ria ſiue maioris, ſiue minoris circuli per nouum punctum <lb></lb>proprium, vlterius non attingat nouum punctum lineæ re<lb></lb>ctæ ſuper quam fertur; nec tempus in quo noua eius pars <lb></lb>nouæ parti illius non commenſuretur. </s>
          <s id="N1656C">Quapropter cum <lb></lb>peripheria minoris circuli, vel non habeat tot partes, quot <lb></lb>habet recta ſuper quam fertur motu maioris circuli; vel cer<lb></lb>tè partes ipſæ, quas habet non ſint æqualis dimenſionis, ſed <lb></lb>proculdubio minoris; non videtur quomodo ad contactum <lb></lb>partis poſt partem mediantibus punctis, poſſit maior linea, <lb></lb>vt eſt recta, ipſi minori, vt eſt circumferentia minoris circuli <lb></lb>adæquari, niſi alia via, ac ratione id comprobetur, &amp; oſten<lb></lb>datur. </s>
          <s id="N1657F"><expan abbr="Idemq.">Idemque</expan> è conuerſo applicari poteſt in contactu pe<lb></lb>ripheriæ maioris circuli cum recta breuiori, quam conficit <lb></lb>ad motum minoris circuli ſuper abſidem per ſe lati. </s>
        </p>
        <p id="N16589" type="main">
          <s id="N1658B">Ad diluendam igitur omnino prædictam difficultatem, <lb></lb>quæ multorum quippe vexauit ingenia, &amp; pene inſuperabi-<pb pagenum="215" xlink:href="005/01/223.jpg"></pb>lis apud aliquos extimatur, liceat aliunde totum negocium <lb></lb>auſpicari, nouumque aliquid in medium affere in eiuſdem <lb></lb>Ariſtotelis, ac veterum Philoſophorum principis funda <lb></lb>tum. </s>
          <s id="N1659D">Ac primò quidem ſtabiliatur, motum cuiuſlibet circu<lb></lb>li ſecundum abſidem, eſſe motum quendam mixtum ex du<lb></lb>plici latione; vna qua circumuoluitur, ſeu circa proprium <lb></lb>centrum fertur in gyrum; altera verò qua ad motum axis <lb></lb>rectà fertur ſuper planum quo verſus tendit ipſemet axis. <lb></lb></s>
          <s id="N165A9">Etenim ſi circulus ſtans abſque ſui rotatione raperetur ſu<lb></lb>per <expan abbr="planũ">planum</expan>, verè moueretur motu recto, ac per vnicum pun<lb></lb>ctum totam plani longitudinem ſuper quam fertur attinge<lb></lb>ret. </s>
          <s id="N165B6">Si verò circumuolueretur abſque progreſſu, aut latio<lb></lb>ne axis, verè moueretur circulariter ac per omnes partes, <lb></lb><expan abbr="punctaq.">punctaque</expan> ſuæ peripheriæ, eandem plani partem, vel punctum <lb></lb>in quo ſiſtebat attingeret. </s>
          <s id="N165C2">Cum itaque ad motum axis re<lb></lb>ctà ſuper planum trahitur, ac ſimul rotatur, ex vtraque la<lb></lb>tione mixtus quidam motus producitur, per quem tota <lb></lb>circumferentia toti longitudini ſuper quam fertur ada<lb></lb>ptatur. </s>
        </p>
        <p id="N165CD" type="main">
          <s id="N165CF">Deinde verò ſtabiliatur lineam, quæ à circulo, prædicto <lb></lb>modo deſcribitur ſuper planum, abſtrahendo à rotatione <lb></lb>ſpontanea, vel coacta ad motum alterius, ex natura ſua non <lb></lb>deſcribi nisi iuxta menſuram lationis, ſeu motus recti, qui ſimul <lb></lb>cum axe conficitur in anteriora, &amp; cuius virtute deſcribitur. <lb></lb></s>
          <s id="N165DB">Etenim ipſa deſcribi poſſet ab eodem circulo etiam ſine ro<lb></lb>tatione, per vnicum punctum vt diximus, non autem ſine re<lb></lb>cta aliqua latione. </s>
          <s id="N165E2">Quamobrem in deſcriptione ipſius lineæ <lb></lb>rectæ ſuper planum, per ſe, &amp; abſolutè loquendo, non habe<lb></lb>tur ratio de motu circulari, nec de ſpatio circulariter pera<lb></lb>grato ab ipſo circulo, ſed de motu recto, ac ſpatio, quod ip<lb></lb>ſe circulus ſimul <expan abbr="cũ">cum</expan> axe percurrit, &amp; ad cuius ſemper men<lb></lb>ſuram ipſa recta linea excitatur. </s>
          <s id="N165F3">Quamuis per accidens con<lb></lb>tingat, circulum deferentem, vel alium ex ſe, ac ſeorſum ro<lb></lb>tando, tantum ſpatium ſimul cum axe recta tranſmittere, <lb></lb>quantum ipſemet circulariter eodem tempore peragrare <lb></lb>valuerit. </s>
          <s id="N165FE">Quia ſcilicet cum tota progreſſio à ſua ipſius ro<pb pagenum="216" xlink:href="005/01/224.jpg"></pb>tatione dependeat, ſicut motus rectus progreſſionis neceſ<lb></lb>ſariò proportionatur motui circulari à quo pendet, ita <lb></lb>etiam linea deſcripta per talem motum proportionari, &amp; <lb></lb>adæquari debet lineæ deſcriptæ, ſeu peragratæ per circui<lb></lb>tionem. </s>
        </p>
        <p id="N1660E" type="main">
          <s id="N16610">His itaque ſic ſtabilitis, atque ſuppoſitis tanquam certis, <lb></lb>&amp; cui dentibus, ad primam partem quæſtionis ſimul, ac dif<lb></lb>ficultatis propoſitæ reſpondetur, circulum delatum ſemper <lb></lb>æquale ſpatium, ac circulum deferentem ſuper planum ro<lb></lb>tando, rectà tranſmittere, ſiue maior eo fuerit, ſiue minor; <lb></lb>quia illud non tranſmittit ex vi ſuæ rotationis, ac iuxta <lb></lb>menſuram ſuæ circumferentiæ, ſed ex vi ſui raptus, &amp; aſpor<lb></lb>tationis. </s>
          <s id="N16621">Siquidem tantum rectà progreditur, quantum à <lb></lb>deferente rapitur, &amp; aſportatur, licet aliàs eodem tempore <lb></lb>maiorem, aut minorem ſimul peragrat circuitum, de quo <lb></lb>nulla per ſe haberi debet ratio, vt præmonuimus. </s>
          <s id="N1662A">Vnde nec <lb></lb>requiritur, vt eius motus circumuolutionis ſit æqualis mo<lb></lb>tui recto, nec vt linea recta, quam percurrit ſit æqualis cir<lb></lb>cunferentiæ ſecundum quam rotando conuoluitur. </s>
        </p>
        <p id="N16633" type="main">
          <s id="N16635">Ad ſecundam verò partem quæſtionis reſpondetur, cir<lb></lb>culum deferentem, vel alium, qui ſeorſum per ſe ſuper pla<lb></lb>num circumuoluatur, quò maior ipſe fuerit, maius ſpatium <lb></lb>rectà in ſua reuolutione percurrere, quò verò minor, minus. <lb></lb></s>
          <s id="N1663F">Quia cum tota eius progreſſio fiat ex vi propriæ rotationis, <lb></lb>non niſi æqualem ſuæ peripheriæ lineam in plano poteſt de<lb></lb>ſcribere; tantum ſcilicet cum ſuo axe rectà progrediendo, <lb></lb>quantum rotatur; ac tantundem ſpatium percurrendo, quan<lb></lb>tum fuerit circumuolutus. </s>
          <s id="N1664A">Quæ reſponſio ad vtramque <lb></lb>difficultatis, ſeu quæſtionis partem, eſt omnino ad mentem <lb></lb>Ariſtotelis, vt patere poteſt ex eius propria, cui hæc maxi<lb></lb>mè congruit, licet aliunde vim, ac diſtinctionem obtinuerit. </s>
        </p>
        <p id="N16653" type="main">
          <s id="N16655">Adhuc tamen ex eiſdem principijs <expan abbr="reſpõderi">reſponderi</expan> poteſt, præ<lb></lb>fata nos experiri, quia minor circulus quando mouetur ad <lb></lb>motum alterius maioris motu mixto iam explicato, magis <lb></lb>participat de latione recta, quàm circulari; citius videlicet <lb></lb>progrediendo quàm rorando. </s>
          <s id="N16664">Cogitur enim rectà progre-<pb pagenum="217" xlink:href="005/01/225.jpg"></pb>di iuxta progreſſum axis, ac circuli maioris, <expan abbr="ſimulq.">ſimulque</expan> tardius <lb></lb>rotari quàm ille, minus ſpatium eodem tempore tranſmit<lb></lb>tendo in ſua minori circumuolutione: <expan abbr="proindeq.">proindeque</expan> per talem <lb></lb>rotationem, rectam quandam lineam deſcribit maiorem, <lb></lb>quam ſit eius circunferentia propria. </s>
          <s id="N1667C">E contra verò, nam <lb></lb>cum circulus maior mouetur ad motum minoris, magis par<lb></lb>ticipat de latione circulari, quàm recta. </s>
          <s id="N16683">Siquidem, cogitur <lb></lb>citius moueri circulariter quàm rectà, cum eodem tempo<lb></lb>re maiorem ambitum, quàm circulus minor, æqualemque <lb></lb>rectam debeat percurrere: <expan abbr="ideoq.">ideoque</expan> minorem rectam in ſua <lb></lb>circumuolutione deſcribit, quàm ſit eiuſmet circumſerentia<lb></lb> qua illam attingit. </s>
          <s id="N16694">Demum quia ſi circulus ex ſe, &amp; inde<lb></lb>pendenter ab alio duplici hac latione feratur, ſiue maior ſit, <lb></lb>ſiue minor, ſemper æquè de vtraque participat. </s>
          <s id="N1669B">Etenim tan<lb></lb>tum rectà progreditur quantum rotatur, nec aliunde rapi<lb></lb>tur, aut detinetur, vt magis vna quàm altera latione dimo<lb></lb>ueatur. </s>
          <s id="N166A4">Quo fit vt linea quam ſuper planum deſcribit, æqua<lb></lb>lis ſit propriæ circumferentiæ eique ſecundum omnes par<lb></lb>tes commenſurata. </s>
        </p>
        <p id="N166AB" type="main">
          <s id="N166AD">Verum vt non ſolum cauſa tam admirabilis effectus, ſed <lb></lb>etiam modus quo ipſe ab illa procedit expreſſius innote<lb></lb>ſcat, ac difficultas vltimò propoſita ex directo penitus eua<lb></lb>datur, vlterius dicendum eſt, circulum delatum non minus <lb></lb>ac deferentem, omnia ac ſingula puncta, quæ ſunt in linea re<lb></lb>cta ſuper quam fertur per totidem puncta propria ſucceſſi<lb></lb>uè attingere; ita vt in quolibet inſtanti per nouum punctum <lb></lb>ſuæ peripheriæ attingat nouum punctum plani. </s>
          <s id="N166C0">Etenim cum <lb></lb>planum à circulo attingatur per puncta, quæ ſunt extremita<lb></lb>tes diametrorum, &amp; vterque circulus ex infinitis diametris <lb></lb>conſtet; imò diametri circuli maioris includant diametros <lb></lb>minoris; tot erunt puncta terminatiua diametrorum in cir<lb></lb>culo minori, quot ſunt in maiori, ſiue delato per quæ ſimili<lb></lb>ter omnia puncta ſui plani valebit attingere. </s>
        </p>
        <p id="N166CF" type="main">
          <s id="N166D1">Rurſus dicendum eſt tam circulum deferentem, quàm <lb></lb>circulum delatum omnes, ac ſingulas partes diuiſibiles, quę <lb></lb>ſunt in eadem linea plani per totidem partes ſuas ſucceſſiuè <pb pagenum="218" xlink:href="005/01/226.jpg"></pb>attingere: hoc tamen diſcrimine, quod circulus deferens <lb></lb>illas attingit commenſuratiuè, &amp; adæquatè, circulus verò <lb></lb>delatus nonniſi inadæquatè. </s>
          <s id="N166E1">Sicut enim circulus deferens <lb></lb>ſiue maior ſit, ſiue minor conſtat ex infinitis partibus inde<lb></lb>terminatis, quæ mediant inter infinita puncta, ita etiam cir<lb></lb>culus delatus, per eaſque non minus attingere poterit infi<lb></lb>nitas partes, quæ ſunt in plano. </s>
          <s id="N166EC">Diximus tamen attingere <lb></lb>inadæquatè. </s>
          <s id="N166F1">Nam contactus adæquatus, &amp; commenſura<lb></lb>tus duarum quantitatum, fit per æqualem applicationem <lb></lb>partium æqualium vtriuſque quantitatis ad coexiſtendum <lb></lb>ſimul in eodem ſpatio loci: partes autem æqualiter appli<lb></lb>cari non poſſunt per lationes inæquales, nam ea eſt inæqua<lb></lb>litas in applicatione, quæ eſt in ipſis lationibus, ſiue lationes <lb></lb>cadant in vtramque quantitatem, ſiue in alteram tantùm. <lb></lb></s>
          <s id="N16701">Quapropter cum tota applicatio partium circumferentiæ <lb></lb>ad attingendas partes plani ſuper quod rotatur, fiat tum ex <lb></lb>vi ipſius rotationis, qua ſucceſſiuè ipſæ partes inclinantur <lb></lb>ad illas, tum ex vi motus recti quo ſucceſſiuè etiam progre<lb></lb>diendo ad eaſdem perueniunt: hinc fit, vt ſi lationes ipſæ <lb></lb>æqualiter procedant, quemadmodum in motu mixto circuli <lb></lb>deferentis, aut alterius per ſe ſeorſum rotantis, æqualiter <lb></lb>etiam alterius quantitatis partes, ad partes alterius appli<lb></lb>centur, ac ſe tangendo ad inuicem commenſurentur, &amp; <lb></lb>adæquentur: E contra verò ſi non procedant æqualiter ip<lb></lb>ſæ lationes, ſed vna alteram excedat in velocitate, aut tardi<lb></lb>tate, vt in motu mixto cuiuſlibet circuli delati, inæqualiter <lb></lb>etiam partes ipſius ad partes plani applicentur, ac inadæ<lb></lb>quatè adinuicem commenſurentur. </s>
        </p>
        <p id="N1671E" type="main">
          <s id="N16720">Quod ſi non poſſit coexiſtere in ſpatio, exempli gratia <lb></lb>bipalmari cum linea recta bipalmari arcus circumferentiæ <lb></lb>palmaris, vel tripalmaris, quacunque rotatione ad inuicem <lb></lb>applicentur; hoc profectò intelligitur in quiete, atque in <lb></lb>termino ipſius motus: alioquin in tranſitu, ac ſucceſsiuè id <lb></lb>nullo modo repugnat, ſicutnec punctum globi rectà ſuper <lb></lb>planum delati poſt punctum ipſius plani, attingere partem <lb></lb>diuiſibilem eiuſdem plani, eique coexiſtendo inadæquatè <pb pagenum="219" xlink:href="005/01/227.jpg"></pb>&amp; ſucceſsiuè commenſurari, vt omnes penè Philoſophi fa<lb></lb>tentur. </s>
          <s id="N16738">Maior enim vel minor velocitas atque ſucceſsio in <lb></lb>tranſitu, &amp; in partium applicatione, ex vi alterius lationis <lb></lb>æquipollet maiori, vel minori extenſioni ipſius quantitatis <lb></lb>ad replendum æquale ſpatium ei, quod occupatur ab alia <lb></lb>quantitate in eodem tempore, qua ratione dicuntur coexi<lb></lb>ſtere, ac inter ſe coaptari. </s>
        </p>
        <p id="N16745" type="main">
          <s id="N16747">Res itaque ſic eſt concipienda, vt in reuolutione circuli <lb></lb>minoris ad motum maioris ſemper pars minor ipſius attin<lb></lb>gat partem plani maiorem, quia velocius tranſit per illam <lb></lb>motu recto, quàm rotando æqualem <expan abbr="dimenſionẽ">dimenſionem</expan> proptiam <lb></lb>poſsit exponere, atque ſecundum ipſam ſe applicare. </s>
          <s id="N16756">Vnde <lb></lb>quod illi deeſt extenſionis compenſatur velociori ſucceſsio<lb></lb>ne, &amp; applicatione ſecundum lationem rectam ad coaptan<lb></lb>dum ſe parti majori. </s>
          <s id="N1675F">Quod certè non eſt intelligendum <lb></lb>fieri per raptationem, quaſi per vnicum delati circuli pun<lb></lb>ctum plura plani puncta, vel per <expan abbr="eandẽ">eandem</expan>. </s>
          <s id="N1676A">omnino circuli par<lb></lb>tem, plures plani partes attingerentur; ſed per propriam, <lb></lb>rotationem. </s>
          <s id="N16771">Quia ita rapitur, ac fertur ſuper illud motu re<lb></lb>cto, vt ſimul quamuis tardius feratur latione circulari per <lb></lb>quam partes, ac puncta ipſius peripheriæ iugiter mutantur. <lb></lb></s>
          <s id="N16779">Cumque numerus infinities infinitus punctorum, ac indeter<lb></lb>minatarum partium vtriuſque circuli ſufficiat ad mutatio<lb></lb>nem ipſam continuam, &amp; correſpondentiam, quam præſta<lb></lb>re debet infinitis punctis, ac partibus plani, nullum relinqui<lb></lb>tur inconueniens, minorem circumferentiam maiori ſpatio, <lb></lb>plani ob diſparem lationem, &amp; applicationem inadæquatè <lb></lb>in tranſitu coaptari. </s>
          <s id="N16788">Idemque è conuerſo dici poteſt in re<lb></lb>uolutione circuli maioris ad <expan abbr="motũ">motum</expan> minoris, vt ſcilicet ſem<lb></lb>per pars maior ipſius eo reſpondeat parti minori in plano <lb></lb>ſuper quod fertur, quia tardius tranſit per illam motu recto, <lb></lb>quàm rotando æqualem ſibi dimenſionem poſſit attingere. <lb></lb></s>
          <s id="N16798">Siquidem velocius rotando, quàm progrediendo, nequit at<lb></lb>tingere tantam dimenſionem in plano, quantam ipſe exhi<lb></lb>bet per circumuolutionem. </s>
          <s id="N1679F">Vnde quod ei ſupereſt exten<lb></lb>ſionis circularis compenſatur tardiori ſucceſſione, &amp; appli-<pb pagenum="220" xlink:href="005/01/228.jpg"></pb>cationem ſecundum lationem rectam ad proportionandum <lb></lb>ſe parti minori. </s>
          <s id="N167AB">Atque hæc in re tam ambigua ſi minus <lb></lb>demonſtraſſe, ſaltem indicaſſe, vel tentaſſe ſufficiat. </s>
        </p>
        <p id="N167B0" type="main">
          <s id="N167B2">Ad exactius denique percipiendam naturam miſtorum <lb></lb>motum, non abs re fuerit affinem aliam quæſtionem diluere, <lb></lb>quæ fortaſſe non minus admirabilem, ac ferè incredibilem <lb></lb>ſupponit experientiam. </s>
          <s id="N167BB">Nimirum cur in prædicta latione <lb></lb>duorum circulorum circa idem centrum ſecundùm abſidem <lb></lb>circuli maioris, aliqua puncta circumferentiæ maioris, mi<lb></lb>nus progrediantur, quàm correſpondentia ſibi puncta cir<lb></lb>cumferentiæ minoris; aliqua verò magis. </s>
          <s id="N167C6">In maiori enim <lb></lb>circulo puncta vnius ſemicirculi minus progrediuntur, quam <lb></lb>puncta ſemicirculi correſpondentis in circulo minori. </s>
          <s id="N167CD">Con<lb></lb>tra verò, puncta alterius ſemicirculi magis progrediuntur in <lb></lb>circulo maiori, quàm in minori, vt de motu particulari Epi<lb></lb>cyclorum docere ſolent Aſtronomi. </s>
          <s id="N167D7">Quod maximè vide<lb></lb>tur admirandum <expan abbr="cū">cum</expan> vterque circulus ſimpliciter, ac ſecun<lb></lb>dum ſe totum ad motum axis progrediendo, æquale ſpa<lb></lb>tium percurrat, vt vidimus, ac probatum eſt in præcedenti<lb></lb>bus. </s>
          <s id="N167E6">Ita tamen rem ſe habere ſic oſtenditur. </s>
        </p>
        <figure id="id.005.01.228.1.jpg" xlink:href="005/01/228/1.jpg"></figure>
        <p id="N167EE" type="main">
          <s id="N167F0">Eſto exempli gratia circulus maior ABCD, minor verò <lb></lb>EFGH circa commune centrum I ſuper planum KL. <expan abbr="Sintq.">Sintque</expan> <lb></lb>duo diametri maioris ad angulos rectos ſeſe interſecantes <lb></lb>AC, &amp; BD; minoris verò in ipſis contenti EG, &amp; FH; ita <pb pagenum="221" xlink:href="005/01/229.jpg"></pb>vt BD ſit perpendicularis ipſi KL. </s>
          <s id="N16803">Rotetur autem vterque <lb></lb>circulus ſimul ſecundum <expan abbr="abſidẽ">abſidem</expan> maioris dextrorſum quouſ<lb></lb>que punctum C perueniat, verbi gratia in L, ac ſemidiame<lb></lb>ter IC conſtituatur in ML perpendicularis ipſi KL: ac <lb></lb>per conſequens IG in MN; ita vt punctum G reperia<lb></lb>tur in N. </s>
          <s id="N16815">Dicimus ergo punctum C in hac reuolutione <lb></lb>minus dextrorſum promoueri, quàm punctum G. </s>
          <s id="N1681B">Demit<lb></lb>tatur enim à puncto C linea CO perpendicularis pariter <lb></lb>ipſi KL, &amp; à puncto G alia perpendicularis GP: &amp; tunc <lb></lb>apparebit punctum C dextrorſum peragraſſe ſpatium CM, <lb></lb>vel OL, quæ ſunt latera oppoſita, ac proinde æqualia re<lb></lb>ctanguli CMLO, vt pater per 34. propoſit. </s>
          <s id="N16828">primi. </s>
          <s id="N1682B">Pun<lb></lb>ctum verò G conſtabit peragraſſe ſpatium GM, ſeu PL <lb></lb>æquale huic. </s>
          <s id="N16832">At GM maior eſt, quàm CM, eo quod <lb></lb>illam contineat, ſicut PL maior eſt ipſa OL propter ean<lb></lb>dem rationem. </s>
          <s id="N16839">Ergo per talem circumuolutionem minus <lb></lb>dextrorſum progreditur punctum C, quod eſt extremum <lb></lb>diametri circuli maioris, quàm punctum G extremum <lb></lb>diametri contenti sit culi minoris. </s>
        </p>
        <p id="N16842" type="main">
          <s id="N16844">Rurſus verò dicimus punctum D eiuſdem circuli maio<lb></lb>ris, minus pariter dextrorſum progredi, quam punctum H, <lb></lb>quod illi correſpondet in circulo minori. </s>
          <s id="N1684B">Etenim poſt præ<lb></lb>dictam reuolutionem centro I tranſlato in M, ac C in <lb></lb>L, punctum D erit in linea AM vbi Q, (nempe in loco, <lb></lb>qui tantum ſanè diſter à puncto M, quantum diſtat extre<lb></lb>mum D ipſius ſemidiametri DI ab ipſo centro I,) pun<lb></lb>ctum verò H ſimiliter erit in R; ita vt ſemidiameter IHD <lb></lb>reperiatur in <expan abbr="MRq.">MRque</expan> Quapropter ſi ex duobus punctis QR <lb></lb>demittantur duæ perpendiculares in planum DL, quæ ſint <lb></lb>QS, &amp; RT, ſpatium progreſſionis ipſius puncti D, erit <lb></lb>linea IQ, æqualis ipſi DS: Spatium verò progreſſionis <lb></lb>puncti H, erit linea IR, ſiue DT. Cum igitur minor ſit linea <lb></lb>DS ipſa DT, ſiquidem continetur in illa, remanet vt pun<lb></lb>ctum D circuli maioris, minus. </s>
          <s id="N1686C">dextrorſum promoueatur <lb></lb>quàm punctum H ſibi correſpondens circuli minoris. </s>
        </p>
        <p id="N16871" type="main">
          <s id="N16873">E contra tamen dicimus punctum A circuli maioris am-<pb pagenum="222" xlink:href="005/01/230.jpg"></pb>plius dextrorſum progredi, quàm punctum E circuli mino<lb></lb>ris quo illi correſpondet. </s>
          <s id="N1687D">Poſita namque eadem reuolu<lb></lb>tione, I exiſtente in M, ac C in L, A erit in V: con<lb></lb>ſtitueretur enim tota diameter AIC in VML, in qua etiam <lb></lb>linea eſſet punctum E, nempe in X. </s>
          <s id="N16887">Quod ſi compleatur <lb></lb>rectangulum AV, ac rectangulum EX, erit ſpatium <lb></lb>peragratum à puncto A dextrorſum idem, quod linea <lb></lb>AM, vt deducitur ex eadem 34. propoſitione primi. </s>
          <s id="N16890">Spa<lb></lb>tium verò ſimiliter peragratum à puncto E, erit EM, quod <lb></lb>continetur in illo. </s>
          <s id="N16897">Magis ergo progreditur A, quàm E. </s>
        </p>
        <p id="N1689B" type="main">
          <s id="N1689D">Id ipſum tandem demonſtratur de puncto B, quod cer<lb></lb>tè magis progreditur quàm F. </s>
          <s id="N168A3">Quandoquidem in deſcri<lb></lb>pta reuolutione ſemidiameter IB conſtitueretur in MY in <lb></lb>qua cum contineatur ſemidiameter IF, ipſum F conſtitue<lb></lb>retur in Z: completiſque rectangulis BY, &amp; BZ, erit ſpa<lb></lb>tium dextrorſum peragratum à B quantum IY; peragra<lb></lb>tum verò ab F; quantum IZ contentum in ipſo IY, quod <lb></lb>propterea maius eſt. </s>
          <s id="N168B2">Erunt igitur duo puncta circuli maio<lb></lb>ris, quæ minus dextrorſum progrediuntur, quàm puncta ſibi <lb></lb>correſpondentia circuli minoris: alia verò duo quæ magis. <lb></lb></s>
          <s id="N168BA">Quod etiam demonſtrari poterit de reliquis punctis eiuſ<lb></lb>dem ſemicirculi cum ſuo correſpondenti in vtroque circulo <lb></lb>ſi vterque bifariam ſecetur per diametrum 3, 4, cuius extre<lb></lb>mitates nempe 3, &amp; 4, in circulo maiori medient inter A, <lb></lb>&amp; D, ac inter B &amp; C. </s>
          <s id="N168C6">Sicut in circulo minori extremita<lb></lb>tes 5, 6. medient inter E, &amp; H, ac inter F, &amp; G. </s>
          <s id="N168CC">Nam <lb></lb>puncta omnia ſemicirculi inferioris 3 DC 4 in circulo <lb></lb>maiori, minus progredi <expan abbr="reperiẽtur">reperientur</expan>, quàm puncta ſemicircu<lb></lb>li inferioris 5 HG 6 ſibi correſpondentis in circulo mino<lb></lb>ri. </s>
          <s id="N168DB">E contra verò omnia puncta ſemicirculi ſuperioris 3 <lb></lb>AB 4 magis progredi, quàm puncta correſpondentis ſemi<lb></lb>circuli 5 EF 6 in circulo minori. </s>
          <s id="N168E2">Ipſa tamen puncta ex<lb></lb>trema diametri 3, 4 in circulo maiori, nec magis, nec mi<lb></lb>nus, ſed æquè progredi conſpicientur, ac extrema diametri <lb></lb>5, 6 in circulo minori. </s>
          <s id="N168EB">Sicut enim per quàm facilè id po<lb></lb>terit eadem ratione qua ſupra demonſtrari, ita hic de-<pb pagenum="223" xlink:href="005/01/231.jpg"></pb>monſtraſſe, inutile, ac prolixum extimaretur. </s>
        </p>
        <p id="N168F5" type="main">
          <s id="N168F7">Eiuſmodi ergo euentus cauſam reddere nullo negocio <lb></lb>quiſque poterit ſuppoſita expoſitione mixti motus, quam <lb></lb>ſupra tradidimus: cum planè ex illa pateat, puncta CD, ſi<lb></lb>cut &amp; puncta GH duabus lationibus ferri, vna dextrorſum, <lb></lb>ſimul cum toto circulo ad motum rectum axis I verſus M: <lb></lb>altero verò ſiniſtrorſum ad proprium rotationis motum quo <lb></lb>obliquè puncta omnia ſemicirculi inferioris CDA, ſicut &amp; <lb></lb>GHE retrocedunt verſus partes AK. </s>
          <s id="N16908">Hinc namque fit, vt <lb></lb>tantum de recta eorum latione dextrorſum ſubtrahatur, <lb></lb>quantum per motum circularem obliquè retroceſſerint. <lb></lb></s>
          <s id="N16910">Cumque minus contingat retrocedere punctum G, ſi<lb></lb>cut &amp; punctum H, quàm ipſa puncta CD iuxta mino<lb></lb>rem ſuum motum, <expan abbr="minoremq.">minoremque</expan> ſemicirculum, quem per il<lb></lb>lum percurrunt; ſequitur, vt ipſa puncta GH, magis quàm <lb></lb>puncta CD participent de latione recta qua tendunt dex<lb></lb>trorſum. </s>
          <s id="N16921">At loquendo de punctis AB, ac de EF, contraria <lb></lb>eſt ratio. </s>
          <s id="N16926">Nam huiuſmodi quatuor puncta ſicut &amp; ipſi toti <lb></lb>ſemicirculi ſuperiores, nempe ABC, &amp; EFG, vtraque la<lb></lb>tione feruntur dextrorſum. </s>
          <s id="N1692D">Quo fit, vt illud punctum ma<lb></lb>gis progrediatur, quod celerius mouetur latione propria, <lb></lb>ſeu maius ſpatium eodem tempore virtute circumuolutio<lb></lb>nis tranſmiſerit. </s>
          <s id="N16936">Cum igitur puncta AB, hoc ipſo, quod ſint <lb></lb>puncta circuli maioris, velocius ferantur, <expan abbr="maioremq.">maioremque</expan> ambi<lb></lb>tum rotando percurrant, quàm puncta EF in circulo mino<lb></lb>ri; magis etiam dextrorſum progredientur. </s>
        </p>
        <p id="N16943" type="main">
          <s id="N16945">Quod ſi puncta, quæ ſunt in arcubus 4 C, &amp; 6 G dex<lb></lb>trorſum vtraque pariter latione ferantur, ſicut reliqua pun<lb></lb>cta, quæ ſunt in ſemicirculis ABC, &amp; EFG; &amp; tamen pun<lb></lb>cta inter 4 C circuli maioris minus progrediantur, quàm <lb></lb>ſibi correſpondentia in 6 G circuli minoris; hoc quidem <lb></lb>fit; nam cum ipſi arcus maximè declinent deorſum, parum <lb></lb>ambo progrediuntur ad dexteram virtute ſuæ circumuolu<lb></lb>tionis; <expan abbr="multumq.">multumque</expan> virtute motus recti, &amp; aſportantis ad mo<lb></lb>tum axis. </s>
          <s id="N1695C">Cumque ratione ſitus, terminus à quo incipit mo<lb></lb>ueri prædictus arcus circuli minoris, magis diſtet à termino, <pb pagenum="224" xlink:href="005/01/232.jpg"></pb>à quo incipit moueri arcus maioris, quàm ſit exceſſus pro<lb></lb>greſſionis ipſius arcus maioris ratione termini, ad quem <lb></lb>poſtea pertingit, ſequitur abſolutè loquendo, magis progre<lb></lb>di dextrorſum prædictum arcum circuli minoris, quàm ar<lb></lb>cum circuli maioris. </s>
          <s id="N1696E"><expan abbr="Idemq.">Idemque</expan> è conuerſo applicari poteſt in <lb></lb>arcubus 3 A, 5 E ad oſtendendum, cur puncta arcus <lb></lb>3 A circuli maioris, magis progrediantur quàm puncta ar<lb></lb>cus 5 E circuli minoris. </s>
          <s id="N1697A">Nam licet vterque arcus per mo<lb></lb>tum circularem retrocedat, ac retrocedendo velocius mo<lb></lb>ueatur arcus maioris, quàm minoris; nihilominus ratione <lb></lb>ſitus, ac termini à quo, <expan abbr="cũ">cum</expan> minor ſit exceſſus retroceſſionis, <lb></lb>quàm anteceſſionis virtute motus recti, eo quod à remotio<lb></lb>ri termino arcus maioris promoueatur; hinc pariter fit, vt <lb></lb>maior ſit progreſſus dextrorſum maioris, quàm minoris ar<lb></lb>cus prædicti, ſicut &amp; totius ſemicirculi 3 AB 4, quàm 5 <lb></lb>EF 6, vt dicebamus. </s>
        </p>
        <p id="N16991" type="head">
          <s id="N16993">Quæſtio Vigeſimaquinta.</s>
        </p>
        <p id="N16996" type="main">
          <s id="N16998">C<emph type="italics"></emph>vr lectulorum ſpondas ſecundum duplam fa<lb></lb>ciunt proportionem, hanc quidem ſex pedum, <lb></lb>vel paulò ampliorem, illam verò trium? </s>
          <s id="N169A2">Curvè <lb></lb>non ſecundum diametrum illos restibus exten<lb></lb>dunt? </s>
          <s id="N169A9">An tantos quidem magnitudine faciunt, <lb></lb>vt corporibus ſint proportionem habentes? <lb></lb></s>
          <s id="N169AF">fiunt enim ſic ſecundum ſpondas dupli, longitudine quidem <lb></lb>cubitorum, latitudine verò duorum. </s>
          <s id="N169B4">Extendunt autem illos <lb></lb>non ſecundum diametrum, ſed ex oppoſito, vt &amp; ligna <lb></lb>minus diſtrahantur. </s>
          <s id="N169BB">Celerrimè enim ſcinduntur ſecundum na<lb></lb>turam diuiſa, &amp; eodem modo distenta laborant maximè. </s>
          <s id="N169C0">Am<lb></lb>plius quoniam opus eſt, vt reſtes pondus ferre poſsint, ſi certè <lb></lb>pondere impoſito minus <expan abbr="laborabũt">laborabunt</expan>, ſi tranſuerſim, quàm ſi obli<lb></lb>què extendantur. </s>
          <s id="N169CD">Præterea hoc etiam modo minus abſumitur <lb></lb>restium. </s>
          <s id="N169D2">Sit enim lectulus AFGK, &amp; bifariam diuidatur ip<lb></lb>ſa FG ſecundum B: æqualia certè foramina ſunt in ipſa <lb></lb>FA: latera enim ſunt æqualia, nam totum FG duplum est. <lb></lb></s>
          <s id="N169DA">Extendunt autem, vt deſcriptum eſt, ab ipſo A ad ipſum B: ita <lb></lb>vbi eſt C ita eſt D, ita vbi H, poſtea vbi E, &amp; <expan abbr="eodẽ">eodem</expan> ſemper mo-<emph.end type="italics"></emph.end><pb pagenum="225" xlink:href="005/01/233.jpg"></pb><emph type="italics"></emph>do, donec ad angulum peruenerint <expan abbr="aliũ">alium</expan>. </s>
          <s id="N169F0">Duo enim anguli restis <lb></lb>habent capita: æquales autem ſunt reſtes ſecundum curuatu<lb></lb>ras, videlicet AB, &amp; BC, ipſis CD, &amp; DH: &amp; aliæ ſimi<lb></lb>li ſe habent modo, quoniam eadem demonſtratio: ipſa enim <lb></lb>AB æqualis est ipſi HE, æqualia enim ſunt latera ſpatij BG, <lb></lb>MA, &amp; foramina æquè distant. </s>
          <s id="N169FD">Ipſa autem BG æqualis eſt <lb></lb>ipſi MA. </s>
          <s id="N16A02">Angulus enim B æqualis eſt angulo G. </s>
          <s id="N16A06">In æquali<lb></lb>bus enim hic quidem intus, ille verò extra, &amp; B quidem est <lb></lb>ſemirectus. </s>
          <s id="N16A0D">Est enim FB æqualis ipſi FA. </s>
          <s id="N16A10">Et angulus vbi <lb></lb>F, rectus eſt, B autem angulus æqualis ei, vbi eſt G quo<lb></lb>niam quadratum altera parte longius, duplum eſt: &amp; ad me<lb></lb>dium eſt curuatura, quamobrem AD ipſi EG eſt æqualis, huic <lb></lb>verò ipſa HM. <expan abbr="Similiq.">Similique</expan> modo demonſtrantur aliæ, quoniam <lb></lb>æquales ſunt duæ, quæ ſecundum curuaturas ſunt, duabus. <lb></lb></s>
          <s id="N16A23">Quare manifestum eſt, quod tot ſunt reſtes in lectulo, quot <lb></lb>ſunt quatuor, ſicut AB. </s>
          <s id="N16A29">Quanta autem foraminum eſt mul<lb></lb>titudo in ipſo FG latere, &amp; in eius dimidio FB eſt medietas. <lb></lb></s>
          <s id="N16A2F">Quamobrem in dimidiato lectulo tantæ reſtium magnitudines <lb></lb>erunt, quantum eſt AB, multitudine verò tot, quot in BG ſunt <lb></lb>foramina. </s>
          <s id="N16A36">Hoc autem nihil refert dicere, quàm quot ſunt in <lb></lb>ipſis AF, &amp; BF ſimul ſumptis. </s>
          <s id="N16A3B">Si autem ſecundum diame<lb></lb>trum extendantur reſtes, quemadmodum ſe habet in lectulo <lb></lb>ABCD: dimidia non tot ſunt, quot amborum latera FAFG, <lb></lb>æqualia autem quot in ipſis FB, FA, ſunt foramina. </s>
          <s id="N16A44">Maio<lb></lb>res autem ſunt ipſæ AF, BF, duæ exiſtentes, quam AB. </s>
          <s id="N16A4A">Qua<lb></lb>re reſtis in tantùm maior, quantùm ambo latera diametro ſunt <lb></lb>maiora.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N16A53" type="head">
          <s id="N16A55">COMMENTARIVS.</s>
        </p>
        <p id="N16A59" type="main">
          <s id="N16A5B">Vt ex re nullius difficultatis, atque momenti, inge<lb></lb>nio iam, ac perdifficilem apud multos excitet dubi<lb></lb>tationem, quærit hic primò Ariſtoteles, cur lectulo<lb></lb>rum ſpondæ ſecundum duplam proportionem longitudinis <lb></lb>ad latitudinem eorum efficiantur, ita vt quæ lectulorum <lb></lb>longitudinem conſtituunt ſex pedum exiſtant, quæ verò la<lb></lb>titudinem, trium. </s>
          <s id="N16A6A"><expan abbr="Statimq.">Statimque</expan> id conſueuiſſe docet, vt huma<lb></lb>norum corporum ratio habeatur, <expan abbr="lectuliq.">lectulique</expan> illis proportio<pb pagenum="226" xlink:href="005/01/234.jpg"></pb>nentur ad cubantium commoditatem. </s>
          <s id="N16A7B">Loquitur autem. <lb></lb></s>
          <s id="N16A7F">Philoſophus de lectulis minoribus cum qui ad vnum dum<lb></lb>taxat capiendum hominem cubantem efficiuntur, tum qui <lb></lb>reſtibus, ſeu funibus quibuſdam ad ſuſtinendam culcitram <lb></lb>ſuper quam ille iaceat ſunt intexti, quemadmodum adhuc <lb></lb>in Italia licet rarò, frequentius tamen in Gallia, atque Hiſpa<lb></lb>nia conſpiciuntur in vſum traducti. </s>
        </p>
        <p id="N16A8C" type="main">
          <s id="N16A8E">Hinc itaque rurſus quaerit cur in huiuſmodi lectulis mu<lb></lb>niendis, reſtes per tranſuerſum, &amp; ex oppoſito, non autem <lb></lb>per diametrum extendantur. </s>
          <s id="N16A97"><expan abbr="Aitq.">Aitque</expan> triplici ex cauſa id fieri; <lb></lb>vel pariter in conſuetudinem abijſſe. </s>
          <s id="N16A9F">Primò nimirum, vt <lb></lb>ſpondarum ligna ab ipſis reſtibus minus diſtrahantur atque <lb></lb>ſcindantur; quandoquidem ſciſſioni magis obnoxia ſunt cum <lb></lb>per diametrum in eis funes inditi fuerint, ac diſtenti. </s>
          <s id="N16AA8">Nam <lb></lb>tunc quaſi per longum iuxta naturales venulas, ac rimulas, <lb></lb>quibus obſequendo facilè ſequitur ſciſsio, ligna ipſa vim pa<lb></lb>terentur, ac veluti ſecarentur; ſecus ac ſi per tranſuerſum, <lb></lb>ac ſecundum latitudinem terebrata ſint, <expan abbr="funesq">funesque</expan> per ipſa <lb></lb>foramina <expan abbr="traducãtur">traducantur</expan>. </s>
          <s id="N16AB9">Quia ſemper lignorum tramites tranſ<lb></lb>uerſi funium preſſioni magis reſiſtunt. </s>
        </p>
        <p id="N16AC0" type="main">
          <s id="N16AC2">Secundo id fieri docet ex eo quod ſic funes traducti, mi<lb></lb>nus laborant, pondus ſuperimpoſitum ſuſtinendo. </s>
          <s id="N16AC7">Quo enim <lb></lb>per breuiores lineas extenſi fuerint, eò fortiores euadunt. <lb></lb></s>
          <s id="N16ACD">Sic è contra cum per longiores, debiliores fiunt, ac facilius <lb></lb>in parte ab extremis remotiſſima diſrumpuntur: longiores <lb></lb>autem lineæ ſunt diametrales in quadrangulari, ac rectan<lb></lb>gula figura de qua loquimur, vt per ſe patet. </s>
        </p>
        <p id="N16AD6" type="main">
          <s id="N16AD8">Tertio denique id ipſum iccirco vſui eſſe inquit, vt in ip<lb></lb>ſa lectulorum textura minus reſtium, ſeu funium abſumatur. <lb></lb></s>
          <s id="N16ADE">Quod licet implexè admodum videatur probare ob textus <lb></lb>corruptionem; Satis tamen ſenſus probationis tenetur, at<lb></lb>que optimè à Piccolomineo dilucidatur. </s>
        </p>
        <p id="N16AE5" type="main">
          <s id="N16AE7">Summatim verò ad hoc, vt clarius probatio ipſa perci<lb></lb>piatur, ſupponimus primò cum ipſo Ariſtotele, quod lectu<lb></lb>lus ſuis reſtibus per tranſuerſum intextus exempli gratia <pb pagenum="227" xlink:href="005/01/235.jpg"></pb><figure id="id.005.01.235.1.jpg" xlink:href="005/01/235/1.jpg"></figure><lb></lb>ſit <expan abbr="rectãgulũ">rectangulum</expan> IGAO, <lb></lb><expan abbr="eiusq.">eiusque</expan> <expan abbr="lõgiores">longiores</expan> <expan abbr="ſpõ-dæ">ſpon<lb></lb>dæ</expan>, nempe ſex <expan abbr="pedũ">pedum</expan> <lb></lb>ſint IG, &amp; AO; bre<lb></lb>uiores verò <expan abbr="triũ">trium</expan> pe<lb></lb>dum IA, &amp; GO, ſin<lb></lb>gulæ in totidem pe<lb></lb>des diuiſæ per ſua <lb></lb>foramina, quibus re<lb></lb>ſtes indantur, prout <lb></lb>hic litteris conſignantur. </s>
          <s id="N16B24">Deinde ſupponimus ex eodem, <lb></lb>hoc pacto reſtes ipſos per tranſuerſum extendi. </s>
          <s id="N16B29">Sumitur ini<lb></lb>tium reſtis, &amp; obfirmatur in A, tunc reſtis ipſa ducitur ad B, <lb></lb>ex quo poſtea per C flectitur in D; hinc per E ad F; exinde <lb></lb>verò per G ad H: ex H autem rurſus ducitur in I, &amp; ex I per <lb></lb>K in L; vnde per M ad N; &amp; ex N per B, <expan abbr="tandẽ">tandem</expan> peruenitur <lb></lb>in O; vbi ſimiliter <expan abbr="alterũ">alterum</expan> reſtis caput deſinendo obfirmatur. </s>
        </p>
        <p id="N16B3E" type="main">
          <s id="N16B40">Quibus poſitis ad <expan abbr="comprehendendã">comprehendendam</expan> huiuſmodi reſtium <lb></lb>quantitatem ſic ferè procedit Ariſtoteles, vel ſaltem obſcu<lb></lb>riuſculè æquiualentia profert. </s>
          <s id="N16B4B">Cum enim triangulus BGO <lb></lb>ex conſtructione ſit rectangulus, quadrata laterum BG, &amp; <lb></lb>GO, per 47. primi, æqualia ſunt quadrato lateris BO. </s>
          <s id="N16B52">Cum<lb></lb>que latus BG, ſicut &amp; latus GO trium exiſtant pedum, ac <lb></lb>ternarij quadratus numerus, ſint nouem; hinc fit, vt ex vtro<lb></lb>que quadrato, ſcilicet lateris BG, &amp; lateris GO, conſti<lb></lb>tuatur numerus 18. totidem pedes contineat quadratum <lb></lb>lateris BO duobus illis æquale, proindeque vt latus ip<lb></lb>ſum BO ſit radix quadrata numeri 18. nempe quatuor <lb></lb>pedum circiter cum quarta. </s>
          <s id="N16B63">At in lectulo non ſunt niſi <lb></lb>octo reſtes æquales, <expan abbr="eiuſdemq.">eiuſdemque</expan> dimenſionis, ac latus BO, <lb></lb>vt patet per 33. primi. </s>
          <s id="N16B6E">Ergo omnes ipſi reſtes ſimul ſum<lb></lb>pti, ac per tranſuerſum intexti erunt quaſi triginta quatuor <lb></lb>pedum: quibus ſi addantur (vt rectè notat Baldus) ſex alij <lb></lb>pedes reſtium qui cadunt extra, nempe à B in C, &amp; à D in <lb></lb>E, &amp; ſic in reliquis, erit reſtis totius longitudo pedum qua<lb></lb>draginta cum dimidio, vel paulò amplius. </s>
        </p>
        <pb pagenum="228" xlink:href="005/01/236.jpg"></pb>
        <p id="N16B7F" type="main">
          <s id="N16B81">Quod ſi reſtes extendantur ſecundum diametrum, vt in <lb></lb>deſcripto lectulo ABCD, plus reſtium abſumi, inquit Phi<lb></lb><figure id="id.005.01.236.1.jpg" xlink:href="005/01/236/1.jpg"></figure><lb></lb>loſophus; &amp; eadem <lb></lb>qua ſupra ratioci<lb></lb>natione poterit de<lb></lb>monſtrari. </s>
          <s id="N16B94"><expan abbr="Nã">Nam</expan> ſin<lb></lb>gulis <expan abbr="quibusq.">quibusque</expan> re<lb></lb>ſtibus, tanquam la<lb></lb>teribus trianguli re<lb></lb>ctanguli conſidera<lb></lb>tis per 47. prop. <lb></lb></s>
          <s id="N16BA9">primi, &amp; per extractionem radicis quadratæ, inueniemus, <lb></lb>eos omnes ſimul ſumptos quadraginta pedum cum dimi<lb></lb>dio obtinere dimenſionem, quibus ſi alios ſeptem, qui ex<lb></lb>tra cadunt adijciamus, erit tota longitudo reſtis pedum 47. <lb></lb>cum dimidio. </s>
          <s id="N16BB4">Quod ſanè ad rei, de qua agitur intelligen<lb></lb>tiam ſufficit indicaſſe, cum exactior ſupputatio fruſtrà ac <lb></lb>prolixius quàm par eſt, ſermonem protraheret. </s>
        </p>
        <p id="N16BBB" type="head">
          <s id="N16BBD">Quæſtio Vigeſimaſexta.</s>
        </p>
        <p id="N16BC0" type="main">
          <s id="N16BC2">C<emph type="italics"></emph>vr difficilius eſt longa ligna ab extremo ſuper <lb></lb>humeros ferre, quàm ſecundum medium, <lb></lb>æquali existente pondere? </s>
          <s id="N16BCD">An quia vibrato li<lb></lb>gno ipſum extremum prohibet ferre, vibratio<lb></lb>ne magis retrahens lationem? </s>
          <s id="N16BD4">An quoniam li<lb></lb>cet nihil inflectatur, neque multam habeat lon<lb></lb>gitudinem, difficilius tamen ad ferendum eſt <lb></lb>ab extremo, quoniam facilius ex medio eleuatur, quàm ab ex<lb></lb>tremo, &amp; ideo ſic ferre eſt facilius. </s>
          <s id="N16BE0">Cauſa autem quoniam <lb></lb>ſecundum medium quidem eleuato ligno ſemper ſeſe inuicem <lb></lb>ſuſpendunt extrema, &amp; altera pars alteram bene ſubleuat. <lb></lb></s>
          <s id="N16BE8">Medium enim veluti centrum fit, vbi habet is qui eleuat, <lb></lb>aut fert. </s>
          <s id="N16BED">Extremorum igitur vtrumque deorſum vergens, <lb></lb>ſurſum ſuſpenditur. </s>
          <s id="N16BF2">Quod ſi ab extremo eleuetur, aut fe<lb></lb>ratur, non ſanè facit: ſed vniuerſum pondus ad vnum ver<lb></lb>git medium, quo eleuatur, aut fertur. </s>
          <s id="N16BF9">Sit medium vbi A, <lb></lb>extrema B, C. </s>
          <s id="N16BFF">Eleuato igitur aut portato ſecundum A,<emph.end type="italics"></emph.end><pb pagenum="229" xlink:href="005/01/237.jpg"></pb><emph type="italics"></emph>ipſum quidem B deorſum nutans, ſurſum eleuat C, ipſum au<lb></lb>tem C deorſum nutans, B ſurſum eleuat, ambo autem ſurſum <lb></lb>eleuata hoc faciunt.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N16C11" type="head">
          <s id="N16C13">COMMENTARIVS.</s>
        </p>
        <p id="N16C17" type="main">
          <s id="N16C19">Dvplicem Ariſtoteles cauſam affert, ob <expan abbr="quã">quam</expan> difficilius <lb></lb>procera ligna ab extremo ſuper <expan abbr="humerũ">humerum</expan> geſtantur, <lb></lb>quàm è medio, æquali exiſtente pondere, à quo to<lb></lb>ta geſtandi difficultas naſci videretur. </s>
          <s id="N16C2C">Vna eſt, quia procera <lb></lb>ligna, vt plurimùm ex ſe flexibiliora ſunt, ac vibrationi, &amp; flu<lb></lb>ctuationi magis obnoxia, quàm breuiora. </s>
          <s id="N16C33">Quapropter ſi to<lb></lb>ta ferè longitudo ligni ſuper humerum geſtati, à tergo po<lb></lb>natur, parte tantum ante relicta qua manu ſuſtineatur, cre<lb></lb>ſcit cum ipſa longitudine flexibilitas: vnde magis agitatio<lb></lb>ne ipſa portantis fluctuando vibratur: vibratio autem non <lb></lb>parum geſtationem impedit, retrahendo quodammodo la<lb></lb>tionem, dum frequentiſſimo motu ſurſum, ac deorſum vi<lb></lb>brati ligni extremitas tendit, <expan abbr="proindeq.">proindeque</expan> non ad partes ante<lb></lb>riores, iuxta motum progreſſiuum ferentis. </s>
          <s id="N16C4A">De quo vibra<lb></lb>tionis effectu iterum redibit ſermo quæſtione ſequenti vbi <lb></lb>fuſiùs, ac luculentiùs declarabitur. </s>
          <s id="N16C51">Interim concluditur ex <lb></lb>Ariſtotele, propter maiorem huiuſmodi fluctuationem, ac <lb></lb>vibrationem difficilius procera ligna ab extremo ſuper hu<lb></lb>merum geſtari, quàm ſi è medio ſuſtinerentur, atque aſpor<lb></lb>tarentur, cum hoc pacto, minus ab humero, seu fulcimen<lb></lb>to producta, minus vibrationi eſſent obnoxia. </s>
        </p>
        <p id="N16C5E" type="main">
          <s id="N16C60">Quoniam verò cauſa hæc vniuerſalis non eſt, nec adæ<lb></lb>quata, ſiquidem nec omnia ligna quantumuis procera fle<lb></lb>xibilia ſunt, aut vibrari poſſunt; nec difficultas geſtationis <lb></lb>à ſola vibratione <expan abbr="intercedẽte">intercedente</expan> procedit; hinc eſt, quod Ariſto<lb></lb>teles alteram propoſitæ difficultatis cauſam, tanquam vni<lb></lb>uerſaliorem in medium afferat. </s>
          <s id="N16C71">Ea autem eſt, quia quæ<lb></lb>cumque difficilius eleuantur, difficilius pariter poſtquam <lb></lb>eleuata fuerint ſuſtinentur, aut geſtantur, cum tàm latio, <lb></lb>quàm ſuſtentatio ſit veluti continuata quædam eleuatio ob <pb pagenum="230" xlink:href="005/01/238.jpg"></pb>longa autem ligna difficilius ab extremo eleuantur, quam <lb></lb>ex medio, ſiquidem eleuato ligno ab eius medio ſemper <lb></lb>ſeſe inuicem ſuſtentant extrema, &amp; altera pars alteram ſub<lb></lb>leuat, ait ipſe Philoſophus. </s>
          <s id="N16C87">Medium enim quaſi centrum <lb></lb>conſtituitur, quod fulcitur in manu eleuantis, aut in humero <lb></lb>deferentis. </s>
          <s id="N16C8E">Quapropter ad depreſsionem alterius extremi, <lb></lb>alterum eleuatur, &amp; ſic viciſsim mutuo ſuſtolluntur. </s>
          <s id="N16C93">At ſi <lb></lb>ab extremo idem lignum eleuetur, vel deferatur, vniuerſo <lb></lb>pondere deorſum vergente, nulla eſſet pars, quæ ad graui<lb></lb>tationem alterius eleuatetur, proindeque laborioſa magis <lb></lb>eſſet geſtatio. </s>
        </p>
        <p id="N16C9E" type="main">
          <s id="N16CA0">Verùm contra huiuſmodi diſcurſum, ac doctrinam Ari<lb></lb>ſtotelis illud obijci poſſet, quod tametſi extrema proceri <lb></lb>ligni è puncto medio delati ſeſe inuicem ſuſtollant vtrum <lb></lb>libet alterum ſuperando: nihilominus ipſa ſimul ſumpta <lb></lb>cum toto ligno ſemper eodem modo grauitant reſpectu <lb></lb>deferentis, ſiue in ęquilibrio, ſiue ſecus conſtituantur. </s>
          <s id="N16CAD">Quan<lb></lb>doquidem deferens tam excedens, quàm exceſſum ſuſti<lb></lb>net, ac defert: <expan abbr="proindeq">proindeque</expan> pondus ipſius ligni, non minus gra<lb></lb>uitare concluditur cum lignum ipſum è medio ſuſtollitur, ac <lb></lb>cum ab extremo. </s>
        </p>
        <p id="N16CB8" type="main">
          <s id="N16CBA">Huic tamen obiectioni occurritur diſtinguendo grauita<lb></lb>tionem procedentem ab ipſo pondere ligni delati ſecun<lb></lb>dum ſe ſumpto ab ea, quæ procedit ratione diſtantiæ à ful<lb></lb>cimento quò ſuſtinetur. </s>
          <s id="N16CC3">Nulli namque dubium eſt grauita<lb></lb>tionem procedentem à naturali pondere ipſius ligni, ean<lb></lb>dem ſemper eſſe, ſiue lignum ex medio, ſiue ab extremo ſu<lb></lb>ſtollatur. </s>
          <s id="N16CCC">Nihilque conducere poſitionem extremorum in <lb></lb>æquilibrio ad diminutionem ponderis naturalis. </s>
          <s id="N16CD1">Vnde non <lb></lb>minus grauitat lignum ſi è medio ſuſpendatur tanquam iu<lb></lb>gum alicuius libræ, ac ſi ab extremo perpendiculariter ad <lb></lb>horizontem erectum ſuſtineatur. </s>
          <s id="N16CDA">At loquendo de grauita<lb></lb>tione, quæ procedit ex diſtantia grauitatis a fulcimento prę<lb></lb>dicto, non ita res ſe habet. </s>
          <s id="N16CE1">Quandoquidem hæc augetur ad <lb></lb>augmentum diſtantiæ, ac minuitur per approximationem; <lb></lb>imò omninò deperditur per <expan abbr="æquilibrationẽ">æquilibrationem</expan>. </s>
          <s id="N16CEC">Porrò brachia <pb pagenum="231" xlink:href="005/01/239.jpg"></pb>libræ, ſiue magis ſiue minus protendantur, dummodo ęqua<lb></lb>lia inter ſe ſint, nihil ponderis, aut grauitationis augent, vel <lb></lb>minuunt; ſecus autem ſi alterum ſit protentius, licet æqualis <lb></lb>ponderis naturalis. </s>
          <s id="N16CFA">Nam libram vertet per exceſſum ſuæ <lb></lb>diſtantiæ à fulcimento, vt ſupra quæſt. </s>
          <s id="N16CFF">prima explicauimus. </s>
        </p>
        <p id="N16D02" type="main">
          <s id="N16D04">Rectè igitur argumentatur Philoſophus, dum ex mutua <lb></lb>victoria, ac ſubleuatione extremorum ligni in medio fulti, <lb></lb>minorem difficultatem, ſeu grauitationem infert, quàm ſi <lb></lb>ab extremo ſuſtolleretur, ac in ſitu ſimili ſuſtentaretur per <lb></lb>lineam horizonti paralellam, ſeu quaſi paralellam. </s>
          <s id="N16D0F">Etenim <lb></lb>in hac ſituatione lignum grauitaret tum iuxta pondus natu<lb></lb>rale, tum etiam iuxta diſtantiam alterius extremi à fulci<lb></lb>mento; in illa verò non niſi iuxta grauitatem naturalem. <lb></lb></s>
          <s id="N16D19">Quo ſit vt ſariſſa, aut lancea perpendiculariter ad planum <lb></lb>horizontis erecta, facilè ab extremo ſuſtineatur, difficilè <lb></lb>verò per lineam horizonti paralellam conſtituta. </s>
          <s id="N16D20">Vnde ad <lb></lb>facilius, præſtandum manubrium in lancea non quidem in <lb></lb>ipſo extremo, ſed prope extremum conſtituitur, nec non <lb></lb>extremum ipſum craſsius, grauiuſque propterea efficitur <lb></lb>ad compenſandam grauitatem ortam ex longitudine, qua <lb></lb>illa cuſpidem verſus protenditur. </s>
          <s id="N16D2D">Imò ex hoc etiam ipſa <lb></lb>productior pars lanceæ cum primò craſſeſcit, ſtriari conſue<lb></lb>uit vſque ad manubrium, vt ipſis excauata ſtrijs, vel ſulcis, <lb></lb>leuior euadat, &amp; ad planum horizontis vergens, facilius va<lb></lb>leat manu geſtari. </s>
          <s id="N16D38">Hinc pariter qui viribus pollent ad oſten<lb></lb>tandum robur brachij, atque lacerti, dum ad confrin<lb></lb>gendam lanceam in deſtinatum locum procur<lb></lb>runt, ab extremo ſubtus manubrium eam <lb></lb>procumbentem in ipſo curſu ſuſten<lb></lb>tant. </s>
          <s id="N16D45">Quæ omnia ſatis con<lb></lb>firmantur ex di<lb></lb>ctis <expan abbr="q.">que</expan> 3. ac <lb></lb>16. </s>
        </p>
        <pb pagenum="232" xlink:href="005/01/240.jpg"></pb>
        <p id="N16D56" type="head">
          <s id="N16D58">Quæſtio Vigeſimaſeptima.</s>
        </p>
        <p id="N16D5B" type="main">
          <s id="N16D5D">C<emph type="italics"></emph>vr ſi valde procerum fuerit idem pondus, dif<lb></lb>ficilius ſuper humeros gestatur, etiamſi me<lb></lb>dium quiſpiam illud ferat, quàm ſi breuius <lb></lb>ſit? </s>
          <s id="N16D69">Quod enim dudum dictum eſt, cauſa non <lb></lb>eſt, ſed vibratio nunc est cauſa. </s>
          <s id="N16D6E">Quando enim <lb></lb>productius fuerit, vibrantur extrema, quam<lb></lb>obrem contingit portantem difficilius geſtare. </s>
          <s id="N16D75">Vibrationis au<lb></lb>tem cauſa eſt, quoniam ab eadem motione magis transferuntur <lb></lb>extrema; quanto procerius fuerit lignum. </s>
          <s id="N16D7E">Humerus quidem <lb></lb>ſit centrum vbi A manet enim is; ipſæ autem A B, A C, quæ <lb></lb>ſunt ex centro, quantò autem maius fuerit id, quod ex centro <lb></lb>eſt, ſiuè A B, ſeu A C, plus transfertur ſpatij. </s>
          <s id="N16D87">Demonſtratum <lb></lb>autem eſt hoc prius.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N16D8E" type="head">
          <s id="N16D90">COMMENTARIVS.</s>
        </p>
        <p id="N16D94" type="main">
          <s id="N16D96">Qvamuis idemmet lignum, vel aliud graue corpus <lb></lb>oblongum facilius ex medio ſuſtineatur, ac defera<lb></lb>tur, quam ab extremo, vt in præcedenti quæſt. </s>
          <s id="N16D9D">di<lb></lb>ctum eſt: nihilominus cum hoc etiam pacto delatum, quò <lb></lb>procerius illud fuerit, eò difficilius geſtetur, quærit hic Ari<lb></lb>ſtoteles vnde maior hæc difficultas oriatur. </s>
          <s id="N16DA6">Concluditque, <lb></lb>vibrationem huius rei cauſam eſſe. </s>
          <s id="N16DAB">Nam quanto produ<lb></lb>ctius fuerit lignum, tantò imbecillius redditur, ac vibrationi <lb></lb>obnoxius: magis enim inflectitur, vt quæſt. </s>
          <s id="N16DB2">16. probatum <lb></lb>eſt magiſque eius extrema iactantur tanquam à centro re<lb></lb>motiora. </s>
          <s id="N16DB9">Magis autem iactatis, ac vibratis extremis, diffi<lb></lb>cilior euadit geſtatio; Idque duplici ex capite, vt rectè Bal<lb></lb>dus obſeruat. </s>
          <s id="N16DC0">Tum ſcilicet quia motus vibrationis, vt præ<lb></lb>cedenti quæſt. </s>
          <s id="N16DC5">docuerat Ariſtoteles, morum progreſsionis, <lb></lb>ſurſum ac deorſum tendendo impedit, ac quodammodo <lb></lb>prohibet, retrahendo ipſum delatum, quod in anteriora fer<lb></lb>tur: tum etiam quia impetum quendam producit quo vltra <pb pagenum="233" xlink:href="005/01/241.jpg"></pb><expan abbr="põdus">pondus</expan> grauatus humerus <expan abbr="deferẽtis">deferentis</expan>. </s>
          <s id="N16DDA">Etenim extrema ipſius <lb></lb>ligni valde ab eius medio, ſeu centro remota, dum inferius, <lb></lb>quantum ex ſe eſt, vibrando flectuntur ipſummet centrum, <lb></lb>ſeu medium ſecum rapere, ac detrahere conantur. </s>
          <s id="N16DE3">Quam<lb></lb>obrem humerus, qui medio ſupponitur, non modo totius li<lb></lb>gni ſuſtinet pondus, quod in ipſo grauitatis centro coacer<lb></lb>uatur, ſed impetum quoque per eandem extremorum in<lb></lb>flexionem ei illatum. </s>
          <s id="N16DEE">Tametſi hoc totum intelligatur non <lb></lb>iugiter, ſed per interualla tantum contingere, vt idem Bal<lb></lb>dus animaduertit; Quandoquidem impetus ex ipſo motu <lb></lb>vibrationis acquiſitus quemadmodum deorſum tendendo <lb></lb>deprimit, ita ſurſum attollens ipſa extrema, portantem alle<lb></lb>uiat, humerumque aliquantiſper nonnihil exonerat, vt milites <lb></lb>ſariſſam in humero geſtantes paſsim experiuntur. </s>
        </p>
        <p id="N16DFD" type="head">
          <s id="N16DFF">Quæſtio Vigeſimaoctaua.</s>
        </p>
        <p id="N16E02" type="main">
          <s id="N16E04">C<emph type="italics"></emph>vr iuxta puteos celonia faciunt eo, quo <lb></lb>viſuntur modo? </s>
          <s id="N16E0C">Ligno enim plumbi adiun<lb></lb>gunt pondus, cùm alioqui vas ipſum &amp; ple<lb></lb>num, &amp; vacuum pondus habeat. </s>
          <s id="N16E13">An quo<lb></lb>niam duobus temporibus hauriendi diuiſo ope<lb></lb>re (intingere enim oportet, &amp; id ſurſum <lb></lb>trahere) continget demittere quidem vacuum faciliter, <lb></lb>trahere verò plenum difficulter. </s>
          <s id="N16E1E">Commodum igitur est pau<lb></lb>lò tardius illud demittere, cùm multò leuiùs effectum ſuſtol<lb></lb>latur pondus: id autem facit in extremo celonio adiunctum: <lb></lb>plumbum, aut lapis. </s>
          <s id="N16E27">Demittendi quidem maius ſit pon<lb></lb>dus, quàm ſi ſolummodò vacuum oporteret demittere: <lb></lb>cùm verò plenum fuerit ſurſum id rapii plumbum, aut quic<lb></lb>quid illi ponderis inerit. </s>
          <s id="N16E30">Quamobrem faciliora hoc modo <lb></lb>ambo ſunt, quàm illo.<emph.end type="italics"></emph.end></s>
        </p>
        <pb pagenum="234" xlink:href="005/01/242.jpg"></pb>
        <p id="N16E3B" type="head">
          <s id="N16E3D">COMMENTARIVS.</s>
        </p>
        <p id="N16E41" type="main">
          <s id="N16E43">Celonium quod &amp; Tellenon apud Latinos appella<lb></lb>tur, machina quædam eſt ad commodius haurien<lb></lb>dam aquam ex puteis, vt frequenter viſitur in hor<lb></lb>tis. </s>
          <s id="N16E4C">Conſtat autem ex tigno quodam prægrandi, quod iux<lb></lb>ta puteos erigitur, ac validè obfirmatur, &amp; ex tranſuerſario <lb></lb>quodam alio ligno tenuiori, quod ſuperiori parti illius tan<lb></lb>quam furculæ per ſui quaſi medium incumbens, in altero <lb></lb>extremo funem habet appenſum <expan abbr="cũ">cum</expan> aquario vaſe; in altero <lb></lb>verò, appoſito pondere prægrauatur, vt ſurſum, ac deorſum <lb></lb>facili negocio pro olitoris arbitrio valeat commoueri. </s>
          <s id="N16E5F">Vſus <lb></lb><expan abbr="namq;">namque</expan> huius machinæ eſt, vt manu funis <expan abbr="apprehẽſus">apprehenſus</expan> vnà <expan abbr="cũ">cum</expan> <lb></lb>vaſe, quod ſuſtinet, in puteum demittatur quouſque vas in <lb></lb><expan abbr="aquã">aquam</expan> immergatur, reclinato ſcilicet ligni extremo cui funis <lb></lb>alligatur. </s>
          <s id="N16E78">Deinde puſilla vi adhibita ob <expan abbr="præponderantiã">præponderantiam</expan> al<lb></lb>terius extremi, quod onere preſſum deſcendit, ac <expan abbr="alterũ">alterum</expan> co<lb></lb>git aſcendere, ipſummet vas aqua plenum ſuſtollatur, &amp; ex<lb></lb>trahatur. </s>
          <s id="N16E89">Quamuis enim vas ipſum aqua <expan abbr="repletũ">repletum</expan>, <expan abbr="deſcriptoq.">deſcriptoque</expan> <lb></lb>ab extremo propendens ex ſe æquiponderare ſoleat oneri, <lb></lb>quod alteri extremo adiungitur, vix tamen vel modicè ma<lb></lb>nu adiuuante eleuatum ſtatim ab onere prædicto vincitur, <lb></lb>ac ſuperatur: non ſecus ac lanx libræ in æquilibrio conſtitu<lb></lb>tæ ab æquali pondere alterius lancis, ſi vel tenuiter manu <lb></lb>aliqua ſuſtollatur. </s>
        </p>
        <p id="N16EA0" type="main">
          <s id="N16EA2">His itaque non aliter ſe habentibus, quærit hic Ariſtote<lb></lb>les, cur ad huiuſmodi machinam facilius promouendam, &amp; <lb></lb>&amp; aquam eius motione exhauriendam, onus oneri adiunga<lb></lb>tur, plumbum nimirum, aut lapidem apponendo in alte<lb></lb>ro extremo tranſuerſarij ligni, cum alioquin tota ipſa ma<lb></lb>china ſit per ſe grauis, ac præſertim idemmet tranſuer<lb></lb>ſarium lignum, quod adhuc prægrauatur pondere vaſis ap<lb></lb>penſi, ſiue vacui, ſiue repleti. </s>
          <s id="N16EB3">Difficilius namque eſt mo<lb></lb>uere machinam grauiorem, quàm leuiorem. </s>
          <s id="N16EB8">Quamob<lb></lb>rem ſit in deſcripta Tellenonis figura A B C D tignum <pb pagenum="235" xlink:href="005/01/243.jpg"></pb>arrectarium ſuper <lb></lb><figure id="id.005.01.243.1.jpg" xlink:href="005/01/243/1.jpg"></figure><lb></lb>planum <expan abbr="erectũ">erectum</expan> AB: <lb></lb>tranſuerſarium ve<lb></lb>rò CD; ac funis <lb></lb>propendens DE, <lb></lb>in cuius ima extre<lb></lb>mitate vbi E, alli<lb></lb>gata ſit vrna, vel ſi<lb></lb>tula, aut ſimile <lb></lb>aliud vas <expan abbr="aquariũ">aquarium</expan>: <lb></lb><expan abbr="Puteusq.">Puteusque</expan> ſubiectus, <lb></lb>ſit vbi F. </s>
          <s id="N16EEA">Tunc in<lb></lb>quam ſi in extremo <lb></lb>C tranſuerſarij li<lb></lb>gni adiungatur <expan abbr="põ-dus">pon<lb></lb>dus</expan> lapidis, aut <expan abbr="plũ-bi">plum<lb></lb>bi</expan>, vt in figura refertur, manus funi admota ad demittendum <lb></lb>vas aquarium, difficilius deprimet extremum D, vnde fu<lb></lb>nis ipſe propendet, cum vltra propriam grauitatem ligni <lb></lb>AC, ſuperare, ac eleuare etiam debeat pondus illi adiun<lb></lb>ctum. </s>
          <s id="N16F07">Quare ex huiuſmodi ponderis additione, potius vi<lb></lb>detur, motionem ipſam explicatæ machinæ retardari, quàm <lb></lb>facilius conſequi, &amp; expediri. </s>
        </p>
        <p id="N16F0E" type="main">
          <s id="N16F10">Nihilominus reſpondet idem Philoſophus, omnemque <lb></lb>dubitandi rationem exterminat, quoniam hauriendi opus <lb></lb>duobus diſtributum temporibus perficitur. </s>
          <s id="N16F17">Primo nimirum <lb></lb>vas demittendo vacuum, vt aquæ immergatur: deinde il<lb></lb>lud extrahendo plenum. </s>
          <s id="N16F1E">Nullo autem addito pondere <lb></lb>in extremo C, facilius quidem vas vacuum demittendum <lb></lb>fore, quia nihil obſtaret; difficilius tamen extrahi poſſet, <lb></lb>quia pondus aquæ, magnopere aſcenſui repugnaret, nec ha<lb></lb>beret à quo ſuſtolleretur ſimul cum parte tranſuerſarij li<lb></lb>gni AD, quæ tanquam productior, ac prægrauata ponde<lb></lb>re vaſis pleni, vinci non poſſet à parte eiuſdem ligni AC, <lb></lb>breuiori, ac omni exonerata pondere. </s>
          <s id="N16F2F">Quoniam verò ma<lb></lb>gis expedit, vt tardius ac difficilius vas demittatur, dum-<pb pagenum="236" xlink:href="005/01/244.jpg"></pb>modò facilius extrahatur; plumbum vel ſimile aliud onus <lb></lb>ſuperimponitur ipſi extremo C, vt eo depreſſo, eleuetur <lb></lb>alterum extremum D, per conuerſionem ipſius ligni CD, <lb></lb>tanquam vectis ſuper fulcimentum A; &amp; ad eleuationem <lb></lb>ipſius extremi D, vas ex eo pendens, pariter euehatur, &amp; è <lb></lb>puteo extrahatur. </s>
          <s id="N16F43">Expedit autem facilitas potius in vaſis <lb></lb>extractione, quàm in demiſſione; <expan abbr="idq.">idque</expan> tam ex parte poten<lb></lb>tiæ, quàm ex parte ponderis. </s>
          <s id="N16F4E">Ex parte quidem potentiæ, <lb></lb>quia laborioſus eſt cum difficultate extrahere, quàm cum <lb></lb>difficultate demittere. </s>
          <s id="N16F55">Nam corpus humanum dum ex<lb></lb>trahendo inclinatur, ſuo præpeditur pondere, ne expeditiùs <lb></lb>erigatur, <expan abbr="funemq.">funemque</expan> paulatim reducat, &amp; per eam vas ipſum <lb></lb>ſubleuet. </s>
          <s id="N16F62">Contra verò dum ad vas demittendum, &amp; immer<lb></lb>gendum, funis cum ligni extremo D trahitur deorſum, illi <lb></lb>naturali quodam nutu incumbit, commodiuſque vires <lb></lb>exerit, ac difficultatem omnem euincit; vt experiri etiam eſt <lb></lb>in vſu trachleæ ad exhauriendam aquam, vel ſuſtollendum <lb></lb>quodlibet aliud pondus per funis detractionem. </s>
          <s id="N16F6F">Deinde <lb></lb>ex parte ponderis, quia minor eſt difficultas demiſsionis, <lb></lb>quàm extractionis prædictæ. </s>
          <s id="N16F76">Siquidem pondus lapidis, aut <lb></lb>plumbi, quod ſuperari debet in vaſis miſsione, æquale eſt <lb></lb>ponderi ſolius aquæ hauriendæ ipſo eodem vaſe, vt dictum <lb></lb>eſt: pondus autem quod ſuperandum eſt in extractione, <lb></lb>non ſolum eſt pondus aquæ hauriendæ, ſed etiam <lb></lb>vaſis, ac funis, ideoque maius conſtituitur, <lb></lb>ac difficilius ſuperatur. </s>
          <s id="N16F85">Conſultius ergo <lb></lb>eſt, maiori difficultati ſuccur<lb></lb>rere ipſo machinæ bene<lb></lb>ficio, ac ponde<lb></lb>re adie<lb></lb>cto <lb></lb>in altero extremo, vt <lb></lb>aiebat Philoſo<lb></lb>phus. </s>
        </p>
        <pb pagenum="237" xlink:href="005/01/245.jpg"></pb>
        <p id="N16F9C" type="head">
          <s id="N16F9E">Quæſtio Vigeſimanona.</s>
        </p>
        <p id="N16FA1" type="main">
          <s id="N16FA3">C<emph type="italics"></emph>vr quando ſuper ligno, aut huiuſmodi quo<lb></lb>piam duo portauerint homines æquale pondus <lb></lb>non ſimiliter præmuntur, ſi ad vnum non de<lb></lb>clinet pondus, ſed magis quanti vicinius fue<lb></lb>rit gestantibus? </s>
          <s id="N16FB1">An quoniam vectis quidem <lb></lb>lignum efficitur: pondus verò hypomochlion: <lb></lb>qui autem propior eſt ponderi ex ijs, qui illud geſtant, id qua<lb></lb>re mouetur: alter vero portantium, quod mouet? </s>
          <s id="N16FBA">Quantò igitur <lb></lb>plus diſtat à pondere, tanto facilius mouet, &amp; alterum premit <lb></lb>magis inferius, velut contra nitente pondere impoſito quod hy<lb></lb>pomochlion factum eſt, ſi autem in medio inerit pondus, nihilo <lb></lb>magis alter alteri fit pondus, aut mouet: ſed eodem modo alteri <lb></lb>alter fit pondus.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N16FC9" type="head">
          <s id="N16FCB">COMMENTARIVS.</s>
        </p>
        <p id="N16FCF" type="main">
          <s id="N16FD1">Cauſam hic inquirit Ariſtoteles cur duo baiuli idem <lb></lb>pondus ſuper lignum, vel quidpiam aliud ſimile fe<lb></lb>rentes, <expan abbr="nõ">non</expan> æquè grauentur, atque <expan abbr="pręmãtur">pręmantur</expan> ſi in <expan abbr="eo-rũ">eo<lb></lb>rum</expan> medio <expan abbr="nõ">non</expan> extiterit ipſum pondus, ſed magis præmatur is, <lb></lb>cui ipſum proximius conſtituitur. </s>
          <s id="N16FEC"><expan abbr="Eamq.">Eamque</expan> mox eſſe ait, quo<lb></lb>niam huiuſmodi lignum in ipſa aſportatione efficitur vectis, <lb></lb>cuius fulcimentum conſtituitur ipſummet pondus quod ge<lb></lb>ſtatur: Onus verò baiulus, qui ponderi eſt propinquior, ac <lb></lb>veluti potentia mouens, baiulus, qui eſt ab illo remotior. <lb></lb></s>
          <s id="N16FFB">Etenim cum onus quodlibet, vecte adhibito, tanto facilius <lb></lb>moueatur, quanto proximius fuerit centro, ſeu fulcimen<lb></lb>to locatum, ac motrix potentia remotius fuerit applicata, <lb></lb>vt ſupra oſtenſum eſt quæſt. </s>
          <s id="N17004">3. hinc fit, vt baiulus, qui one<lb></lb>ris loco ſuccedit, hoc ipſo, quod propinquius centro con<lb></lb>ſtituitur, quàm alter qui potentiæ vices obtinet, magis <lb></lb>præmatur, contra nitente pondere impoſito, tanquam fulci<lb></lb>mento validè obfirmato, cui vectis innititur in ipſo motu. <pb pagenum="238" xlink:href="005/01/246.jpg"></pb><figure id="id.005.01.246.1.jpg" xlink:href="005/01/246/1.jpg"></figure><lb></lb>Quod vt præ ocu<lb></lb>lis habeatur eſto <lb></lb>lignum AB, pon<lb></lb>dus C appenſum <lb></lb>in D proximius <lb></lb>ipſi A; baiulorum <lb></lb>verò alter hume<lb></lb>rum, vel manum <lb></lb>ſupponat in A; al<lb></lb>ter in B. </s>
          <s id="N1702E">Dicimus ergo cum Ariſtotele, lignum ipſum AB, <lb></lb>vectem conſtitui ſuffultum in D, tanquam fulcimento in<lb></lb>uerſo ad deprimendum humerum aſportantis in A, per mo<lb></lb>tum aſportantis in B, qui baiulando, ſemper eleuare cona<lb></lb>tur extremitatem ſibi incumbentem in B. </s>
          <s id="N17039">Quandoquidem <lb></lb>punctum D, quod conſtituitur centrum in motione ipſius <lb></lb>vectis, ita à pendente pondere præmitur, &amp; figitur, ac ſi im<lb></lb>mobile omnino eſſet ad fulciendum ipſum vectem. </s>
          <s id="N17042">Quod <lb></lb>euidentius fiet ſi eundem vectem inuerſo modo conſidere<lb></lb><figure id="id.005.01.246.2.jpg" xlink:href="005/01/246/2.jpg"></figure><lb></lb>mus, in ſequenti fi<lb></lb>gura; Nimirum vt <lb></lb>ſi vectis A B ſu<lb></lb>ſpendatur in C ex <lb></lb>puncto intermedio <lb></lb>vbi D, ad eleuan<lb></lb>dum onus impo<lb></lb>ſitum in extremo A <lb></lb>per depreſsionem alterius extremi B. </s>
          <s id="N1705F">His namque po<lb></lb>ſitis ad primam figuram redeuntes facilè intelligitur cur <lb></lb>baiulus geſtans in A magis grauetur à pondere C, <lb></lb>quàm geſtans in B. </s>
          <s id="N17068">Quanto enim longior eſt pars vectis <lb></lb>DB, ipſa DA, eo facilius geſtans in B eleuat, vel ſuſti<lb></lb>net ipſum extremum B reſpectu ſuſtinentis in A tanquam <lb></lb>in loco centro vectis propinquiori quàm ſit ipſum B. </s>
        </p>
        <p id="N17071" type="main">
          <s id="N17073">Quod autem cum Ariſtotele explicuimus per rationem <lb></lb>vnius vectis, Piccolomineus explicat per rationem duplicis <pb pagenum="239" xlink:href="005/01/247.jpg"></pb>vectis, ita vt idem lignum AB rationem ſubeat vtriuſque <lb></lb>vectis, vnius nempe per quem geſtans in A prematur ad <lb></lb>motum geſtantis in B: alterius verò per quem geſtans in <lb></lb>B, prematur ad motum geſtantis in A, eodem ſemper exi<lb></lb>ſtente fulcimento D. </s>
          <s id="N17086">Siquidem ambo geſtantes eleuare <lb></lb>conantur ſua extrema, &amp; ambo deprimuntur adinuicem, <lb></lb>ita vt alter alteri conſtituatur onus, ac mouens potentia; li<lb></lb>cet ille magis moueat, minuſque grauetur, qui longius diſtat <lb></lb>à fulcimento. </s>
          <s id="N17091">Quæ profectò explicatio à mente Ariſtotelise <lb></lb>tradita doctrina non abhorret, imò maximè congruit cum <lb></lb>eo, quod ipſemet Philoſophus tandem adiecit: Nimirum <lb></lb>quòd ſi pondus in medio vectis conſtitueretur, non magis <lb></lb>vnus, quam alter baiulus grauaretur; atque moueret; ſed <lb></lb>eodem pacto alter alteri eſſet onus, &amp; potentia. </s>
        </p>
        <p id="N1709E" type="main">
          <s id="N170A0">Baldus verò eandem Piccolominei expoſitionem appro<lb></lb>bando doctrinam Ariſtotelis à qua illa deſumpta eſt, &amp; cui <lb></lb>omnino congruit, reprobat, rationem fulcimenti in ipſo <lb></lb>pondere conſideratam, <expan abbr="figmentũ">figmentum</expan> vocans Ariſtotelis. </s>
          <s id="N170AE">Qua<lb></lb>propter geſtatum pondus, ait verè eſſe pondus, lignum ve<lb></lb>rò vectem, ac duos qui pondus ſuſtinent in ipſius ligni ex<lb></lb>tremi pro duplici fulcimento haberi. </s>
          <s id="N170B7">Non tamen apparet <lb></lb>quo fundamento lignum prædictum, vectis dici poſſit, ſi <lb></lb>duobus fulcimentis ponatur innixum; cum tota ratio vectis <lb></lb>ad libram, ac circulum referatur, quibus non niſi vnum eſſe <lb></lb>poteſt centrum ac fulcimentum circa quod conuertantur. <lb></lb></s>
          <s id="N170C3">Rectè autem ſubiungit poſſe alterum eorum, ſcilicet aſpor<lb></lb>tantium pro potentia mouente, alterum pro fulcimento ha<lb></lb>beri, &amp; ſic viciſsim, ita vt pondus ſit inter <expan abbr="fulcimentũ">fulcimentum</expan>, &amp; po<lb></lb>tentiam. </s>
          <s id="N170D0">Nam hoc pacto præfatum lignum conſtitueretur <lb></lb>vectis eius generis, quod fulturam habet in altero extremo, <lb></lb>vt 1. par. </s>
          <s id="N170D7">tex. vltimo, Addit. </s>
          <s id="N170DC">1. explicuimus. </s>
          <s id="N170DF">Nihil enim pro<lb></lb>hibet idem lignum ſecundum diuerſas conſiderationes <lb></lb>adhuc in diuerſo genere vectis conſtitui. </s>
        </p>
        <p id="N170E6" type="main">
          <s id="N170E8">Ad hæc idem Baldus affines quaſdam huic dubitationes, <lb></lb><expan abbr="eanumq.">eanumque</expan> ſolutiones ſubnectit, quarum illa præcipuè ad rem <lb></lb>facit; Num ſcilicet pondere in vectis medio conſtituto, <pb pagenum="240" xlink:href="005/01/248.jpg"></pb>idem prorſus contingat ſi alterum eorum, qui ſuſtinent ſit <lb></lb>ſtatura procerior, alter verò humilior: Vel ſi ſtatura quidem <lb></lb>pares fueritne, per viam tamen accliuem, aut decliuem ince<lb></lb>dant. </s>
          <s id="N170FD">Etenim ſi pondus liberè pendeat optimè reſpondet, <lb></lb>idem omnino contingere, quia ſemper eadem ſeruaretur <lb></lb>æqualitas partium vectis, ac diſtantia baiulorum à loco vbi <lb></lb>pondus deprimeret, vt clarè ipſe demonſtrat: Si autem <lb></lb>pondus nequaquam liberè pendeat, ſed firmiter ſit infra <lb></lb>vectem alligatum, tunc magis grauari eum, qui extremum <lb></lb>vectis magis ab horizonte eleuatum ſuſtinet. </s>
          <s id="N1710C">Quando qui<lb></lb>dem pondus grauitat in parte vectis propinquiori ipſi ex<lb></lb>tremo magis eleuato, quamuis in medio ſit conſtiturum. <lb></lb></s>
          <s id="N17114">Cuius oppoſitum contingeret ſi pondus ſupra vectem, li<lb></lb>cet pariter in medio collocaretur, quod non tetigit Baldus, <lb></lb>&amp; vtrumque facilè erit ſimul probare. </s>
        </p>
        <figure id="id.005.01.248.1.jpg" xlink:href="005/01/248/1.jpg"></figure>
        <p id="N17120" type="main">
          <s id="N17122">Eſto enim vectis AB bifariam diuiſa in C; cuius extre<lb></lb>mum B ſit magis eleuatum ab horizonte, quàm extremum <lb></lb>A: Pondus verò infra poſitum ſit corpus DE, cuius graui<lb></lb>tatis centrum F ad angulos rectos per lineam CF propen-<pb pagenum="241" xlink:href="005/01/249.jpg"></pb>dens ex AB: geſtantes itidem ſint AG, &amp; BH, ſtatura <lb></lb>quidem pares, ſed per accliue GH aſcendentes. </s>
          <s id="N17132">Demitta<lb></lb>tur autem perpendicularis ad planum horizontis per ipſum <lb></lb>centrum grauitatis F, quæ ſit linea IFK ſecans in I ipſam <lb></lb>AB. </s>
          <s id="N1713C">Grauitabit igitur centrum F in ipſo puncto I, in <lb></lb><expan abbr="eoq.">eoque</expan> vices fulcimenti exercebit, vt explicatum eſt. </s>
          <s id="N17144">At pun<lb></lb>ctum I propinquius eſt ipſi B, quàm ipſi A, cùm ſit inter <lb></lb>C &amp; B; <expan abbr="proindeq.">proindeque</expan> pars AI ſit pluſquam dimidium vectis <lb></lb>IB verò minus. </s>
          <s id="N17151">Ergo geſtans in B, magis grauabitur, quàm <lb></lb>qui in A. </s>
          <s id="N17157">Modò ſupponamus idem pondus ſuper eundem <lb></lb>vectem collocari vbi LM; <expan abbr="eiusq.">eiusque</expan> grauitatis centrum in N, à <lb></lb>quo demittatur perpendicularis horizonti NO; <expan abbr="punctumq.">punctumque</expan> <lb></lb>in quo ſecuerit rectam AB, ſignetur P. </s>
          <s id="N17169">His itaque ſic ſta<lb></lb>bilitis, centrum N grauitabit in P; <expan abbr="eritq.">eritque</expan> AP minor quàm <lb></lb>PB, <expan abbr="ideoq.">ideoque</expan> baiulus portans in A, tanquam fulcimento vi<lb></lb>cinior, grauabitur magis, quàm ſuſtinens in ipſo B, ratione <lb></lb>ſuperius explicata. </s>
          <s id="N1717C">Quod exactius demonſtraſſe moleſtum, <lb></lb>ac in utile fore exiſtimauimus. </s>
        </p>
        <p id="N17181" type="head">
          <s id="N17183">Quæſtio Trigeſima.</s>
        </p>
        <p id="N17186" type="main">
          <s id="N17188">C<emph type="italics"></emph>vr ſurgentes omnes femori eius ad acutum <lb></lb>conſtituentes angulum, &amp; thoraci ſimiliter fe<lb></lb>mur ſurgunt? </s>
          <s id="N17192">quod ſi non, haudquaquam ſur<lb></lb>gere poterunt. </s>
          <s id="N17197">An quia id quod æquale eſt, quie<lb></lb>tis <expan abbr="vbiq.">vbique</expan> eſt cauſa: rectus autem angulus æqua<lb></lb>litatis eſt, <expan abbr="ſtationemq.">ſtationemque</expan> facit, quamobrem ad ſi<lb></lb>miles fertur angulos ipſi terræ circumferentiæ, <lb></lb>non enim quod ad rectum est ipſi pauimento. </s>
          <s id="N171AA">An quoniam ſur<lb></lb>gens ſit rectus, ſtantem verò neceſſe eſt perpendiculum eſſe ad <lb></lb>terram. </s>
          <s id="N171B1">Siquidem igitur ad rectum debet eſſe, hoc autem eſt ca<lb></lb>put ſecundum pedes habere, &amp; fieri oportet cum ſurgit. </s>
          <s id="N171B6">Quan<lb></lb>doquidem igitur fuerit ſedens, ſecundum paralellam pedes <lb></lb>habet &amp; caput, &amp; non inæquali. </s>
          <s id="N171BD">Caput ſit A, thorax AB, ſe<lb></lb>mur BC, crura CD. </s>
          <s id="N171C3">Ad rectum autem fit &amp; thorax vbi AB <lb></lb>ipſi femori, &amp; cruri femur, ſic ſedente. </s>
          <s id="N171C8">Quamobrem eo ſe <lb></lb>habentem modo ſurgere est impoſsibile. </s>
          <s id="N171CD">Neceſſe autem est crus <lb></lb><expan abbr="rēelinare">rem elinare</expan>, <expan abbr="pedesq.">pedesque</expan> conſtituere ſub capite, hoc autem erit, ſi<emph.end type="italics"></emph.end><pb pagenum="242" xlink:href="005/01/250.jpg"></pb><emph type="italics"></emph>CD fiet, vbi CF, &amp; ſimul ſurgere continget, &amp; in eadem <lb></lb>æquali habere caput, &amp; pedes, ipſa autem CF acutum facit <lb></lb>angulum ad ipſam BG.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N171E9" type="head">
          <s id="N171EB">COMMENTARIVS.</s>
        </p>
        <p id="N171EF" type="main">
          <s id="N171F1">Svpponit Ariſtoteles, quod ſatis per ſe notum eſt, <lb></lb>commodè, &amp; appoſitè ſedentes duos angulos rectos <lb></lb>poſitione ſui corporis conſtituere iuxta propriam ſe<lb></lb>dis formam: Vnum quippe quem facit thorax cum femore, <lb></lb>alterum verò quem efficit femur cum tibia. </s>
          <s id="N171FC">Vt exempli <lb></lb>gratia ſi linea AB rectitudinem <lb></lb>humani corporis referat à capite <lb></lb><figure id="id.005.01.250.1.jpg" xlink:href="005/01/250/1.jpg"></figure><lb></lb>vſque ad ventrem, BC verò fe<lb></lb>morum longitudinem vſque ad <lb></lb>genua, tanquam duo latera recti <lb></lb>anguli ABC; &amp; CD crucium al<lb></lb>titudinem deſignet, quæ pariter <lb></lb>cum BC alterum angulum re<lb></lb>ctum conſtituat BCD. </s>
          <s id="N17218">Quo ſup<lb></lb>poſito quærit cur ſedentes cum <lb></lb>ſurgere voluerint, in ipſo ſurgendi <lb></lb>actu prædictos angulos rectos in <lb></lb>acutos commutare ſoleant, nec <lb></lb>aliter ſurgere valeant? </s>
          <s id="N17225">Vt ſiſten<lb></lb>do in eadem figura propoſita, ca<lb></lb>put ab A declinando in E ad <lb></lb>efficiendum angulum acutum <lb></lb>EBC, ac tibias retrahendo cum pedibus ex D in F ad con<lb></lb>ſtituendum acutum angulum BCF. </s>
        </p>
        <p id="N17232" type="main">
          <s id="N17234">Cuius rei duplicem cauſam ſtatim ipſemet Philoſophus <lb></lb>affert, <expan abbr="docetq.">docetque</expan> primò id fieri ex eo, quod æqualitas vbique <lb></lb>eſt cauſa quietis. </s>
          <s id="N1723F">Motus enim quilibet, vt alibi dixerat 1. <lb></lb>de generat. </s>
          <s id="N17244">tex. 4 8. debet eſſe ab inæquali proportione. <lb></lb></s>
          <s id="N1724A">Angulus autem rectus, eſt angulus æqualitatis non modò <lb></lb>quia cuilibet alter irecto ſemper eſt æqualis, ſed quia æqui-<pb pagenum="243" xlink:href="005/01/251.jpg"></pb>ponderantiam in corporibus cauſat, vel certè conſequitur, <lb></lb>vt patet in libra, quæ dum in æquilibrio conſtituitur duos <lb></lb>vtrinque efficit angulos rectos cum trutina. </s>
          <s id="N17258"><expan abbr="Itemq.">Itemque</expan> nam <lb></lb>corpora perpendiculariter ad angulos rectos ſuper planum <lb></lb>horizontis conſtituta, dum terræ ſuperficiei incumbunt, <lb></lb>æqualiter omni ex parte diſtant à ſolo, <expan abbr="ſtareq.">ſtareque</expan> propterea <lb></lb>dicuntur, hoc eſt in ſua propria mole conſiſtere. </s>
          <s id="N1726A">Quare cu<lb></lb>bus eo quod non niſi ex rectis angulis conſtet, &amp; vndique <lb></lb>ſit æqualis, maximè omnium corporum valet conſiſtere, at<lb></lb>que ſolo inhæréndo quieſcere: Ita vt Pythagorici ad tuendam <lb></lb>terræ immobilitatem, eam dixerint eſſe cubicam. </s>
          <s id="N17275">Quod <lb></lb>autem dicitur de toto corpore ſtante, idem reſpectiuè dici <lb></lb>poteſt de partibus, quæ ſimiliter ad angulos rectos ſupra <lb></lb>planum horizontis erectæ quieſcunt, vt thorax, vel tibiæ in <lb></lb>homine ſedente. </s>
          <s id="N17280">Cum igitur à ſeſſione ſurgentes, quietem <lb></lb>qua ſedendo ad angulos rectos potiebantur aſſurgendo re<lb></lb>linquant, ipſos angulos rectos in acutos commutare co<lb></lb>guntur, hoc ipſo quod moueantur, &amp; acuti anguli, non au<lb></lb>tem obtuſi ad ipſum ſurrectionis motum ſint idonei, at que <lb></lb>accommodati, vt mox infrà conſtabit. </s>
        </p>
        <p id="N1728D" type="main">
          <s id="N1728F">Secundò igitur id fieri docet Philoſophus, nam qui ſur<lb></lb>git, ad hoc tendit, vt totus conſtituatur erectus, ac perpen<lb></lb>dicularis ſuperficiei terræ ſecundum eandem rectitudinem <lb></lb>vnius lineæ cadentis ad centrum, ſecus ac cum ſederet. <lb></lb></s>
          <s id="N17299">Quantumuis enim tunc caput &amp; thorax, ſicut &amp; crura per<lb></lb>pendiculariter haberet ſupra horizontem erecta, non tamen <lb></lb>femora ſic erant conſtituta, nec crura in eadem erant linea, <lb></lb>ac thorax &amp; caput, ſed in alia paralella. </s>
          <s id="N172A2">Quare vt totus <lb></lb>erigatur, &amp; ſecundum eandem lineam perpendiculariter <lb></lb>horizonti inſiſtat, opus eſt, pedes retrahere, vt dicebamus, <lb></lb>ex D in F, <expan abbr="caputq.">caputque</expan> cum ſubiecto thorace reclinare ex A <lb></lb>in E; quod eſt prædictos angulos rectos in acutos conuerte<lb></lb>re, vt pedibus ſub capite conſtitutis, per eandem perperdi<lb></lb>cularem EF totum corpus erigi poſſit, ac ſtare. </s>
          <s id="N172B5">Alioquia <lb></lb>eandem angulorum rectitudinem ſeruando, non fieret mo<lb></lb>tus; atque rectos angulos in obtuſos commutando, non mo<pb pagenum="244" xlink:href="005/01/252.jpg"></pb>do pedes ſub thorace, vel capite perpendiculariter, vt opus <lb></lb>eſt, conſtituerentur; ſed magis à perpen diculo, in quo con<lb></lb>uenire debent ad erectionem pedes, &amp; caput, diſtarent, vt <lb></lb>per ſe patet. </s>
        </p>
        <p id="N172C7" type="main">
          <s id="N172C9">Cæterum Baldus obijcit Ariſtoteli; ſedentem non ideo <lb></lb>quieſcere quod rectus angulus quietis ſit cauſa, ſed propte<lb></lb>rea quod eius thoracis tum etiam femorum pondus ab ip<lb></lb>ſa ſede ſuſtineatur; crura verò &amp; pedes ideo non laborent, <lb></lb>quod partim ſuſpenſa ſint, partim ipſi ſolo innitantur. </s>
          <s id="N172D4">Sed <lb></lb>hoc nihil contra ipſius Philoſophi doctrinam concludit. <lb></lb></s>
          <s id="N172DA">Non enim dixit Ariſtoteles, ſedentem abſolutè quieſcere <lb></lb>ex eo, quod rectus angulus quietis ſit cauſa, nulla habi<lb></lb>ta ratione fulcimenti, cui ſedens innititur, ſed præſup<lb></lb>poſita ſede, cui ſedens incumbendo ad angulos rectos <lb></lb>quieſcit, ait illum ad hoc vt ſurgat, angulos rectos in <lb></lb>acutos neceſſariò commutare. </s>
          <s id="N172E7">Quando quidem ſeruata re<lb></lb>ctitudine angulorum moueri non poſſet, nec ſe totum ere<lb></lb>ctum conſtituere ſuper planum horizontis per angulos re<lb></lb>ctos. </s>
          <s id="N172F0">Quod ſi rurſus obijciat Baldus, angulos acutos non <lb></lb>eſſe cauſam ſurrectionis, ſed cauſam cauſæ illius, hoc eſt, vt <lb></lb>totum pondus corporis humani, vel centrum grauitatis il<lb></lb>lius ſimul cum pedibus, quibus fulcitur in eadem linea <lb></lb>perpendiculari, vt diximus, collocetur; Nam ex hoc imme<lb></lb>diatè procedit ſurrectio: Hoc inquam nihil, aut pa<lb></lb>rum refert, dummodo concedatur, quod nega<lb></lb>ri non poteſt, rectè ſcilicet Ariſtotelem <lb></lb>quæſtionem ſoluiſſe, dum quærenti <lb></lb>cur ſurgentes, prædictos angu<lb></lb>los acutos thorace, ac fe<lb></lb>more ſimul cum tibia <lb></lb>efficiant, inter <lb></lb>alia reſpon<lb></lb>dit, <lb></lb>vt pedes ſub capite conſtituant <lb></lb>&amp; ſic poſſint aſſur<lb></lb>gere. </s>
        </p>
        <pb pagenum="245" xlink:href="005/01/253.jpg"></pb>
        <p id="N17319" type="head">
          <s id="N1731B">Quæſtio Trigeſimaprima.</s>
        </p>
        <p id="N1731E" type="main">
          <s id="N17320">C<emph type="italics"></emph>vr faciliùs mouetur commotum, quàm ma<lb></lb>nens? </s>
          <s id="N17328">Veluti currus citiùs commotos agitant, <lb></lb>quàm moueri incipientes. </s>
          <s id="N1732D">An quia difficilli<lb></lb>mum est pondus mouere, quod in contrarium <lb></lb>mouetur, aufert enim quiddam ex motoris po<lb></lb>tentia, licet multò ſit velocior, neceſſe namque <lb></lb>eſt tardiorem eſſe impulsionem illius, quod re<lb></lb>pellitur. </s>
          <s id="N1733A">Secundo autem loco ſi quieuerit, reſistit enim ipſum <lb></lb>quieſcens. </s>
          <s id="N1733F">Quod autem mouetur ad id ipſum ad quod impelli<lb></lb>tur, impellenti ſimile facit, ceu ſi quiſpiam mouentis poten<lb></lb>tiam, &amp; celeritatem augeret, quod enim ab illo pateretur, vti<lb></lb>que ipſum facit ex ſe commotum.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1734A" type="head">
          <s id="N1734C">COMMENTARIVS.</s>
        </p>
        <p id="N17350" type="main">
          <s id="N17352">Facilius deinceps moueri corpus, quod iam moueri <lb></lb>cœperit, quàm cum primò ei moueri <expan abbr="cõtingit">contingit</expan>, aper<lb></lb>tiſſima experientia comprobatur in pluribus, ac præ<lb></lb>ſertim in curribus, vt hic ſupponit Ariſtoteles. </s>
          <s id="N17360">Cuius rei <lb></lb>cauſam indagando præmittit, difficillimum eſſe mouere <lb></lb>pondus, quod ex ſe mouetur in contrarium. </s>
          <s id="N17367">Quippe cum <lb></lb>ſemper aliquid minuat de motoris virtute, &amp; efficacitate, <lb></lb>quamuis motor ipſo commoto ſit longè potentior, atque <lb></lb>in agendo velocior. </s>
          <s id="N17370">Neceſſe enim eſt imbecilliorem, ac <lb></lb>tardiorem reddi potentiam eiuſque impulſionem, quæ ab <lb></lb>alio repellitur; nec poteſt potentia, vel conatus motoris, ip<lb></lb>ſa vi in contrarium commoti non repelli. </s>
        </p>
        <p id="N17379" type="main">
          <s id="N1737B">Ex quo tanquam à ſimili argumentando ipſe Philoſo<lb></lb>phus, cauſam propoſiti experimenti ait eſſe, tum reſiſten<lb></lb>tiam corporis quieſcentis quando primo incipit moueri; <lb></lb>tum nutum, quem habet ad vlteriorem motum idem cor<lb></lb>pus poſtquam reperitur in motu. </s>
          <s id="N17386">Cum enim à quiete tran<lb></lb>ſit in motum, &amp; aliquo transfertur, reſiſtit non ſecus, vel <lb></lb>paulò minus, ac ſi ex ſe in contrarium raperetur. </s>
          <s id="N1738D">Ex ſe <pb pagenum="246" xlink:href="005/01/254.jpg"></pb>namque graue quodlibet quieſcendo, corpori cui adiacet <lb></lb>adhæret, ac perpetua quadam preſſione deorſum mundi <lb></lb>centrum iugiter petit. </s>
          <s id="N17399">Quapropter dum aliò transferri con<lb></lb>tigerit, reſiſtit quaſi per contrarium motum. </s>
          <s id="N1739E">Vice autem <lb></lb>verſa cum iam moueri cœperit per impulſum tunc acce<lb></lb>ptum, non modò adhuc refrænatur grauitas, <expan abbr="minuiturq.">minuiturque</expan> ef<lb></lb>fectus preſsionis illius qua tendit deorſum, ſed iam graue <lb></lb>ipſum ad vlteriorem motum progreſsionis reperitur diſpo<lb></lb>ſitum, vt adueniente nouo impetu quaſi duplicato principio <lb></lb>transferatur. </s>
          <s id="N173B1">Imo ipſa quoque grauitas in corpore agita<lb></lb>to ſi ex parte illud tendat deorſum, vt in decliue vrget quo <lb></lb>verſum graue proijcitur, ita vt vis quæ merè deorſum ten<lb></lb>debat, in vim quæ aliò transfert per accidens refundatur. <lb></lb></s>
          <s id="N173BB">Facilius ergo deinceps fertur graue proximè commotum <lb></lb>quàm cum primò quietem relinquit: quia mouetur ad no<lb></lb>uum ipſum impulſum ſimul cum reliquijs impetus prius im<lb></lb>preſsi, quo adhuc grauitas compeſcitur, ac moderatur ne <lb></lb>progreſsioni obſiſtat, ſed potius ad illam <expan abbr="quandoq.">quandoque</expan> per ac<lb></lb>cidens conferat, at que concurrat. </s>
        </p>
        <p id="N173CC" type="main">
          <s id="N173CE">Quod autem dictum eſt de motione, &amp; commotione <lb></lb>violenta idipſum, vel quid ſimile communiter obſeruatur in <lb></lb>motione naturali grauium deorſum, ac leuium ſurſum; vt <lb></lb>ſcilicet hæc corpora facilius, ac velocius moueantur in pro<lb></lb>greſſu poſtquam commota iam fuerint, quàm in principio <lb></lb>quando tunc ſe mouere incipiunt; imò tanto facilius ac ve<lb></lb>locius, quantò magis à principio motus diſceſſerint. </s>
          <s id="N173DD">Sed <lb></lb>qua ratione id eueniat, diuerſo exiſtente principio motus <lb></lb>naturalis à principio motus violenti, non conuenit inter Phi<lb></lb>loſophos, qui propterea in varias, ac diſcrepantes abierunt <lb></lb>ſententias. </s>
          <s id="N173E8">Inter quas ea videtur aliqua cum probabilitate <lb></lb>percrebuiſſe, quæ totam hanc maiorem facilitatem, ac velo<lb></lb>citatem, refert ad medium per quod mobile tranſit: non <lb></lb>ſolum ob minorem eius reſiſtentiam, quæ reperitur in pro<lb></lb>greſſu, ac prope finem, ſed præcipuè propter accurſum eiuſ<lb></lb>dem poſt terga ipſius mobilis ad replendum vacuum, quod <lb></lb>relinquit. </s>
          <s id="N173F7">Nam is cum celerrimè fiat, impingere videtur in <pb pagenum="247" xlink:href="005/01/255.jpg"></pb>ipſum mobile, <expan abbr="proindeq.">proindeque</expan> impetu incuſſo, motum eius acce<lb></lb>lerare; ex qua acceleratione velocior adhuc redditur no<lb></lb>uus accurſus, quo rurſus mobile magis impellitur, &amp; ſic <lb></lb>deinceps. </s>
          <s id="N17409"><expan abbr="Citaturq.">Citaturque</expan> pro hac ſententia Ariſtoteles 3. de cæ<lb></lb>lo tex. 28. vbi loquendo de diſtinctione motus naturalis à <lb></lb>violento, &amp; acceleratione vtriuſque inquit: Ad ambo au<lb></lb>tem tanquam inſtrumento vtitur aere: nempe ipſum princi<lb></lb>pium à quo principaliter prouenit motus. </s>
          <s id="N17419"><expan abbr="Rurſumq.">Rurſumque</expan> paulò <lb></lb>inferius loquens adhuc de aere, ſubdit: Veluti enim impri<lb></lb>mens tradit vtrique. </s>
          <s id="N17423">Impulſum ſcilicet vtrique mobili ad <lb></lb>proprium motum impertiendo. </s>
          <s id="N1742A">Verum ex hoc loco ad ſum<lb></lb>mum tantum colligitur de mente Ariſtotelis, aerem ad <lb></lb>vtrunque motum perficiendum, videlicet tam naturalem, <lb></lb>quàm violentum deſeruire, ac tanquam inſtrumentum con<lb></lb>currere. </s>
          <s id="N17435">Alioquin præcisè loquendo de maiori celeritate <lb></lb>motus naturalis deorſum quò proprius graue ad imum ac<lb></lb>ceſſerit, potius ibidem docet Philoſophus, eam ab adiuncta <lb></lb>virtute præternaturali oriri; inquiens, eum motum, qui eſt <lb></lb>ſecundum naturam (vt in lapide dum fertur deorſum) velo<lb></lb>ciorem fieri ab eo, qui eſt ſecundum potentiam: vocat au<lb></lb>tem potentiam ipſam virtutem motiuam, quæ per violen<lb></lb>tiam imprimitur, aut producitur in corporibus, vt patet ex <lb></lb>contextu. </s>
        </p>
        <p id="N17448" type="main">
          <s id="N1744A">Quare dicendum eſt ex eo facilius, ac velocius grauia <lb></lb>deorſum moueri in progreſſu, quanto magis à principio mo<lb></lb>tus diſceſſerint; quia nimirum per ipſum motum naturalem <lb></lb>augetur in eis virtus motiua, qua feruntur in proprium lo<lb></lb>cum. </s>
          <s id="N17455">Producunt enim in ſe impetum, cumque ſucceſsiuè <lb></lb>ſemper magis ac magis intendunt per grauitatem tanquam <lb></lb>per formam principaliter agendi. </s>
          <s id="N1745C">Ita vt poſt primam grauis <lb></lb>motionem deorſum, non modo duplicetur deinceps prin<lb></lb>cipium ipſius motionis, ſeu virtus motiua, per productionem <lb></lb>impetus in eundem locum tendentis; ſed creſcente diſtan<lb></lb>tia creſcat pariter impetus, &amp; cum eo velocitas in immen<lb></lb>ſum. </s>
          <s id="N17469">Quam ſententiam expreſsè fuiſſe Ariſtotelis decla<lb></lb>rant tum eius verba proximè a nobis expoſita, tum ea quæ <pb pagenum="248" xlink:href="005/01/256.jpg"></pb>protulit ſupra quæſt. </s>
          <s id="N17473">19. dum vim quam habet commota <lb></lb>ſecuris ad ſcindendum inquirens, dixit: An quia omnia cum <lb></lb>motu fiunt, &amp; graue ipſum magis aſſumit grauitatis dum <lb></lb>mouetur, quàm dum quieſcit? </s>
          <s id="N1747C">Vbi impetum ſuperadditum <lb></lb>grauitati ad deſcendendum, vocat grauitatem aſſumptam, <lb></lb>quia mouet quo verſum ipſa grauitas mouet: vnde ab alijs <lb></lb>vocatur grauitas accidentalis, &amp; adſcititia. </s>
          <s id="N17485">Senſus autem <lb></lb>ipſorum verborum eſt. </s>
          <s id="N1748A">Nam etſi ſemper grauitas premat, <lb></lb>&amp; grauitet, ſiue moueatur, ſiue quieſcat, quando tamen <lb></lb>mouetur, multo magis conatur, ideoque impetum facit, <lb></lb><expan abbr="eumq.">eumque</expan> ſucceſsiuè intendit, quanto vlterius mouetur. </s>
          <s id="N17496">Præ<lb></lb>terea idem Philoſophus lib.

1. de cœlo tex. 88. docet <expan abbr="cele-ritatẽ">cele<lb></lb>ritatem</expan> motus naturalis in progreſſu augeri propter <expan abbr="augmen-tũ">augmen<lb></lb>tum</expan> virtutis motiuæ grauitatis, aut leuitatis, quæ ſcilicet <expan abbr="au-gẽtur">au<lb></lb>gentur</expan> in motu. </s>
          <s id="N174AF">Vnde infert, quod ſi motus prederet in <expan abbr="infi-nitũ">infi<lb></lb>nitum</expan>, <expan abbr="etiã">etiam</expan> grauitas, aut leuitas, &amp; velocitas ex illis orta creſce <lb></lb>ret in <expan abbr="infinitũ">infinitum</expan>. </s>
          <s id="N174C2">Loquitur <expan abbr="autẽ">autem</expan> de <expan abbr="augmẽto">augmento</expan>, &amp; <expan abbr="incremẽto">incremento</expan> gra. <lb></lb></s>
          <s id="N174D2">uitatis <expan abbr="accidẽtalis">accidentalis</expan>, ſeu impetus acquiſiti; <expan abbr="cũ">cum</expan> ſatis <expan abbr="cõſtet">conſtet</expan>, nec <lb></lb><expan abbr="grauitatẽ">grauitatem</expan>, nec <expan abbr="leuitatẽ">leuitatem</expan> naturalem formaliter in ſeipſa augeri. </s>
        </p>
        <p id="N174EA" type="main">
          <s id="N174EC">Primum autem fundamentum huius aſſertionis, ac Peri<lb></lb>pateticæ doctrinæ ſumendum eſt ex reiectione prioris, ac re<lb></lb>latæ ſententiæ (cum cæteræ ſatis reiectæ ſint ab alijs, ac <lb></lb>reij ci poſsint ex dicendis) quia licet aer, qui à graui de<lb></lb>ſcendente truditur, ac deorſum pellitur ob ſuam tenuitatem <lb></lb>partim ſcindatur, ac diſsipetur, <expan abbr="partimq.">partimque</expan> impetu accepto, vl<lb></lb>terius abire cogatur verſus eundem locum, <expan abbr="minusq.">minusque</expan> propte<lb></lb>rea reſiſtat: atque hoc ex capite motus grauium deorſum <lb></lb>non parum acceleretur: nullo tamen pacto is accelerari po<lb></lb>terit accurſu aeris ſubſequentis, qui retro terga grauis im<lb></lb>pellat, <expan abbr="tantaq.">tantaque</expan> vi magis ac magis promoueat, vt relata ſen<lb></lb>tentia aſſerebat. </s>
          <s id="N17511">Quoniam &amp; ſi partes aeris pulſæ, ac diuul<lb></lb>ſæ in ſpacium ab eodem graue relictum ſubire conentur, <lb></lb>nunquam ob ſuam tenuitatem tanta vi poſſunt confluere, <lb></lb>vt vehementiam, quam in motu ſuſcipit ingens aliquod gra<lb></lb>ue deſcendens valeant cauſare, <expan abbr="augereq.">augereque</expan> vſque in finem. <lb></lb></s>
          <s id="N17521">Præſertim cum videamus, nec tenuiſsimam lanam, vel quid <pb pagenum="249" xlink:href="005/01/257.jpg"></pb>ſimile, quod à quolibet vento agitari ſoleat, deſcendenti <lb></lb>graui poſt terga alligatam, eas poſſe deprimere: nec caden<lb></lb>tem candelam extinguere ſi flamma ſit in parte ſuperiori. <lb></lb></s>
          <s id="N1752E">Imò nec ipſam <expan abbr="flammulã">flammulam</expan> à rectitudine ſuæ pyramidis auer<lb></lb>tere, quamuis tali ex altitudine decidat, vt in motu accele<lb></lb>rationis incrementa ſuſcipiat. </s>
          <s id="N17539">Quod cum ſenſu conſtet, &amp; <lb></lb>à grauiſsimis Philoſophis acceperimus obſeruatum, gratis à <lb></lb>nonnullis negatur, qui parui quoque momenti faciunt vim <lb></lb>aeris ſubſequentis cum per poros lanæ inquiunt illum inſi<lb></lb>nuari, &amp; ſic graue depellere abſque vlla lanæ depreſsione. </s>
        </p>
        <p id="N17544" type="main">
          <s id="N17546">Cum igitur huiuſmodi accurſus aeris ſuccedentis in eun<lb></lb>dem locum non ſuffragetur; nec ſufficiat minor illa reſiſten<lb></lb>tia explicata; grauitas verò ipſa corporis augeri non poſsit <lb></lb>à ſeipſa, ſicut nec vlla qualitas per acquiſitionem noui gra<lb></lb>dus eiuſdem ſpecificæ qualitatis, qui ſi daretur, perſeuera<lb></lb>ret etiam poſt motum, quod experientiæ repugnat; aliaque <lb></lb>non appareat probabilis cauſa ipſius maioris velocitatis, <lb></lb>quam graue acquirit in motu; remanet vt illam non niſi ab <lb></lb>impetu ab eodem graui in ipſa naturali motione producto <lb></lb>oriri dicamus cum Ariſtotele, <expan abbr="alijsq.">alijsque</expan> magni nominis tum <lb></lb>veteribus, tum neotericis Philoſophis, qui hac de re fusè <lb></lb>ſcripſerunt. </s>
        </p>
        <p id="N17563" type="main">
          <s id="N17565">Secundum verò fundamentum eiuſdem veritatis, ac no<lb></lb>ſtræ ſententiæ ſumendum eſt ab obſeruationibus, &amp; expe<lb></lb>rientijs. </s>
          <s id="N1756C">Primò enim conſtat, grauia quò ex altiori loco <lb></lb>deciderint, non modò eo velocius ferri prope finem, quàm <lb></lb>in principio, ſed etiam validius obuiantia pellere <expan abbr="fortiusq.">fortiusque</expan> <lb></lb>impingere: quod non contingit quando ad latera, vel ſur<lb></lb>ſum feruntur, langueſcente impetu prope finem. </s>
          <s id="N1757B"><expan abbr="Indiciumq.">Indiciumque</expan> <lb></lb>propterea eſt, non prouenire à ſola grauitate, eodem ſem<lb></lb>per modo ſe habente, ſed etiam ab impetu acquiſito, qui <lb></lb>cum in motu naturali ſucceſsiuè ſemper intendatur, in vio<lb></lb>lento verò remittatur, magis præualet in illo, quàm in iſto, <lb></lb>quo longius ipſa grauia à principio fuerint remota. </s>
        </p>
        <p id="N1758B" type="main">
          <s id="N1758D">Deinde obſeruamus ipſa grauia quanto ex ſublimiori ſi<lb></lb>tu demittantur, tantò altius reſilire, quod euenire nequit <pb pagenum="250" xlink:href="005/01/258.jpg"></pb>ex vi præciſæ grauitatis, quæ ſanè vbi primò ſolum vel de<lb></lb>tinens quippiam attingeret, ſiſteret, nec ſineret graue ipſum <lb></lb>rurſus attolli. </s>
          <s id="N1759B">Contra verò admiſſa productione impetus in <lb></lb>deſcenſu illorum, cum hic ſucceſsiuè intendatur in progreſ<lb></lb>su, facilè intelligitur magis ea reſilire iuxta maiorem impe<lb></lb>tum acquiſitum in maiori via. </s>
          <s id="N175A4">Quod ſi dicas impetum ad <lb></lb>reſiliendum produci ab ipſo plano, vel ſolo in <expan abbr="pilã">pilam</expan> luſoriam, <lb></lb>vel decidens quodlibet corpus, quod reſilit: hoc in primis <lb></lb>expreſsè eſt contra Ariſtotelem 8. phyſic. </s>
          <s id="N175B1">tex. 32. Qui <lb></lb>ſphæram ait à proijciente, non à pariete virtutem accipere <lb></lb>ad reſiliendum: nec minus contra experientiam cum teſta <lb></lb>impetu lata, &amp; obliquè in aquarum ſuperficiem incidens, <lb></lb>longius inde reſiliat, tametſi paruam, aut nullam in fluido <lb></lb>corpore adinuenerit reſiſtentiam, <expan abbr="nullumq.">nullumque</expan> propterea pro<lb></lb>prii impetus acquiſierit incrementum. </s>
          <s id="N175C6">Corpus enim quod <lb></lb>ſeritur, aut percutitur à proiectis, repellere illa dicitur non <lb></lb>producendo, nec augendo, ſed retorquendo in eis impe<lb></lb>tum incuſſum à proijciente. </s>
          <s id="N175CF">Item non ſatis intelligitur im<lb></lb>pulſum ad reſiliendum effici abſque motu locali impellentis <lb></lb>ſicut in reliquis omnibus impulſibus experimur. </s>
          <s id="N175D6"><expan abbr="Probaturq.">Probaturque</expan> <lb></lb>ex receptiſsimo illo Ariſtotelis axiomate, quod nullum <lb></lb>moueat niſi commotum, vt quæſt. </s>
          <s id="N175E0">33. explicabitur. </s>
        </p>
        <p id="N175E3" type="main">
          <s id="N175E5">Præterea videmus corpus fune appenſum huc atque il<lb></lb>luc circumferri, per vnum quippe arcum deſcendendo, ac <lb></lb>per alium aſcendendo: ſed nequit aſcendere virtute graui<lb></lb>tatis, qua ſolùm poteſt deſcendere: Ergo neceſſariò conce<lb></lb>denda eſt alia virtus motiua, qua poſsit aſcendere; &amp; hanc <lb></lb>vocamus impetum. </s>
          <s id="N175F2">Qui cum à nulla alia cauſa tunc poſsit <lb></lb>oriri, remanet, vt producatur ab eodem corpore agitato in <lb></lb>ipſo deſcenſu virtute ſuæ grauitatis, quæ eſt illi ratio princi<lb></lb>paliter agendi, vt infra rurſus patebit. </s>
        </p>
        <p id="N175FD" type="main">
          <s id="N175FF">Neminem denique fugit celſis ex cacuminibus montium <lb></lb>cadentia ſaxa diſcindi per aera, nullis alijs illiſa corporibus; <lb></lb>&amp; aquam ſupernè cadentem in progreſſu magis ac magis <lb></lb>d uelli, &amp; in guttas reſolui. </s>
          <s id="N17608">Quod abſque impetu ab eo<lb></lb>dem graui producto non poteſt intelligi; Cum aer nec ſaxa <pb pagenum="251" xlink:href="005/01/259.jpg"></pb>diſrumpere magis quàm lana; nec aquæ partes diſcontinua<lb></lb>re valeat potius in progreſſu, vel fine, quàm in principio ca<lb></lb>ſus quando non eſt adhuc ipſe deorſum commotus. </s>
          <s id="N17616">Hinc <lb></lb>enim obſeruare eſt, aquam per Epiſtomium fluentem, vel <lb></lb>aliquod foramen, nullo pacto ſub initio ab aere diuelli, quò <lb></lb>magis tamen deſcendit, magis extenuari, ita vt pyramidis <lb></lb>figuram referat. </s>
          <s id="N17621">Nam quantò magis à foramine elongatur <lb></lb>tantò velocius cogitur moueri, quod eſt in eodem tempore <lb></lb>maius ſpatium non ſolum percurrere, ſed etiam occupare. <lb></lb></s>
          <s id="N17629"><expan abbr="Fieriq.">Fierique</expan> non poſſet ſeruando continuationem, eandemque <lb></lb>craſsitiem quam prius. </s>
          <s id="N17631">Vnde ſucceſsiuè creſcente veloci<lb></lb>tate, creſcit extenuatio ad occupandam maiorem longitu<lb></lb>dinem ſpatij, quouſque deperdita continuatione in guttas <lb></lb>reſoluatur. </s>
          <s id="N1763A">Itaque aquæ diuulſio, ac diſcontinuatio, ſicut <lb></lb>&amp; ipſa maior veloçitas caſus, cum non proueniat ab aere <lb></lb>intermedio, nec immediatè ab ipſa grauitate eodem pacto <lb></lb>ſe habente, remanet vt proximè oriatur ex impetu iugiter <lb></lb>aucto, quo partes aquæ ſucceſsiuè ſemper magis vrgentur. </s>
        </p>
        <p id="N17645" type="main">
          <s id="N17647">Nec obſtat qualitatem impetus eſſe præter naturam gra<lb></lb>uium ad hoc, vt dicamus ab ipſismet per motum naturalem <lb></lb>deorſum tendendo produci. </s>
          <s id="N1764E">Quandoquidem multa per <lb></lb>accidens producuntur à cauſis naturalibus, quæ illis con<lb></lb>ueniunt præter naturam. </s>
          <s id="N17655">Vt cum per motum localem pro<lb></lb>ducitur in ſe calor ab aqua, vel ferro, quibus conuenit præ<lb></lb>ter naturam; ſicut &amp; præferentia localis in ſpatio à centro re<lb></lb>motiori, quæ producitur ab eiſdem grauibus ſurſum ten<lb></lb>dentibus, at que promotis; &amp; ſimilia. </s>
        </p>
        <p id="N17660" type="main">
          <s id="N17662">Nec tandem ſequitur, quod ſi talis impetus à deſcenden<lb></lb>te graui produceretur, natura ſua tenderet in eundem Io<lb></lb>cum in quem tendit grauitas, à qua propterea non ſatis poſ<lb></lb>ſet diſtingui. </s>
          <s id="N1766B">Porrò determinatio qua impetus tendit in <lb></lb>hunc potius quàm illum locum, pendet à dirigente, vel im<lb></lb>primente, atque adeo non niſi per accidens ei conuenit, &amp; <lb></lb>ab extrinſeco. </s>
          <s id="N17674">Vnde ſicut indifferens eſt ex natura ſua, vt <lb></lb>producatur à proijciente, vel à graui deſcendente, aut leui <lb></lb>aſcendente: ita pariter eſt in differens ad tenden dum potius <pb pagenum="252" xlink:href="005/01/260.jpg"></pb>iſtuc quàm illuc; determinatur autem à cauſa impellente <lb></lb>per modum quo applicatur, ac iuxta poſitionem qua vrget, <lb></lb>ac diligit mobile in ipſa impulſione. </s>
        </p>
        <p id="N17684" type="main">
          <s id="N17686">Cæterum ex dictis in hac quæſtione colligitur, non eſſe <lb></lb>eandem rationem de maiori facilitate motus violenti, ac <lb></lb>naturalis poſt principium motus; cum maior facilitas, quæ <lb></lb>reperitur in violenta motione corporis iam commoti, oria<lb></lb>tur ex reduplicatione illa impetus explicata: maior autem <lb></lb>facilitas, ac velocitas motus naturalis <expan abbr="poſtquã">poſtquam</expan> corpus mo<lb></lb>ueri cœperit in ſolum <expan abbr="locũ">locum</expan>, procedat ab impetu aduenien<lb></lb>te vltra grauitatem, aut leuitatem, qui adhuc ſucceſſiuè in<lb></lb>tenditur, <expan abbr="promouetq.">promouetque</expan> magis ac magis vſque in <expan abbr="finẽ">finem</expan>. </s>
          <s id="N176AB">Quam<lb></lb>obrem abſque fundamento nonnulli oppoſitum putantes, <lb></lb>aiunt eandem eſſe vtrique motui facilitatis, ac velocitatis <lb></lb>rationem, <expan abbr="eamq.">eamque</expan> conſiſtere in diſpoſitione prioris motus, <lb></lb>quo diſponatur ſubiectum ad motum poſteriorem: cum <lb></lb>nec motus, nec alia actio per ſe diſponere valeat ſubiectum <lb></lb>abſque formæ alicuius productione; nec vlla forma produ<lb></lb>ci poſſit per motum localem præter: præſentiam ipſam lo<lb></lb>calem, quæ ad nihil diſponit. </s>
        </p>
        <p id="N176C2" type="head">
          <s id="N176C4">Quæſtio Trigeſimaſecunda.</s>
        </p>
        <p id="N176C7" type="main">
          <s id="N176C9">C<emph type="italics"></emph>vr ea quæ proijciuntur, ceſſant à latione? <lb></lb></s>
          <s id="N176D0">An quia impellens deſinit potentia, vel pro<lb></lb>pter retractionem, vel propter rei proiectæ in<lb></lb>clinarionem, quando ea valentior fuerit, <lb></lb>quàm pro&lt;03&gt;cientis vires. </s>
          <s id="N176D9">Aut isthæc ambi<lb></lb>gere, principium relinquentes, abſurdum eſt.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N176E0" type="head">
          <s id="N176E2">COMMENTARIVS.</s>
        </p>
        <p id="N176E6" type="main">
          <s id="N176E8">De motu proiectorum ſermonem inſtituens Ariſto<lb></lb>teles inuerſo ordine videtur procedere dum prius <lb></lb>hic quærit cur illa ceſſent à latione, deinde verò in <pb pagenum="253" xlink:href="005/01/261.jpg"></pb>ſequenti quæſtione de ipſa latione pertractat. </s>
          <s id="N176F4">Vnde poſt <lb></lb>breuem ſolutionem huius quæſtionis, addit: An potius ab<lb></lb>ſurdum eſſe videtur, nos iſthæc quærere, ac in dubitationem <lb></lb>vocare, principium relinquentes. </s>
          <s id="N176FD">Nempe cauſam huius ceſ<lb></lb>ſationis conſiſtentem in ipſa natura virtutis, qua proiecta; <lb></lb>feruntur, ac de qua acturus erat in ſequenti quæſtione. </s>
          <s id="N17704">Ve<lb></lb>rùm totam huius rei doctrinam ſpectando non immeritò <lb></lb>Ariſtotelem id egiſſe comperiemus, cùm ad explicandam <lb></lb>tam occultæ qualitatis naturam non parum conducat illam <lb></lb>à proprio interitu explorare. </s>
        </p>
        <p id="N1770F" type="main">
          <s id="N17711">Rectè igitur primo loco hìc quærit Ariſtoteles, cur ea, <lb></lb>quæ proijciuntur ceſſent à latione. </s>
          <s id="N17716">Et ratio dubitandi eſt, <lb></lb>quia proiecta ceſſare non poſſunt à latione, niſi eius cauſa, <lb></lb>ceſſante, quæ eſt virtus impreſſa à proijciente, vt quæſt. </s>
          <s id="N1771D">ſe<lb></lb>quen. </s>
          <s id="N17722">patebit: virtus autem hæc ſemel impreſſa non vide<lb></lb>tur poſſe ceſſare. </s>
          <s id="N17727">Nam vel hoc contingeret per defectum <lb></lb>cauſæ conſeruantis, vel per aduentum alicuius formæ con<lb></lb>trariæ: ſed talis virtus exiſtens in proiecto iam ſeparato à <lb></lb>proijciente, non poteſt deſinere ob defectum cauſæ con<lb></lb>ſeruantis: Siquidem iam perijſſet vbi primo ſeiunctum fuit <lb></lb>fuit proiectum ipſum à proijciente; ſicut lumen quando ſe<lb></lb>paratur illuminatum ab illuminante: nec per aduentum <lb></lb>formæ contrariæ, cum nulla talis forma de nouo produca<lb></lb>tur in proiecto quando ceſſat à motu: Ergo virtus prædicta <lb></lb>non videtur poſſe deſinere, <expan abbr="ideoq.">ideoque</expan> nec proiectum à latione <lb></lb>ceſſare. </s>
        </p>
        <p id="N17742" type="main">
          <s id="N17744">Nonnulli tamen reſpondent, virtutem illam impreſſam <lb></lb>in proiectis paulatim remitti, ac tandem penitus corrumpi <lb></lb>per reproductionem deperditæ grauitatis ad impreſſionem <lb></lb>illius. </s>
          <s id="N1774D">Putant enim in ipſo actu impreſsionis impetus, mul<lb></lb>tùm minui de grauitate naturali ipsius corporis proiecti; <lb></lb>quod cùm violenter fiat, <expan abbr="ipſum̃">ipſum</expan> &amp; corpus cum primò ſepa<lb></lb>ratur à proijciente paulatimue reducit in priſtinam grauita<lb></lb>tem, per <expan abbr="quã">quam</expan> ſenſim etiam expellitur virtus illa à proijcien<lb></lb>te impreſſa, quæ vocatur impetus, ſiue impulſus, &amp; ſic proie<lb></lb>ctum ceſſat à latione. </s>
          <s id="N17768">Quod explicant atque confirmant <pb pagenum="254" xlink:href="005/01/262.jpg"></pb>exemplo caloris introducti in aquam, qui ſanè ad remotio<lb></lb>nem calefacientis paulatim extinguitur, dum aqua ſe redu<lb></lb>cit in priſtinam frigiditatem. </s>
        </p>
        <p id="N17774" type="main">
          <s id="N17776">Sed ratio eſt valde diuerſa, vnde facilè hæc reſponſio im<lb></lb>pugnatur. </s>
          <s id="N1777B">Primò quia graui dum impetu feruntur, ſi in <lb></lb>medio curſu ſiſtantur, nihil ſuæ naturalis grauitatis perdidiſ<lb></lb>ſe comperiuntur; vt manu experiri potestin paruis proie<lb></lb>ctis. </s>
          <s id="N17784">Nec talis grauitas in inſtanti ad eandem menſuram <lb></lb>potuiſſet reproduci, cum primo ipſa grauia incipiunt deti<lb></lb>neri. </s>
          <s id="N1778B">Nam qualitates quæ habent contrarium nonniſi in <lb></lb>tempore intenduntur, ac remittuntur per proprium mo<lb></lb>tum alterationis, vt patet in eadem calefactione aquæ, ea <lb></lb>reproductione frigiditatis eiuſdem. </s>
          <s id="N17794">Secundò quia non eſt <lb></lb>admittenda diminutio, ac reproductio grauitatis abſque <lb></lb>propria contrarietate, quam ipſa grauitas habeat cum virtu<lb></lb>te illa impreſſa. </s>
          <s id="N1779D">Nullam autem eſſe huiuſmodi contrarie<lb></lb>tatem, argumento eſt, quia in motu violento quo deorſum <lb></lb>aliqua corpora depelluntur, nec aufertur, nec minuitur gra<lb></lb>uitas per ipſam violentiam illatam, <expan abbr="virtutemq.">virtutemque</expan> motiuam in <lb></lb>illis impreſſam; nec virtus ipſa motiua deperditur, aut cor<lb></lb>rumpitur à grauitate, quia potius augetur, <expan abbr="magisq.">magisque</expan> corrobo<lb></lb>ratur. </s>
          <s id="N177B4">Imò ab ipſo ſolo corpore graui operante per graui<lb></lb>tatem in deſcenſu producitur, vt quæſtione præcedenti di<lb></lb>cebamus: Quod certè non contingeret, ſi qualitas illa vir<lb></lb>tutis impreſſæ, quæ ſemper eſt eiuſdem ſpeciei, ex natura <lb></lb>ſua incompoſsibilis eſſet cum grauitate, <expan abbr="contrarietatemq.">contrarietatemque</expan> <lb></lb>habeent ad inuicem. </s>
        </p>
        <p id="N177C5" type="main">
          <s id="N177C7">Præterea tota contrarietas excogitabilis inter grauita<lb></lb>tem, &amp; impetum colligitur ex repugnantia, quam grauitas <lb></lb>habet cum illo quando grauia ſurſum proijciuntur: Quæ ta<lb></lb>men repugnantia non minus obſeruatur inter eandem qua<lb></lb>litatem impetus, &amp; leuitatem, quando leuia proijciuntur <lb></lb>deorſum. </s>
          <s id="N177D4">At eadem qualitas ex genere ſuo non poteſt eſſe <lb></lb>ſimul contraria duabus qualitaribus inter ſe contrarijs: nam <lb></lb>hoc ipſo quod opponatur vni, non poteſt opponi alteri illi <lb></lb>contrariæ: Ergo qualitas impetus ex genere ſuo nullam ha-<pb pagenum="255" xlink:href="005/01/263.jpg"></pb>bet contrarietatem cum grauitate, aut leuitate, quæ ſunt <lb></lb>qualitates inter ſe contrariæ. </s>
          <s id="N177E4">Et confirmari adhuc poteſt, <lb></lb>quia ſi gradus aliquis grauitatis expelleretur è proiecto, id <lb></lb>fieret per introductionem ſimilis gradus leuitatis, vt gradus <lb></lb>frigoris per gradum caloris; atque adeò non per introdu<lb></lb>ctionem qualitatis impetus, quæ indifferens eſt ad coexi<lb></lb>ſtendum cum grauitate, aut leuitate. </s>
          <s id="N177F1">Licet <expan abbr="quandoq.">quandoque</expan> ex <lb></lb>prædominio impediat effectum, ſeu motum vtriuſque vel <lb></lb>alterutræ qualitatis oppoſitæ. </s>
          <s id="N177FC">Nam ſi dirigatur ad latera <lb></lb>per lineam horizonti paralellam, nec ſinit proiectum aſcen<lb></lb>dere, nec deſcendere; ac ſurſum ferens pondera prohibet <lb></lb>deſcenſum, non minus ac aſcenſum leuium dum ea deorſum <lb></lb>deprimit. </s>
          <s id="N17807">Quod ſi <expan abbr="pleraq.">pleraque</expan> grauia nimia grauitate proijci <lb></lb>minimè valeant, <expan abbr="nullamq.">nullamque</expan> propterea impetus introductio<lb></lb>nem, aut productionem in ſe admittant: hoc certè non pro<lb></lb>uenit ex contrarietate, quam formaliter grauitas habeat <lb></lb>cum impetu; ſed ex repugnantia, quam dicit ad motum <lb></lb>præter naturalem, ac requiſitum tanquam conditionem ad <lb></lb>hoc vt impetus producatur, &amp; incutiatur. </s>
          <s id="N1781E">Etenim quod mo<lb></lb>neri nequit, nec poteſt impelli, &amp; abſque impulſu, nulla fieri <lb></lb>valet proiectio. </s>
          <s id="N17825">Sicut contrà quantò plus, aut velociùs <lb></lb>graue aliquod à proijciente agitatur, tantò maiorem ab eo <lb></lb>impetum recipit, <expan abbr="longiusq.">longiusque</expan> proijcitur. </s>
        </p>
        <p id="N17830" type="main">
          <s id="N17832">Soluit igitur quæſtionem Ariſtoteles dicens, proiecta ex <lb></lb>eo à latione ceſſare, quod virtus motiua impellens, quam <lb></lb>vocat potentiam, &amp; qua ipſa ferebantur, tandem deſinat, <lb></lb>atque marceſcat. </s>
          <s id="N1783B">Quod profectò duplici ex cauſa euenire <lb></lb>poſſe ſubiungit. </s>
          <s id="N17840">Nimirum vel propter ſimplicem retractio<lb></lb>nem, vt cum proiecta alterius corporis obiectu, ſiue repulſu <lb></lb>retrahuntur à tali motu, ac ſiſtere coguntur: ( Nam quippe <lb></lb>tunc ceſſante progreſſu, ac motu, ceſſat &amp; impetus, qui ſicut <lb></lb>præuio motu producitur, ita quamdiu durat conſeruatur in <lb></lb>motu tanquam cum propria diſpoſitione;) vel propter in<lb></lb>clinationem, quam potius ipſa proiecta habeant ad alium <lb></lb>motum, vt ſurſum, vel deorſum per naturalem grauitatem, <lb></lb>aut leuitatem quando talis inclinatio rurſus coeperit præ-<pb pagenum="256" xlink:href="005/01/264.jpg"></pb>ualere magis quàm virtus illa impreſſa à proijciente. </s>
          <s id="N17858">Quod <lb></lb>vtique ſi attentè conſideretur non poteſt verificari per pro<lb></lb>priam contrarietatem, &amp; incompoſsibilitatem ipſarum for<lb></lb>marum grauitatis, aut leuitatis cum impetu in eodem ſubie<lb></lb>cto; ſed potius per quandam reluctantiam ex parte effectus, <lb></lb>diuerſorum ſcilicet motuum, quos cauſare conſueuerunt. <lb></lb></s>
          <s id="N17866">Idque optimè intelligitur in tractione, qua graue aliquod <lb></lb>hinc inde ſimul diſtrahitur. </s>
          <s id="N1786B">Quandoquidem virtutes tra<lb></lb>hentes non ſunt contrariæ, ſed motus ipſi, ſeu tractiones, <lb></lb>quæ vel mutuò ſe impediunt, vel mixtum quendam motum <lb></lb>componunt ab vtraque diuerſum: vel poſt reluctantiam, al<lb></lb>tera tandem præualet ob validiorem virtutem à qua proce<lb></lb>dit. </s>
          <s id="N17878"><expan abbr="Idemq.">Idemque</expan> exemplificari poterit in motibus mixtis proce<lb></lb>dentibus à duobus impulſibus in diuerſa tendentibus. </s>
          <s id="N17880">Nam <lb></lb>ſimiliter nulla exiſtente contrarietate inter ipſos impulſus, <lb></lb>motus per eos producti aduerſantur <expan abbr="adinuicẽ">adinuicem</expan>, <expan abbr="impediuntq.">impediuntque</expan> <lb></lb>ſeſe omnino, vel in tertium quendam motum degenerant, <lb></lb>qui dicitur mixtus ex vtroque. </s>
        </p>
        <p id="N17893" type="main">
          <s id="N17895">Alioquin ſi grauitas, aut leuitas proiecti, quod actu fertur <lb></lb>per impetum acceptum ex ſe obſtitiſſet introductioni, ac <lb></lb>radicationi illius in ſubiecto, nec ſineret proiectum moueri <lb></lb>ad nutum illius. </s>
          <s id="N1789E">Quod ſi non à principio, ſed poſtea in pro<lb></lb>greſſu naturalis ipſa inclinatio grauitatis, aut leuitatis inci<lb></lb>piat præualere, indicium eſt, vel tunc augeri ipſam graui<lb></lb>tatem, aut leuitatem, quod, vt diximus, eſt improbabile; vel <lb></lb>tunc impetum langueſcere, aut remitti per naturalem, ac <lb></lb>veluti ſpontaneam deſitionem: qua ſemel admiſſa, iam <lb></lb>optimè intelligitur, effectum grauitatis, aut leuitatis præua<lb></lb>lere contra lationem diuerſam ac violentam. </s>
          <s id="N178AF">Nam tenden<lb></lb>tia grauis deorſum, aut leuis ſurſum, non poteſt impediri à <lb></lb>quacunque latione impetus remiſsi, ſed potius impetu lan<lb></lb>gueſcente, grauitate autem, aut leuitate in ſuo robore per<lb></lb>ſiſtente, paulatim motus degenerat à latione violenta <lb></lb>quouſque abſolutè fiat iuxta inclinationem naturalem, cum <lb></lb>ſcilicet impetus omninò deſierit. </s>
          <s id="N178BE">Abſoluta igitur cauſa <lb></lb>ceſſationis à latione in proiectis, eſt ipſa deſitio impetus, <pb pagenum="257" xlink:href="005/01/265.jpg"></pb>qui cum contrarium non habeat, <expan abbr="ſitq.">ſitque</expan> ſemper eiuſdem ſpe<lb></lb>ciei quocunque tendat, ex ſe incipit langueſcere, &amp; hebeta<lb></lb>ri poſt moram aliquam à ſua productione ob defectum cau<lb></lb>ſæ conſeruantis, &amp; commune eſt pluribus qualitatibus in <lb></lb>genere diſpoſitionis facilè mobilis à ſubiecto, ac paſſibilis <lb></lb>qualitatis, &amp; paſsionis propriè dictæ; imò &amp; in genere natu<lb></lb>ralis potentiæ, &amp; impotentiæ. </s>
          <s id="N178D8">Nam &amp; ſonus, &amp; odor, &amp; ſa<lb></lb>por, poſtquam aliquantiſper viguerint, ex ſe remittuntur, ac <lb></lb>deſinunt abſque proprio contrario expellente in eodem <lb></lb>ſubiecto. </s>
          <s id="N178E1">Sicut &amp; rubedo, quæ procedit ex verecundia, &amp; <lb></lb>ab Ariſtotele inter paſsiones enumeratur. </s>
          <s id="N178E6">Itemque ſpecies <lb></lb>intentionales expreſſæ, imò &amp; impreſſæ poſt diuturnam ceſ<lb></lb>ſationem ab vſu, ac renouatione illarum. </s>
        </p>
        <p id="N178ED" type="main">
          <s id="N178EF">Nec obſtat, quòd impetus lati corporis, vel proiecti in, <lb></lb>medio curſu detenti non vltrò ac ſponte ſua, ſed vi detinen<lb></lb>ris corrumpi videatur; <expan abbr="itemq.">itemque</expan> non ſucceſsiuè, ſed in inſtan<lb></lb>ti cum primò ceſſat à motu. </s>
          <s id="N178FC">Nam virtus detinentis non <lb></lb>opponitur virtuti motiuæ, ſiue naturali, ſiue violentæ; ſed <lb></lb>effectui illarum: Vnde ſicut per detentionem corporis non <lb></lb>corrumpitur grauitas, aut leuitas illius, ſic neque impetus. <lb></lb></s>
          <s id="N17906">Per accidens tamen acceleratur corruptio, ac deſitio impe<lb></lb>tus in ipſa detentione, quia vt diximus, ceſſante motu ceſſat <lb></lb>diſpoſitio, atque conditio, qua maximè impetus conſerua<lb></lb>tur. </s>
          <s id="N1790F"><expan abbr="Nullumq.">Nullumque</expan> eſt inconueniens, effectum concurrere ad <lb></lb>conſeruationem cauſæ tanquam diſpoſitionem, aut condi<lb></lb>tionem. </s>
          <s id="N17919">Nec propterea talis deſitio fit tota ſimul in in<lb></lb>ſtanti; Quandoquidem licet impetus poſt primum impul<lb></lb>ſum, ac repulſum amplius à detinente non ſentiatur, videli<lb></lb>cet propter exuperantiam virtutis illius qua vincitur, &amp; ſu<lb></lb>peratur: hoc tamen non arguit cum totum simul in primo <lb></lb>inſtanti deperijſſe; ſed tantum propter obſtaculum ad ceſſa<lb></lb>tionem motus breui morula remiſſum paulatim fuiſſe, ac <lb></lb>tandem penitus deſiſſe. </s>
          <s id="N1792A">Etenim niſi omni ex parte ipſum <lb></lb>proiectum detineatur, adhuc poſt acceptum repulſum vide<lb></lb>mus illud reſilire, ac pauliſper impetum eius quamuis retor<lb></lb>tum, ac langueſcentem non nihil vrgere. </s>
        </p>
        <pb pagenum="258" xlink:href="005/01/266.jpg"></pb>
        <p id="N17937" type="main">
          <s id="N17939">Sed contra etiam eſt, quia ſi qualitas prædicta&#039; impetus <lb></lb>impreſsi deficeret per meram deſitionem ad remotionem <lb></lb>impellentis, vel proijcientis, ſtatim atque proiectum elabi<lb></lb>tur è manu proijcientis, inciperet ipſa impetus remiſsio, <lb></lb><expan abbr="creſceretq.">creſceretque</expan> vſque ad totalem deſitionem. </s>
          <s id="N17947">At non ita con<lb></lb>tingit, cum potius proiecta è manibus proijcientium egreſ<lb></lb>ſa, tardius moueantur à principio, quàm in progreſſu vſque <lb></lb>ad certum terminum, ad quem virtus impulſiua valet per<lb></lb>tingere, <expan abbr="validiusq.">validiusque</expan> propterea feriant in proportionata qua<lb></lb>dam diſtantia, quàm prope nimis ipſum proijciens: Ergo <lb></lb>indicium eſt ipſam impetus qualitatem, non deficere, nec <lb></lb>remitti ſtatim ad defectum cauſæ conſeruantis, &amp; impel<lb></lb>lentis, ſed potius augeri per aliquod tempus, deinde paula<lb></lb>tim remitti.ac tandem diſcedere ad expulſionem ortam ex <lb></lb>qualitate contraria. </s>
        </p>
        <p id="N17962" type="main">
          <s id="N17964">Verùm huic obiectioni facilè occurritur dicendo, impe<lb></lb>tum poſt remotionem impellentis, nullum ex ſe incremen<lb></lb>tum poſſe ſuſcipere, ſiue habeat, ſiue non habeat qualitatem <lb></lb>contrariam; cauſamque tarditatis, ſeu minoris velocitatis <lb></lb>prædictæ in principio, eſſe maiorem reſiſtentiam, quam ſub <lb></lb>ipſo initio proiectum reperit in intermedio. </s>
          <s id="N17971">Nam aer, verbi <lb></lb>gratia, vel aqua quieſcens, cum primo à proiecto impellitur <lb></lb>magis valet reſiſtere, quàm cum paulatim dimota per no<lb></lb>uum ſemper impulſum vlterius abire cogitur, vt locum re<lb></lb>linquat ipſi proiecto. </s>
          <s id="N1797C">Impetus enim in eodem aere, vel <lb></lb>aqua impreſſus creſcit ſemper cum motu, quia proiectum <lb></lb>dum fertur ſemper impellit, ac impellendo ſucceſsiuè in<lb></lb>tendit effectum: magis autem intenſus impetus in ipſo me<lb></lb>dio, magis ac magis difſfunditur in vlteriores partes eiuſdem <lb></lb>medij, quod propterea velocius diſcedit, ac locum, quem <lb></lb>habet relinquendo, minus reſiſtit. </s>
          <s id="N1798B">Quod idem in cauſa <lb></lb>eſt ſaltem ex parte, vt motus grauium è ſuperno aliquo lo<lb></lb>co <expan abbr="decidẽtium">decidentium</expan> velocior ſit in progreſſu, quàm in principio, <lb></lb>vt ſupra innuimus. </s>
          <s id="N17998">Etenim inter motum grauium natura<lb></lb>lem, quo illa tendunt deorſum, ac motum violentum, quo <lb></lb>tendunt ſurſum, vel ad latera, hoc ſolum intereſt in propoſi-<pb pagenum="259" xlink:href="005/01/267.jpg"></pb>to, quod motus naturalis ſucceſsiuè ſemper fiat velocior, <lb></lb>at que velocior in partibus poſterioribus vſque in finem <lb></lb>cum ſemper grauitas perſeueret in eadem intentione, <expan abbr="mi-nusq.">mi<lb></lb>nusque</expan> reſiſtat intermedium, nec non &amp; maiori ſemper feran<lb></lb>tur impulſu ab eiſdem grauibus in eodem motu produ<lb></lb>cto: motus autem violentus licet in progreſſu vſque ad <lb></lb>certum terminum ſimiliter fiat velocior, tandem lan<lb></lb>gueſcente impetu rurſus incipiat retardari quouſque deſi<lb></lb>nat in quietem, vel degeneret in motum naturalem cor<lb></lb>rupta penitus virtute motiua ipſius impetus à proijciente <lb></lb>impreſſa. </s>
        </p>
        <p id="N179BC" type="main">
          <s id="N179BE">Cæterum hic etiam determinandum videtur, qua ratio<lb></lb>ne, vel cauſa corpus pendens à fune poſtquam aliquandiu <lb></lb>fuerit ex ſe huc atque illuc circulariter agitatum, ſeu per <lb></lb>portionem peripheriæ <expan abbr="circumlatũ">circumlatum</expan>, <expan abbr="tandẽ">tandem</expan> ceſſet à latione, ac <lb></lb>per lineam tendentem ad mundi centrum quieſcat. </s>
          <s id="N179D1">Suppo<lb></lb>nimus enim id ſæpè contingere, nulla adhibita violentia per <lb></lb>ſolam remotionem prohibentis. </s>
          <s id="N179D8">Nam ſi per funem alicubi <lb></lb>religatum corpus aliquod inde propendens detineatur, non <lb></lb>quidem perpendiculariter ad horizontem, ſed aliquantu<lb></lb>lum ex latere, ac liberè poſtea relinquatur ſtatim ex ſe cir<lb></lb>culariter illud deſcendere, ac rurſus aſcendere conſpicie<lb></lb>mus, huc atque illuc arcus deſcribendo, <expan abbr="eosq;">eosque</expan> ſucceſsiuè <lb></lb>diminuendo quouſque tandem quieſcat in puncto per quod <lb></lb>à loco detentionis funis ad mundi centrum rectà deduci<lb></lb>tur. </s>
          <s id="N179EF">Difficultas autem in eo conſiſtit, quod cum huiuſmodi <lb></lb>motus ex parte ſit obliquus <expan abbr="quidã">quidam</expan> aſcenſus, &amp; ex parte <expan abbr="de-ſcẽſus">de<lb></lb>ſcenſus</expan>, nec à grauitate <expan abbr="dũtaxat">duntaxat</expan> videtur poſſe procedere, nec <lb></lb>ab alia ſimul virtute impreſſa, quæ moueat in <expan abbr="cõtrariũ">contrarium</expan>: præ<lb></lb>ſertim <expan abbr="cũ">cum</expan> nulla appareat cauſa effectiua talis virtutis; niſi di<lb></lb>catur ab eodem graui manare ( vt præcedenti quæſtione <lb></lb>probatum eſt ) quod cum operetur per grauitatem intrinſe<lb></lb>cam, quæ iugiter perſeuerat in ipſo, iugiter etiam talem vir<lb></lb>tutem in ſe conſeruaret, quæ propterea nunquam ceſſaret à <lb></lb>motu alterno iam explicato, <expan abbr="ſicq.">ſicque</expan> corpus per funem pro<lb></lb>pendens, ſemel promotum, alternatim ac ſemper, ſeu pe<pb pagenum="260" xlink:href="005/01/268.jpg"></pb>renniter moueretur; partim ſcilicet à grauitate, ac partim <lb></lb>à virtute impreſſa, perſeuerante ſemper grauitate cum tali <lb></lb>virtute impulſiua. </s>
        </p>
        <p id="N17A27" type="main">
          <s id="N17A29"><expan abbr="Dicendũ">Dicendum</expan> tàmen eſt, corpus <expan abbr="prædictũ">prædictum</expan> <expan abbr="ſtatimatq.">ſtatim atque</expan> relinqui<lb></lb>tur in ſua libertate <expan abbr="deſcẽdere">deſcendere</expan> ex vi propriæ grauitatis ea via <lb></lb>qua poteſt, nempe obliquè per arcum, <expan abbr="deſcribẽdo">deſcribendo</expan> <expan abbr="portionẽ">portionem</expan> <lb></lb>circumferentiæ circa punctum, in quo funis eſt religatus <lb></lb>tanquam circa centrum: Per hunc autem deſcenſum impe<lb></lb>tum quendam in ſe ab eodem corpore produci, quod cum <lb></lb>vlterius deorſum tendere nequeat ob funis detentionem, <lb></lb>quaſi reſilire cogitur, ac denuò ſurſum attolli per oppoſitum <lb></lb>arcum ſeu viam, ita vt corpus poſtquam à dextris deſcendit <lb></lb>per grauitatem; aſcendit ad læuam per impetum, quo lan<lb></lb>gueſcente, ac deſinente rurſus per eandem viam corpus ip<lb></lb>ſum grauitate vrgente deſcendat: Per quem deſcenſum <lb></lb>nouus impetus producitur ad nouum aſcenſum perficien<lb></lb>dum, &amp; ſic deinceps. </s>
          <s id="N17A5D">Quoniam verò corpus ipſùm per im<lb></lb>petum in ſe media grauitate productum, nunquam poteſt <lb></lb>tantum aſcendere, quantum per ipſam grauitatem deſcen<lb></lb>dit ob reſiſtentiam, quam reperit in aſcenſu ſecus ac in de<lb></lb>ſcenſu: hinc eſt, vt ſecundus deſcenſus per minorem arcum <lb></lb>etiam fiat, per <expan abbr="eumq.">eumque</expan> minor impetus producatur, quàm per <lb></lb>primum; ex quo minori impetu adhuc minor conſtituatur <lb></lb>alius aſcenſus, ac deſcenſus, &amp; ſic paulatim per minores, ac <lb></lb>minores arcus corpus ipſum dimoueatur, quouſque penitus <lb></lb>quieſcat in puncto explicato. </s>
        </p>
        <p id="N17A77" type="head">
          <s id="N17A79">Quæſtio Trigeſimatertia.</s>
        </p>
        <p id="N17A7C" type="main">
          <s id="N17A7E">C<emph type="italics"></emph>vr quippiam non peculiarem ſibi fertur la<lb></lb>tionem, impulſore alioquin non conſequenter?</s>
<s id="N17A82">An videlicet quoniam primum id efficit, vt <lb></lb>alterum impellat: <expan abbr="illudq.">illudque</expan> rurſum vt alte<lb></lb>rum? </s>
          <s id="N17A90">Ce&lt;32&gt;at autem quando non poteſt am<lb></lb>plius facere primum impelleat, id quod <emph.end type="italics"></emph.end><pb pagenum="261" xlink:href="005/01/269.jpg"></pb><emph type="italics"></emph>fertur, vt impellat: &amp; quoniam ipſius lati grauitas nutu <lb></lb>ſuo declinat magis, quàm impellentis in ante ſit potentia.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N17AA2" type="head">
          <s id="N17AA4">COMMENTARIVS.</s>
        </p>
        <p id="N17AA8" type="main">
          <s id="N17AAA">Cvm frequentiſſimè de impetu, ſiue impulſu, quo <lb></lb>grauia in diuerſa loca feruntur ſermo in his quæſtio<lb></lb>nibus incidiſſet, nunquam quod ille ſit, huiuſque de<lb></lb>terminauerat Ariſtoteles. </s>
          <s id="N17AB4">Quod licet obſcurinſculè, op<lb></lb>portunè tamen hic præſtat agendo de motu proiectorum, <lb></lb>poſt proximam quæſtionem, qua de ceſſatione illorum à <lb></lb>motu, ac deſitione eiuſdem impulſus, vt vidimus pertran<lb></lb>ſiuit. </s>
        </p>
        <p id="N17ABF" type="main">
          <s id="N17AC1">Quærit igitur cur proiecta moueantur, quamuis impel<lb></lb>lens, ea impellendo, non conſequatur; ſed ab eis rema<lb></lb>neat ſeiunctum, cum certè ſibi naturalis ac propria non <lb></lb>ſit ea latio vel motus. </s>
          <s id="N17ACA">Aitque id fieri quoniam proijciens, <lb></lb>quod eſt primum impellens efficit, vt proiectum quoque <lb></lb>ipſum impellat alterum (nempe aerem, vel aliud interme<lb></lb>dium) quouſque eò deueniat, vt nequeat amplius illud im<lb></lb>pellere, langueſcente nimirum, ac tandem deficiente virtu<lb></lb>te à primo impulſore accepta. </s>
          <s id="N17AD7">Nam tunc ipſius lati gra<lb></lb>uitas nutu ſuo declinat magis, ſeu deorſum mouere magis <lb></lb>præualet, quàm virtus illa deficiens impellentis in ante. </s>
          <s id="N17ADE">Im<lb></lb>plicitè igitur docet Ariſtoteles, formam intrinſecam à qua <lb></lb>efficienter, &amp; immediatè prouenit motus proiectorum <lb></lb>poſtquam è manibus proijcientium ea fuerint egreſſa, eſſe <lb></lb>virtutem quandam motiuam ab impulſore <expan abbr="productã">productam</expan>, &amp; in <lb></lb>illis <expan abbr="receptã">receptam</expan>, ex natura ſua defectibilem, qua tamen perdu<lb></lb>rante, dum ea informantur, ipſa quoque proiecta valent alia <lb></lb>corpora impellere, ac præſertim aerem, vel aquam, aut <lb></lb>aliud intermedium, vt ſibi locum cedant, ac procedant vlte<lb></lb>rius, tendendo ſecundum eandem directionem. </s>
          <s id="N17AFB">Non ſecus <lb></lb>ac per inhærentem grauitatem, aut leuitatem ſimilia corpo<lb></lb>ra ſurſum, aut deorſum mouentur, <expan abbr="aliaq.">aliaque</expan> ſibi occurrentia <lb></lb>promouent verſus eundem locum. </s>
          <s id="N17B08">Quamobrem idem Ari<lb></lb><pb pagenum="262" xlink:href="005/01/270.jpg"></pb>ſtoteles 1. de Cælo tex. 89. &amp; 8. Phyſic. tex. 27. docuit <lb></lb>per violentiam mota, fieri quaſi per ſe mobilia: hoc eſt ſi<lb></lb>mili quadam intrinſeca virtute inhærente, at que à proijcien<lb></lb>te recepta. </s>
          <s id="N17B1D">Alioqui proijciens efficere non poſſet, vt proie<lb></lb>ctum etiam poſtquam ab ipſo ſeiunctum fuerit, alterum im<lb></lb>pellat, vt hic ipſe aiebat, niſi in actu proiectionis, talem in <lb></lb>eo virtutem impulſiuam imprimeret. </s>
        </p>
        <p id="N17B26" type="main">
          <s id="N17B28">Contra tamen huiuſcemodi expoſitionem eſt, quòd ſæ<lb></lb>pè Ariſtoteles alibi docuerit, proiecta ab aere, vel aqua, aut <lb></lb>alio non abſunili medio deferri, vt 4. Phyſic. tex. 68. &amp; <lb></lb>lib.

8. tex. 82. &amp; lib.

3. de cælo tex. 28. Quod idem ſuppo<lb></lb>nit lib. de Somnijs, ac de Diuinatione per ſomn. </s>
          <s id="N17B3F">&amp; 11. ſect. <lb></lb></s>
          <s id="N17B43">problem. </s>
          <s id="N17B46">quæſt. </s>
          <s id="N17B49">6. Ex quo aliqui Peripatetici ſumpſerunt, <lb></lb>nullam in proiectis dari virtutem motiuam à proijciente <lb></lb>impreſſam. </s>
          <s id="N17B50">Sequeretur enim poſt remotionem proijcien<lb></lb>tis, ipſa proiecta per illam, tanquam à ſe per proprium prin<lb></lb>cipium intrinſecum moueri præter naturam, quod impoſſi<lb></lb>bile eſſe ſtatuit ipſemet Ariſtoteles 8. Phyſicor. tex. 29. Vi<lb></lb>tale namque (hoc eſt animatorum) ait eſſe proprium. </s>
          <s id="N17B5F">Cum <lb></lb>pariter tex. 27. dixiſſet. </s>
          <s id="N17B66">Quorumcunque motus principium <lb></lb>in ſe ipſis eſt, hæc natura dicimus moueri, non autem vio<lb></lb>lentia. </s>
        </p>
        <p id="N17B6D" type="main">
          <s id="N17B6F">Verum ſi Ariſtotelis doctrina in locis citatis attentius <lb></lb>expendatur, nihil omnino illam contra explicatam virtutem <lb></lb>impreſſam continere comperietur. </s>
          <s id="N17B76">Tantum enim per eam <lb></lb>intendit Philoſophus proiecta non modo prius à proijcien<lb></lb>te, ſed etiam à medio poſtea ſemper impelli; nec ob remo<lb></lb>tionem, aut ceſſationem proijcientis à ſeipſis moueri, ſed <lb></lb>adhuc ab alio extrinſeco nempe à contiguo ambiente. <lb></lb></s>
          <s id="N17B82">Alioqui non negat virtutem aliquam à proijciente cum in <lb></lb>ipſis proiectis, tum etiam in aere, vel alio medio imprimi. <lb></lb></s>
          <s id="N17B88">Nam vt docet 8. Phyſicor. tex. 82. vbi hac de re fuſiùs ac <lb></lb>magis ex profeſſo pertractat: Neceſſe eſt (inquit) dicere, <lb></lb>quod primum mouens facit, vt medium poſſit mouere, <lb></lb>nempe contiguus aer vel aqua. </s>
          <s id="N17B95">Quod verificari non poſſet <lb></lb>abſque impreſsione, ac diffuſione alicuius virtutis motiuæ, <pb pagenum="263" xlink:href="005/01/271.jpg"></pb>qua in abſentia primi motoris moueat. </s>
          <s id="N17B9F"><expan abbr="Ideoq.">Ideoque</expan> concludit: <lb></lb>Ceſſat autem cum in ipſo contiguo minor fuerit virtus, <lb></lb>quàm vt moueat. </s>
          <s id="N17BA9">Quæ ſanè virtus cum naturaliter aeri, <lb></lb>vel aquæ non inſit, ſatis conuincitur, eam ab alio, ſcilicet à <lb></lb>primo motore mutuari debere. </s>
          <s id="N17BB0">Nec oppoſitum Ariſtote<lb></lb>lem ſenſiſſe, quippe qui paulò inferius tex. 85. loquens ad<lb></lb>huc de medio tanquam inſtrumento continuè mouente <lb></lb>ait: Aut ipſum oportet pellere, aut trahere, vel vtrumque <lb></lb>aliquid aliud excipiens ab alio (videlicet virtutem impreſ<lb></lb>ſam à primo motore) ſicut dudum dictum eſt in ijs, quæ <lb></lb>proijciuntur. </s>
          <s id="N17BC1">Quibus conſentanea protulit 11. ſect. </s>
          <s id="N17BC4">pro<lb></lb>blem quæſt. </s>
          <s id="N17BC9">6. vbi perpetuè motum mouere docet, ac mo<lb></lb>tum aerem motori ſuccedere, donec omnis conatus mo<lb></lb>uendi emarceſcat cum aer non amplius impellere, vel te<lb></lb>lum, vel aerem poteſt. </s>
          <s id="N17BD2">Concedit igitur proprium cona<lb></lb>tum in aere, tanquam in inſtrumento ſeparato motoris, tan<lb></lb>dem marceſcere ob deſitionem potentiæ, ſeu virtutis im<lb></lb>pulſiuæ, qua eliciebatur in abſentia ipſius primi motoris. <lb></lb></s>
          <s id="N17BDC">Item 3. de Cælo tex. 28. loquendo de motione naturali, ac <lb></lb>violenta, ait, vtrique aerem, tanquam inſtrumentum extrin<lb></lb>ſecum, deſeruire. </s>
          <s id="N17BE5">Sicut 8. Phyſicor. tex. 33. etiam dixerat, <lb></lb>afferens illud exemplum: Vt baculus (inquit) mouet lapi<lb></lb>dem, &amp; mouetur à manu mota ab homine. </s>
          <s id="N17BF0">Vnde colligit <lb></lb>vtraque mouere, &amp; primum, &amp; vltimum. </s>
        </p>
        <p id="N17BF5" type="main">
          <s id="N17BF7">Illud autem his in locis magnopere obſeruandum eſt, <lb></lb>Ariſtotelem ſemper loqui de motore extrinſeco, quem in <lb></lb>motibus quoque naturalibus grauium, &amp; leuium ibidem <lb></lb>admittit, ne concedere cogatur corpora inanimata moueri <lb></lb>à ſeipſis, huiuſmodi motus referens ad generantem grauita<lb></lb>tem, aut leuitatem, vel ad remouentem impedimenta. <lb></lb></s>
          <s id="N17C05">Quamobrem ſicut ipſe Philoſophus non per hoc negat, <lb></lb>grauia, &amp; leuia habere formam quandam inhærentem, at<lb></lb>que intrinſecam, quæ natura ſua tendunt ſurſum, aut deor<lb></lb>ſum, vt apertè conceſſerat tex. præcedenti nempe 8. Phyſic. <lb></lb>tex. 32. ita nec poteſt negare, proiecta præter causam ex<lb></lb>trinſecam ſuæ motionis præternaturalis, videlicet primum <pb pagenum="264" xlink:href="005/01/272.jpg"></pb>motorem, aut aerem impellentem, habere propriam virtu<lb></lb>tem motiuam intrinſecam, ipſis à proijciente, vel ambiente <lb></lb>impreſſam, per quam proximè feruntur quò diriguntur, ſicut <lb></lb>per leuitatem ſurſum, ac per grauitatem deorſum. </s>
          <s id="N17C22">Quam <lb></lb>quidem virtutem, vt vidimus, ſæpè ipſe inſinuat, &amp; à neote<lb></lb>ricis rem diſtinctius pertractantibus vocatur impetus, ſeu <lb></lb>impulſus. </s>
          <s id="N17C2B">Qui cum diu non perſeueret in ſubiecto, nec ei <lb></lb>competat ex natura ſua: <expan abbr="Cumq">Cumque</expan> determinatè tantum va<lb></lb>leat mouere iuxta proijcientis directionem, non ſequitur il<lb></lb>lud inconueniens, quod Ariſtoteles pro ratione dubitandi <lb></lb>propoſuerat, nimirum fore, vt proiecta <expan abbr="mouerẽtur">mouerentur</expan> à ſeipſis, <lb></lb>&amp; ab intrinſeco, non ſecus ac animalia, vel ſaltem corpora, <lb></lb>quæ natura mouentur, non violentia. </s>
          <s id="N17C3E">Non ſufficit enim mo<lb></lb>ueri à principio intrinſeco ad conſtituendum motum natu<lb></lb>ralem, ſed amplius requiritur, vt ipſum principium ſit ſtabi<lb></lb>le, ac naturæ debitum, cuiuſmodi non eſt virtus impreſſa <lb></lb>proiectis. </s>
        </p>
        <p id="N17C49" type="main">
          <s id="N17C4B">Iam verò quàm neceſſariò admittenda ſit talis qualitas, <lb></lb>ſeu virtus impreſſa, quidquid ſenſerit Ariſtoteles, ex eo vel <lb></lb>maximè intelligitur, quòd abſque illa inſufficiens ſit ſolus <lb></lb>aer concitatus ad perficiendum motum proiectorum, etſi <lb></lb>ad ipſum <expan abbr="quandoq.">quandoque</expan> concurrat. </s>
          <s id="N17C5A">Senſu enim conſtat, nulla <lb></lb>ventorum irruentium vi quieſcentem lapidem, aut plum<lb></lb>beam pilam poſſe ſuſtolli, &amp; in longinqua transferri, ſicut <lb></lb>nec ligneam, aut ferream rotam conuolui, &amp; alia eiuſmodi <lb></lb>corpora promoueri; quæ tamen impetu incuſſo, facilè præ<lb></lb>ſtantur à manu, etiam contra omnem ventorum conatum <lb></lb>vehementiſſimè ex aduerſo perflantium. </s>
          <s id="N17C69">Imò &amp; ferreas <lb></lb>pilas contra eundem flatum videmus è tormentis explodi, <lb></lb>ac non minus mænia quatere; &amp; ingentia ſaxa eminus ac <lb></lb>ſumma celeritate per aera ferri, ipſo aere in contrarium ni<lb></lb>tente, ac repellente. </s>
          <s id="N17C74">Vanumque videtur illud effugium, <lb></lb>flante vento, quamuis totus aer commoueatur, pars tamen <lb></lb>aeris, quæ tangit proiectum, cum vnitè magis moueatur à <lb></lb>proijciente, maiorem vim obtinere ad promouendum, quàm <lb></lb>vllum ventum in contrarium. </s>
          <s id="N17C7F">Siquidem veluti per follem, <pb pagenum="265" xlink:href="005/01/273.jpg"></pb>aut fiſtulam aer emittendus eſſet, ac pellendus à proijcien<lb></lb>te poſt terga proiecti, poſterioremque partem, qua neruo <lb></lb>aptari ſolet ſagitta ex directo feriret, tanquam ventus na<lb></lb>uem in puppi: <expan abbr="tantaq.">tantaque</expan> demum eſſet virtus ipſius aeris in <lb></lb>tam paruam quantitatem incidentis, vt totum corpus emi<lb></lb>nus impellere contra quamcunque reliqui aeris vniuerſi ve<lb></lb>hementiam præualeret, quod eſt abſurdum. </s>
        </p>
        <p id="N17C97" type="main">
          <s id="N17C99">Accedit quia nec aquam comitari, atque impellere vi<lb></lb>demus nauiculas, ac triremes quemcunque curſum in mari <lb></lb>tenentes, quippe quæ ſæpius contra fluxum, ac fluctus illius <lb></lb>ſolo remorum pulſu feruntur: Nec aerem circumobſiſten<lb></lb>tem conſtat, rotam figuli, vel ſimilem, quæ in gyrum velo<lb></lb>ciſſimè ducitur promouere, cum accenſum lumen prope <lb></lb>illam extinguere, aut inflectere quamuis concitatus ipſe <lb></lb>minimè valeat. </s>
          <s id="N17CAA">Præterea ſi ſolus aer ad proiectorum la<lb></lb>tionem valeret, faciliùs, ac longiùs transferre deberet le<lb></lb>uiora proiecta, quàm grauiora; at ſi quis proijciat plumam, <lb></lb>vel paleam, minus illam promouere valebit, quam plum<lb></lb>beum quippiam, vel æneum, quod non excedat vires proij<lb></lb>cientis: Ergo non ſolo aere proiecta ipſa feruntur: Neque <lb></lb>vim huius argumenti effugiunt nonnulli dum aiunt, ob ni<lb></lb>miam leuitatem minus proijci corpora poſſe, à quocunque <lb></lb>proijciantur, aut ferantur, eo quod proportio quædam re<lb></lb>quiratur inter proijciens, &amp; proiectum, ac ſicut nimia reſi<lb></lb>ſtentia, ita imbecillitas nimia ipſius proiecti, motum proie<lb></lb>ctionis impediat, vt ſequenti quæſt. </s>
          <s id="N17CC3">optimè docet Ariſto<lb></lb>teles. </s>
          <s id="N17CC9">Quandoquidem ſi latio proiectorum perficeretur <lb></lb>ab aere nulla eſſet imbecillitas leuium ad talem motum, <lb></lb>quæ ſanè tota conſiſtit in eo, quod ſuperare, &amp; expellere <lb></lb>nequeant aerem, in cuius locum vlterius tendendo deberent <lb></lb>ſuccedere, vt ipſemet Ariſtoteles ibidem aduertit. </s>
          <s id="N17CD4">Si enim <lb></lb>aer deferret proiecta, non vtique illis obſtaret, ac ſine ob<lb></lb>ſtaculo nulla haberetur ratio imbecillitatis eorum. </s>
          <s id="N17CDB">Quare <lb></lb>non modò leuia nimis, æquè ac moderatè grauia proijci <lb></lb>poſſent, ſed multò longiùs, ac faciliùs propter minorem <pb pagenum="266" xlink:href="005/01/274.jpg"></pb>reſiſtentiam ex parte grauitatis, vt dicebamus; quod eſt <lb></lb>contra experientiam. </s>
        </p>
        <p id="N17CE9" type="main">
          <s id="N17CEB">Demum ratio à priori videtur, quoniam aer ex ſe quie<lb></lb>tus eſt, nec poteſt aliud mouere, niſi ipſe ab alio moueatur, <lb></lb>&amp; impellatur: dum autem impellitur, vel accipit virtutem <lb></lb>aliquam ab impellente, vel nullam: ſi aliquam accipit, eam <lb></lb>potius, vel ſimilem dicemus accipere proiectum immedia<lb></lb>tè: ſi nullam accipit; ergo tamdiu poterit impellere quam. <lb></lb></s>
          <s id="N17CF9">diu actu impellitur (vt baculus, vel aliud inſtrumentum ma<lb></lb>nu dimotum ad aliud impellendum) ceſſante verò impul<lb></lb>ſore, ipſe quoque ab impulſu deſiſtet. </s>
          <s id="N17D00">Quod idem conclu<lb></lb>ditur de pluribus, ac pluribus intermedijs, quan do alterum <lb></lb>ab altero nullam accipit virtutem inhærentem, ſed pendent <lb></lb>ab actuali influxu, ac motione prioris. </s>
          <s id="N17D09">At ſenſu conſtat ceſ<lb></lb>ſante primo motore, ſeu proijciente, adhuc proiecta perfer<lb></lb>ri vlteriuſque propelli: Ergo vel non propelluntur ab aere, <lb></lb>vel aer propellens non abſque virtute à proijciente recepta <lb></lb>propellit. </s>
          <s id="N17D14">Semel autem admiſſa huiuſmodi virtute impul<lb></lb>ſiua in aere, multo magis ac potiori iure admittenda erit <lb></lb>in ipſis proiectis. </s>
        </p>
        <p id="N17D1B" type="main">
          <s id="N17D1D">Quod ſi dicatur proiectum ſemper impelli ab aere ſucce<lb></lb>dente à tergo ad replendum vacuum, quod ab ipſo proiecto <lb></lb>relinquitur, nulla vi ab alio recepta, vel in vlteriores partes <lb></lb>aeris transfuſa; tunc concluderetur, huiuſmodi motum ne<lb></lb>ceſſario eſſe perennem. </s>
          <s id="N17D28">Quandoquidem ſicut nunquam <lb></lb>ceſsat naturalis illa propenſio, qua corpora feruntur ad re<lb></lb>plendum vacuum, ita nunquam ceſſare poſſet effectus ma<lb></lb>nans ab illa; quod cum ſit falſum, remanet, &amp; falſum eſſe il<lb></lb>lud, ex quo ſequitur. </s>
        </p>
        <p id="N17D33" type="main">
          <s id="N17D35">Cum igitur aer commotus, vel aliud medium, tanquam <lb></lb>inſtrumentum proijcientis, non ſufficiat ad <expan abbr="perficiẽdum">perficiendum</expan> mo<lb></lb>tum proiectorum, poſtquam ea ab ipſo proijciente receſſe<lb></lb>rint, nec aliud ad id præſtandam appareat, remanet cauſam <lb></lb>proximam, ac principalem motus prædicti eſſe ipſamet cor<lb></lb>pora proiecta, prout informata qualitate impetus, quem <pb pagenum="267" xlink:href="005/01/275.jpg"></pb>hactenus à proijciente in actu proiectionis acceperunt. </s>
          <s id="N17D4B">Ita <lb></lb>vt corpora proiecta præcisè vt corpora ſunt, ſint cauſa ma<lb></lb>terialis huius motus, quem recipiunt; ipſe verò impetus ſit <lb></lb>ratio formalis principaliter agendi, &amp; influendi, hoc eſt, lo<lb></lb>caliter ſe mouendi, producendo in eiſdem corporibus no<lb></lb>uas, ac nouas præſentias locales, quouſque viguerit, ac per<lb></lb>durauerit: Cum natura ſua, vt diximus, paulatim remitta<lb></lb>tur, ac tandem penitus deſinat. </s>
        </p>
        <p id="N17D5C" type="main">
          <s id="N17D5E">Dicimus autem præfatum impetum, ſeu virtutem moti<lb></lb>uam impreſſam, eſſe propriam qualitatem de ſecunda ſpe<lb></lb>cie, quæ dicitur potentia in prædicamento qualitatis, diuer<lb></lb>ſam tamen eſſentialiter à virtute motiua naturali, vt eſt gra<lb></lb>uitas, aut leuitas. </s>
          <s id="N17D69">Quatenus nimirum eſt principium forma<lb></lb>le intrinſecum quo producitur motus localis, non debitus <lb></lb>naturæ, ſed præter vel contra inclinationem illius secus ac <lb></lb>motus, qui producitur à grauitate, aut leuitate, qui ſemper <lb></lb>eſt determinatus ad vnum locum, iuxta inclinationem pro<lb></lb>priæ naturæ. </s>
          <s id="N17D76">Motus enim productus ab impetu indifferens <lb></lb>eſt ad quamcunque poſitionem, vel locum, ita vt quoquo<lb></lb>uerſum ab eo proiecta ferantur: Imò &amp; pila, vt Ariſtoteles <lb></lb>aduertit. </s>
          <s id="N17D7F">8. Phyſicor. tex. 22. per eundem impetum à proij<lb></lb>ciente receptum in parietem illidit, ac inde reſilit, qui mo<lb></lb>tus ſunt inter ſe contrarij. </s>
          <s id="N17D8A">Et crocæ, vel teſtulæ eodem, <lb></lb>impetu, quo in ſuperficiem aquæ proijciuntur, vix ad con<lb></lb>tactum peruenientes, per aliam lineam inde reſiliunt, ite<lb></lb>rumque vlterius, tanquam per ſaltus pluries in eandem ſu<lb></lb>perficiem incidunt, quouſque impetu extincto immergan<lb></lb>tur. </s>
        </p>
        <p id="N17D98" type="main">
          <s id="N17D9A">Vnde colligitur ipſam qualitatem impetus eiuſdem eſſe <lb></lb>infimæ ſpeciei in omnibus proiectis, ac motibus violentis. <lb></lb></s>
          <s id="N17DA0">Tum quia quodlibet proiectum per eam in infinitas loci <lb></lb>partes poſſet moueri, vt à centro ad circumferentiam; im<lb></lb>poſſibile autem eſt dari infinitas qualitates ſpecie diuerſas: <lb></lb>tum etiam quia omnis impetus ordinatur, ac tendit ad pro<lb></lb>ducendam præſentiam localem eiuſdem ſpeciei, abſtrahen<lb></lb>do à diſtantia, vel propinquitate cæli, à qua differentia non <pb pagenum="268" xlink:href="005/01/276.jpg"></pb>abſtrahunt grauitas, &amp; leuitas, quæ proinde ſpecie differunt <lb></lb>inter ſe, &amp; ab ipſo impetu. </s>
          <s id="N17DB4">Præterquam quod impetus dif<lb></lb>fert à grauitate, &amp; leuitate ratione principij extrinſeci, à <lb></lb>quo per <expan abbr="accidẽs">accidens</expan> procedit abſque exigentia naturæ, nec non <lb></lb>ratione deſitionis abſque introductione qualitatis contra<lb></lb>riæ. </s>
          <s id="N17DC3">Quare diximus non eſſe virtutem innatam, ac perma<lb></lb>nentem in ſubiecto, ſicut eſt grauitas, &amp; leuitas, quæ vnicui<lb></lb>que corpori debentur à propria natura. </s>
        </p>
        <p id="N17DCA" type="main">
          <s id="N17DCC">Denique dicimus, hanc virtutem motiuam impetus à <lb></lb>proijciente in ipſo actu proiectionis produci, non quidem <lb></lb>formaliter per motum localem, qui ſolùm eſt productiuus <lb></lb>præſentiæ localis ſed concomitanter ad illum per actionem <lb></lb>diſtinctam, quæ prout tendit ad qualitatem dici poteſt alte<lb></lb>ratio latè ſumpta; tum vel maximè qualitatis productio non <lb></lb>fit in inſtanti, ſed in tempore attamen breuiſſimo. </s>
          <s id="N17DDB">Etenim <lb></lb>licet impetus propriè non habeat contrarium, nihilominus <lb></lb>cum eius productio neceſſariò ſequatur motum <expan abbr="localẽ">localem</expan>, tan<lb></lb>quam conditionem requiſitam ad exerendas, &amp; applican<lb></lb>das vires proijcientis, neceſſariò etiam ipſa proportiando ſe <lb></lb>illi, fit ſucceſsiuè, atque in tempore. </s>
          <s id="N17DEC">Quare impetus pau<lb></lb>latim intenditur ab eodem proijciente magis, ac magis ſe <lb></lb>applicante in parua illa morula, <expan abbr="paulatimq.">paulatimque</expan> nec ſtatim per <lb></lb>omnes proiecti partes ſecundum eandem intentionem, vt <lb></lb>in lumine, quod pariter non in qualibet diſtantia diffunditur <lb></lb>ſecundum eandem intentionem, ſed ſucceſsiuè, quamuis ab<lb></lb>ſolutè in inſtanti producatur. </s>
          <s id="N17DFF">Poſt emiſsionem verò pro<lb></lb>iecti, nullam fieri intenſionem, nec diffuſionem explicatæ <lb></lb>qualitatis in eodem ſubiecto conſentaneum eſt; ſed tantum <lb></lb>in aerem quem offendit, quemque commotum facilius va<lb></lb>let vlterius pellere. </s>
          <s id="N17E0A">Vnde prouenit, vt velocior ſit motus <lb></lb>proiecti in poſterioribus partibus, quàm in prioribus, quouſ<lb></lb>que talis virtus hebetata langueſcat, vt præcedenti quæſt. <lb></lb></s>
          <s id="N17E12">explicatum eſt. </s>
        </p>
        <p id="N17E15" type="main">
          <s id="N17E17">Ex quo pariter intelligitur, cur proiecta in vacuo non <lb></lb>mouerentur proprio motu, vt docet Ariſtoteles 4. Phyſic. <lb></lb>tex. 68. Nam præcipua ratio ſucceſsionis in motu locali <pb pagenum="269" xlink:href="005/01/277.jpg"></pb>prouenit à reſiſtentia medij locum non ſtatim cedentis, vs <lb></lb>ipſemet Philoſophus poſtea docet tex. 70. quod cum non <lb></lb>eſſet in vacuo, non poſſet reſiſtere; <expan abbr="proindeq.">proindeque</expan> confeſtim de <lb></lb>loco ad locum cuncta proiecta transferri contingeret per <lb></lb>vnicum mutatum eſſe. </s>
          <s id="N17E35">Quod ſatis eſt inſinuaſſe ad suaden<lb></lb>das difficultates, quæ contra explicatam virtutem congere<lb></lb>re plerique conantur. </s>
        </p>
        <p id="N17E3C" type="head">
          <s id="N17E3E">Quæſtio Trigeſimaquarta.</s>
        </p>
        <p id="N17E41" type="main">
          <s id="N17E43">C<emph type="italics"></emph>vr neque parua valde, neque magna longè <lb></lb>proÿci queunt, ſed commenſurationem quan<lb></lb>dam illa habere oportet ad id quod proÿcit? </s>
          <s id="N17E4D">An <lb></lb>quia neceſſe est, quod proÿcitur, &amp; impellitur, <lb></lb>contraniti ei vnde impellitur quod autem <lb></lb>magnitudine ſua nihil cedit, c ut imbecillita<lb></lb>te nihil contranititur, non efficit pròiectionem <lb></lb>neque impulſionem. </s>
          <s id="N17E5E">Quod enim muliò impellentis excedit vi<lb></lb>res, haud quaquam cedit: quod verò multò eſt imbecillius, nihil <lb></lb>contranititur. </s>
          <s id="N17E6B">An quia tantum fertur id quod fertur, quan<lb></lb>tum aëris mouerit ad profundum: quod autem non mouetur, <lb></lb>neque mouebit quippiam, accidit auiem illis ambo illbæc babe<lb></lb>ve. </s>
          <s id="N17E76">Valde enim magnum, &amp; valde paruum, ceu non mota exi<lb></lb>ſtant: alterum namque nihil mouet, alterum verò nihil mo<lb></lb>uetur.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N17E80" type="head">
          <s id="N17E82">COMMENTARIVS.</s>
        </p>
        <p id="N17E86" type="main">
          <s id="N17E88">Qvid in cauſa ſit quærit hic Ariſtoteles, vt neque <lb></lb>parua valde, <expan abbr="neq;">neque</expan> magna nimis longè proijci queant, <lb></lb>ſed proportionem quandum habere debeant ipſa <lb></lb>proiecta cum proijciente. </s>
          <s id="N17E95">Docetque primò id eſſe, quòd <lb></lb>in proiectione ſemper ac neceſſariò intercedat aliqua proie<lb></lb>cti reſiſtentia, quæ tamen à proijciente vincitur, ea ſupera<lb></lb>tur. </s>
          <s id="N17E9E">Vnde quod magnitudine ſua, ac pondero ſitate ita reſi<lb></lb>ſtit, vt nihil cedat, nec eius renitentia valeat ſuperari; aut <lb></lb>ex oppoſito paruitate, &amp; imbecillitate propria, nihil omni-<pb pagenum="270" xlink:href="005/01/278.jpg"></pb>no reſiſtit, nequit aliquo pacto proijci, aut ab alio moueri. </s>
        </p>
        <p id="N17EAB" type="main">
          <s id="N17EAD">Qua in ſolutione illud non paruam continet difficulta<lb></lb>tem, quod quæ nihil contranituntur, ſiue reſiſtunt, proijci <lb></lb>minime poſſe Philoſophus velit. </s>
          <s id="N17EB4">Cum potius ab experien<lb></lb>tia inferri videatur contrarium. </s>
          <s id="N17EB9">Nam ſi quæ minus reſiſtunt <lb></lb>facilius mouentur, multò magis, <expan abbr="longèq.">longèque</expan> facilius quæ nihil <lb></lb>reſiſtunt abſolutè poterunt proijci, ac moueri. </s>
        </p>
        <p id="N17EC4" type="main">
          <s id="N17EC6">Pro huius autem difficultatis explicatione, atque intelli<lb></lb>gentia duo hic animaduertere oportet: Vnum eſt totam ra<lb></lb>tionem ſucceſſionis in motu, qua conſtituitur propriè mo<lb></lb>tus, ac diſtinguitur à mutatione inſtantanea, quæ fit tota ſi<lb></lb>mul, prouenire ex reſiſtentia corporis moti, quæ non niſi in <lb></lb>tempore ſuperatur. </s>
          <s id="N17ED3">Alterum verò eſt reſiſtentiam proie<lb></lb>ctorum in motu locali partim prouenire ab effectu grauita<lb></lb>tis, aut leuitatis quo ipſa proiecta diuerſas in poſitiones ten<lb></lb>dunt, atque inclinantur: partim quoque ab aere expellen<lb></lb>do, vt ipſa dum feruntur, in eius locum ſuccedant, ita vt re<lb></lb>ſiſtant motioni proijcientis, eò quod moueri nequeant niſi <lb></lb>mouendo aerem circumfuſum, quem debent expellere, &amp; <lb></lb>in cuius locum debent ſuccedere. </s>
        </p>
        <p id="N17EE4" type="main">
          <s id="N17EE6">His ergo præmonitis, liquidò conſtat, quod ab Ariſtotele <lb></lb>dictum eſt, nimirum proijci non poſſe, quæ nihil reſiſtunt. <lb></lb></s>
          <s id="N17EEC">Tum quia proiectio, ſeu proiecti latio non eſſet propriè mo<lb></lb>tus, nec fieret in tempore, ſed in inſtanti, quod eſt contra <lb></lb>experientiam: tum etiam quia vbi non adeſt reſiſtentia, <lb></lb>nec eius cauſa poteſt adeſſe, quæ in proiectis eſt circumob<lb></lb>ſiſtentia medij expellendi, &amp; inclinatio grauitatis, aut leui<lb></lb>tatis eorum. </s>
          <s id="N17EF9">Quæ autem nec grauitatem, nec leuitatem <lb></lb>habent, <expan abbr="nullamq.">nullamque</expan> medij circumobſiſtentis repugnantiam, <lb></lb>nullam pati poſſunt violentiam qualis eſt ea, quæ infertur <lb></lb>per impetum in ipſa proiecta grauia,aut leuia. </s>
          <s id="N17F06">Licet itaque <lb></lb>defectus reſiſtentiæ per ſe, &amp; abſtractè loquendo, non impe<lb></lb>diat, ſed potius iuuet actionem agentis: nihilominus tamen <lb></lb>in propoſito, cum arguat incapacitatem quandam ſubiecti <lb></lb>ad recipiendum impulſum proijcientis per vim illatam, &amp; <lb></lb>ſuperan dam aliquam intermedij contrarietatem, ſufficit vt <pb pagenum="271" xlink:href="005/01/279.jpg"></pb>ex eo nulla fieri poſſit proiectio, vt Ariſtoteles aſſerebat. </s>
          <s id="N17F18">Vn<lb></lb>de colligitur in orbium cæleſtium circumuolutione nullam <lb></lb>ab intelligentijs impetus qualitatem in illis produci; cum <lb></lb>nec illi ſint alterabiles nec grauitatem, aut <expan abbr="leuitatẽ">leuitatem</expan> habeant, <lb></lb>ſiue inclinationem aliquam ad reſiſtendum impulſui, <expan abbr="patien-damq.">patien<lb></lb>damque</expan> formam contrariam, aut violentiam ab impulſore. </s>
        </p>
        <p id="N17F2D" type="main">
          <s id="N17F2F">Sed contrà adhuc vrgeri poteſt, quia ex præfato diſcurſu <lb></lb>tantum concluditur, iuxta rerum ordinem fieri non poſſe <lb></lb>grauium aut leuium proiectionem abſque aliqua reſiſtentia, <lb></lb>qua data non ſequitur, vt quò minorilla fuerit, eò minus cor<lb></lb>pora proijci valeant; ſed potius oppoſitum. </s>
          <s id="N17F3A">Nam quæ mi<lb></lb>nus contranituntur, facilius ſuperantur, <expan abbr="longiusq.">longiusque</expan> propterea <lb></lb>proijci poſſunt. </s>
          <s id="N17F45"><expan abbr="Cumq.">Cumque</expan> parua valde, ſua imbecillitate mi<lb></lb>nus contranitantur, reſtat vt facilius ſuperari debeant, <expan abbr="lon-giusq.">lon<lb></lb>giusque</expan> à proijciente emittantur. </s>
        </p>
        <p id="N17F53" type="main">
          <s id="N17F55">Reſpondendum tamen eſt iuxta prædicta, corpora valde <lb></lb>parua minus quidem reſiſtere imbecillitate ſua, eo quod mi<lb></lb>norem habeant grauitatem, aut leuitatem; ex eadem autem <lb></lb>magnitudinis paruitate naſci minorem capacitatem illorum <lb></lb>ad recipiendum impulſum, quo pellere poſsint circumobſi<lb></lb>ſtentem aerem, vel aquam, &amp; in eius <expan abbr="locũ">locum</expan> ſucceſsiuè abeun<lb></lb>do ſuccedere. </s>
          <s id="N17F68">Impulſus enim, ſicut omnis alia ſimilis qua<lb></lb>litas, minus ex natura ſua imprimi valet in parua quantitate, <lb></lb>quàm in maiori, <expan abbr="minusq.">minusque</expan> in leuiori, ac rariori, quàm in gra<lb></lb>uiori, ac denſiori. </s>
          <s id="N17F75">Siquidem multiplicantur partes quali<lb></lb>tatis ad multitudinem partium quantitatis, quæ ſanè plures <lb></lb>ſunt in maiori, ac denſiori materia, quæ propterea etiam fit <lb></lb>grauior. </s>
          <s id="N17F7E">Ad agendum verò non tantum valet, ac requiri<lb></lb>tur proportionata quædam intenſio qualitatis actiuæ, ſed <lb></lb>etiam extenſio; vt patet in paruo, aut magno lumine vel ca<lb></lb>lore, qui licet ſit ſemper æquè intenſus in igne. </s>
          <s id="N17F87">minus ta<lb></lb>men, aut magis operatur iuxta maiorem, aut minorem ex<lb></lb>tenſionem, quam habet in magno, vel paruo igne. </s>
          <s id="N17F8E">Quare <lb></lb>huiuſmodi minuſcula corpora, de quibus loquebamur, poſt <lb></lb>acceptum impulſum adhuc imbecilliora remanent, quam <lb></lb>alia grandiora ad ſuperandam reluctantiam intermedij per <pb pagenum="272" xlink:href="005/01/280.jpg"></pb>quod debent tranſire. </s>
          <s id="N17F9C">Vnde optimè intulit Ariſtoteles, ip<lb></lb>ſa proiecta commenſurationem, ac proportionem quandam <lb></lb>cum proijciente requirere, vt eminus proijciantur. </s>
          <s id="N17FA3">Nam <lb></lb>in magnis valde deficit virtus motiua ipſius proijcientis ad <lb></lb>ſuperandam inclinationem, ac preſſionem grauitatis: in ad<lb></lb>modum verò paruis deficit capacitas ad recipiendam tan<lb></lb>tam virtutem motiuam, qua pellere poſſint intermedium, <lb></lb>ac per illud vlterius tranſilire. </s>
        </p>
        <p id="N17FB1" type="main">
          <s id="N17FB3">Ex quibus perquàm facilè patebit, quod Ariſtoteles ad<lb></lb>dit poſt explicatam ſolutionem, inquiens, idipſum fortaſſe, <lb></lb>ex eo adhuc contingere, quia tantum fertur id quod proij<lb></lb>citur, quantum aeris moucerit in profundum, videlicet ver<lb></lb>ſus eam partem, in quam tendit. </s>
          <s id="N17FBE">Siquidem in eius locum, <lb></lb>tranſeundo debet ſuccedere; nec poſſet, niſi dimouendo <lb></lb>illum à proprio loco. </s>
          <s id="N17FC5">At valde parua, vel magna nimis, di<lb></lb>mouere nequeunt ipſum aerem, eo quod nihil mouet im<lb></lb>motum; ipſa autem ſe habeant tanquam immota: parua <lb></lb>quidem propter imbecillitatem impetus recepti, qui non <lb></lb>ſufficit ad motum: magna verò propter exuperantiam gra<lb></lb>uitatis cuius preſſione non ſinuntur ab impellente moueri: <lb></lb>Ergo ipſa valde parua, ac nimis magna proijci nullo modo <lb></lb>poſſunt, quod erat probandum. </s>
        </p>
        <p id="N17FD6" type="head">
          <s id="N17FD8">Quæſtio Trigeſimaquinta.</s>
        </p>
        <p id="N17FDB" type="main">
          <s id="N17FDD">C<emph type="italics"></emph>vr ea quæ in vorticoſis feruntur aquis, ad me<lb></lb>dium tandem aguntur omnia? </s>
          <s id="N17FE5">An quia magni<lb></lb>tudinem habet quodcunque fertur, quamobrem <lb></lb>illius extrema in duobus ſunt circulis, hoc qui<lb></lb>dem minori, illo verò maiori: quare maior di<lb></lb>strahit: quoniam sceleriùs fertur, &amp; tranſuer<lb></lb>ſum impellit illud ad minorem: quoniam autem id quod fer<lb></lb>tur, latitudinem habet, &amp; iste rurſum idem efficit, &amp; ad inte<lb></lb>riorem propellit, donec ad mediam perueniat. </s>
          <s id="N17FF6">An quia quod <lb></lb>fertur, ſimili ſe habet modo ad omnes circulos propter medium, <lb></lb>medium enim in vnoquoque circulo æqualiter diſtat. </s>
          <s id="N17FFD">An <lb></lb>quia quorum quidem circumactæ aqua latio non ſuperior pro-<emph.end type="italics"></emph.end><pb pagenum="273" xlink:href="005/01/281.jpg"></pb><emph type="italics"></emph>pter magnitudinem, ſed grauitate ſua circuli celeritatem ex<lb></lb>cellunt, ea neceſſe est relinqui, &amp; tardius ferri, tardius au<lb></lb>tem minor circulus fertur; non idem enim in tempore æquali <lb></lb>magnus cum paruo reuoluitur circulus, quando circa idem <lb></lb>fuerint medium, quamobrem in minori circulo relinqui neceſ<lb></lb>se eſt, donec ad medium perueniant. </s>
          <s id="N18017">Quorumcumque autem <lb></lb>ſuperior à principio fuerit latio, &amp; finiens idem efficiet; opor<lb></lb>tet enim hunc quidem ſtatim, alterum verò celeritate ſupera<lb></lb>re grauitatem, quamobrem ad interiorem ſemper circulum re<lb></lb>linquetur quodcumque. </s>
          <s id="N18022">Neceſſe enim eſt quod non ſuperatur, <lb></lb>aut in exteriori, aut in interiori moueri, in illo autem in quo <lb></lb>eſt, impoſsibile eſt ferri, quod non ſuperatur: adhuc verò mi<lb></lb>nus in exteriori, celerior enim exterioris circuli eſt latio, re<lb></lb>stat igitur, vt id quod non ſuperatur, ad interiorem transfe<lb></lb>ratur, ſemper autem vnumquodque proficit, vt non ſuperetur. <lb></lb></s>
          <s id="N18030">Quoniam verò peruenire ad medium, finem quidem efficit, vt <lb></lb>quippiam non moueatur, ſtat autem ſolummodò ipſum cen<lb></lb>trum, ad hoc ſanè-omnia congregari neceſſe eſt.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N18039" type="head">
          <s id="N1803B">COMMENTARIVS.</s>
        </p>
        <p id="N1803F" type="main">
          <s id="N18041">Vltima <expan abbr="tãdem">tandem</expan> hac in quæſtione cauſam perſcrutatur <lb></lb>Ariſtoteles cur ea, quæ in aquarum vorticibus, ac <lb></lb>reuolutionibus ferri cernuntur, ad medium poſtre<lb></lb>mo ferantur. </s>
          <s id="N1804E"><expan abbr="Primumq.">Primumque</expan> id ex eo fortaſſe euenire docet, <lb></lb>quod lata corporis magnitudo dum circumagitur vortice, <lb></lb>inter duos veluti circulos circa idem centrum ductos con<lb></lb>uoluitur, quorum exterior, ac maior, cum velocius feratur, <lb></lb>quàm minor, atque interior, velocius, ac facilius pariter de<lb></lb>fert, <expan abbr="vehitq.">vehitque</expan> correſpondens ſibi extremum magnitudinis in<lb></lb>termediæ. </s>
          <s id="N18064">Quo fit vt altero extremo minus, ac tardius com<lb></lb>moto, tota ipſa magnitudo quaſi in tranſuerſum dimota, ab <lb></lb>exteriori in interiorem circulum vergendo transferatur: Ex <lb></lb>quo ſimiliter in alium, atque alium minorem perueniat, <lb></lb>quouſque ad centrum agatur: Etenim quod fertur ſimili ſe <lb></lb>habet modo ad omnes circulos circa idem centrum per <lb></lb>quos conuoluitur, vt ipſemet Philoſophus quaſi nouo me<lb></lb>dio argumentando ſubiungit. </s>
        </p>
        <pb pagenum="274" xlink:href="005/01/282.jpg"></pb>
        <p id="N18079" type="main">
          <s id="N1807B">Secundò verò idipſum confirmat ex eo, nam delati cor<lb></lb>poris magnitudo diuerſimodè ſecundum diuerſas ſui partes <lb></lb>ſe habet ad circulos à quibus mouetur; Quandoquidem ſe<lb></lb>cundum partes à centro vorticis remotiores, velocius mo<lb></lb>uetur à circulis maioribus, quàm ſecundum partes vicinio<lb></lb>res à circulis minoribus. </s>
          <s id="N18088">Ex quo fit, vt magnitudo ipſa non <lb></lb>æqualiter ſuperetur, ac ſecundum ſe totam deferri poſsit ad <lb></lb>motum circuli maioris, <expan abbr="proindeq.">proindeque</expan> vel extra, vel intra illum <lb></lb>eam tranſmitti debere: ſed nequit extra, cum adhuc cele<lb></lb>rior ibi fiat latio cui non poſſet correſpondere ſecundum <lb></lb>omnes ſuas partes; ergo reſtat, vt ab ipſa exuperantia cir<lb></lb>culi maioris in extimam eius partem incidentis, magnitu<lb></lb>do ipſa tranſmittatur intra, nempe ad interiores circulos, &amp; <lb></lb>ſic deinceps ad alios interiores vſque ad centrum illis <lb></lb>commune in quo tandem omnia congregantur, atque <lb></lb>quieſcunt. </s>
        </p>
        <p id="N180A3" type="main">
          <s id="N180A5">Quod ſanè non ita concipiendum eſt, vt ipſis portionibus <lb></lb>circuli, quibus agitata magnitudo conuoluitur, circulum <lb></lb>abſoluentibus, ac perfectum motum circularem complen<lb></lb>tibus, diuerſum ea curſum teneat, ac aliter quàm aqua ipſa <lb></lb>deferens moueatur. </s>
          <s id="N180B0">Siquidem tàm aqua, quàm corpus in <lb></lb>ea latum, ac ſupernatans, cum primò circularem motum in<lb></lb>choauerit ob cauſam prædictam, circumferentias quas de<lb></lb>ſcribere cæperat, in ſpiras commutat, &amp; à perfecto motu <lb></lb>circulari ſenſim degenerat. </s>
          <s id="N180BB">Eodem enim eſt vtriuſque ra<lb></lb>tio, vt partes exteriores in gyrum ductæ, tanquam à centro <lb></lb>remotiores, velociùs ferantur, <expan abbr="prænaleantq.">præualeantque</expan> interioribus, <lb></lb>quas propterea cum ſecum rapere nequeant pari paſſu per <lb></lb>lineas æquales, nec ab eis diſiungi permittantur, ſe illis ag<lb></lb>glomerando interius magis, circumiendo contorqueant, <lb></lb>quouſque ſimul in centrum perueniant. </s>
          <s id="N180CE">Quod eſt per ſpi<lb></lb>ras tam aquam, quàm corpus in ea latum deferri, vt ſenſu <lb></lb>manifeſtiſsimè conſtat, ac perſpicuè videre eſt in magnis <lb></lb>vorticibus fluminum, quæ rapidè fluunt, <expan abbr="amplosq.">amplosque</expan> non ha<lb></lb>bent ſinus. </s>
          <s id="N180DD">Nam incidens aqua in ſinus ipſos, anguſtos, <lb></lb>turbinatim quidem ac per ſpiras, non autem per abſolutos <pb pagenum="275" xlink:href="005/01/283.jpg"></pb>circulos cogitur circumuolui. </s>
          <s id="N180E7">Id quod nec Ariſtoteles ne<lb></lb>gauit, aut tantus vir potuit ignorare; nec alienum eſt à tra<lb></lb>dita eius doctrina, vt Baldus contendit, quaſi Philoſophus <lb></lb>dixiſſet, aquam in vorticibus circumferri per circulos perfe<lb></lb>ctos, acta<expan abbr="q.">que</expan> diſtinctos, &amp; corpus in ea latum ab vno in alium <lb></lb>circulum pertranſire; hoc eſt ab exterioribus in interiores <lb></lb>appropinquando ſe magis ad centrum. </s>
          <s id="N180FB">Quod proculdubio <lb></lb>falſum eſſet, cum ſenſu, vt diximus conſtet, aquam non mo<lb></lb>ueri per circulos, ſed per ſpiras: ac minimè conſentaneum <lb></lb>ſit rationi, corpus delatum, diuerſum à deferente iter tenere. <lb></lb></s>
          <s id="N18107">Præsertim cum latio corporis ſupernatantis in aqua, ſit ve<lb></lb>ctio, &amp; non impulſio. </s>
        </p>
        <p id="N1810C" type="main">
          <s id="N1810E">Ad faciliorem tamen captum eorum, quæ de mente <lb></lb>Ariſtotelis à nobis relata ſunt, ſit aqua primò rectà decur<lb></lb>rens AB, quæ incidat in curuam ripam BC, vnde repul<lb></lb>ſa vergere cogatur in gyrum deſcribendo quaſi portionem <lb></lb><figure id="id.005.01.283.1.jpg" xlink:href="005/01/283/1.jpg"></figure><lb></lb>quandam circuli iuxta figuram eiuſdem ripæ, cui aquæ mo<lb></lb>les neceſsariò adaptatur, vt BCD. </s>
          <s id="N18122">Sitque corpus latum in <lb></lb>aqua vbi E. </s>
          <s id="N18128">Dicimus ergo quod aqua ceptum iter, ſeu mo<lb></lb>tum circularem ſecundans nequit circulum abſolutum per<lb></lb>ficere, quem punctis BCDF hic expreſſimus, eodemque <lb></lb>circulo iniectam, ac ſupernatantem magnitudinem E ſecum <pb pagenum="276" xlink:href="005/01/284.jpg"></pb>abripiens, circumagere: Quia poſtquam aqua è loco ripæ <lb></lb>continentis diſceſſerit, &amp; vltrò ſe in gyrum mouere cæperit <lb></lb>per impetum repulſionis inde acceptum, partes eius exte<lb></lb>riores, ſeu maioris circumferentiæ, ob maiorem velocitatem <lb></lb>propriam, <expan abbr="maioremq.">maioremque</expan> impetum ex incidentia receptum, ef<lb></lb>ficaciùs agunt quàm interiores, quæ per minorem circum<lb></lb>ferentiam commouentur, ac nullum immediatè repulſum <lb></lb>acceperunt à conſiſtenti ripa prædicta. </s>
          <s id="N18148"><expan abbr="Ideoq.">Ideoque</expan> non tantum <lb></lb>correſpondentem ſibi partem exteriorem lati corporis E, <lb></lb>nempe quæ remotior eſt à centro vorticis magis valent vl<lb></lb>terius promouere, quàm illæ partem eiuſdem corporis in<lb></lb>teriorem; ſed ipſaſmet partes aquæ interiores, quæ per mi<lb></lb>nores ambitus circumuoluuntur magis compellere, ac in <lb></lb>minores circuitus reſtringere, quibus ſeſe adaptando ſimul <lb></lb>in ſpiras degenerant. </s>
          <s id="N1815E">Et ſic lata corporis magnitudo vnà <lb></lb>cum aqua tandem ad vorticis centrum reducitur. </s>
        </p>
        <p id="N18163" type="main">
          <s id="N18165">Quod ſi abſtractè loquendo quælibet maior, ac exterior <lb></lb>circumferentia velocius moueatur, quàm minor, &amp; interior <lb></lb>circa idem centrum, <expan abbr="validiusq.">validiusque</expan> propterea corpora impelle<lb></lb>re, aut ſecum rapere poſſe intelligatur, abſque eo, quod ad <lb></lb>hoc præſtandum circularem motum relinquat, ac in ſpiras <lb></lb>conuertatur, compellendo etiam circumferentias interiores <lb></lb>ad ſecum degenerandum ſimili modo. </s>
          <s id="N18179">Id tamen in propo<lb></lb>ſito locum non habet, tum quia aquæ fluenti, &amp; ob inciden<lb></lb>tiam aliquam ſe retorquenti, nullus in rigore præſcribitur <lb></lb>circulus, quem debeat perficere, nec partibus eius exterio<lb></lb>ribus interdicitur acceſſus ad interiores, ſicut circumferen<lb></lb>tiæ exteriori ſolidi corporis ad interiorem, à qua profectò <lb></lb>æquè diſtat in circulo: tum quia non eſt eadem proportio <lb></lb>exceſſus in velocitate, &amp; efficacitate inter circumferentiam <lb></lb>exteriorem, &amp; interiorem in circulo conſiſtentis materiæ <lb></lb>dum rotatur, atque inter partes exteriores, &amp; interiores <lb></lb>aquæ per incidentiam quandam circumuolutas. </s>
          <s id="N18190">Quando<lb></lb>quidem ſemper eſt maior exceſſus in iſtis, quàm in illis. </s>
          <s id="N18195">Vt <lb></lb>qui duplici ex cauſa proficiſcatur; tàm ſcilicet ex maiori <lb></lb>ambitu, quem perficiunt in æquali tempore, quàm ex maio-<pb pagenum="277" xlink:href="005/01/285.jpg"></pb>ri repulſu, quem immediatè per incidentiam acceperunt à <lb></lb>ripa. </s>
          <s id="N181A3">Admiſſo autem hoc exceſſu maiori, conſequens eſt <lb></lb>admittere adhuc maiorem circuitum, qui cum reperiri non <lb></lb>poſſit in figura perfectè circulari, concedendum eſt, circu<lb></lb>lum in ſpiras conuerti, in quibus extima linea longè maior <lb></lb>eſt reſpectu interioris, quàm æqualis extima peripheria re<lb></lb>ſpectu circumferentiæ interioris, vt obſeruare quiſque po<lb></lb>terit; Quod ſuperuacaneum eſſet hic ſermonem vlterius <lb></lb>protrahendo probare, cum ſatis dictum ſit ad textus Ariſto<lb></lb>telis expoſitionem, <expan abbr="veritatisq.">veritatisque</expan> dilucidationem quantum no<lb></lb>bis aſſequi datum eſt in hac <expan abbr="cæterisq.">cæterisque</expan> explicatis quæſtioni<lb></lb>bus, quibus veluti in profundo Peripateticæ doctrinæ pela<lb></lb>go, poſt tot ſpeculationum circuitus, <expan abbr="variarumq.">variarumque</expan> diſputatio<lb></lb>num anfractus, ac vortices, vtinam tandem ad centrum il<lb></lb>lud ageretur mens noſtra, ad quod omnia referuntur, &amp; in. <lb></lb></s>
          <s id="N181CD">quo ſolo poſt huius vitæ multiplices flexus, ac ſpiras tan<lb></lb>quam ſummo bono immobiliter adhærendo poteſt quie<lb></lb>ſcere. </s>
        </p>
        <p id="N181D4" type="head">
          <s id="N181D6"><emph type="italics"></emph>FINIS.<emph.end type="italics"></emph.end></s>
        </p>
        <pb xlink:href="005/01/286.jpg"></pb>
        <p id="N181E1" type="head">
          <s id="N181E3">INDEX TEXTVVM <lb></lb>ATQVE ADDITIONVM</s>
        </p>
        <p id="N181E8" type="head">
          <s id="N181EA">Primæ partis huius Mechanicæ Tra<lb></lb>ctationis.<lb></lb>O<emph type="italics"></emph>peris argumen<lb></lb>tum.                                                   pag.<emph.end type="italics"></emph.end> 1 <lb></lb><emph type="italics"></emph>Quæ ſit artis Me<lb></lb>chanicæ facul<lb></lb>tas Textus pri<lb></lb>mus pag.<emph.end type="italics"></emph.end>                                                    4 <lb></lb><emph type="italics"></emph>De nomine, &amp; origine faculta<lb></lb>tis Mechan. </s>
          <s id="N1820D">Addit prima. </s>
          <s id="N18210">pag<emph.end type="italics"></emph.end>                                6 <lb></lb><emph type="italics"></emph>De obiecto circa quod Mechani<lb></lb>ca facultas verſatur. </s>
          <s id="N1821C">Addi<lb></lb>tio<emph.end type="italics"></emph.end> 2. <emph type="italics"></emph>pag.<emph.end type="italics"></emph.end>                                          9 <lb></lb><emph type="italics"></emph>Qua ratione facultas Mechani<lb></lb>ca conſtituatur ars &amp; ſcien<lb></lb>tia. </s>
          <s id="N18232">Additio<emph.end type="italics"></emph.end> 3.                                            12 <lb></lb><emph type="italics"></emph>Mechanicam facultatem verè, <lb></lb>  ac propriè eſſe ſcientiam Ma<lb></lb>thematicam. </s>
          <s id="N18240">Addit.<emph.end type="italics"></emph.end> 4.                                      17 <lb></lb><emph type="italics"></emph>Quænam deſcriptio quid ditatiua <lb></lb>  huius facultatis colligatur ex <lb></lb>  dictis, &amp; quo pacto ab alÿs <lb></lb>  ſcientÿs distinguatur. </s>
          <s id="N18250">Addi<lb></lb>tio<emph.end type="italics"></emph.end> 5.                                                     25 <lb></lb><emph type="italics"></emph>De vnitate ſcientiæ Mechanicæ, <lb></lb>  eiuſque partibus. </s>
          <s id="N1825E">Additio<emph.end type="italics"></emph.end> 6. <lb></lb>  <emph type="italics"></emph>pag.<emph.end type="italics"></emph.end>                                                    26 <lb></lb><emph type="italics"></emph>Quem gradum perfectionis, aut <lb></lb>  dignitatis facultas Mechani<lb></lb>ca obtineat. </s>
          <s id="N18274">inter ſcientias. <lb></lb>  Addit.<emph.end type="italics"></emph.end> 7. <emph type="italics"></emph>pag.<emph.end type="italics"></emph.end>                                      30 <lb></lb><emph type="italics"></emph>De dignitatibus, admirandiſque <lb></lb>  circuli proprietatibus. </s>
          <s id="N18288">Tex.<emph.end type="italics"></emph.end> 2. <lb></lb>  <emph type="italics"></emph>pag.<emph.end type="italics"></emph.end>                                                    33 <lb></lb><emph type="italics"></emph>De prima circuli admiranda <lb></lb>  proprietate. </s>
          <s id="N1829C">Tex.<emph.end type="italics"></emph.end> 3.                                       34 <lb></lb><emph type="italics"></emph>De ſecunda circuli proprietate. <lb></lb>  Textus<emph.end type="italics"></emph.end> 4.                                                  35 <lb></lb><emph type="italics"></emph>De tertia circuli proprietate. <lb></lb>  Textus<emph.end type="italics"></emph.end> 5.                                                  36 <lb></lb><emph type="italics"></emph>De quarta circuli proprietate. <lb></lb>  Tex.<emph.end type="italics"></emph.end> 6.                                                    39 <lb></lb><emph type="italics"></emph>Quo pacto linea circulum deſcri<lb></lb>bens duabus feratur lationi<lb></lb>bus. </s>
          <s id="N182C5">Tex.<emph.end type="italics"></emph.end> 7.                                               40 <lb></lb><emph type="italics"></emph>Quo ratione partes diametri à <lb></lb>  centro remotiores magis parti<lb></lb>cipent de motu naturali, pro<lb></lb>pinquiores verò magis de præ<lb></lb>ternaturali. </s>
          <s id="N182D7">Tex.<emph.end type="italics"></emph.end> 8.                                       49 <lb></lb><emph type="italics"></emph>De instrumentis, ac machinis <lb></lb>  naturam circuli in motione <lb></lb>  partticipantibus. </s>
          <s id="N182E5">Addit.<emph.end type="italics"></emph.end> 1.                                53 <lb></lb><emph type="italics"></emph>De Libra.<emph.end type="italics"></emph.end>                                                 55 <lb></lb><emph type="italics"></emph>De Veste.<emph.end type="italics"></emph.end>                                                 56 <lb></lb><emph type="italics"></emph>De Trochlea.<emph.end type="italics"></emph.end>                                              58 <lb></lb><emph type="italics"></emph>De Axe in Peritrochio.<emph.end type="italics"></emph.end>                                    60 <lb></lb><emph type="italics"></emph>De Cuneo.<emph.end type="italics"></emph.end>                                                 61 <lb></lb><emph type="italics"></emph>De Choclea.<emph.end type="italics"></emph.end>                                               63 <lb></lb><emph type="italics"></emph>De Centro grauitatis, naturalique <lb></lb>mobilitate grauium, &amp; <expan abbr="leuiũ">leuium</expan>. <lb></lb>  Additio<emph.end type="italics"></emph.end> 2.                                                 64 <lb></lb><emph type="italics"></emph>De præternaturali, &amp; artificioſa <lb></lb>  grauium, &amp; leuium. </s>
          <s id="N1832A">Additio<emph.end type="italics"></emph.end> 3. <lb></lb>  <emph type="italics"></emph>pag.<emph.end type="italics"></emph.end>                                                    68 </s>
        </p>
        <pb xlink:href="005/01/287.jpg"></pb>
        <p id="N1833B" type="head">
          <s id="N1833D">INDEX <lb></lb>QVAESTIONVM <lb></lb>SECVNDAE PARTIS.<lb></lb>Q<emph type="italics"></emph>vestio prima Cum <lb></lb>  maiores libræ exa<lb></lb>ctiores ſint minori<lb></lb>bus. </s>
          <s id="N1834F">pag.<emph.end type="italics"></emph.end>                                                  73 <lb></lb>Quæſtio 2. <emph type="italics"></emph>Cur ſi ſpartum lo<lb></lb>cetur ſupra iugum libræ ip<lb></lb>ſaque ab altero extremo depri<lb></lb>matur, rurſum illud aſcen<lb></lb>dat, ſecus ac ſi ſpartum loce<lb></lb>tur infra.<emph.end type="italics"></emph.end>                                                 77 <lb></lb>Quæſtio 3. <emph type="italics"></emph>Cur exiguæ vires <lb></lb>  adhibito vecte magna moueant <lb></lb>  pondera.<emph.end type="italics"></emph.end>                                                   85 <lb></lb>Quæſtio 4. <emph type="italics"></emph>Cur ÿ, qui in nauis <lb></lb>  medio ſunt remiges, magis na<lb></lb>uem moueant quam qui in alio <lb></lb>  ſitu.<emph.end type="italics"></emph.end>                                                      91 <lb></lb>Quæſtio 5. <emph type="italics"></emph>Cur paruum exiſtens <lb></lb>  gubernaculum tantas habeat <lb></lb>  vires ad circumferenda naui<lb></lb>gia.<emph.end type="italics"></emph.end>                                                       98 <lb></lb>Quæſtio 6. <emph type="italics"></emph>Cur quanto antenna <lb></lb>  ſublimior ſuerit ÿſdem velis, <lb></lb>  &amp; eodem vento, celerius fe<lb></lb>rantur nauigia.<emph.end type="italics"></emph.end>                                           118 <lb></lb>Quæſtio 7. <emph type="italics"></emph>Cur nautæ vento ex <lb></lb>  tranſuerſo perflante, veli par<lb></lb>tem quæ ad puppim vergit <expan abbr="cõ-">con<lb></lb></expan>stringunt, quæ verò ad pro<lb></lb>ra relaxant.<emph.end type="italics"></emph.end>                                              124 <lb></lb>Quæſtio 8. <emph type="italics"></emph>Cur ex figurarum <lb></lb>  genere, quæcunque rotundæ <lb></lb>  ſunt facilius moueantur.<emph.end type="italics"></emph.end>                                  129 <lb></lb>Quæſtio 9. <emph type="italics"></emph>Cun ea quæ per maio<lb></lb>res circulos tolluntur citius ac <lb></lb>  facilius moueantur.<emph.end type="italics"></emph.end>                                       139 <lb></lb>Quæſtio 10. <emph type="italics"></emph>Cur facilius quan<lb></lb>do ſine pondere eſt mouetur li<lb></lb>bra.<emph.end type="italics"></emph.end>                                                      143 <lb></lb>Quæſtio 11. <emph type="italics"></emph>Cur ſuper ſcytalas <lb></lb>  facilius portentur onera quàm <lb></lb>  ſuper currus.<emph.end type="italics"></emph.end>                                             147 <lb></lb>Quæſtio 12. <emph type="italics"></emph>Cur longius feran<lb></lb>tur miſſilia funda, quam ma<lb></lb>nu miſſa.<emph.end type="italics"></emph.end>                                                 149 <lb></lb>Quæſtio 13. <emph type="italics"></emph>Cur ſi longiores fue<lb></lb>rint collopes circa. </s>
          <s id="N183F3">idem iu<lb></lb>gum, facilius circumagatur. <lb></lb>  Itemque cur graciliores ſuc<lb></lb>culæ facilius pariter ab eadem, <lb></lb>  potentia circumuoluantur. </s>
          <s id="N183FE">pa<lb></lb>gina.<emph.end type="italics"></emph.end>                                                     154 <lb></lb>Quæſtio 14. <emph type="italics"></emph>Cur lignum faci<lb></lb>lius genu frangitur, cum ab <lb></lb>  extremis apprehenditur, quàm <lb></lb>  cum prope genu.<emph.end type="italics"></emph.end>                                           157 <lb></lb>Quæſtio 15. <emph type="italics"></emph>Cur ea quæ circa <lb></lb>  litora appellantur. </s>
          <s id="N1841B">Crocæ, ro<lb></lb>tunda ſint figura.<emph.end type="italics"></emph.end>                                        160 <lb></lb>Quæſtio 16. <emph type="italics"></emph>Cur. </s>
          <s id="N18429">quanto longio<lb></lb>ra ſunt ligna, tanto imbecil<lb></lb>liora fiant, magisque infle<lb></lb>ctantur.<emph.end type="italics"></emph.end>                                                  163 <lb></lb>Quæſtio 17. <emph type="italics"></emph>Cur paruo existen-<pb xlink:href="005/01/288.jpg"></pb>  te cuneo eius adminiculo ma<lb></lb>gna ſcindantur corpora.<emph.end type="italics"></emph.end>                                   167 <lb></lb>Quæſtio 18. <emph type="italics"></emph>Cur duabus tro<lb></lb>chleis adinuicem ex oppoſito <lb></lb>  compoſitis, ac fune circumdu<lb></lb>cto, magna trahantur ponde<lb></lb>ra, quamuis imbecilla ſit vir<lb></lb>tus trahentis.<emph.end type="italics"></emph.end>                                            171 <lb></lb>Quæſtio 19. <emph type="italics"></emph>Cur ſecuris, per<lb></lb>cuſsione potius quàm ſupera<lb></lb>diecto pondere, lignum ſcin<lb></lb>dere valeat.<emph.end type="italics"></emph.end>                                              177 <lb></lb>Quæſtio 20. <emph type="italics"></emph>Cur ſtatera paruo <lb></lb>  appendiculo magna trutinet <lb></lb>  onera.<emph.end type="italics"></emph.end>                                                    184 <lb></lb>Quæſtio 21. <emph type="italics"></emph>Cur dentes facilius <lb></lb>  <expan abbr="extrabãtur">extrabantur</expan> dentiforcipis adhi<lb></lb>bito inſtrumento, quàm ſola <lb></lb>  manu.<emph.end type="italics"></emph.end>                                                     189 <lb></lb>Quæſtio 22. <emph type="italics"></emph>Cur nuces abſque <lb></lb>  ictu facile confringantur in <lb></lb>  strumento ad eum vſum inſti<lb></lb>tuto.<emph.end type="italics"></emph.end>                                                     193 <lb></lb>Quæſtio 23. <emph type="italics"></emph>Cur ſi duo puncta <lb></lb>  extrema vnius lateris in <lb></lb>  Rombo duabus ſimul ferantur <lb></lb>lationibus cum eadem veloci<lb></lb>tate, vnum maius, alterum <lb></lb>  minus ſpacium percurrat. <lb></lb>  Item cur quod ſuper latus <lb></lb>  fertur minus <expan abbr="pertrãſeat">pertranſeat</expan>, quàm <lb></lb>  ipſum latus.<emph.end type="italics"></emph.end>                                              200 <lb></lb>Quæſtio 24. <emph type="italics"></emph>Cur ex duobus cir<lb></lb>culis circa idem centrum coap<lb></lb>tati, ac reuoluti ſecundum <lb></lb>  abſidem, maior minori æqua<lb></lb>le ſpacium percurrit. </s>
          <s id="N184B9">Seor<lb></lb>ſum verò conuoluti, maior <lb></lb>  maius, minor verò minus iux<lb></lb>ta proportionem circumferen<lb></lb>tiæ vnius ad circumferentiam <lb></lb>  alterius.<emph.end type="italics"></emph.end>                                                 205 <lb></lb>Quæſtio 25. <emph type="italics"></emph>Cur lectulorum <lb></lb>  ſpondæ ſecundum duplam <lb></lb>  proportionem longitudinis ad <lb></lb> latitudinem efficiantur. </s>
          <s id="N184D6">Cur <lb></lb>  verè in illis muniendis resies <lb></lb>  per tranſuerſum, non autem <lb></lb>  per diametrum extendantur. <lb></lb>  pag.<emph.end type="italics"></emph.end>                                                      225 <lb></lb>Quæſtio 26. <emph type="italics"></emph>Cur difficilius pro<lb></lb>cera ligna ab extremo ſuper <lb></lb>  humerum geſtentur, quam <lb></lb>  è medio, æquali exiſtente pon<lb></lb>dere.<emph.end type="italics"></emph.end>                                                     228 <lb></lb>Quæſtio 27. <emph type="italics"></emph>Cur ſi valde pro<lb></lb>cerum fuerit lignum, quam<lb></lb>uis eiuſdem ſit ponderis, &amp; è <lb></lb>  medio ſustineatur, difficilius <lb></lb>  tamen ſuper humerum geſte<lb></lb>tur.<emph.end type="italics"></emph.end>                                                      232 <lb></lb>Quæſtio 28. <emph type="italics"></emph>Cur iuxta puteos <lb></lb>  conſtituta Celonia ad aquam <lb></lb>  hauriendam facilius mouen<lb></lb>tur, onus in altero extremo <lb></lb>  tranſuerſarÿ ligni apponendo. <lb></lb>  pag.<emph.end type="italics"></emph.end>                                                      233 <lb></lb>Quæſtio 29. <emph type="italics"></emph>Cur duo ſuper li<lb></lb>gnum aliquod pondus feren<lb></lb>tes non æquè grauentur ſi in <lb></lb>  eorum medio non extiterit ip<lb></lb>ſum pondus, ſed magis is cui <lb></lb>  ipſum proximius fuerit. </s>
          <s id="N18527">pa<lb></lb>gina.<emph.end type="italics"></emph.end>                                                     237 <lb></lb>Quæſtio 30. <emph type="italics"></emph>Cur à ſeſsione ſur<lb></lb>gentes angulos rectos, quos <lb></lb>  efficiebat thorax cum femore, <lb></lb>  ac femur cum tibia; in acu<lb></lb>tos commutant.<emph.end type="italics"></emph.end>                                            241 <lb></lb>Quæſtio 31. <emph type="italics"></emph>Cur facilius moue<lb></lb>tur commotum, quàm manens. <lb></lb>  pag.<emph.end type="italics"></emph.end>                                                      245 <lb></lb>Quæſtio 32. <emph type="italics"></emph>Cur ea quæ proÿ<lb></lb>ciuntur ceſſent à latione.<emph.end type="italics"></emph.end>                         252 <pb xlink:href="005/01/289.jpg"></pb>Quæſtio 33. <emph type="italics"></emph>Cur proiecta mo<lb></lb>ueantur quamuis impellens <lb></lb>  ea non conſequatur.<emph.end type="italics"></emph.end>                                       260 <lb></lb>Quæſtio 34. <emph type="italics"></emph>Cur neque parua <lb></lb>  valde, neque magna nimis lon<lb></lb>gè proÿci queant.<emph.end type="italics"></emph.end>                             269 <lb></lb>Quæſtio 35. <emph type="italics"></emph>Cur ea quæ in <lb></lb>  aquarum vorticibus ferun<lb></lb>tur, ad medium tandem agan<lb></lb>tur.<emph.end type="italics"></emph.end>                                                      272 </s>
        </p>
        <figure id="id.005.01.289.1.jpg" xlink:href="005/01/289/1.jpg"></figure>
        <pb xlink:href="005/01/290.jpg"></pb>
        <p id="N18585" type="head">
          <s id="N18587">INDEX RERVM</s>
        </p>
        <p id="N1858A" type="head">
          <s id="N1858C">A <lb></lb>Absidem ſecun<lb></lb>dum quam per <lb></lb>  ſe <expan abbr="cõuoluitur">conuoluitur</expan> cir<lb></lb>culus <expan abbr="commẽſu-">commenſu<lb></lb></expan>  rari plano ſuper <lb></lb>  quod rotatur. <lb></lb>  pag.                                                          216 <lb></lb>Abſidem verò circuli delati ad ro<lb></lb>tationem alterius, non ita. </s>
          <s id="N185A8">ibi<lb></lb>dem, &amp; ſequente. <lb></lb></s>
          <s id="N185AE">Motum circuli ſecundum Abſi<lb></lb>dem eſſe motum quendam mix<lb></lb>tum ex duplici latione.                                       215 <lb></lb>Secundum Abſidem dimotis cir<lb></lb>culis, dimouetur &amp; centrum il<lb></lb>lorum.                                                        130 <lb></lb>Accidentia nonnulla à cauſis na<lb></lb>turalibus producta conueniunt <lb></lb>  illis præter naturam. </s>
          <s id="N185C1">pag. </s>
          <s id="N185C4">70. <lb></lb>  &amp;                                                         251 <lb></lb>Actio debet eſſe ab inæquali pro<lb></lb>portione.                                                      70 <lb></lb>Actio qua producitur impetus <lb></lb>  non eſt motus localis, ſed alte<lb></lb>ratio.                                                        268 <lb></lb>Admiranda omnia ad duo rerum <lb></lb>  genera poſſe reuocari.                                          5 <lb></lb>Admirandam eſſe naturam circuli. <lb></lb>  pag.                                                           33 <lb></lb>Aequalitas cur dicatur cauſa quie<lb></lb>tis.                                                          242 <lb></lb>Aequilibrium quid.                                               55 <lb></lb>In Aequilibris tam vectis, quam <lb></lb>  libræ ita ſe habet i od <gap></gap>d pon<lb></lb>dus, vt brachium <gap></gap>brachium <lb></lb>  ex commutata proportione. <lb></lb>  pag.                                                           88 <lb></lb>Aere incluſo varij emittuntur ſo<lb></lb>nitus ad motum, vel percuſſio<lb></lb>nem aquæ.                                                29 <lb></lb>Aëris reſiſtentia, &amp; accurſus in <lb></lb>  motu grauium.                                      246. &amp; 248 <lb></lb>Aër quid valeat ad motum natu<lb></lb>ralem grauium, &amp; <expan abbr="proiectorũ">proiectorum</expan>. <lb></lb>  ibid.&amp; 265 <lb></lb><expan abbr="Aẽr">Aer</expan> quomodo feriret ſagittam ſi <lb></lb>  eam ipſe pelleret in deſtina<lb></lb>tum locum.                                                    265 <lb></lb>Angulus <expan abbr="cõtingentiæ">contingentiæ</expan> minoris cir<lb></lb>cumferentiæ maior eſt quàm <lb></lb>  circunferentiæ maioris.                                 137 <lb></lb>Angulus rectus quo ſenſu dicatur <lb></lb>  angulus æqualitatis.                                    242 <lb></lb>Angulus circuli apud Ariſtotelem <lb></lb>  quinam ſit.                             134. &amp; 136. &amp; 208 <lb></lb>Antenna altus ſublimata, cur <lb></lb>  celerius feratur nauigium. <lb></lb>  pag.                                                          119 <lb></lb>Antenna abſque velo quò altius <lb></lb>  ſublimatur, fluctuante mare, <lb></lb>  minus iactatur nauigium.                                      122 <lb></lb>Antennæ corolla non minus quàm <lb></lb>  malus vrgent antrorſum, na<lb></lb>uemque trahunt per funes opi<lb></lb>feros ac propedes.                                            106 <lb></lb>Aquæ eade<gap></gap>ntes cur diuertantur. <lb></lb>  pag.                                                          250 <lb></lb>Aqua ſupernè cadens per aliquod <lb></lb>  foramen cur pyramidalem fi<lb></lb>guram referat.                                                251 <pb xlink:href="005/01/291.jpg"></pb>Archimedis opera poſt Ariſtote<lb></lb>lem facultas Mechanica in<lb></lb>crementa ſuſcepit.                                              8 <lb></lb>Archimedem diuerſa ab Ariſtote<lb></lb>le principia non tradidiſſe. <lb></lb>  pag.                                                           71 <lb></lb>Archita ligneam columbam vo<lb></lb>lantem exhibuit.                                                8 <lb></lb>Ariſtoteles poſt Architam Mecha<lb></lb>nicæ artis modo <expan abbr="ſciẽtiſico">ſcientifico</expan> fun<lb></lb>damenta iecit.                                                  8 <lb></lb>Ars quomodo &amp; <expan abbr="quãdo">quando</expan> diſtingua<lb></lb>tur à ſcientia.                                         12 <lb></lb>Arte nos ſuperare ea à quibus na<lb></lb>tura vincimur.                                                  5 <lb></lb>Artis <expan abbr="raturã">raturam</expan> verè ac propriè par<lb></lb>ticipari à facultate Mechanica. <lb></lb>  pag.                                                           13 <lb></lb>Auctores Mechanicæ facultatis. <lb></lb>  pag.                                                   8. &amp; 9 <lb></lb>Axis in Libra. </s>
          <s id="N18677">Vide Libram. </s>
          <s id="N1867B">55. <lb></lb> s&amp;s                                                             74 <lb></lb>Axis in Peritrochio quid.                                        60 <lb></lb>Axiculus Trochleæ                               58. &amp; 172 </s>
        </p>
        <p id="N18684" type="head">
          <s id="N18686">B <lb></lb>Baculi extrema permutantur <lb></lb> in aëre quando in eius proie<lb></lb>ctione anteponitur quod eſt le<lb></lb>uius.                                                         105 <lb></lb>Baculus nullo accepto impetu <expan abbr="tã-">tan<lb></lb></expan>tum poteſt impellere, quantum <lb></lb>  act<gap></gap>u mouetur à manu.                                  166 <lb></lb>Baiuli idem pondus ſuper lignum <lb></lb>  ſimul geſtantes cur non ſemper <lb></lb>  æquè grauentur. <lb></lb></s>
          <s id="N186A3">Baiulorum ſi alter fuerit ſtatura <lb></lb>  procerior, alter verò humilior, <lb></lb>  num æquè grauentur.                              240 <lb></lb>Item ſi ſtatura <expan abbr="quidẽ">quidem</expan> pares fue<lb></lb>rint, per viam tamen <expan abbr="acliuẽ">acliue</expan> in<lb></lb>cedant, <expan abbr="nũ">num</expan> idem contingat. </s>
          <s id="N186BC">ibid. <lb></lb></s>
          <s id="N186C0">Bellica inſtrumenta, vel machi<lb></lb>nas conſiderare pertinet ad Po<lb></lb>liorceticam.                                                   28 <lb></lb>Bilancis iugum, axis, ac trutina. <lb></lb>  74. Vide Libram. <lb></lb></s>
          <s id="N186CD">Bipennis vnde vim habeat ad fe<lb></lb>riendum.                                                      182 <lb></lb>Brachia libræ inę qualia quo pacto <lb></lb>  decipiant. </s>
          <s id="N186D6">pag. </s>
          <s id="N186D9">76. Vide Libram. <lb></lb></s>
          <s id="N186DE">Brachia dentiforcipis.                                          190 <lb></lb>Brachia inſtrumenti ad confrin<lb></lb>gendas nuces quo amplius dila<lb></lb><expan abbr="tãtur">tantur</expan>, eò velocius comprimunt. <lb></lb>  pag.                                                          196 </s>
        </p>
        <p id="N186EC" type="head">
          <s id="N186EE">C <lb></lb>Candelæ rectà <expan abbr="decidẽt">decident</expan> is flam<lb></lb>mula non extinguitur, nec in<lb></lb>flectitur.                                                    249 <lb></lb>Item nec prope rotam agitatam <lb></lb>  poſita.                                                       165 <lb></lb>Cardo in cuſpide puppis <expan abbr="fulcimẽ-">fulcimen<lb></lb></expan>  <expan abbr="tũ">tum</expan> gubernaculi, ac temonis.                            102 <lb></lb>Catapulta quid.                                                  28 <lb></lb>Cathectus in motione libræ.                                83 <lb></lb>Celonium quid.                                                  234 <lb></lb>Ad Celonium promouendum cur <lb></lb>  onus oneri adiungatur.                                      ibid. <lb></lb></s>
          <s id="N18715">Centrobarica ſcientia quæ.                                 28 <lb></lb>Centrum grauitatis quid.                                         64 <lb></lb>In Centro grauitatis omnis gra<lb></lb>uitas corporis colligitur, &amp; <lb></lb>  coaceruatur.                                                   67 <lb></lb>Centro grauitatis corpora recta <lb></lb>  feruntur deorſum.                                              67 <lb></lb><expan abbr="Centrũ">Centrum</expan> grauitatis ſtatim corpus <lb></lb>  <expan abbr="aliũde">aliunde</expan> ſuſpenſum cóuertit.                    ibid. <lb></lb></s>
          <s id="N18730">Circuli proprietates quatuor, &amp; <lb></lb>  quæ. </s>
          <s id="N18735">34. &amp; ſequentibus. <lb></lb></s>
          <s id="N18739">In Circulo quæ plus à centro di<lb></lb>ſtat linea eadem vi commota, <lb></lb>  citius fertur.                                                 40 <pb xlink:href="005/01/292.jpg"></pb>Circulos maiores mobiliores eſſe <lb></lb>  minoribus. </s>
          <s id="N18746">pag.                                               133 <lb></lb>Circuli contrarium nixum non <lb></lb>  habent quo reſiſtant motui, aut <lb></lb>  motori, ſicut corpora manen<lb></lb>tia.                                                          133 <lb></lb>Ex duobus circulis circa idem <lb></lb>  centrum reuolutis ſecundum <lb></lb>  <expan abbr="abſidẽ">abſidem</expan>, cur maior minori æqua<lb></lb>le ſpatium pertranſit.                                        207 <lb></lb>Circulum maiorem ſeorſum reuo<lb></lb>lutum, maius ſpatium pertran<lb></lb>ſire.                                                         208 <lb></lb>Circuli motum ſecundum abſidem <lb></lb>  eſſe motum quendam mixtum <lb></lb>  ex duabus lationibus,                                         215 <lb></lb>Circulum minorem delatum ad <lb></lb>  motum alterius maioris magis <lb></lb>  participare de latione recta, <lb></lb>  quàm circulari.                                        216 <lb></lb>Circulum maiorem delatum ad <lb></lb>  motum minoris magis partici<lb></lb>pare de latione circulari, quàm <lb></lb>  recta.                                                        217 <lb></lb>Circulum quemlibet per ſe ſeor<lb></lb>ſum rotatum ſemper æquè de <lb></lb>  <expan abbr="vtraq;">vtraque</expan> latione participare.                                   217 <lb></lb>Circunferentia idem quod ambi<lb></lb>tus circuli,                                                  208 <lb></lb>Circunferentiæ <expan abbr="cõmenſuratur">commenſuratur</expan> li<lb></lb>nea deſcripta per circumuolu<lb></lb>tionem circuli ſuper <expan abbr="planũ">planum</expan>.                            209 <lb></lb>Cur aliqua puncta circunferentiæ <lb></lb>  maioris ſecundum <expan abbr="propriã">propriam</expan> ab<lb></lb>ſidem latæ minus <expan abbr="progrediãtur">progrediantur</expan>, <lb></lb>  quàm puncta ſibi <expan abbr="correſpõden-">correſponden<lb></lb></expan>tia circunferentiæ minoris ſe<lb></lb><expan abbr="cũ">cum</expan> delatæ; alia verò magis.               220 <lb></lb>Claua cur maximè valeat ad per<lb></lb>cutiendom.                                                    182 <lb></lb>Cleopatræ nauigium, &amp; remi.                            29 <lb></lb>Cochlea quid.                                                    63 <lb></lb>Cochleæ vſus ad mouenda ponde<lb></lb>ra.                                                         ibid. <lb></lb></s>
          <s id="N187BC">Concauum, &amp; conuexum ſe habent <lb></lb>  ſicut magnum, &amp; paruum.                                    35 <lb></lb>Conſtipatio, &amp; laxatio partium <lb></lb>  neceſſaria ad inflexionem con<lb></lb>tinui.                                                        165 <lb></lb>Crocæ quid, idemque quod vmbi<lb></lb>lici.                                                         160 <lb></lb>Crocæ cur <expan abbr="rotũda">rotunda</expan> ſint figura.                    ibid. <lb></lb></s>
          <s id="N187D2">Crocæ, vel teſtulæ quomodo per <lb></lb>  ſaltus in aqua reſiliant. </s>
          <s id="N187D7">267. Vi<lb></lb>de Teſta. <lb></lb></s>
          <s id="N187DD">Cuneus quid.                                                     61 <lb></lb>Cuneus vnde vim habeat ad ſcin<lb></lb>dendum.                                                       168 <lb></lb>Cuneum duos continere vectes li<lb></lb>bi inuicem aduerſos.                                          168 </s>
        </p>
        <p id="N187E8" type="head">
          <s id="N187EA">D <lb></lb>Dedali ſtatua motus veluti <lb></lb>  animatos præſtabat.                                      29 <lb></lb>Democritus Mileſius antequam <lb></lb>  Eudoxius, &amp; Archita opus ferè <lb></lb>  mechan. </s>
          <s id="N187F7">ediderat.                                               8 <lb></lb>Dentes cur facilius extrahantur <lb></lb>  dentiforcipis adhibito inſtru<lb></lb>mento, quam ſola manu.                                        189 <lb></lb>Dentiforcipem duos <expan abbr="cõtinere">continere</expan> ve<lb></lb>ctes ſibi <expan abbr="inuicẽ">inuicem</expan> contrarios.                           190 <lb></lb>Dentem dentiforcipe conſtrictum <lb></lb>  vnà cum ipſo inſtrumento, <expan abbr="aliũ">alium</expan> <lb></lb>  <expan abbr="quendã">quendam</expan> conſtituere <expan abbr="vectẽ">vectem</expan>.                       191 <lb></lb>Dentem <expan abbr="commotũ">commotum</expan> facilius manu <lb></lb>  ſola <expan abbr="quã">quam</expan> inſtrumento ſimul au<lb></lb>ferri, quo pacto verificetur.                                  192 <lb></lb><expan abbr="Deſcẽſus">Deſcenſus</expan>, &amp; deorſum. </s>
          <s id="N18831">Vide Motus. <lb></lb></s>
          <s id="N18836">Deſcriptio quid ditatiua Mecha<lb></lb>nicæ facultatis.                                         25 <lb></lb><expan abbr="Deſitionẽ">Deſitionem</expan> impetus impreſſi nó fie<lb></lb>ri in <expan abbr="inſtãti">inſtanti</expan>, ſed in <expan abbr="tẽpore">tempore</expan>.                   257 <pb xlink:href="005/01/293.jpg"></pb>Differentia inter Mechanicam, <lb></lb>  Architectonicam, &amp; Nauticam <lb></lb>  facultatem.                                                    29 <lb></lb>Dignitas Mechanicæ facultatis. <lb></lb>  30. &amp; ſequen. <lb></lb></s>
          <s id="N18857">Diſtantia potentiæ à fulcimento <lb></lb>  vectis, mouendi facilitatem au<lb></lb>geat.                                                          88 <lb></lb>Diuiſio ſcientiæ Mechanicæ in <lb></lb>  ſuas partes.                                                   27 <lb></lb>Doctrina Ariſtotelis&#039; in priori par<lb></lb>te huius libri tradita, applica<lb></lb>tur in ſecunda.                                      2. &amp; 73 <lb></lb>Duplicari virtutem motiv<expan abbr="ã">am</expan> quan<lb></lb>do mouetur commotim.                                          246 <lb></lb>Duplicari deinceps principium <lb></lb>  motus in deſcenſu grauis deor<lb></lb>ſum.                                                          247 </s>
        </p>
        <p id="N18876" type="head">
          <s id="N18878">E <lb></lb>Effectum <expan abbr="quandoq.">quandoque</expan> concurre<lb></lb>re ad conſeruationem cauſæ <lb></lb>  <expan abbr="tanquã">tanquam</expan> diſpoſitionem, aut con<lb></lb>ditionem.                                                     257 <lb></lb>Efficiens cauſa impetus in motu <lb></lb>  naturali eſt ipſum graue, aue <lb></lb>  leue.                                                         247 <lb></lb>Efficiens cauſa impetus in motu <lb></lb>  violento eſt ipſum proijciens, <lb></lb>  vel impellens.                                                268 <lb></lb>Enſis ictum validiorem eſſe in cu<lb></lb>ſpide quam in medio.                                          183 <lb></lb>Enſis ictus facilius diuertitur <expan abbr="cũ">cum</expan> <lb></lb>  quis enſi obuiat verſus cuſpi<lb></lb>dem.                                                          183 <lb></lb>Enſem non cedere ſecundum pro<lb></lb>priam contrarietatem, ſed cum <lb></lb>  exlatere eius cuſpis dimouetur <lb></lb>  ad latus.                                                 ibid. <lb></lb></s>
          <s id="N188B0"><expan abbr="Erumpẽres">Erumperis</expan> ignitos lapides moue<lb></lb>ri motu præternaturali.                                  70 <lb></lb>Eudoxius Gnidius, &amp; Archita Ta<lb></lb>rentinus primò Geometrica <lb></lb>  principia ad vſum Mechanicum <lb></lb>  tranſtulerunt.                                                  8 <lb></lb>Exercitus mechanicis artibus pro <lb></lb>  ſtrati.                                                         7 <lb></lb>Expulſio quid.                                                   70 <lb></lb>Extractio diſſicilior quàm demiſ<lb></lb>ſio.                                                          236 </s>
        </p>
        <p id="N188CA" type="head">
          <s id="N188CC">F <lb></lb>Faber eſt opifex eorum, quæ <lb></lb>  ingenio ſimul, &amp; manibus <lb></lb>  fiunt.                                                          7 <lb></lb>Femur sedertis ſimul cum tibia, <lb></lb>  ac thorace duos conſtituit an<lb></lb>gulos tectos, quos ille ſurgen<lb></lb>do commutat.                                                  242 <lb></lb>Finis ad quem ars Mechanica or<lb></lb>dinatur.                                                        9 <lb></lb>Finis cuiusque practicæ ſcientiæ <lb></lb>  eſt opus.                                                      15 <lb></lb>Foramen libræ cum axe triplici in <lb></lb>  ſitu collocari poteſt.                               78. &amp; 84 <lb></lb>Foramen vnde malus emergit in <lb></lb>  naui excipit impulſum ipſius <lb></lb>  mali.                                                         120 <lb></lb>Fractio ligni genu, ac manibus <lb></lb>  vtrinque adhibitis dupliciter <lb></lb>  poteſt contingere.                                            157 <lb></lb>Et cur facilius contingat longè <lb></lb>  quàm prope genu admotis ma<lb></lb>nibus.                                                        158 <lb></lb>Fractio ligni per eius complica<lb></lb>tionem cur ſequatur prius ex <lb></lb>  parte exteriori, quàm interiori <lb></lb>pag.                                                          158 <lb></lb><expan abbr="Fulcimentũ">Fulcimentum</expan> græcè hypomochlion <lb></lb>  appellatur.                                                    56 <lb></lb>Fulcimentum axis vicem gerit, <lb></lb>  <expan abbr="habetq.">habetque</expan> ſe tanquam centrum <lb></lb>  immotum.                                                       86 <pb xlink:href="005/01/294.jpg"></pb>Fulcimentum dentiforcipis in ex<lb></lb>tractione dentis vbi conſtitua<lb></lb>tur. </s>
          <s id="N1891C">pag.                                                     191 <lb></lb>Fulcimentum libræ trutina, ſeu <lb></lb>  ſpartum.                                                       55 <lb></lb>Fulcimentum vectis quantò pro<lb></lb>pinquius oneri locatur, tantò <lb></lb>  facilius onus ipſum leuatum <lb></lb>pag.                                                 56. &amp; 87 <lb></lb>Fulcimentum vectis, quandoque: eſt <lb></lb>  in altera eius extremitate, vt <lb></lb>  plurimum tamen inter onus, &amp; <lb></lb>  potentiam.                                                     56 <lb></lb>Punda cur longius ſerantur miſſi<lb></lb>lia quam manumiſſa.                                           250 <lb></lb>Fundatores cur tardius potius <lb></lb>  quàm cito <expan abbr="fundã">fundam</expan> irrotare con<lb></lb>ſueuerunt.                                                    151 <lb></lb>Fundæ motus circularis quo pa<lb></lb>cto ad motum rectum proie<lb></lb>ctionis vim poſſit adijcere.                                  153 <lb></lb>Funis ductarius vbi ſit alligandus <lb></lb>  in trochleis.                                                 172 <lb></lb>Fune corpus appenſum qua virtu<lb></lb>te huc, atque illuc circumfera<lb></lb>tur.                                                          250 <lb></lb>Item qua ratione tandem quie<lb></lb>ſcat.                                               259.&amp; 260 <lb></lb>Funes opiferi, ac propedes.                                     106 </s>
        </p>
        <p id="N18957" type="head">
          <s id="N18959">G <lb></lb>Geodeſia quo pacto diſtin<lb></lb>guatur à Mechanica.                                     26 <lb></lb>Geometria item in quo differat à <lb></lb>  Mechanica.                                                  ibid. <lb></lb></s>
          <s id="N18965">Geometricæ, &amp; non alteri ſcientię <lb></lb>  ſubalternatur Mechanica.                                       20 <lb></lb>Geometricis concluſionibus vti<lb></lb>tur Mechanica tanquam pro<lb></lb>prijs principijs.                                            20 <lb></lb>Grauia, &amp; leuia quomodo apud <lb></lb>  Mechanicos vſurpentur.                                        10 <lb></lb>Grauia, &amp; leuia cum virtute qua <lb></lb>  moueri debent conſtituunt ſub<lb></lb>iectum materiale adæquatum <lb></lb>  Mechan.                                                        11 <lb></lb>Grauia quibus præcipuè inſtru<lb></lb>mentis à Mechamcis mouean<lb></lb>tur.                                                           54 <lb></lb>Graue <expan abbr="librandũ">librandum</expan> tanto magis gra<lb></lb>uitat, quanto plus diſtauerit à <lb></lb>  catectu.                                                       82 <lb></lb>Graue cadens ex alto in ſe impe<lb></lb>tum producit.                                                   247 <lb></lb>Grauitas corporis tanquam pro<lb></lb>prium operandi principium, eſt <lb></lb>  illi ratio, vt moueatur deorſum. <lb></lb>  pag.                                                           67 <lb></lb>Grauitas quo ſenſu augeri dica<lb></lb>tur in motu.                                                  179 <lb></lb>Gubernaculum quo pacto à temo<lb></lb>ne diſtinguatur.                                              100 <lb></lb>Et quomodo vnum cum illo con<lb></lb>ſt iouat inſtrumentum.                                        100 <lb></lb><expan abbr="Gubernaculũ">Gubernaculum</expan> cum temone, quan<lb></lb>doque, ſe habet ſicut remus in <lb></lb>  cuſpide puppis.                                               100 <lb></lb>Gubernaculi virtus ad circumſe<lb></lb>renda nauigia. </s>
          <s id="N189B5">Vide Temonem. <lb></lb></s>
          <s id="N189BA">Gubernator <expan abbr="quandoq.">quandoque</expan> non minus <lb></lb>  conſtituitur. </s>
          <s id="N189C3">mouens quam re<lb></lb>miger.                                                        102 <lb></lb>Gubernator quo pacto obſtare ſo<lb></lb>let nauis demerſioni cum nimis <lb></lb>  ad latus illa vergerit ventorum <lb></lb>  impulſu.                                                      129 </s>
        </p>
        <p id="N189D0" type="head">
          <s id="N189D2">H<lb></lb> Hauriendi opus duobus di<lb></lb>ſtributum temporibus per<lb></lb>fici, &amp; quo pacto.                                        235 <lb></lb>Helices in Cochlea quomodo <expan abbr="põ-">pon<lb></lb></expan>  dera ſubleuent.                                                63 <pb xlink:href="005/01/295.jpg"></pb>Hero Alexandrinus Philoſophus <lb></lb>  multa monumenta Mechan. <lb></lb>  protulit.                                                       9 <lb></lb>Hero Mechanicus de Geodeſia, ac <lb></lb>  de machinis bellicis ſcripſit.                                  9 <lb></lb>Hominem ſtatura proceriorem <lb></lb>  magis grauari à pondere infra <lb></lb>  vectem alligatum, quod cum <lb></lb>  alio ſtatura humiliori ſuſtinet. <lb></lb>  pag.                                                          240 <lb></lb> Quod ſi onus ſupra vectem ſit al<lb></lb>ligatum magis grauari homi<lb></lb>nem ſtatura humiliorem.                                   ibid. <lb></lb> Si autem onus liberè pendeat, <lb></lb>  vtrumque hominem æquè gra<lb></lb>uari.                                                       ibid. <lb></lb></s>
          <s id="N18A07">Hominem ſcytalis, ac trochleis, <lb></lb>  axe<expan abbr="q.">que</expan> in peritrochio, ore tan<lb></lb>tum perflando dimoueri poſſe. <lb></lb>  pag.                                                          177 <lb></lb>Homo dum commodè ſedet, duos <lb></lb>  angulos rectos poſitione ſui <lb></lb>  corporis efficit: cum verò ſur<lb></lb>git, eos in acutos commutat. <lb></lb>  pag.                                                          242 <lb></lb>Humeri iunctura conſtituitur cen<lb></lb>trum motionis qua ſecuris ad <lb></lb>  ſcindendum adhibetur.                                         180 <lb></lb>Humeri iunctura <expan abbr="cõſtituitur">conſtituitur</expan> cen<lb></lb>trum motionis qua circumagi<lb></lb>tur funda.                                                    151 <lb></lb>Hydraulicas machinas à Cteſibo <lb></lb>  primò inuentas fuiſſe.                                   9 <lb></lb>Hypomochlion idem quod fulci<lb></lb>mentum.                                                        86 </s>
        </p>
        <p id="N18A37" type="head">
          <s id="N18A39">I <lb></lb>Iacula quomodo manu emit<lb></lb>tantur.                                                       150 <lb></lb>Iaculationem fieri non poſſe <expan abbr="abſq;">abſque</expan> <lb></lb>  præuio motu iaculantis.                                 151 <lb></lb>Ictus ſecuris ſicut &amp; mallei, ac ſi<lb></lb>milium vnde validus conſtitua<lb></lb>tur.                                                          179 <lb></lb>Ictus enſis. </s>
          <s id="N18A50">Vide Enſem. <lb></lb></s>
          <s id="N18A55">Ignes miſſiles cur huc, atque illuc <lb></lb>  interdum diſcurrant.                                          153 <lb></lb>Impetus, ſeu impulſus quid.                                     267 <lb></lb>Impetum non produci formaliter <lb></lb>  per motum localem, ſed per <lb></lb>  aliam actionem.                                             <gap></gap>68 <lb></lb>Impetum non produci in inſtanti. <lb></lb>  ibid. <lb></lb></s>
          <s id="N18A69">Impetum minus imprimi in par<lb></lb>ua quantitate quam in maiori: <lb></lb>  minuſque in leuiori, &amp; rariori, <lb></lb>  quàm in grauiori, ac denſiori. <lb></lb>  pag.                                                          271 <lb></lb>Impetum per ſe ordinari ad <expan abbr="motũ">motum</expan> <lb></lb>  rectum, ad cæteros verò per ac<lb></lb>cidens.                                                       153 <lb></lb>Impetus ad <expan abbr="reſiliendũ">reſiliendum</expan> à quo pro<lb></lb>ducatur.                                                      250 <lb></lb>Impetus velis exceptus in quam <lb></lb>  nauis partem refundatur.                                      119 <lb></lb>Impetum non corrumpi in inſtan<lb></lb>ti, ſed in tempore. </s>
          <s id="N18A8E">257. Vide <lb></lb>  Qualitas impetus. <lb></lb></s>
          <s id="N18A94">Inflexio continui ab altero extre<lb></lb>mo eleuati quomodo fiat.                                      164 <lb></lb>Inflexio proceris ligni ex medio <lb></lb>  ſuſpenſi, vel ambabus extremi<lb></lb>tatibus quo etiam pacto proce<lb></lb>dat.                                                          166 <lb></lb>Inſtrumenta naturam circuli in <lb></lb>   motione participantia quæ.                              53 <lb></lb>Inſtrumenta præcipua Mechani<lb></lb>corum ſex.                                                 ibid. <lb></lb></s>
          <s id="N18AAA">Iugum Libræ. </s>
          <s id="N18AAD">Vide Libram. <lb></lb></s>
          <s id="N18AB2">Iugum in machina textoria cur <lb></lb>  facilius volutetur maioribus, <lb></lb>  quàm minoribus collopibus. <lb></lb>  pag.                                                           15 <pb xlink:href="005/01/296.jpg"></pb>Iunctura humeri, vel brachij. </s>
          <s id="N18ABF">Vide <lb></lb>  Humeri. </s>
        </p>
        <p id="N18AC4" type="head">
          <s id="N18AC6">L <lb></lb>Lana quamuis tenuiſsima de<lb></lb>ſcendenti graui poſt terga <lb></lb>  alligata ab aëre non deprimi<lb></lb>tur. </s>
          <s id="N18AD1">pag.                                                     249 <lb></lb>Lancea cur facilius ſuſtineatur <lb></lb>  erecta, quàm inclinata.                                231 <lb></lb>Lancea inclinata cur facilius è <lb></lb>  manubrio, quàm ab extremo <lb></lb>  geſtetur.                                                     231 <lb></lb>In lancea cur manubrium prope <lb></lb>  extremum, &amp; non in ipſo extre<lb></lb>mo conſtituatur.                                            ibid. <lb></lb></s>
          <s id="N18AE5">Lancea cur ſtriari conſueuit.                                 ibid. <lb></lb> Ad lanceam confringendam in<lb></lb>curſu quomodo robur brachij <lb></lb>  oſtentatur.                                                 ibid. <lb></lb></s>
          <s id="N18AEF">Lances libræ non pertinent eſſen<lb></lb>tialiter ad conſtitutionem li<lb></lb>bræ.                                                     55 <lb></lb>Lapillus complanatus quomodo <lb></lb>  eminus proijciatur. </s>
          <s id="N18AFA">Vide Teſta. <lb></lb>  pag.                                                          152 <lb></lb>Latio duplex, naturalis, ac præter<lb></lb>naturalis.                                           41. &amp; 47 <lb></lb>Lati continui in fine imbecilliſſi<lb></lb>mam eſſe lationem, quando ve<lb></lb>rificetur.                                                    105 <lb></lb>Lectulorum ſpondæ cur ſecundum <lb></lb>  duplam proportionem effician<lb></lb>tur.                                                          225 <lb></lb>In. </s>
          <s id="N18B11">lectulis muniendis cur reſtes <lb></lb>  per tranſuerſum, non per dia<lb></lb>metrum extendantur.                                           226 <lb></lb>Libra quid &amp; quomodo in ſui mo<lb></lb>tione naturam circuli partici<lb></lb>pet.                                                           55 <lb></lb>Libra cur facilius moueatur <expan abbr="quā-">quan<lb></lb></expan>  do eſt vacua.                                                 144 <lb></lb>Libræ maiores cur exactiores ſint <lb></lb>  minoribus.                                                     74 <lb></lb>Libræ inæqualibus brachijs de<lb></lb><expan abbr="ſraudātur">fraudantur</expan> <expan abbr="merciũ">mercium</expan> emptores.                        76 <lb></lb> Ad libræ <expan abbr="motionẽ">motionem</expan> exceſſus pon<lb></lb>deris proportionem quandam <lb></lb>  requirit cum parte oppoſita <lb></lb>  quam excedit. </s>
          <s id="N18B40">145. &amp; ſequen. <lb></lb></s>
          <s id="N18B44">Libræ iugum ſuſpenditur ſparto, <lb></lb>  vel trutina.                                                   55 <lb></lb>Libræ ſpartum locari poteſt in <lb></lb>  medio, ſupra vel infra lineam <lb></lb>  iugum diuidentem per longum. <lb></lb>  pag.                                                 78. &amp; 84 <lb></lb> Cur quando ponitur ſupra ſi al<lb></lb>terum extremum demittatur, <lb></lb>  libra ex ſe reducitur in priſti<lb></lb>num ſtatum.                                                    79 <lb></lb> Cur quando conſtituitur infra <lb></lb>  non item.                                                      80 <lb></lb> Cur quando conſtituitur in pun<lb></lb>cto medio maneat quomodo<lb></lb>cunque relinquatur.                                            84 <lb></lb>Ligna oblonga cur difficilius ab <lb></lb>  extremo ſuper <expan abbr="humerū">humerum</expan> geſten<lb></lb>tur, quàm ex medio.                                    229 <lb></lb> Cur item difficilius ab extremo <lb></lb>  eleuentur.                                                    230 <lb></lb>Ligna cur eo difficilius quò pro<lb></lb>ceriora ſunt etiam ex medio <lb></lb>  aſportentur.                                                  232 <lb></lb>Lignum cur facilius genu franga<lb></lb>tur ſi ab extremis apprehenda<lb></lb>tur.                                                          157 <lb></lb>Ligna graciliora cur facilius fran<lb></lb>gantur, quàm craſſiora.                                158 <lb></lb>Ligna cur prius frangantur in <lb></lb>  parte exteriori, quàm interiori <lb></lb>  reſpectu frangentes.                                          158 <lb></lb>Ligna cur quanto longiora ſunt <lb></lb>  tanto imbecilliora fiant.                                     163 <lb></lb>Ligna ab aliquo extremo eleuata <pb xlink:href="005/01/297.jpg"></pb>  ſi longiora ſint, cur magis infle<lb></lb>ctantur.                                                      163 <lb></lb>Locus antennæ.                                            119 <lb></lb>Locus vbi fulcitur malus in naui. <lb></lb>  pag.                                                          120 <lb></lb>Locus proprius temonis.                                         105 <lb></lb>Locus vbi applicatur gubernacu<lb></lb>lum eſt veluti ſcalmus.                                       112 <lb></lb>Longitudo vectis vtrinque ex ful<lb></lb>cimento protenſa iugum refert <lb></lb>  libræ in partes inæquales diui<lb></lb>ſum.                                                           86 <lb></lb>Longitudo patitur ad longitudi<lb></lb>nem, quod motum pondus ad <lb></lb>  mouens in vecte.                                               88 <lb></lb>Lorati ſtipites vnde vim tantam <lb></lb>  habeant ad percutiendum.                                      182 <lb></lb>Lumen accenſum prope rotam <lb></lb>  agitatam, ab aëre non inflecti, <lb></lb>  nec extingui.                                                 265 <lb></lb>Lumen candelæ rectà <expan abbr="decidẽtis">decidentis</expan> ſi<lb></lb>militer, nec inflecti, nec extin<lb></lb>gui.                                                          249 <lb></lb>Luſoriam pilam non reſilere per <lb></lb>  nouum impetum acceptum à <lb></lb>  ſolo vel pariete.                                             250 </s>
        </p>
        <p id="N18BC7" type="head">
          <s id="N18BC9">M<lb></lb> Machinaria ſcientia quænam <lb></lb>  ſit.                                                           28 <lb></lb>Malleus dum clauos reuellit con<lb></lb>ſtituitur vectis.                                             121 <lb></lb>Malleus vnde vim habeat ad per<lb></lb>cutiendum.                                                    182 <lb></lb>Malus in ventorum impulſionibus <lb></lb>  conſtituitur vectis.                                          119 <lb></lb>Malum duplicem habere poſſe ra<lb></lb>tionem vectis.                                     119. &amp; 120 <lb></lb>Mali ſedes, ac fulcimentum.                                     119 <lb></lb>Mali pars qua ipſe vrget, ac pro<lb></lb>mouet nauem.                                                  119 <lb></lb>Malus quo verſus vrgeat flante <lb></lb>  vento ex tranſuerſo.                                          128 <lb></lb>Manganaria ſcientia quæ.                                   28 <lb></lb>Mare in remigatione conſtituitur <lb></lb>  onus, quod per remum <expan abbr="tanquã">tanquam</expan> <lb></lb>  per vectem repellitur.                                         91 <lb></lb>Mare ſe habet tanquam onus re<lb></lb>ſpectu vectis in motione guber<lb></lb>naculi.                                            101. &amp; 102 <lb></lb>Mechanopetica ſcientia quæ.                                28 <lb></lb>Mechanicæ facultatis nomen à <lb></lb>  quo deriuetur.                                                  6 <lb></lb>Mechanica facultas in <expan abbr="rationalẽ">rationalem</expan>, <lb></lb>  &amp; manualem diſtinguitur.                                    7 <lb></lb>Mechanicæ facultatis origo.                                 7 <lb></lb>Mechanicæ facultatis obiectum, <lb></lb>  atque ſubiectum.                                               11 <lb></lb>Mechan. finis ad quem ordinatur. <lb></lb>  pag.                                                  9. &amp; 71 <lb></lb>Mechan. facult. </s>
          <s id="N18C18">verè eſſe artem ſi<lb></lb>mul &amp; ſcientiam.                                           13 <lb></lb> <expan abbr="Nõ">non</expan> ſubalternari Philoſophiæ na<lb></lb>turali, ſed Mathematicæ.                                 20 <lb></lb> Quam habeat vnitatem, &amp; par<lb></lb>tes.                                                 27. &amp; 28 <lb></lb>Mechan. facultat, deſcriptio.                                    25 <lb></lb>Mechan. facultat. </s>
          <s id="N18C2D">dignitas, atque <lb></lb>  perfectio.                                                     30 <lb></lb>Mechan. facultat. </s>
          <s id="N18C34">vtilitas.                                      32 <lb></lb>Mechanica problemata quomodo <lb></lb>  a Phiſicis differant.                                           5 <lb></lb>Miraculo habentur quæ natura, <lb></lb>  ſed præter conſuetudinem con<lb></lb>tingunt; &amp; quæ præter naturam <lb></lb>  arte patrantur.                                                 5 <lb></lb>Miraculorum omnium cauſas in <lb></lb>  hac materia Ariſt.

refert ad na<lb></lb>turam circuli.                                                 33 <lb></lb>Mobilitas naturalis grauium quæ. <lb></lb>  pag.                                                           66 <lb></lb>Mobilitas verò præternaturalis<lb></lb> pag.                                                           68 <pb xlink:href="005/01/298.jpg"></pb>Mobilitas artificioſa.                                           70 <lb></lb>Motus præternaturales, qui à cau<lb></lb>ſis naturalibus oriuntur.                                      70 <lb></lb>Motum corpus facilius deinceps <lb></lb>  moueri.                                                       245 <lb></lb><expan abbr="Idq.">Idque</expan> verificari tàm in motione <lb></lb>  violenta, quàm in naturali.                            246 <lb></lb>Motus naturalis cur in progreſſu, <lb></lb>  &amp; in fine velocior. </s>
          <s id="N18C68">247. &amp; ſe<lb></lb>quen. <lb></lb></s>
          <s id="N18C6E">Motus violentus cur velocior ſit <lb></lb>  in medio, quàm in principio, vel <lb></lb>  fine.                                                         258 <lb></lb>Motus productus ab impetu indif<lb></lb>ferens eſt ad quamcunque poſi<lb></lb>tionem.                                                       267 <lb></lb>Motus acceleratio in proiectis <expan abbr="nõ">non</expan> <lb></lb>  prouenire ab aëris ſubſequentis <lb></lb>  accurſu.                                                      248 <lb></lb>Motus quomodo ponderi addat <lb></lb>  pondus, &amp; grauitas augeatur <lb></lb>  in motu.                                                      178 <lb></lb>Motus <expan abbr="reſiliẽdi">reſiliendi</expan> quomodo fiat.                            250 <lb></lb>Motus circularis corporis fune <lb></lb>  appenſi qua virtute perficiatur. <lb></lb>  pag.                                                          250 <lb></lb>Mutatio appendiculi, vel eius <expan abbr="trãſ-">tranſ<lb></lb></expan>  latio de loco ad locum, mutat <lb></lb>  etiam ſtateram.                                               188 <lb></lb>Multiplicare trutinas in ſtatera <lb></lb>  ad ponderum differentias, labo<lb></lb>rioſum, &amp; inutile.                                        188 </s>
        </p>
        <p id="N18CA6" type="head">
          <s id="N18CA8">N <lb></lb>Nauis progreſſus per velifi<lb></lb>cationem quomodo fiat. <lb></lb>  pag.                                                119.&amp; 120 <lb></lb>Nauis progreſsus in anteriora <expan abbr="nõ">non</expan> <lb></lb>  flante ex puppi vento.                                        125 <lb></lb>Nauis progreſſus per remigatio<lb></lb>nem quo pacto procedat. </s>
          <s id="N18CBD">108. <lb></lb>  &amp; ſequentib. </s>
          <s id="N18CC2">Vide Remus. <lb></lb></s>
          <s id="N18CC7">Nauis recta incedendo cur quan<lb></lb>doque non pertingat ad deſti<lb></lb>natum locum.                                                  114 <lb></lb>Nauis abſque velo cur minus ia<lb></lb>ctetur fluctibus ſi altius ſubli<lb></lb>metur antenna.                                                122 <lb></lb>Nauigia qua ratione paruo cir<lb></lb>cumferantur gubernaculo. </s>
          <s id="N18CD8">101. <lb></lb>  Vide Temonem. <lb></lb></s>
          <s id="N18CDF">Nauis æquabiliter à dextris, &amp; à <lb></lb>  ſiniſtris recipiendo maris im<lb></lb>pulſum, ſe habet tanquam libra <lb></lb>  in æquilibrio.                                          117 <lb></lb>Nauis conſtituitur etiam onus, <lb></lb>  quod per malum tanquam per <lb></lb>  vectem mouetur.                                               119 <lb></lb>Nauis quo pacto abſque remis ſo<lb></lb>lo temone conuertatur in por<lb></lb>tu.                                                           101 <lb></lb>Nixum non habet peripheria quo <lb></lb>  retardetur à proprio motu.                             133 <lb></lb>Nixus corporum quieſcentium. <lb></lb>  ibid. <lb></lb></s>
          <s id="N18CFD">Nuces cur abſque ictu facile in<lb></lb>ſtrumento ad id opus fabrefa<lb></lb>cto confringantur.                                            194 <lb></lb>Nuces facilius confringi quo lon<lb></lb>giora fuerint brachia huius in<lb></lb>ſtrumenti à connexione ipſo<lb></lb>rum.                                                          195 <lb></lb>Nutus quem habent corpora ro<lb></lb>tunda ad motum. </s>
          <s id="N18D10">131. &amp; ſe<lb></lb>quentibus. <lb></lb></s>
          <s id="N18D16">Nutu ſuo celerrime deorſum ro<lb></lb>tando feruntur indecliue cor<lb></lb>pora orbiculata. </s>
        </p>
        <p id="N18D1D" type="head">
          <s id="N18D1F">O<lb></lb>Obiectum totale adæquatum <lb></lb>  Mechanicæ facultatis.                                    11 <pb xlink:href="005/01/299.jpg"></pb>Obiectum formale eiuſdem.                                     ibid. <lb></lb></s>
          <s id="N18D2B">Obliqua temonis conſtitutio quo<lb></lb>modo nauem inclinet.                                          103 <lb></lb>Obliqua, ac magna declinatio pro<lb></lb>ræ per paruam temonis conuer<lb></lb>ſionem.                                             106.&amp; 107 <lb></lb>Odor ex ſe remittitur, ac deſinit <lb></lb>  <expan abbr="abſq;">abſque</expan> contrario expellente.                                   257 <lb></lb>Offenſant minus corpora rotunda <lb></lb>  quàm alia ſuper planum.                                131 <lb></lb>Onus, vel potentiam augeri, ac <lb></lb>  minui iuxta maiorem, aut mi<lb></lb>norem diſtantiam à fulcimento <lb></lb>  vectis.                                                        88 <lb></lb>Onus proportionem quandam re<lb></lb>quirere cum potentia.                                         269 <lb></lb>Onus oneri cur adiungatur ad ce<lb></lb>lonium facilius promouendum. <lb></lb>  pag.                                                          235 <lb></lb>Onus antennæ aliquando reſiſtit <lb></lb>  nauis inclinationi.                                           123 <lb></lb> Aliquando verò nihil obſtat, ſed <lb></lb>  potius vicem gerit potentiæ in<lb></lb>clinantis.                                                  ibid. <lb></lb></s>
          <s id="N18D5F">Opifex eorum, quæ ingenio ſimul <lb></lb>  &amp; manibus fiunt, dicitur etiam <lb></lb>  Mechanicus.                                                     7 <lb></lb>Opiferi funes quodnam in naui <lb></lb>  munvs exerceant.                                              106 <lb></lb>Oppugnationum aſtutias in bello <lb></lb>  ad Mechanicam pertinere.                                        6 <lb></lb>Organopetica scientia quæ.                                 28 <lb></lb>Orbiculis multiplicatis in tro<lb></lb>chlea, augetur virtus motiua. <lb></lb>  pag.                                                          173 </s>
        </p>
        <p id="N18D76" type="head">
          <s id="N18D78">P<lb></lb> Palmula. </s>
          <s id="N18D7D">Vide Remi palmula. <lb></lb>  Parua nimis ſicut &amp; magna <lb></lb>  valde cur proijci minimè va<lb></lb>leant,                                                        269 <lb></lb>Pedem facere in velificatione <lb></lb>  quid. </s>
          <s id="N18D8A">pag.                                          124.&amp; 127 <lb></lb>Pedes retrahere, ac perpendicula<lb></lb>riter ſub capite conſtituere de<lb></lb>bet is, qui à ſeſſione vult ſurge<lb></lb>re.                                                           243 <lb></lb>Pila per eundem impetum à proij<lb></lb>ciente <expan abbr="receptũ">receptum</expan> in parietem illi<lb></lb>dit, ac inde reſilit.                                         267 <lb></lb>Poliorcetica ſcientia quæ.                                 28 <lb></lb>Proiectorum latio non perficitur <lb></lb>  ab aëre, 248. &amp; ſequent. </s>
          <s id="N18DA5">&amp; 265. <lb></lb>  &amp; ſequent. <lb></lb></s>
          <s id="N18DAB">Proiecta qua ratione è minus ſe<lb></lb>rantur.                                                       261 <lb></lb>Proiecta cur ceſſent à latione.                          253 <lb></lb>Proiecta cur velocius ferantur in <lb></lb>  progreſſu, quàm in principio, <lb></lb>  vel fine.                                                     258 <lb></lb> In proiectis virtutem aliquam à <lb></lb>  proijciente imprimi, ac produ<lb></lb>ci.                                                           262 <lb></lb>Proiectorum reſiſtentia in motu <lb></lb>  locali à quo proueniat.                                270 <lb></lb>Proiecta <expan abbr="commenſurationẽ">commenſurationem</expan> quan<lb></lb>dam cum proijciente require<lb></lb>re.                                                           272 <lb></lb>Propedes veli inferiora retrorſum <lb></lb>  tendere, nauemque ſecum abri<lb></lb>pere.                                                         106 <lb></lb>Propedes repentino ſuperuenien<lb></lb>te turbine relaxantur.                                      ibid. <lb></lb></s>
          <s id="N18DD7">Prora in eodem exiftente, totum <lb></lb>  transferri nauigium, quomodo <lb></lb>  intelligatur.                                                 115 <lb></lb>Proræ multa ſit tranſpoſitio temo<lb></lb>ne paululum quid tranſpoſito. <lb></lb>  pag.                                                107.&amp; 117 <lb></lb> In prora, vel puppi remigantes <lb></lb>  minus quàm in medio nauem <lb></lb>  promouent.                                                     91 <lb></lb>Prora an <expan abbr="maiorẽ">maiorem</expan> <expan abbr="impetũ">impetum</expan> recipiat <lb></lb>  in nauigatione <expan abbr="quã">quam</expan> puppis.                             106 <pb xlink:href="005/01/300.jpg"></pb>Proram verſus pauciores remiges <lb></lb>  adhibentur in triremibus.                                     106 <lb></lb>Proram verſus totus impetus it. <lb></lb>  velo collectus etiam ex tranſ<lb></lb>uerſo perflante vento refundi<lb></lb>tur.                                                          128 <lb></lb>Puppis an maneat omnino dum <lb></lb>  ad motum temonis circumfer<lb></lb>tur longitudo nauigij.                                        113 <lb></lb>Puppi parum dimota, multa ſit <lb></lb>  proræ tranſpoſitio.                          106. &amp; 113 <lb></lb>Puppis qua ratione feratur quo <lb></lb>  gubernaculum vergit.                                          114 <lb></lb>Puppim verſus ad latus tenditur <lb></lb>  velum flante vento ex tranſuer<lb></lb>ſo.                                                           124 <lb></lb>Puppis aliquando ſe habet <expan abbr="tanquã">tanquam</expan> <lb></lb>  onus in vecte anguloſo.                                       122 </s>
        </p>
        <p id="N18E24" type="head">
          <s id="N18E26">Q<lb></lb>Qvalitates quæ habent con<lb></lb>trarium non niſi in tempore <lb></lb>  intenduntur, ac remittuntur. <lb></lb>  pag.                                                          254 <lb></lb>Qualitates nonnullæ deficientes <lb></lb>  per propriam <expan abbr="deſitionẽ">deſitionem</expan> abſque <lb></lb>  contrario.                                                    257 <lb></lb>Qualitatem impetus eſſe præter <lb></lb>  naturam grauium.                                              251 <lb></lb>Qualitatem impetus ſemper eſſe <lb></lb>  eiuſdem ſpeciei.                                              267 <lb></lb>Qualitatem impetus non habere <lb></lb>  qualitatem contrariam. </s>
          <s id="N18E47">254. &amp; <lb></lb>  256. vide Impetum. <lb></lb></s>
          <s id="N18E4E">Quantitas ponderis, &amp; quantitas <lb></lb>  virtutis motiuæ ſimul à Mecha<lb></lb>nico conſideranda.                                             10 <lb></lb>Quantitas ponderis tum grauitas <lb></lb>  tum leuitas reſpectu diuerſo<lb></lb>rum apud Mechanicos nuncu<lb></lb>patur.                                                         10 <lb></lb>Quæſtiones Mechanicæ quomodo <lb></lb>  à naturalibus diſtinguantur.                            6 </s>
        </p>
        <p id="N18E61" type="head">
          <s id="N18E63">R <lb></lb>Rami amputatio, quæ ſurſum <lb></lb>  fit ab vnico tantum impulſu <lb></lb>  procedit.                                                     179 <lb></lb>Remi longiores in medio nauis, <lb></lb>  quàm in puppi, vel prora.                               91 <lb></lb>Remi argentei Cleopatrę Reginæ. <lb></lb>  pag.                                                           29 <lb></lb>Remi palmula, quandoque in pro<lb></lb>greſſu nauigij non retrocedit. <lb></lb>  pag.                                                109.&amp; 111 <lb></lb>Remi palmula tantum <expan abbr="quandoq.">quandoque</expan> <lb></lb>  retrocedit quantum progredi<lb></lb>tur nauigium.                                                 111 <lb></lb>Remi palmula, vt plurimum minus <lb></lb>  retrocedit, quàm nauis progre<lb></lb>diatur.                                                     ibid. <lb></lb></s>
          <s id="N18E8B">Remigantes in nauis medio, ma<lb></lb>gis nauem mouere.                                              91 <lb></lb>Remum in remigatione, vectis ra<lb></lb>tionem habere.                                                 91 <lb></lb> In remigatione ſcalmum eſſe ful<lb></lb>cimentum, mare onus.                                        ibid. <lb></lb></s>
          <s id="N18E99">Remigationem fieri per modum <lb></lb>  circuli circa ſcalmum,                                         97 <lb></lb> In remigatione ex duplici motu <lb></lb>  circulari contrario reſultare <lb></lb>  vnum rectum quo progreditur <lb></lb>  nauis.                                                         97 <lb></lb>Reſiliendo proiectum nullus in eo <lb></lb>  producitur impetus nouus, ſed <lb></lb>  retorquetur idem à proijciente <lb></lb>  incuſsus.                                                     250 <lb></lb>Reſiliendi motus. </s>
          <s id="N18EB0">Vide Motus. <lb></lb></s>
          <s id="N18EB5">Rimulæ <expan abbr="ſpondarũ">ſpondarum</expan> cauſa ſciſſionis <lb></lb>  earum cum reſtes in lectulis ex<lb></lb>tenduntur per diametrum.                                      226 <lb></lb>Ripa quomodo per repulſum con-<pb xlink:href="005/01/301.jpg"></pb> currat ad circulationem aqua<lb></lb>rum in vorticibus. </s>
          <s id="N18EC8">275. &amp; ſe<lb></lb>quen. <lb></lb></s>
          <s id="N18ECE">Romanos ad remigium in arena <lb></lb>  aliquando ſe exercuiſſe.                                       93 <lb></lb>Rombi puncta extrema vnius la<lb></lb>teris ſi duabus ſimul ſerantur <lb></lb>  lationibus cum eadem veloci<lb></lb>tate, cur vnum maius, alterum <lb></lb>  minus ſpatium percurrat.                                      200 <lb></lb> In Rombo cur quod ſuper eius <lb></lb>  latus fertur, minus ſpatium per<lb></lb>tranſit, quàm ipſum latus.                             204 <lb></lb>Rotas tripliciter in orbem poſſe <lb></lb>  conuerti.                                                     130 <lb></lb>Rota leuior cur facilius mouea<lb></lb>tur quàm grauior.                                      144 <lb></lb> Quæ per maiores rotas trahun<lb></lb>tur, facilius ac citius moueri. <lb></lb>  pag. </s>
          <s id="N18EF1">140. &amp; 142. Vide <expan abbr="Circulũ">Circulum</expan>. <lb></lb></s>
          <s id="N18EF9">Rotunda corpora cur facilius mo<lb></lb>ueantur.                                            130.&amp; 137 <lb></lb>Runca vnde efficaciam ſortiatur <lb></lb>  ad ſcindendum.                                                182 </s>
        </p>
        <p id="N18F02" type="head">
          <s id="N18F04">S <lb></lb>Sariſſam ab extremo eleuatam <lb></lb>  magis inclinari, quàm furca, <lb></lb>  lum.                                                          164 <lb></lb>Sariſſa perpendiculariter ad pla<lb></lb>num horizontis erecta, cur fa<lb></lb>cile ab extremo ſuſtineatur.                                  231 <lb></lb>Cur non item per lineam hori<lb></lb>zonti parallelam conſtituta. <lb></lb>  ibid. <lb></lb></s>
          <s id="N18F1A">Sariſſam in humero geſtantes, ef<lb></lb>fectum vibrationis experiun<lb></lb>tur.                                                          233 <lb></lb>Saxa <expan abbr="decidẽtia">decidentia</expan> cur interdum ſcin<lb></lb>dantur per aëre.                                         250 <lb></lb>Scalmus quomodo ſe habeat in <lb></lb>  remigatione.                                                   91 <lb></lb>Scalmus per remigationem illuc <lb></lb>  transfertur vbi remi eſt princi<lb></lb>pium, ſeu manubrium.                                          172 <lb></lb>Scalmus conſtituitur medium ma<lb></lb>nens inter duos motus contra<lb></lb>rios.                                                         108 <lb></lb>Scytala quid, &amp; quotuplex. </s>
          <s id="N18F3B">141. <lb></lb>  &amp; 147 <lb></lb> Super Scytalas cur facilius por<lb></lb>tentur onera.                                                 148 <lb></lb>Securis cur ia cta, lignum facile <lb></lb>  ſcindat, ſecus autem ſuper illud <lb></lb>  impoſita <expan abbr="etiã">etiam</expan> ingenti ſuperadie<lb></lb>cto pondere.                                                  178 <lb></lb>Securis percuſſio ex circulatione <lb></lb>  vim maximam adipiſcitur.                                      179 <lb></lb>Securis manubrium quomodo ve<lb></lb>ctis vicem ſubeat.                                            181 <lb></lb>Securis in ſciſſione conſtituitur <lb></lb>  veluti cuneus.                                                182 <lb></lb>Securis eſt malleus cuneatus, vel <lb></lb>  cuneus malleatus.                                           ibid. <lb></lb></s>
          <s id="N18F61">Semidiametrum in deſcriptione <lb></lb>  circuli moueri motu quoddam <lb></lb>  miſto ex duabus lationibus. <lb></lb>  41. &amp; 47. <lb></lb>Semidiameter ex quo puncto inci<lb></lb>pit circumduci ad idem poſtre<lb></lb>mo reuertitur.                                                 38 <lb></lb>Semidiametri puncta quo remo<lb></lb>tiora erunt à centro eò velo<lb></lb>cius mouebuntur.                                               41 <lb></lb>Semidiametri puncta à centro re<lb></lb>motiora, cur magis participent <lb></lb>  de motu naturali; propinquiora <lb></lb>  de præternaturali.                                       94 <lb></lb>Spheropeia <expan abbr="quænã">quænam</expan> ſcientia ſit.                      28 <lb></lb>Statera quomodo paruo appendi<lb></lb>culo magna leuet onera.                                       184 <lb></lb>Statera, libræ ſimul, ac vectis ra<lb></lb>tionem obtinet.                                               185 <pb xlink:href="005/01/302.jpg"></pb>Stateram eſſe veluti libram in qua <lb></lb>  plures ſint libræ, quomodo in<lb></lb>telligendum.                                                  187 <lb></lb>Statera tanto maius onus valet <lb></lb>  leuare quanto propinquius illi <lb></lb>  conſtituitur ſpartum.                                         188 <lb></lb>Stipites lorati vnde tantam vim <lb></lb>  <expan abbr="obtineãt">obtineant</expan> ad percutiendum.                              182 <lb></lb>Stipites lorati adhiberi ſolent ad <lb></lb>  enucleandum triticum.                                       ibid. <lb></lb></s>
          <s id="N18FA7">Succula quænam machina ſit.                               115 <lb></lb>Succulæ graciliores cur facilius <lb></lb>  ab eadem potentia circumuol<lb></lb>uantur.                                                       115 <lb></lb>Surgentes à ſeſſione angulos re<lb></lb>ctos in acutos commutant.                                     242 </s>
        </p>
        <p id="N18FB4" type="head">
          <s id="N18FB6">T <lb></lb>Temo quid, &amp; quomodo con<lb></lb>ſtituat vnum inſtrumentum <lb></lb>  ſimul cum gubernaculo.                                        100 <lb></lb>Temonis motu dupliciter nauem <lb></lb>  poſſe circumferri.                                            100 <lb></lb>Temo vnde tantas vires habeat. <lb></lb>  pag.                                                          101 <lb></lb>Temonem conſtitui vectem, gu<lb></lb>bernatorem potentiam, ac ma<lb></lb>re, onus.                                                     102 <lb></lb>Temo cur in extremo nauigij col<lb></lb>locetur.                                                      104 <lb></lb><expan abbr="Temonẽ">Temonem</expan> nihil nauigio ad id quod <lb></lb>  in ante progredi eſt, conferre. <lb></lb>  pag.                                                          113 <lb></lb>Temonis motio explicatur per <lb></lb>  eius <expan abbr="reductionẽ">reductionem</expan> ad libram.                             117 <lb></lb> Per temonem nautæ cum vento <lb></lb>  contendunt.                                                   125 <lb></lb>Teſta obliquè in aquarum ſuperfi<lb></lb>ciem incidens cur longius inde <lb></lb>  reſiliat.                                                     150 <lb></lb> Et cur pluries tanquam per ſal<lb></lb>tus in eandem ſuperficiem inci<lb></lb>dat.                                                          267 <lb></lb>Teſta quomodo inter digitos col<lb></lb>locetur ad hoc, vt eminus proij<lb></lb>ciatur.                                                       152 <lb></lb>Taumaturgica ſcientia quæ.                                 28 <lb></lb> Et in quas partes diuidatur.                                    29 <lb></lb>Tollenon idem quod <expan abbr="Celoniũ">Celonium</expan>.                              234 <lb></lb>Tractio quid.                                                    70 <lb></lb>Triremes cur prope puppim plu<lb></lb>res remiges in ſingulis remis <lb></lb>  habere conſueuerint.                                          106 <lb></lb>Trochlea quid.                                                   58 <lb></lb>Trochleis duabus adinuicem op<lb></lb>poſitis cur facile magna leuen<lb></lb>tur onera.                                                    172 <lb></lb>Trochleæ orbiculum, vectis vicem <lb></lb>  obtinere.                                                   ibid. <lb></lb></s>
          <s id="N19018">Trochlearum beneficio tanto ma<lb></lb>ius pondus leuari, quantò plu<lb></lb>res extiterint in eis rotulę.                          173 <lb></lb>Trochleam ſuperiorem non tam <lb></lb>  auxilium, quàm commoditatem <lb></lb>  ad leuandum praeſtare.                                         174 <lb></lb> Ex inferiori trochlea totam vim <lb></lb>  quæ potentiæ adiungitur eſſe <lb></lb>  petendam.                                                     175 <lb></lb>Tylum quid.                                                      63 <lb></lb>Tympanus quid.                                                   60 </s>
        </p>
        <p id="N1902F" type="head">
          <s id="N19031">V<lb></lb> Vectio quid &amp; quotuplex.                                     70 <lb></lb>Vectis quid &amp; quotuplex.                                     56 <lb></lb>Vecte adhibito cur exigua virtu<lb></lb>te magna leuentur pondera.                                     86 <lb></lb>Vectis quomodo habeat rationem <lb></lb>  libræ.                                                ibid. <lb></lb></s>
          <s id="N19041">Vectis longitudo atque proportio <lb></lb>  ad potentiam, &amp; pondus.                                    88 <lb></lb>Velis antrorſum pergere quomo<lb></lb>do valeat nauis.                                    119 &amp; 124 <pb xlink:href="005/01/303.jpg"></pb>Velificando vbi totus ventorum <lb></lb>  impetus refundatur.                                           106 <lb></lb>Vento ex tranſuerſo perflante, ac <lb></lb>  directè nihilominus nauigia in<lb></lb>cedendo, cur tandem non per<lb></lb>tingant quò præcisè tendebant. <lb></lb>  pag.                                                          114 <lb></lb>Vento ex latere flante, <expan abbr="veloq.">veloque</expan> ad <lb></lb>  oppoſitum inclinante, cur non <lb></lb>  ſequatur nauis ſubmerſio.                                     128 <lb></lb>Imo cur ſic ſecurius ipſa nauis <lb></lb>  incedat.                                                    ibid. <lb></lb></s>
          <s id="N19069">Verticilla ex papiro quomodo ab <lb></lb>  aëre circumuoluantur.                                    101 <lb></lb>Vertigo quid.                                                    70 <lb></lb>Vibratio quid.                                                  229 <lb></lb>Vibrationis motus, geſtationem <lb></lb>  ligni retardat.                                     229.&amp; 232 <lb></lb>Violentia quot modis poſsit in<lb></lb>ferri.                                                         69 <lb></lb>Per violentiam mota, fieri quaſi <lb></lb>  per ſe mobilia.                                               262 <lb></lb>Virtus impreſſa cur neceſſario ad <lb></lb>  motum violentum ſit coceden<lb></lb>da, 264. Vide Impetum. <lb></lb></s>
          <s id="N19086">Vortex per lineas ſpirales, non <lb></lb>  autem per proprias circunfe<lb></lb>rentias perfici.                                              274 <lb></lb>Vortice circumlata, cur ad me<lb></lb>dium tandem agantur. </s>
          <s id="N19091">273. &amp; <lb></lb>  ſequentibus, </s>
        </p>
        <p id="N19096" type="head">
          <s id="N19098">FINIS.</s>
        </p>
        <p id="N1909C" type="head">
          <s id="N1909E">ERRATA.<lb></lb><emph type="italics"></emph>Pag. </s>
          <s id="N190A5">Lin. </s>
          <s id="N190A9">Errata.                  Correctio.<emph.end type="italics"></emph.end><lb></lb> 13  8 pro                            per <lb></lb> 14 24 inefſabiliter                  infallibiliter <lb></lb> 38 35 non eſt <expan abbr="incõ-">incon-</expan>           non eſt <expan abbr="incõuenlens">inconuenlens</expan> cir <lb></lb>       <expan abbr="ueniẽs">ueniens</expan> ex                 qulum ex ipſa <lb></lb>       ipſa <lb></lb> 51  2 paralellam                     parallelam, Sic lege <lb></lb>                                        pag.5 2 80. 231. 243. <lb></lb>                                        255. <lb></lb> 71 16 enumera-                      enumeratas pertineat <lb></lb>        ras <lb></lb><emph type="italics"></emph>Pag. Lin. </s>
          <s id="N190D5">Errata.                  Correctio.<emph.end type="italics"></emph.end><lb></lb> 82 17 quam eleua-                   quam extremum <lb></lb>        tæ                       partis eleuatæ <lb></lb> 82 33 aliena                         à linea <lb></lb>105 21 ipſis                          ipſius <lb></lb>108 24 impoſito                       in propoſito <lb></lb>109 13 procedi                        procedere <lb></lb>188 29 diuerſum                       diujſum <lb></lb>191 32 Philolophas                    philoſophatus <lb></lb>200  5 confert                        conferat <lb></lb>238 18 ucidentius                     euidentius </s>
        </p>
        <p id="N190EE" type="head">
          <s id="N190F0">REGESTVM.</s>
        </p>
        <p id="N190F3" type="head">
          <s id="N190F5">a ABCDEFGHIKLMNOPQRST.</s>
        </p>
        <p id="N190F9" type="head">
          <s id="N190FB">Omnes ſunt Quaterniones, præter a, &amp; T, Duerniones.</s>
        </p>
      </chap>
    </body>
    <back></back>
  </text>
</archimedes>
author	Klaus Thoden <kthoden@mpiwg-berlin.mpg.de>
date	Thu, 02 May 2013 11:08:12 +0200
parents	22d6a63640c6
children