Alvarus, Thomas, Liber de triplici motu, 1509

Table of Notes

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                <p xml:id="N21C13">
                  <s xml:id="N21C14" xml:space="preserve">
                    <pb chead="De motu rarefactionis  condenſationis." file="0182" n="182"/>
                  cut lux eſt quedam qualitas: et tenebre ſunt eiꝰ pri-
                    <lb/>
                  uatio. </s>
                  <s xml:id="N21C24" xml:space="preserve">et intenſio eſt quedaꝫ qualitas: et remiſſio eiꝰ
                    <lb/>
                  priuatio: ita  quando aliquid rarefit aliqua qua­
                    <lb/>
                  litas que dicitur raritas ei acquiritur cum vero cõ­
                    <lb/>
                  denſatur non acquiritur ei aliqua qualitas que di­
                    <lb/>
                  catur denſitas: ſed tale corpus deperdit raritatem
                    <lb/>
                  </s>
                  <s xml:id="N21C30" xml:space="preserve">Alii aūt aliter intelligunt hanc opinionem dicen-
                    <lb/>
                  tes  ſecundum eaꝫ, ne raritas, ne denſitas ſūt
                    <lb/>
                  qualitates: ſed ipſa raritas eſt ipſamet res rara: et
                    <lb/>
                  ipſa denſitas ipſammet res denſa. </s>
                  <s xml:id="N21C39" xml:space="preserve">Dicitur tamen
                    <lb/>
                  raritas poſitiuum ſecundum hanc opinionem: q2
                    <lb/>
                  quando aliquid rarefit ei acquiritur quantitas ip­
                    <lb/>
                  ſum efficitur maius: quando viro condenſatur ip­
                    <lb/>
                  ſum efficitur minus. </s>
                  <s xml:id="N21C44" xml:space="preserve">Et ideo raritas dicitur poſiti­
                    <lb/>
                  ue: denſitas vero priuatiue: quia per denſitatē ſub-
                    <lb/>
                  iectum aliqua quãtitate priuatur per raritatē ve-
                    <lb/>
                  ro aliquam quantitatem acquirit.</s>
                </p>
                <p xml:id="N21C4D">
                  <s xml:id="N21C4E" xml:space="preserve">Tertia opinio eſt /  denſitas dicitur
                    <lb/>
                  poſitiue et raritas priuatiue non tamen dicit den­
                    <lb/>
                  ſitatem eſſe qualitatem: et addit  ex vniformi rare­
                    <lb/>
                  factione alicuius per tempus ſecundum ſe totuꝫ ac­
                    <lb/>
                  quiritur vniformiter quãtitas: addit ſecundo  ſi
                    <lb/>
                  rarius et denſius equalis quantitatis eque veloci-
                    <lb/>
                  ter rarefiunt: denſius maiorem quantitatem acqui­
                    <lb/>
                  rit ꝙ̄ rarius.</s>
                </p>
                <p xml:id="N21C5F">
                  <s xml:id="N21C60" xml:space="preserve">Quarta vero poſitio eſt /  denſitas di­
                    <lb/>
                  ditur poſitiue. </s>
                  <s xml:id="N21C65" xml:space="preserve">et raritas priuatiue: et  raritas eſt
                    <lb/>
                  ipſamet res rara: et denſitas ſimiliter: et differt hec
                    <lb/>
                  opinio a tertia. quia addit contradictorias ꝓpoſi­
                    <lb/>
                  tiones duabus propoſitionibus quas addit tertia /
                    <lb/>
                  vt poſtea plus declarabitur. </s>
                  <s xml:id="N21C70" xml:space="preserve">Hãc autem opinionē
                    <lb/>
                  principaliter intendo ſuſtentare et declarare. </s>
                  <s xml:id="N21C75" xml:space="preserve">q2 ea
                    <lb/>
                  eſt quã deffenſat calculator in hac materia ceteros
                    <lb/>
                  excellens. </s>
                  <s xml:id="N21C7C" xml:space="preserve">et quia ipſa et dictis philoſophorum et
                    <lb/>
                  naturalibus experimentis conformior ceteris opi­
                    <lb/>
                  nionibus apparet. </s>
                  <s xml:id="N21C83" xml:space="preserve">Hic oponionibus ſic recitatis.</s>
                </p>
                <p xml:id="N21C86">
                  <s xml:id="N21C87" xml:space="preserve">Querit̄̄ vtrum ipſe ſint ſuſtentabiles
                    <lb/>
                  et ſignãter de tribꝰ primis. </s>
                  <s xml:id="N21C8C" xml:space="preserve">¶ Et argr̄ primo /  ṗma
                    <lb/>
                  nõ ſit poſſiblis per argumentū primū ante oppo-
                    <lb/>
                  ſitū in quo ꝓbatur /  raritas et denſitas nõ poſſūt
                    <lb/>
                  poſitiue accipi ſicut albedo et nigredo.</s>
                </p>
                <p xml:id="N21C95">
                  <s xml:id="N21C96" xml:space="preserve">Secundo arguit̄̄. </s>
                  <s xml:id="N21C99" xml:space="preserve">Si raritas  den-
                    <lb/>
                  ſitas eſſent qualitates et ſignanter contrarie / vt di­
                    <lb/>
                  cit opinio. </s>
                  <s xml:id="N21CA0" xml:space="preserve">Sequeretur /  aliquid nec eſſet rarum
                    <lb/>
                  nec denſum: et contineret finitam materiam ſub fi-
                    <lb/>
                  nita quãtitate / ↄ̨ñs eſt falſum: ergo et ãtecedēs. </s>
                  <s xml:id="N21CA7" xml:space="preserve">Se­
                    <lb/>
                  quela ꝓbatur: et pono /  ſit a. corpꝰ pedale habens
                    <lb/>
                  duos g̈dus materie: et habeat q̈tuor gradus rarita­
                    <lb/>
                  tis et quatuor denſitatis quo poſito illud nec eſt ra­
                    <lb/>
                  rum: nec eſt denſum: q2 raritas et dēſitas ſunt qua-
                    <lb/>
                  litates cõtrarie equales in ipſo: et ſic ſe īpediunt: et
                    <lb/>
                  tñ ipſum certã materiã cõtinet ſub finita quãtitate /
                    <lb/>
                  vt ponit caſus igr̄. </s>
                  <s xml:id="N21CB8" xml:space="preserve">Sed iam probo falſitatē ↄ̨ñtis: q2
                    <lb/>
                  ſeq̇tur bene cõtinet finitã materiã ſub finita quãti-
                    <lb/>
                  tate: g̊ ſequit̄̄ /  eſt rarū / vt ptꝫ ex diffinitione rari: et
                    <lb/>
                  nõ eſt rarum ꝑ te: igr̄ ↄ̨tradictio.</s>
                </p>
                <p xml:id="N21CC1">
                  <s xml:id="N21CC2" xml:space="preserve">Tertio contra eandem opinionem ar­
                    <lb/>
                  guitur: quia ſi illa eſſet vera ſequeretur /  aliquid
                    <lb/>
                  eſſet infinite rarū quod eſſet etiam denſum: ↄ̨ñs im­
                    <lb/>
                  plicat: igr̄. </s>
                  <s xml:id="N21CCB" xml:space="preserve">Argr̄ añs, et pono /  a. ſit vnū corpꝰ di-
                    <lb/>
                  uiſum ꝑ partes ꝓportionales ꝓportione dupla: et
                    <lb/>
                  prima pars ꝓportionalis ſit aliqualiter rara: et ſe­
                    <lb/>
                  cunda in duplo magis et tertia in duplo magis ̄
                    <lb/>
                  ſecūda: et quarta in duplo magis ꝙ̄ tertia: et ſic in
                    <lb/>
                  infinitū: quo poſito argr̄ ſic / a. eſt infinite rarum: et
                    <lb/>
                  eſt dēſuꝫ: igr̄ ꝓpoſitū </s>
                  <s xml:id="N21CDA" xml:space="preserve">Probatur maior / q2 raritas
                    <cb chead="De motu rarefactionis  condenſationis."/>
                  prime partis ꝓportionalis denoīat ipſum aliqua­
                    <lb/>
                  liter raꝝ: et raritas ſecūde partis tm̄ (cū ſit dupla
                    <lb/>
                  in ſubdupla parte) et raritas tertie tm̄ ſicut rari-
                    <lb/>
                  tas ſecūde (cū ſit dupla in ſubduplo ſubiecto) et ſic
                    <lb/>
                  in infinitū: igr̄ q̄libet pars ꝓportiõalis alia a pri-
                    <lb/>
                  ma denoīat tm̄ illud corpꝰ rarum ſicut prima: et ſūt
                    <lb/>
                  infinite: igr̄ infinite rarum denominãt illud corpꝰ:
                    <lb/>
                  et ſic eſt infinite rarum </s>
                  <s xml:id="N21CEE" xml:space="preserve">Sed  ſit denſum probatur /
                    <lb/>
                  quia habet finitam materiam vt notum eſt ſub fini­
                    <lb/>
                  ta quantitate vt ponitur: igitur eſt denſum.</s>
                </p>
                <p xml:id="N21CF5">
                  <s xml:id="N21CF6" xml:space="preserve">Contra ſcḋam opinionē quarto argr̄ ſic / q2 ſi
                    <lb/>
                  illa eſſet a ſeq̄ret̄̄ / q2 oē raꝝ eſſet īfinite deſū
                    <lb/>
                  et ſic eſſet raꝝ et nõ eēt raꝝ: qḋ īplicat: ꝓbatur ſeq̄la /
                    <lb/>
                  q2 in oī raro m illã opinionē eſt infinita denſitas:
                    <lb/>
                  igr̄ oē rarum eſt īfinite denſum. </s>
                  <s xml:id="N21D01" xml:space="preserve">Argr̄ añs: et capio
                    <lb/>
                  aliquod raꝝ in quo ſit ꝑ totū raritas vt quatuor q̄
                    <lb/>
                  ꝑ te eſt quedã qualitas aut poſitiue dr̄. </s>
                  <s xml:id="N21D08" xml:space="preserve">Diuido igr̄
                    <lb/>
                  illã raritatē ꝑ partes ꝓportionales m intenſionē
                    <lb/>
                  et hoc ꝓportione dupla: et arguo ſic / prima pars ꝓ-
                    <lb/>
                  portionalis illius raritatis eſt aliqualiter denſa,
                    <lb/>
                  ſiue hꝫ aliquã denſitatē: ſicut pars intēſa qualita-
                    <lb/>
                  tis hꝫ aliquã remiſſionē: et ſecūda pars ꝓportiona­
                    <lb/>
                  lis eſt in duplo minor raritas: igr̄ in duplo maior
                    <lb/>
                  denſitas et tertia in quadruplo minor raritas quã
                    <lb/>
                  prima: igr̄ in quadruplo maior dēſitas: et quarta
                    <lb/>
                  in octuplo minor raritas / g̊ in octuplo maior dēſi-
                    <lb/>
                  tas: et ſic in īfinitū: g̊ īfinita dēſitas eſt in tali corꝑe.
                    <lb/>
                    <note position="right" xlink:href="note-0182-01a" xlink:label="note-0182-01" xml:id="N21D4E" xml:space="preserve">Confir-
                      <lb/>
                    matio</note>
                  </s>
                  <s xml:id="N21D26" xml:space="preserve">¶ Et cõfirmat̄̄. </s>
                  <s xml:id="N21D29" xml:space="preserve">Quia vbicū eſt aliquod poſituū
                    <lb/>
                  ibi eſt in īfinitū de ſuo priuatiuo (dūmodo priua-
                    <lb/>
                  tiuū et poſitiuū ſe cõpatiant̄̄) ſed raritas ſe hꝫ po-
                    <lb/>
                  ſitiue: et denſitas priuatiue: et ſe cõpatiunter: ergo
                    <lb/>
                  vbicū eſt aliqua raritas ibi eſt infinita denſitas
                    <lb/>
                  ſeu in īfinitū magna denſitas. </s>
                  <s xml:id="N21D36" xml:space="preserve">Probat̄̄ maior īdu­
                    <lb/>
                  ctiue / q2 vbi eſt aliq̈ magnitudo ibi eſt in īfinitū par­
                    <lb/>
                  ua quantitas: et vbi eſt aliqua diſtãtia ibi eſt in īfi-
                    <lb/>
                  nitū magna ꝓpinq̇tas: q2 ꝓpinq̇tas dr̄ priuatiue
                    <lb/>
                  ad diſtantiã. </s>
                  <s xml:id="N21D41" xml:space="preserve">et vbicū eſt aliqua intenſio ibi īfinita
                    <lb/>
                  remiſſio eſt vt facile eſt intueri: q2 ibi eſt aliqualis
                    <lb/>
                  intenſio: et ſubdupla, et ſubquadrupla, et ſic in īfini­
                    <lb/>
                  tum: et ſic de aliis priuatiue ſi que ſint talia.</s>
                </p>
                <p xml:id="N21D56">
                  <s xml:id="N21D57" xml:space="preserve">Quninto contra eandē arguo ſic. </s>
                  <s xml:id="N21D5A" xml:space="preserve">Si
                    <lb/>
                  raritas diceret̄̄ poſitiue ſeq̄ret̄̄ /  aliquod corpus
                    <lb/>
                  aliqualiter rarū ꝑ ſolã rarefactionē ſiue inductio-
                    <lb/>
                  nē raritatis: et motū ↄ̨ñtem raritatē q̇ motꝰ eſt aug­
                    <lb/>
                  mentatio: ipſum efficiret̄̄ denſius: ſed ↄ̨ñs eſt mani­
                    <lb/>
                  feſte falſum: q2 tunc ipſum efficiret̄̄ maiꝰ equaliter
                    <lb/>
                  cõtinens de materia: ergo nõ efficeretur denſiꝰ: īmo
                    <lb/>
                  rariꝰ / et ſic illud ↄ̨ñs eſt falſum. </s>
                  <s xml:id="N21D6B" xml:space="preserve">Sed iã ꝓbo ſequelã
                    <lb/>
                  et capio vnū corpꝰ tripedale cuius vna medietas ſit
                    <lb/>
                  rara vt duodecim: et alia rara vt duo: et volo /  illa
                    <lb/>
                  rara vt duo acq̇rat duos g̈dus raritatis quieſcēte
                    <lb/>
                  altera rara vt duodecim. </s>
                  <s xml:id="N21D76" xml:space="preserve">Quo poſito argr̄ ſic in fi­
                    <lb/>
                  ne illiꝰ rarefactionis illud corpꝰ eſt minꝰ rarū ꝙ̄ an­
                    <lb/>
                  tea: igr̄ ꝓpoſitū </s>
                  <s xml:id="N21D7D" xml:space="preserve">Añs argr̄: q2 antea illud corpꝰ erat
                    <lb/>
                  rarum vt ſeptē: q2 medietas rara vt .12. denoīabat
                    <lb/>
                  vt ſex: et medietas rara vt duo denoīabat vt vnum /
                    <lb/>
                  igr̄ tota illa raritas erat vt ſeptē: et modo eſt vt ſex
                    <lb/>
                  cū duabꝰ tertiis p̄ciſe: igr̄ eſt minꝰ rarum ꝙ̄ antea.
                    <lb/>
                  </s>
                  <s xml:id="N21D89" xml:space="preserve">Sed iam ꝓbo /  modo eſt rarū vt ſex cū duabꝰ ter-
                    <lb/>
                  tiis p̄ciſe: q2 illud corpꝰ eſt modo tripedale, q2 ãtea
                    <lb/>
                  erat bipedale et eius vna medietas pedalis effecta
                    <lb/>
                  eſt in duplo maior: et ſic effecta eſt bipedalis et per
                    <lb/>
                  conſequens effecta eſt due tertie totiꝰ et ille due ter-
                    <lb/>
                  tie habent raritatem vt quatuor per totum: et ſic il-
                    <lb/>
                  la raritas denominat totum rarum vt duo cū dua­
                    <lb/>
                  bus tertiis. </s>
                  <s xml:id="N21D9A" xml:space="preserve">Reliquuꝫ vero pedale que eſt vna tertia
                    <lb/>
                  eſt rarum vt duodecim: et ſic denominat totum vt q̈­
                    <lb/>
                  tuor: modo quatuor et duo cum duabus tertiis ſūt </s>
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