Alvarus, Thomas, Liber de triplici motu, 1509

Table of Notes

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              <div xml:id="N1C8BC" level="4" n="1" type="chapter" type-free="capitulum">
                <p xml:id="N1CCC5">
                  <s xml:id="N1CCDC" xml:space="preserve">
                    <pb chead="De motu locali quo ad effectum." file="0132" n="132"/>
                  a quarto vſ ad duodecimū (volo enim /  talis ro­
                    <lb/>
                  ta ſit flexibilis q2 alias non video quomodo / hoc eſ­
                    <lb/>
                  ſet poſſibile) / quo poſito arguitur ſic / motus ille nõ
                    <lb/>
                  eſt vniformiter difformis et tamen omnes partes ī-
                    <lb/>
                  mediate ſecundū extenſionem ſunt īmediate ſecun-
                    <lb/>
                  dū intēſionē: igitur illa definitio cõuenit aliis a dif­
                    <lb/>
                  finito / et per ↄ̨ñs non eſt bona. </s>
                  <s xml:id="N1CCFC" xml:space="preserve">Minor eſt nota ex ca-
                    <lb/>
                  ſu: et maior probatur / quia ſi eſſet vniformiter dif-
                    <lb/>
                  formis cū incipiat a. duodecim et terminat̄̄ ad non
                    <lb/>
                  gradū pūctꝰ mediꝰ ſemidiametri moueret̄̄ velocita­
                    <lb/>
                  te q̄ eſt gradus medius inter duodecim et nõ gradū:
                    <lb/>
                  ſed hoc eſt falſum / vt patet ex caſu qm̄ talis punctus
                    <lb/>
                  mouetur vt quatuor vt ponitur:</s>
                </p>
                <p xml:id="N1CD0B">
                  <s xml:id="N1CD0C" xml:space="preserve">Secunda cõcluſio </s>
                  <s xml:id="N1CD0F" xml:space="preserve">Motus vniformi­
                    <lb/>
                  ter difformis quo ad ſubiectum nõ bene definitur
                    <lb/>
                  iſto modo </s>
                  <s xml:id="N1CD16" xml:space="preserve">Motꝰ vniformiter difformis quo ad ſub­
                    <lb/>
                  iectum eſt quando cuiuſcun partis ſubiecti pun-
                    <lb/>
                  ctus qui eſt in medio (loquor de puncto vero vel ima­
                    <lb/>
                  ginario) tanto exceditur in velocitate ab extremo il­
                    <lb/>
                  lius partis velociſſime moto quantuꝫ excedit extre­
                    <lb/>
                  mum remiſſiſſime motum eiuſdem partis ſiue non
                    <lb/>
                  motum (quod dico propter motum terminatum ad
                    <lb/>
                  non gradum) </s>
                  <s xml:id="N1CD27" xml:space="preserve">Hec concluſio bene probatur per pri­
                    <lb/>
                  mum argumentum principale ante oppoſitum et ꝑ
                    <lb/>
                  ſecundam confirmationem eius. </s>
                  <s xml:id="N1CD2E" xml:space="preserve">Illud em̄ argumē­
                    <lb/>
                  tum et confirmatio oſtendunt /  non oportet mediū
                    <lb/>
                  gradum motus vniformiter difformis / quo ad ſub-
                    <lb/>
                  iectum eſſe in medio magnitudinis corporis moti
                    <lb/>
                  vniformiter difformiter quo ad ſubiectum: ſed bene
                    <lb/>
                  oportet /  ſit in medio longitudinis talis corporis
                    <lb/>
                  modo expoſito in argumento.</s>
                </p>
                <p xml:id="N1CD3D">
                  <s xml:id="N1CD3E" xml:space="preserve">Tertia cõcluſio </s>
                  <s xml:id="N1CD41" xml:space="preserve">Motus vniformiter
                    <lb/>
                  difformis quo ad ſubiectum non bñ definitur ſic.</s>
                </p>
                <p xml:id="N1CD46">
                  <s xml:id="N1CD47" xml:space="preserve">Motus vniformiter difformis quo ad ſubiectū eſt
                    <lb/>
                  quando cuiuſcun partis ſubiecti dimidium ſiue
                    <lb/>
                  punctus qui eſt in medio talis partis (in medio in-
                    <lb/>
                  quã ſecundum longitudinem) tantum exceditur ī ve­
                    <lb/>
                  locitate a puncto ſiue ab extremo velociſſime moto
                    <lb/>
                  quantum excedit punctum ſiue extremuꝫ tardiſſime
                    <lb/>
                  motum in velocitate ſiue extremum nõ motuꝫ (quod
                    <lb/>
                  dico propter motum terminatum ad non gradum)
                    <lb/>
                  </s>
                  <s xml:id="N1CD59" xml:space="preserve">Probatur hec concluſio per vltimam replicam pri­
                    <lb/>
                  mi argumenti huius dubitatiõis: et per ſecundū ar­
                    <lb/>
                  gumentum: </s>
                  <s xml:id="N1CD60" xml:space="preserve">Nam ſi illa definitio eſſet bona / ſeque-
                    <lb/>
                  retur /  quelibet pars illius quod vniformiter dif-
                    <lb/>
                  formiter mouetur quo ad ſubiectum etiam vnifor-
                    <lb/>
                  miter difformiter moueretur quo ad ſubiectū vt fa­
                    <lb/>
                  cile deducitur ex illa definitione: ſed tenendo illã de­
                    <lb/>
                  finitionem / ſequitur oppoſitum videlicet /  non que­
                    <lb/>
                  libet pars illius quod vniformiter difformiter mo­
                    <lb/>
                  uetur etc. / vt probat vltima replica primi argumēti
                    <lb/>
                  et ſecūdum argumentum.</s>
                </p>
                <note position="left" xml:id="N1CD73" xml:space="preserve">definitio
                  <lb/>
                motꝰ vni­
                  <lb/>
                formiter
                  <lb/>
                diffor-
                  <lb/>
                mis q̊ ad
                  <lb/>
                ſubiectū.</note>
                <p xml:id="N1CD81">
                  <s xml:id="N1CD82" xml:space="preserve">Quarta concluſio </s>
                  <s xml:id="N1CD85" xml:space="preserve">Motus vniformi­
                    <lb/>
                  ter difformis quo ad ſubiectum / vt pro nūc mihi ap­
                    <lb/>
                  paret bene definitur ſic </s>
                  <s xml:id="N1CD8C" xml:space="preserve">Motus vniformiter diffor­
                    <lb/>
                  mis quo ad ſubiectum eſt quando quilibet punctus
                    <lb/>
                  ſubiecti intrinſecus et etiam extrinſecus velociſſime
                    <lb/>
                  motus in ea proportione velocius mouetur in qua
                    <lb/>
                  magis diſtat a centro talis motus. </s>
                  <s xml:id="N1CD97" xml:space="preserve">Exemplum / vt ſi
                    <lb/>
                  rota moueatur vniformiter difformiter: requiri-
                    <lb/>
                  tur /  in quacun ꝓportione puncta magis diſtãt
                    <lb/>
                  a centro ipſius rote in ea ꝓportione velocius moue­
                    <lb/>
                  antur </s>
                  <s xml:id="N1CDA2" xml:space="preserve">Et per centrū in propoſito ego intelligo pū-
                    <lb/>
                  ctum quieſcens exiſtens in illo corpore quod ſic mo­
                    <lb/>
                  uetur vniformiter difformiter vel a quo imagina-
                    <lb/>
                  rie ꝓcedit talis motus. </s>
                  <s xml:id="N1CDAB" xml:space="preserve">Et volo dicere /  ſi corpus
                    <lb/>
                  moueatur vniformiter difformiter quo ad ſubiectū
                    <lb/>
                  a non gradu vſ ad certum gradum, oportet /  in
                    <cb chead="De motu locali quo ad effectum."/>
                  quacun proportione puncta magis diſtant a pū-
                    <lb/>
                  cto illius ſubiecti in quo eſt non gradus motus in
                    <lb/>
                  ea velocius moueantur. </s>
                  <s xml:id="N1CDB9" xml:space="preserve">Si vero tale corpus qḋ mo­
                    <lb/>
                  uetur vniformiter difformiter quo ad ſubiectū ita
                    <lb/>
                  ſe habeat /  quilibet punctus eius moueatur ita 
                    <lb/>
                  motus eius incipiat a certo gradu remiſſiori et ter-
                    <lb/>
                  minetur ad certum gradum intenſiorē vt verbi gra­
                    <lb/>
                  tia incipiat a quarto et terminetur ad octauuꝫ ſicut
                    <lb/>
                  eſt de motu totius reſidui a circulo minori exiſtente
                    <lb/>
                  intra rotam in caſu primi argumenti: tunc ad inue­
                    <lb/>
                  niendum centruꝫ talis motus oportet addere cor-
                    <lb/>
                  pori aliquod corpus quod moueatur vniformiter
                    <lb/>
                  difformiter a non gradu ad gradum vt quatuor vĺ
                    <lb/>
                  remiſſimum quo mouetur aliud corpus cuius mo-
                    <lb/>
                  tus vtrim terminatur ad gradum: et ſi tunc omīa
                    <lb/>
                  puncta illius corporis cuius motus in vtro extre­
                    <lb/>
                  mo terminatur ad gradum in ea ꝓportione velociꝰ
                    <lb/>
                  moueantur in qua plus diſtant a puncto non moto
                    <lb/>
                  corporis dati qui quidem punctus tunc eſt centrum
                    <lb/>
                  illius motus tunc tale corpus vniformiter difformi­
                    <lb/>
                  ter mouetur quo ad ſubiectum. </s>
                  <s xml:id="N1CDE0" xml:space="preserve">Probatur hec con-
                    <lb/>
                  cluſio / quia illa definitio cõuenit omni et ſoli etc. / igi­
                    <lb/>
                  tur eſt bona: et antecedens pro nunc alio modo non
                    <lb/>
                  probatur niſi quia omni motui q̇ cõmuniter cõcedi­
                    <lb/>
                  tur vniformiter difformis quo ad ſubiectum con-
                    <lb/>
                  uenit illa definitio, et ſoli tali: igitur propoſitum.</s>
                </p>
                <note position="right" xml:id="N1CDED" xml:space="preserve">1. correl.</note>
                <p xml:id="N1CDF1">
                  <s xml:id="N1CDF2" xml:space="preserve">¶ Ex hac concluſione et predictis ſequitur /  cuiuſli­
                    <lb/>
                  bet quod vniformiter difformiter mouetur quo ad
                    <lb/>
                  ſubiectum quelibet pars quantitiua vniformiter
                    <lb/>
                  difformiter mouetur quo ad ſubiectum. </s>
                  <s xml:id="N1CDFB" xml:space="preserve">Probatur /
                    <lb/>
                  quia cuiuſlibet talis partis quilibet punctus in ea
                    <lb/>
                  proportione velocius mouetur in qua plus diſtat a
                    <lb/>
                  centro illius motus / ergo ſequitur /  quelibet pars
                    <lb/>
                  quantitatiua illius quod vniformiter difformiter
                    <lb/>
                  mouetur quo ad ſubiectum etiam vniformiter dif-
                    <lb/>
                  formiter mouetur quo ad ſubiectum </s>
                  <s xml:id="N1CE0A" xml:space="preserve">Conſequentia
                    <lb/>
                  patet ex definitione: et antecedens patet / quoniam ſi­
                    <lb/>
                  cut illa puncta mouentur in toto ita etiam in illa ꝑ­
                    <lb/>
                  te totius in qua ſunt / vt notū eſt.
                    <note position="right" xlink:href="note-0132-01a" xlink:label="note-0132-01" xml:id="N1CE33" xml:space="preserve">.2correl.</note>
                  </s>
                  <s xml:id="N1CE18" xml:space="preserve">¶ Sequitur ſecūdo /
                    <lb/>
                   non oportet /  motus vniformiter difformis quo
                    <lb/>
                  ad ſubiectum correſpondeat gradui motus exiſten­
                    <lb/>
                  ti in medio magnitudinis talis corporis: nec in me­
                    <lb/>
                  dio longitudinis. </s>
                  <s xml:id="N1CE23" xml:space="preserve">Probatur hoc correlarium / quo
                    <lb/>
                  ad primam partem ex primo argumento et eius ſe­
                    <lb/>
                  cunda confirmatione: </s>
                  <s xml:id="N1CE2A" xml:space="preserve">Et quo ad ſecundam partem
                    <lb/>
                  ex confirmatione ſecundi argumenti.</s>
                </p>
                <note position="right" xml:id="N1CE39" xml:space="preserve">3. correl.</note>
                <p xml:id="N1CE3D">
                  <s xml:id="N1CE3E" xml:space="preserve">¶ Sequitur tertio /  motus vniformiter difformis
                    <lb/>
                  quo ad ſubiectum cõmenſurari habet penes gradū
                    <lb/>
                  medium inter ſummã et infimū vel non gradum vbi­
                    <lb/>
                  cun ſit talis gradus. </s>
                  <s xml:id="N1CE47" xml:space="preserve">Patet / quia non videtur aliꝰ
                    <lb/>
                  modus cognoſcendi totalem velocitatem motꝰ vni­
                    <lb/>
                  formiter difformis quo ad ſubiectuꝫ. </s>
                  <s xml:id="N1CE4E" xml:space="preserve">Et per hoc pa­
                    <lb/>
                  tet concluſio reſponſiua ad dubitationem / q̄ talis ē.</s>
                </p>
                <p xml:id="N1CE53">
                  <s xml:id="N1CE54" xml:space="preserve">Definitio illa / que cõmuniter dat̄̄ de
                    <lb/>
                  motu vniformiter difformi quo ad ſubiectum non
                    <lb/>
                  eſt ſufficienter aſſignata: quoniã nec valet ſi intelli­
                    <lb/>
                  gatur de medio magnitudinis nec ſi ītelligatur de
                    <lb/>
                  medio longitudinis / vt declaratum eſt in ſecūdo cor­
                    <lb/>
                  relario. </s>
                  <s xml:id="N1CE61" xml:space="preserve">His poſitis.</s>
                </p>
                <p xml:id="N1CE64">
                  <s xml:id="N1CE65" xml:space="preserve">Reſpondeo ad argumenta ante oppo­
                    <lb/>
                  ſitum /  illa ſunt pro concluſione reſpoſiua. </s>
                  <s xml:id="N1CE6A" xml:space="preserve">Quia
                    <lb/>
                  tamen in primo argumēto queritur an in motu vni­
                    <lb/>
                  formiter difformi quo ad ſubiectum gradus mediꝰ
                    <lb/>
                  debeat eſſe in medio corporis quo ad magnitudinē
                    <lb/>
                  vel quo ad longitudinem / dico /  neuter illoruꝫ me­
                    <lb/>
                  diorum requiritur /  ſit in medio corporis / vt dicit
                    <lb/>
                  ſecundum correlarium. </s>
                  <s xml:id="N1CE79" xml:space="preserve">¶ Ad replicam tamen reſ-
                    <lb/>
                  pondetur negando antecedens / vt ibi dicitur / quam­ </s>
                </p>
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