Alvarus, Thomas, Liber de triplici motu, 1509

Table of figures

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                <p xml:id="N1C91E">
                  <s xml:id="N1C994" xml:space="preserve">
                    <pb chead="De motu locali quo ad effectum." file="0130" n="130"/>
                  motꝰ ſit vniformis quo ad ſubiectū ſiue difformis.
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                  </s>
                  <s xml:id="N1C9A5" xml:space="preserve">¶ Sed qm̄ definitio motꝰ vniformiter difformis q̊
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                  ad ſubiectū q̄ cõiter dat̄̄ michi ſufficiēs nõ videtur.
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                  </s>
                  <s xml:id="N1C9AB" xml:space="preserve">Ideo vt definitio motꝰ vniformiter difformis adī-
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                  ueniat̄̄ vt poſſibile erit.
                    <note position="left" xlink:href="note-0130-01a" xlink:label="note-0130-01" xml:id="N1C9D8" xml:space="preserve">Queſtio
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                    vtrū defi­
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                    nitio mo­
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                    tus vni-
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                    formiter
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                    difforīs
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                    q̊ ad ſub­
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                    iectuꝫ ſit
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                    bene aſſi­
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                    gnata.</note>
                  </s>
                  <s xml:id="N1C9B5" xml:space="preserve">Querit̄̄ an definitio illa mo­
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                  tus vniformiṫ difformis q̊ ad ſubiectū ſit bñ aſſig̈ta</s>
                </p>
                <p xml:id="N1C9F0">
                  <s xml:id="N1C9F1" xml:space="preserve">Et arguit̄̄ primo /  non q2 ſcḋ3 illã nul­
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                  lus ē motꝰ vniformiter difformis q̊ ad ſubiectū igr̄
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                  </s>
                  <s xml:id="N1C9F7" xml:space="preserve">Argr̄ añs / q2 ſi eſſet aliq̇s motꝰ vniformiter diffor-
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                  mis quo ad ſubiectū maxīe effet motꝰ rote quo mo-
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                  uet̄̄ circulariter: ſꝫ talis motꝰ nõ eſt vniformitēr dif-
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                  formis q̊ ad ſubiectū: igr̄ ↄ̨ña ptꝫ cū maiore: et argr̄
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                  mīor / q2 ſi talis motꝰ ē vniformiter difformis capio
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                  vnã rotã q̄ moueat̄̄ vniformiṫ difformiṫ a nõ g̈du in
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                  cētro vſ ad octauū in circūferētia: et arguo ſic / taĺ
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                  motꝰ ꝑ te ē vniformiṫ difformis a nõ gradu vſ adu
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                  octauū / g̊ velocitas eius corrñdet g̈dui medio puta
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                  vt .4. q̇ mediꝰ g̈dus vt .4. eſt in pūcto medio taĺ rote /
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                  ſꝫ ↄ̨ñs eſt falſū: igr̄ illud ex quo ſeq̇tur, ↄ̨ña ptꝫ ſup-
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                  poſita opinione tenēte motū vniformiter difformē
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                  corrñdere motui exiſtēti in medio corporis mobilis
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                  </s>
                  <s xml:id="N1CA13" xml:space="preserve">Falſitas ↄ̨ñtis ꝓbat̄̄ / q2 aliq̇s pūctus qui tardiꝰ mo­
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                  uet̄̄ ꝙ̄ punctꝰ exiſtēs in medio illiꝰ rote mouet̄̄ veloci­
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                  tate vt .4. / g̊ ſeq̇tur /  alter pūctꝰ puta medius talis
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                  rote velociꝰ mouet̄̄ ꝙ̄ vt .4. </s>
                  <s xml:id="N1CA1C" xml:space="preserve">Cõſequentia ptꝫ, et argr̄
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                  añs, q2 pūctus exiſtēs in medio ſemidiametri inter
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                  centrū et circūferētiã mouet̄̄ velocitate vt .4. et talis
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                  pūctꝰ tardiꝰ mouet̄̄ ꝙ̄ pūctus exiſtēs in medio rote:
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                  igr̄ ꝓpoſitū. </s>
                  <s xml:id="N1CA27" xml:space="preserve">Argr̄ maior capio vnã rotã a.b.c. / et vo­
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                  lo /  ītra illã deſcribat̄̄ vnꝰ circulꝰ ei cõcētricꝰ cuiꝰ
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                  diameter ſit ſubdupla ad diametrū totius rote, et
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                  trãſeat talis circulꝰ ꝑ mediū pūcti ſemidiametri, q̇
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                  circulꝰ ſit f.gh. / vt ſcribit̄̄ in figura. </s>
                  <s xml:id="N1CA32" xml:space="preserve">Quo poſito ſic
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                    <figure xlink:href="fig-0130-01a" xlink:label="fig-0130-01" xml:id="N1CAC0" number="9">
                      <image file="0130-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0130-01"/>
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                  argumētor pūctꝰ mediꝰ
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                  ſemidiametri deſcribit
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                  circulū f.g.h. et talis cir­
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                  culꝰ ſiue talis linea cir-
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                  cularꝪ eſt ſubdupla ad
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                  circulū a.b.c. ſiue ad li-
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                  neã circūferētialē talis
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                  rote / q̄ deſcribit̄̄ a pun-
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                  cto velociſſime moto ta­
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                  lis rote, q2 circūferētia
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                  circuli cuiꝰ diameter eſt
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                  dupla ad diametrū alteriꝰ circuli mīoris eſt dupla
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                  ad circūferentiã mīoris circuli. </s>
                  <s xml:id="N1CA54" xml:space="preserve">Modo ſic eſt ī ꝓpo­
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                  ſito de diametrꝪ, et ꝑ ↄ̨ñs de circūferētiis illoꝝ duo­
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                  rū circuloꝝ: igr̄ ille pūctꝰ ſemidiametri mouet̄̄ velo­
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                  citate vt .4. </s>
                  <s xml:id="N1CA5D" xml:space="preserve">Probat̄̄ hec ↄ̨ña / q2 ſubduplã lineã de-
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                  ſcribit ad lineã deſcriptã a pūcto velociſſime moto
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                  et talis pūctꝰ mouet̄̄ velocitate vt .8. vt poſitū ē: igr̄
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                  ille pūctꝰ mediꝰ ſemidiametri (qm̄ mouet̄̄ ſubdupla
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                  velocitate) mouet̄̄ vt .4. / qḋ fuit ꝓbandū. </s>
                  <s xml:id="N1CA68" xml:space="preserve">Sꝫ iã ꝓbat̄̄
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                  mīor vcꝫ /  talis pūctꝰ tardiꝰ mouet̄̄ ꝙ̄ pūctꝰ exiſtēs
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                  in medio rote (et nõ loquor hic de medio centrali q2
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                  tale mediū nõ mouet̄̄: ſꝫ de medio qḋ eſt īter cētrū et
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                  circūferētiã) / et arguo ſic / talis pūctꝰ mediꝰ ſemidia-
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                  metri eſt in fine tertie q̈rte totiꝰ corporis illiꝰ rote et
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                  in prīcipio vltīe q̈rte ꝓcedendo ſus cētrū: igr̄ pū-
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                  ctus exiſtēs in medio totiꝰ magnitudinis ipſiꝰ rote
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                  eſt ꝓximior circūferētie ꝙ̄ ille pūctꝰ mediꝰ ſemidia-
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                  metri / et ꝑ ↄ̨ñs mouet̄̄ velociꝰ ꝙ̄ ille pūctꝰ mediꝰ ſemi­
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                  diametri / qḋ fuit ꝓbãdu. </s>
                  <s xml:id="N1CA7F" xml:space="preserve">Ptꝫ ↄ̨ña ītelligēti naturã
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                  motꝰ vniformiṫ difformis.
                    <note position="left" xlink:href="note-0130-02a" xlink:label="note-0130-02" xml:id="N1CAC6" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N1CA89" xml:space="preserve">¶ Dices forte / et bene ne-
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                  gãdo añs, et ad ꝓbationē ↄ̨cedēdo maiorē, et negã-
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                  do mīorē, et cū ꝓbat̄̄ admitto caſū cū his q̄ ibi ſup-
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                  ponūtur, et ↄ̨cedo añs et ↄ̨ñam, et diſtīguo ↄ̨ñs ̄tuꝫ
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                  ad illã particulã in qua dr̄ /  talis g̈dus mediꝰ eſt ī
                    <cb chead="De motu locali quo ad effectum."/>
                  pūcto exiſtēti in medio talis rote, q2 aut tu ītelligꝪ
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                  de medio magnitudīs illiꝰ rote qḋ quidē mediū eſt
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                  in medio īter cētrū et circūferētiã talis rote diuidē-
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                  do illã rotã in duas rotas cõcētricas eq̈lis magni-
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                  tudinis ̄uis ſint īeq̈lis ãbitꝰ et circūferētie / vt ptꝫ in
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                  figura: et ſic nego, aut loqueris de pūcto exiſtēte in
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                  medio lõgitudinis īter cētrū et circūferetiã, et ſic bñ
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                  ↄ̨cedo /  ibi eſt gradꝰ mediꝰ / vt bene ꝓbat argumētū
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                  </s>
                  <s xml:id="N1CAA6" xml:space="preserve">Unde dico /  ̄uis in q̈litate vniformiter difformi
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                  mediꝰ gradꝰ debeat eſſe in medio corporis ̄tū ad
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                  magnitudinē </s>
                  <s xml:id="N1CAAD" xml:space="preserve">In motu tñ vniformiter difformi nõ
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                  oportet /  g̈dus mediꝰ ſit in medio corporis ̄tū ad
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                  magnitudinē: ſꝫ oportet /  ſit in medio corꝑis ̄tū
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                  ad lõgitudinē (ſumēdo lõgitudinē eius a puncto nõ
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                  moto ſiue tardiſſime moto vſ ad punctū velociſſi-
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                  me motū) q2 ſcḋm illū modū p̄cedit ille motꝰ vnifor­
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                  miter difformis.</s>
                </p>
                <p xml:id="N1CACC">
                  <s xml:id="N1CACD" xml:space="preserve">Sed ↄ̨̨tra arguit̄̄ ſic / q2 aliqua pars il­
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                  liꝰ rote nõ mouet̄̄ vniformiter difformiter: g̊ ſequit̄̄ /
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                   ipſa tota rota nõ mouet̄̄ vniformiter difformiter
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                  </s>
                  <s xml:id="N1CAD5" xml:space="preserve">Cõſequētia ptꝫ ſcḋm hãc opinionē / q2 oportet /  in
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                  motu vniformiter difformi cuiuſlꝫ partꝪ g̈dꝰ mediꝰ
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                  (id eſt q̇ eſt in medio lõgitudinis / vt dictū eſt) / tm̄ ex-
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                  cedat īfimū ̄tū excedit̄̄ a ſūmo (vt ptꝫ ex definitõe) /
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                  ꝓbat̄̄ añs / q2 datur ibi vna pars in illa rota cuius
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                  pūctꝰ mediꝰ ſcḋm lõgitudinē nõ tm̄ excedit vnū ex-
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                  tremã ̄tū excedit̄̄ ab altero in velocitate: igr̄ talis
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                  pars nõ mouet̄̄ vniformiter difformiter. </s>
                  <s xml:id="N1CAE6" xml:space="preserve">Probat̄̄
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                  añs, et ſigno in tali rota vnū q̈dratū nõ equaliū la-
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                  teꝝ cuiꝰ pūctꝰ mediꝰ ſit pūctꝰ mediꝰ ſemidiametri in­
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                  ter cētrū et circūferētiã et tangat tale q̈dratū extre-
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                  mitates circunferentie ex vtro latere / vt patuit in
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                  ī figura ſupra poſita: ſit illud quadratū .a.b.c.d. /
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                  et arguo ſic / pūctꝰ exiſtēs in medio illiꝰ q̈drati moue­
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                  tur vt .4. cū ſit pūctꝰ mediꝰ ſemidiametri īter centrū
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                  et circūferentiã illiꝰ rote quē ſuperiꝰ ꝓbauimꝰ moue­
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                  ri velocitate vt .4. et pūcta extrema q̄ tãgūt extremi­
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                  tates rote mouetur velocitate vt .8. </s>
                  <s xml:id="N1CAFD" xml:space="preserve">Ergo g̈dus me­
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                  dius neutrū extremoꝝ excedit, et ꝑ ↄ̨ñs nõ tm̄ q̈tum
                    <lb/>
                  excedit̄̄ ab vno excedit reliquū / qḋ fuit ꝓbãdū
                    <note position="right" xlink:href="note-0130-03a" xlink:label="note-0130-03" xml:id="N1CB30" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N1CB09" xml:space="preserve">¶ Di-
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                  ces forte negãdo añs: et ad probationē negãdo iteꝝ
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                  añs / et cū probat̄̄ ↄ̨cedo /  pūctꝰ mediꝰ illiꝰ q̈drati mo-
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                  uetur velocitate vt q̈tuor, et ↄ̨cedo etiã /  duo pūcta
                    <lb/>
                  extrema talis quadrati applicata circūferētie rote
                    <lb/>
                  mouētur velocitate vt .8. </s>
                  <s xml:id="N1CB16" xml:space="preserve">Sed nõ debēt capi extre-
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                  ma motꝰ illiꝰ partꝪ ſcḋm talē lõgitudinē ̄uis de fa­
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                  cto illa ſit lõgitudo talis partis: ſed d3 ſumi in tali
                    <lb/>
                  parte ꝓcedēdo m latitudinē ꝑ lineã rectã a centro
                    <lb/>
                  rote ꝓcedentē ꝑ mediū talis partis vſ ad circūfe-
                    <lb/>
                  tiã / vt ptꝫ in figura ſuperiꝰ poſita. </s>
                  <s xml:id="N1CB23" xml:space="preserve">Modo poteſt dici
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                  īmo de facto ita eſt /  quãto gradꝰ mediꝰ excedit̄̄ a
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                  g̈du velociſſime moto illiꝰ ꝑtis exiſtētis in tali linea
                    <lb/>
                  tantū excedit tardiſſimum exiſtentem in tali parte.</s>
                </p>
                <p xml:id="N1CB36">
                  <s xml:id="N1CB37" xml:space="preserve">Sed cõtra q2 vtra medietas illius
                    <lb/>
                  q̈drati a.b.c.d. mouet̄̄ velociꝰ ꝙ̄ vt .4. / g̊ ſeq̇tur /  to-
                    <lb/>
                  tū illud q̈dratū mouet̄̄ velociꝰ ꝙ̄ vt .4. / ↄ̨ña ptꝫ / q2 to-
                    <lb/>
                  tius velocitas cõficit̄̄ ex partiū velocitatibꝰ, et velo-
                    <lb/>
                  citatis denoīatio ex vtriuſ medietatis denoīatio­
                    <lb/>
                  nibus cõſtat̄̄. </s>
                  <s xml:id="N1CB44" xml:space="preserve">Sed ꝓbat̄̄ añs / q2 vtra medietas il-
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                  lius q̈drati equaliter mouet̄̄ puta medietas e. et me­
                    <lb/>
                  dietas f. cum equaliter diſtent a centro illiꝰ rote, et
                    <lb/>
                  vtra illaꝝ velociꝰ mouetur ꝙ̄ vt .4. / igitur ꝓpoſi-
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                  tum. </s>
                  <s xml:id="N1CB4F" xml:space="preserve">Cõſquētia ptꝫ / et arguit̄̄ minor / q2 vtriuſ me-
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                  dietatis pūctus mediꝰ mouet̄̄ velocius ꝙ̄ vt .4. cum
                    <lb/>
                  vtriuſ medietatis tam e. ꝙ̄ f. punctus mediꝰ plus
                    <lb/>
                  diſtet a centro quã punctus medius totius: vt patꝫ
                    <lb/>
                  in figura: igit̄̄ vtra illaꝝ medietatū f. et e. velocius
                    <lb/>
                  mouetur quam vt quatuor / quod fuit probandum.</s>
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