Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Inductionis gradus ſūmi ↄ̨̨ſideratio.
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per quod in horas inducetur gradꝰ ſūmꝰ rarefiat
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ſus gradū ſūmū tardiꝰ tñ rarefiat m oēm eius
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pūctū ꝙ̄ g̈dꝰ ſūmꝰ īducat̄̄ q̇eſcēte rēiſſiori extremo.
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</
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<
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xml:space
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">Tūc manifeſtū ē / ↄ̨tinuo pūcta in q̇bꝰ erit grg̈dꝰ
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ſūmꝰ magꝪ diſtabūt ab extremo q̇eſcēte ꝙ̄ ſi nõ eēt
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rarefactio: g̊ continuo inter ipſa et punctum a quo
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incipit induci gradus ſummꝰ erit minꝰ de ſpacio
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fixo ꝙ̄ ſi nõ rareficeret: et penes tale ſpacium cõmē
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ſuranda eſt inductionis gradꝰ ſūmi velocitas / vt
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dicit ſolutio: ergo quãdocun ſubiectū rarefit -
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ſus gradus ſūmū continuo gradus ſummus tar-
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dius inducitur ꝙ̄ ſi nõ rarefieret. </
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<
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xml:space
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">Iã ꝓbatur falſi-
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tas ↄ̨ſequētis: et pono / a. alteret̄̄ per totã partē
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nõ ſummã alteratione vniformi: et arguo ſic: eque
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cito erit gra. ſū. ad punctuꝫ ſiue extremuꝫ remiſſiꝰ
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quieſcens ſiċ ſi nõ rarefieret ſubiectum / vt conſtat:
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et nõ citius deueniet ad extremū remiſſiꝰ ꝙ̄ ad oīa
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puncta intrinſeca ſimul: igitur eque cito a. erit ſū-
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mū ac ſi nõ rarefieret: et per cõſequens nõ tradius
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inducetur gradꝰ ſummꝰ ꝙ̄ ſi nõ rarefieret / quod eſt
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opppſitum illati.
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">ↄ̨firma°.</
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<
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xml:space
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">¶ Et cõfiirmatur / q2 ſi velocitas
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inductionis gradꝰ ſummꝰ deberet attendi penes
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ſubiectū per quod adequate inducitur in eodem tē
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pore deductis aliis motibus: ſequeretur / a. et b.
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nūc ſunt oīno cõſimilia quãtitatiue et qualitatiue
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vnifor. diffor. termīata ad ſum: et incipiūt alterari
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cõſimili latitudine vniformi. </
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<
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xml:space
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">Et tamē ī duplo aut
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in maiori proportione inducetur gradꝰ ſummus
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velociꝰ in a. ꝙ̄ in b. ceteris aliis motibus deductis
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</
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<
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ſequitur </
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">Seq̄la probatur et pono / ſint a. et b. oī
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no ſimilia / vt ponitur: et inducat̄̄ pertibiliṫ latitu-
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do equalis alterationis vniformis per a. et per b.
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eo mõ quo inducitur reſiſtētia in mediū nõ reſiſtēs
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et ī vtro progrediatur vniformiter cõtinuo quo
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ad partes ſubiecti in duplo tamē velociꝰ cõtinuo
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progrediatur per a. ꝙ̄ per b. </
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xml:space
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">Quo poſito manife-
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ſtū eſt ꝙ̄ in duplo citius quilibet pūctus a. efficiet̄̄
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ſummus ꝙ̄ correſpõdens punctꝰ in b. cum ad illū
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in duplo citius deueniat alteratio et illa puncta
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ſint cõſimilia in a. et b. / igitur in duplo velocius
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inducetur gradus ſummus in a. ꝙ̄ in b. </
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<
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a. et b. ſunt equalia oīo etc̈. / et alterantur conſimili
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latitudine vniformi etc̈. / quod fuit inferendum.</
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<
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">Quia inductio
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gradus ſummi nõ eſt niſi quedã particĺis progreſ
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ſio per partes ſubiecti: ergo ſequitur / quãto pro
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greſſio eſt maior tanto inductio gradus ſummi eſt
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velocior: tanto autem progreſſio eſt maior quãto
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fit per maiorem partem ſubiecti vel per maiꝰ ſub-
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iectum. </
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<
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xml:space
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">igitur tanto inductio gradꝰ ſummi eſt ve-
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locior quanto fit per maius ſubiectum.</
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ponuntur notabilia. </
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tio ſoluentur rationes ante oppoſitum.</
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<
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ſūmꝰ et q̇d eiꝰ īductio. </
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">Uñ ꝓprie gradꝰ ſūmꝰ eſt in
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tenſiſſima q̈litas naturalr̄ in ſua ſp̄e poſſibilis q̈
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ꝓduct̄̄ a. agēs ceſſat agere ad pūctū ad quē ipſa ē
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ꝓducta </
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">Utrū aūt ſit dabilis gradꝰ ſūmꝰ ſimpĺr di
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co / illḋ eſt mihi dubiū. </
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3. ſic. </
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mõ.
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g̈dꝰ ſūmꝰ</
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">Inductio gradꝰ ſūmꝰ eſt ꝓgreſſio illiꝰ gradꝰ
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ſūmi ſiue ꝑtialis acq̇ſitio eiꝰ q̊ ad ꝑtes ſubiecti. </
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ſi g̈dꝰ octauꝰ q̇ ſignet̄̄ ſūmus ꝓgrediat̄̄ ſiue īducat̄̄
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ꝑtibilr̄ quo ad ꝑtes ſubiecti: ita ad omnē pūctū
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ꝓpinquiꝰ extremo a q̊ īcipit induci citiꝰ ꝓducat̄̄ ̄
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ad remotiꝰ ac ſi eſſet vnꝰ punctꝰ mouēs ſupra idē
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ſubiectū illud ſubiectū ꝑtialr̄ ꝑtrãſiens. </
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greſſio ſiue a ſiue ymagīaris dr̄ īductio gra. ſū.
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Inductionis gradus ſūmi ↄ̨̨ſideratio.
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</
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<
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cipio c. huiꝰ materie.
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poſſit ꝓduci gra. ſūmꝰ </
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ſūmꝰ. </
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<
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iectū
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<
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">¶ Sequit̄̄ .2. / ſi aliqḋ vniforme alteret̄̄ lati-
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tudīe vni. ꝑ totū ita eq̄ cito ſit ꝑ totū gradꝰ ſū.
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talis alteratio ad gra. ſū: ſiue acq̇ſitio gra. ſū. nõ
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eſt īductio gra. ſūmi. </
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<
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<
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ꝑ nullã alteratione vn. vniformiṫ extēſã ꝑ ali-
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qḋ vniforme ꝑ totū: v3 aliquo° īduci gra. ſū. ad
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vnū pūctū ꝙ̄ ad alteꝝ / qḋ eſt ↄ̈ rõnē īductiõis. </
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tñ nõ obſtãte põt ꝑ alṫationē vniformē īduci gra.
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ſū. ſubiectū vni. dū mõ alṫatio ꝓgrediat̄̄ ꝑtibiĺr q̊
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ad ſubiectū: ſꝫ tūc illq̈ totale ſubiectū īcipit eē dif-
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for̄e / vt ↄ̨ſtat </
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<
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<
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<
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aliqñ īducit̄̄ in ſubiectū ab aliis motibꝰ alienū: ali
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qñ o īducit̄̄ in ſubectū qḋ localr̄ mouet̄̄ vt viſū eſt
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in argumētꝪ. </
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<
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dēſat̄̄. </
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<
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">Et hoc duplr̄ aut extremo remiſſiori, aut nõ
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g̈. q̇eſcēte a rarefactiõe, aut extrēo ītēſiori. </
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q̇eſcit extremū rēiſſiꝰ aut ītēſiꝰ mouēt̄̄ velociꝰ ꝑ ra
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refactionē ꝙ̄ gra. ſū. īcipiat īduci: aut eq̄uelociter
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aut tardiꝰ. </
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<
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q̇eſcit, aut rarefit ſcḋm ſe totū: aut rarefit p̄ciſe m
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partē remiſſã. </
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<
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">multꝪ aliis modis põt ymagīari g̈.
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ſūmꝰ īduci ī ſubiectū aliis motibꝰ mutatū. </
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<
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dicas de ↄ̨dēſatiõe. </
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">Ad hñdã aūt vĺr notitiã veloci
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tatis īductiõis gra. ſūmi. </
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<
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xml:space
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">¶ Prīa ꝓpõ velocitas īductiõis gra. ſū nõ d3 vĺr
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attēdi penes manitudinē ſubiecti per qḋ īducitur
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</
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<
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">Probat̄̄ / q2 obſtat rarefactio et ↄ̨dēſatio / vt ptꝫ ex
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4. argumēto ãte oppoſitū
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īductiõis gra. ſū. nõ eſt vĺr attēdēda penes ſpaciū
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fixū īterceptū in fine īductiõis īter pūctū a q̊ incipit
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īduci g̈. ſū. et pūctū ad quē terīat̄̄ īductio gra. ſū. / pꝫ
<
lb
/>
hec clare ex deductiõe argumēti 4. obſtat em̄ motꝰ
<
lb
/>
localis
<
note
position
="
right
"
xlink:href
="
note-0279-09a
"
xlink:label
="
note-0279-09
"
xml:id
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N2CEC4
"
xml:space
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">3. propõ.</
note
>
</
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<
s
xml:id
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N2CE06
"
xml:space
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">¶ Tertia ꝓpõ. </
s
>
<
s
xml:id
="
N2CE09
"
xml:space
="
preserve
">Uelocitas īductiõis gra. ſū.
<
lb
/>
nõ d3 vĺr attēdi penes motū imagīariū pūcti exi-
<
lb
/>
ſtētis ↄ̨tinuo cū gra. ſū. </
s
>
<
s
xml:id
="
N2CE10
"
xml:space
="
preserve
">Ptꝫ etiã hec ꝓpõ ex p̄alle-
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lb
/>
grato argumēto
<
note
position
="
right
"
xlink:href
="
note-0279-10a
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xlink:label
="
note-0279-10
"
xml:id
="
N2CECA
"
xml:space
="
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">4. propõ</
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>
</
s
>
<
s
xml:id
="
N2CE1A
"
xml:space
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">¶ Quarta ꝓpõ. </
s
>
<
s
xml:id
="
N2CE1D
"
xml:space
="
preserve
">Uelocitas īducti
<
lb
/>
onis g̈. ſū. ī ſubiectū: nec rarefactū nec ↄ̨dēſatū ſiue
<
lb
/>
moueat̄̄ localr̄ ſiue nõ: ſꝑ attēdenda eſt penes ma-
<
lb
/>
gnitudinē ſubiecti. </
s
>
<
s
xml:id
="
N2CE26
"
xml:space
="
preserve
">pꝫ / q2 nõ apparet alter modꝰ
<
lb
/>
cognoſcēde velocitatꝪ. </
s
>
<
s
xml:id
="
N2CE2B
"
xml:space
="
preserve
">īductiõis gra. ſū. ī tali caſu
<
lb
/>
<
note
position
="
right
"
xlink:href
="
note-0279-11a
"
xlink:label
="
note-0279-11
"
xml:id
="
N2CED0
"
xml:space
="
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">5. propõ.</
note
>
</
s
>
<
s
xml:id
="
N2CE35
"
xml:space
="
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">¶ Quīta ꝓpõ </
s
>
<
s
xml:id
="
N2CE38
"
xml:space
="
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">Uelocitas īductiõis g̈. ſū. cū ſubiectū
<
lb
/>
rarefit aut ↄ̨dēſat̄̄ gra. ſū. ↄ̨tīuo manēte ī eodē pū
<
lb
/>
cto ſpacii fixi d3 attēdi penes ſpaciū īterceptū īter
<
lb
/>
tale pūctū ſpacii fixi ī q̊ ↄ̨tinuo eſt gra. ſū. et pūctū
<
lb
/>
fixū in q̊ erat pūctꝰ ſubiecti in quē mõ ṗmo inducit̄̄
<
lb
/>
exēplū / vt poſito / a. in qḋ īducit̄̄ g̈. ſū. in prīcipio
<
lb
/>
fit bipedale: et rarefiat ſus gra. ſū. et īductio g̈. ſū.
<
lb
/>
maneat in eodē pūcto fixo: tūc dico / cū g̈. ſū. ṗmo
<
lb
/>
fuerit īductꝰ ꝑ totū ṗmū pedale qḋ tã tūc erit maiꝰ
<
lb
/>
tã velociṫ fuit īductꝰ g̈. cū. ac ſi pedale q̇euiſſet a mo
<
lb
/>
in rarefactiõis.
<
note
position
="
right
"
xlink:href
="
note-0279-12a
"
xlink:label
="
note-0279-12
"
xml:id
="
N2CED6
"
xml:space
="
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">6. propõ.</
note
>
</
s
>
<
s
xml:id
="
N2CE54
"
xml:space
="
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">¶ Sexta ꝓpõ. </
s
>
<
s
xml:id
="
N2CE57
"
xml:space
="
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">Uelocitas īductiõis
<
lb
/>
g̈. ſū. cū. g̈. ſū. mouet̄̄ in ordine ad ſpaciū fixū motu
<
lb
/>
o vĺ imagīario et ſubiectū rarefit vĺ ↄ̨dēſat̄̄ d3 at
<
lb
/>
tēdi penes ſpaciū fixū qḋ deſcribit. </
s
>
<
s
xml:id
="
N2CE60
"
xml:space
="
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">exemplū habes
<
lb
/>
in argumēto .4.
<
note
position
="
right
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xlink:href
="
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xlink:label
="
note-0279-13
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xml:id
="
N2CEDC
"
xml:space
="
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">Correĺ.</
note
>
</
s
>
<
s
xml:id
="
N2CE6A
"
xml:space
="
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">¶ Ex hoc ſeq̇t̄̄ / in caſu p̄cedēti cõ
<
lb
/>
cĺonis in toto tꝑe q̊ gra. ſū. īducit̄̄ ꝑ totū gra. ſū. eq̄
<
lb
/>
uelociṫ īducit̄̄ ac ſi q̇eſceret a rarefactiõe. </
s
>
<
s
xml:id
="
N2CE71
"
xml:space
="
preserve
">et ī q̈lꝫ ꝑte
<
lb
/>
illiꝰ tꝑis terīata ad prīcipiū totiꝰ tꝑis īducit̄̄ tar-
<
lb
/>
diꝰ et ī q̈lꝫ terīata ad finē īducit̄̄ velociꝰ </
s
>
<
s
xml:id
="
N2CE78
"
xml:space
="
preserve
">Hoc correĺ.
<
lb
/>
pꝫ bñ ↄ̨ſiderati vltimã replicã .4. argumēti ãte op
<
lb
/>
poſitū. </
s
>
<
s
xml:id
="
N2CE7F
"
xml:space
="
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">Et hec ſūt dicta cõforīter ad opinionē quã
<
lb
/>
recitat et īpugnare nititur calcu. quaſi ī principio
<
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/>
2. c. de inducti. g̈. ſ. </
s
>
<
s
xml:id
="
N2CE86
"
xml:space
="
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">Sed tenēdo modum dicendi cal
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lb
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cu. pono .7. ꝓpoſitionem
<
note
position
="
right
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xlink:href
="
note-0279-14a
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xlink:label
="
note-0279-14
"
xml:id
="
N2CEE2
"
xml:space
="
preserve
">7. propõ</
note
>
</
s
>
<
s
xml:id
="
N2CE90
"
xml:space
="
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">¶ Septīa propoſitio. </
s
>
<
s
xml:id
="
N2CE93
"
xml:space
="
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">Ue- </
s
>
</
p
>
</
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>
</
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>
</
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>
</
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>
</
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>
</
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>
