Alvarus, Thomas
,
Liber de triplici motu
,
1509
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De motu locali quo ad effectū ſcḋm ſubiectū difformi.
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que dicta ſunt in ſecunda parte huius operis capi
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te quarto. </
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<
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xml:space
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">Infinita alia correlaria poſſūt ex hac ꝓ
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poſitione inferri. </
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<
s
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N1E996
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xml:space
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poſitionis habenda.</
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</
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<
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<
s
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xml:space
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">Quīta ꝓpoſitio. </
s
>
<
s
xml:id
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N1E99F
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xml:space
="
preserve
">Si maior velocitas
<
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tēpori minori coextendat̄̄ et minor maiori, et ꝓpor-
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tio velocitatis maioris ad velocitatem minoris ſit
<
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equalis ꝓportioni tēporis maioris ad tēpus minꝰ
<
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tūc illa mobilia equalia ſpacia ꝑtranſeūt. </
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>
<
s
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xml:space
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">Exēplū /
<
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vt ſi a. mobile per mediã horã moueatur velocitate
<
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vt .4. et b. mobile per horã velocitate vt .2. tunc quia
<
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/>
proportio tēporis ad tēpus eſt dupla / et velocitatis
<
lb
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etiã ad velocitatē dupla ſequitur / a. et b. equalia
<
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ſpacia ꝑtranſeūt. </
s
>
<
s
xml:id
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xml:space
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preserve
">Probat̄̄ hec ꝓpoſitio: ſit a. mo-
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bile qḋ moueatur ꝑ aliqḋ tēpus: et b. mouetur ꝑ tē-
<
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pus in f. ꝓportione maius: et in f. ꝓportione minori
<
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velocitate: tūc ibi ꝓportio velocitatū et tēpoꝝ ſunt
<
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/>
equales q2 vtra f. / igit̄̄ ſi a. moueat̄̄ equali veloci-
<
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/>
tate cū b. tunc in f. ꝓportione b. maius ſpaciū per-
<
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/>
tranſit quã a. q2 in ꝓportiõe tēporis / vt ptꝫ ex ſcḋa
<
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/>
parte prime propoſitionis: ſed modo a. mouet̄̄ in f.
<
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/>
ꝓportione velocius quã tunc: ergo in f. ꝓportione
<
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/>
maius ſpacium ꝑtranſit quã tunc in eodē tēpore: vt
<
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ptꝫ ex ſecūda ꝓpoſitione: ergo tantū ſicut b. </
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>
<
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xml:space
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ↄ̨ña per hanc maximã quãdo aliqua duo ſe habent
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in aliqua ꝓportione vt puta f. </
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>
<
s
xml:id
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xml:space
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">Si minꝰ illoꝝ acqui
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rit illã ꝓportionē f. ſupra ſe, efficitur equale alteri /
<
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/>
quod erat maius: vt ſi quaternariꝰ ad quē octona-
<
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rius habet ꝓportionē duplã acquirat ſupra ſe ꝓ-
<
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portionē duplã efficiet̄̄ equalis octauario / vt ptꝫ de
<
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ſe: et ſic ptꝫ ꝓpoſitio.
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</
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<
s
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xml:space
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">¶ Ex hac ꝓpoſitione ſequitur /
<
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ſi a. mobile moueatur per horã velocitate vt .4.
<
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et b. mobile per duas tertias hore velocitate vt ſex
<
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b. et a. equalia ſpacia ꝑtranſeūt. </
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>
<
s
xml:id
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xml:space
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">Probatio / q2 qua
<
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lis eſt ꝓportio tꝑis maioris ad tempus minꝰ: talis
<
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/>
eſt ꝓportio velocitatis fluentis per tēpus minꝰ ad
<
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/>
velocitatem per maius tēpus labentem. </
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>
<
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xml:space
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">(Utrobi
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enim ſexquialtera proportio reperitur.</
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<
s
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">Quīta ꝓpoſitio. </
s
>
<
s
xml:id
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N1EA0C
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xml:space
="
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">Si maior velocitas
<
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/>
tēpori et extendatur minori, et minor velocitas ma
<
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/>
iori tēpori: ꝓportio velocitatis tēporis ꝓportio
<
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/>
nē exuperet: tūc mobile minori tēpore motū maius
<
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/>
ſpaciū deſcribet ꝙ̄ mobile motū in maiori tēpore
<
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in ea ꝓportione per quã velocitatū ꝓportio tēpoꝝ
<
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ꝓportionē excedit. </
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<
s
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xml:space
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">Exemplū / vt ſi a. mobile moueat̄̄
<
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per horã velocitate vt .2. et b. mobile per mediã ho-
<
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ram velocitate vt .8. tunc b. mobile maius ſpacium
<
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/>
ꝑtranſit quã a. mobile in ea ꝓportione per quã pro
<
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portio quadrupla velocitatū excedit ꝓportitioneꝫ
<
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duplã tēpoꝝ. </
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>
<
s
xml:id
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xml:space
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">Et q2 quadrupla velocitatū duplam
<
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tēpoꝝ per duplã antecedit notū euadet ſpaciū a b.
<
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mobili pertrãſitū ad ſpaciū ab a. mobili ꝑtranſi-
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tū duplū eſſe. </
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<
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">Uniuerſalitcr tamen mathematico
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ordine hanc quintã ꝓpoſitiouē inducamus. </
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<
s
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">Sit em̄
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a. mobile quod per aliquod tēpus aliqua velocita
<
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te moueatur: et b. mobile moueatur per tēpus in f.
<
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ꝓportione minus: et velocitate in g. ꝓportione ma-
<
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iori quã velocitas qua mouetur a. ſit g. ꝓportio
<
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maior f. excedat g. ꝓportio ꝓportionē f. per h. ꝓ-
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portionē. </
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<
s
xml:id
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xml:space
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">quibꝰ ſtructis ſic argr̄: ſi ꝓportio veloci-
<
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tatis b. ad velocitatē a. eſſet equalis ꝓportiõi tēpo-
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ris tn quo mouet̄̄ a. ad tēpus in quo mouetur b. que
<
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eſt f.a. et b. equalia ſpacia ꝑtranſirent in illis tēpo-
<
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ribus in equallbꝰ / vt p̄cedens ꝓpoſitio demonſtrat
<
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puta quarta. </
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>
<
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xml:space
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">Sed modo velocitas qua mouet̄̄ b. eſt
<
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in h. ꝓportione mãior velocitate / qua tunc moueret̄̄ /
<
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ergo in h. ꝓportione maius ſpaciū pertranſit mo-
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De motu locali quo ad effectū ſcḋm ſubiectū difformi.
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do b. quã tunc: qm̄ ſicut ſe habent velocitates in a-
<
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/>
liquo tēpore: ita ſpacia pertranſita in eodē / vt ptꝫ
<
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ex ſecūda ꝓpoſitione: et ex conſequenti ſequitur /
<
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/>
modo b. in h. proportione maius ſpaciū pertrãſit ̄
<
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a. qm̄ a. et b. tunc equalia ſpacia pertranſirent: et h.
<
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ꝓportio eſt ꝓportio per quã g. ꝓportio velocitatū
<
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excedit f. proportionē tēpoꝝ: igr̄ b. mouetur velocius
<
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ipſo a. in ꝓportione per quã ꝓportio velocitatum
<
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temporum proportionem excedit: quod fuit ꝓban-
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dum: et ſic patet propoſitio.</
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note
>
<
p
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<
s
xml:id
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xml:space
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preserve
">¶ Ex hac propoſitione ſequitur / ſi a. mobile mo-
<
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ueatur per horã velocitate vt duo: et b. mobile per
<
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/>
mediã horam, velocitate vt .6. b. mobile in ſexqui
<
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altero maius ſpaciū pertranſit quã a. vt ſi a. per-
<
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trãſit bipedale b. tripedale ꝑtrãſit. </
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<
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xml:space
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">Probat̄̄ / q2 ibi
<
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velocitates inequales in equalibus temporibus co
<
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extenduntur: et mbior velocitas maiori tempori co
<
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extenditur / vt notū eſt: et proportio velocitatū que
<
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tripla eſt, proportionē tēporum duplã per ꝓporti-
<
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onem ſexquialterã antecedit. </
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>
<
s
xml:id
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xml:space
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">Hec igitur ſignum eſt
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et fidem facit auxilio precedentis propoſitionis b.
<
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/>
mobile in ſuo tēpore quo mouetur ſexquialterum
<
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/>
ſpaciuꝫ ad ſpaciū ab a. exactū abſoluiſſe: quod ab
<
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iniitio ꝓpoſitū fuit </
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>
<
s
xml:id
="
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xml:space
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">¶ Inferas tuo marte mĺta huic
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ſimilia correlaria que ex hac quīta propoſitiõe
<
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ſuã demonſtrationem facile ſortiūtur. </
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<
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xml:space
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">Hoc em̄ cor-
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relariū: ideo poſitū eſt: quia neceſſe intelligentem
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particularia fantaſmata ſpeculari.
<
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right
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xlink:href
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note-0150-02
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xml:id
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xml:space
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">phdot;us .2.
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de aīa</
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>
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<
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xml:space
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">teſte philoſo-
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pho ſecūdo de aīa: nichil eſt in īteliectu quin priꝰ
<
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quodammodo ſingulariter preceſſerit in ſenſu de
<
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ſenſu et ſeaſato aſſerente philoſopho.</
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>
</
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<
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">Sexta ꝓpoſitio. </
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>
<
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xml:space
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">Ubicun maior ve
<
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locitas tꝑri coaſſiſtit mīori, mīor o maiori eſt ꝓ
<
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portio velocitatū tp̄m ꝓportiõe īferior et mīor, tūc
<
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mobile qḋ maiori velocitate mouent̄̄ mīori tp̄e mīo
<
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/>
rem magnitudinē deſcribet quã mobile motū ma-
<
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iori tēpore in ea ꝓportione per quã temporū ꝓpor
<
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tio velocitatū ꝓportioni effertur. </
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>
<
s
xml:id
="
N1EAD1
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xml:space
="
preserve
">Exemplū / vt ſi a.
<
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/>
mobile per horan moueatur velocitate vt duo ade-
<
lb
/>
quate, et b. per mediã horam moueatur velocitate
<
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/>
vt .3. tunc b. minꝰ ſpaciū pertranſit quã a (minꝰ in-
<
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/>
quam) in ꝓportione ſexquitertia per quã ſexquiter
<
lb
/>
tiam ꝓportio dupla tēporuꝫ ꝓportionē ſexq̇alterã
<
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velocitatū excedit: ſi igitur a. pedale pertrãſeat: b.
<
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tres quartas deſcribet. </
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>
<
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xml:id
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xml:space
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">Generaliṫ tñ iudicat̄̄ ↄ̨clu-
<
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ſio iſto modo. </
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>
<
s
xml:id
="
N1EAE7
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xml:space
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">Sit a. mobile per aliquod tēpus mo
<
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tum aliqua velocitate, b. vero per tēpus in g. ꝓpor-
<
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tione minus, et moueatur b. in f. ꝓportione minori
<
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/>
tamen g. velocius ipſo a. excedat g. ꝓportio pro-
<
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portionē f. per h. ꝓportionē: tunc a. maius ſpaciuꝫ
<
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/>
pertranſit in h. ꝓportione ꝙ̄ b. </
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>
<
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xml:space
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">Quod ꝓbatur ſic.
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</
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<
s
xml:id
="
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"
xml:space
="
preserve
">quia ſi proportio velocitatis qua moueatur b. mobi
<
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le per tempus minus eſſet equalis proportioni tē-
<
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/>
porum: tunc b: equale ſpaciū pertranſiret adequa-
<
lb
/>
te in tempore in quo mouetur ſpacio pertrãſito ab
<
lb
/>
a. in tempore in quo a. mouetur, vt patet ex quarta
<
lb
/>
prppoſitione: ſed modo mouetur b. velocitate in h.
<
lb
/>
proportione minori quam tunc: igitur b. pertran-
<
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/>
ſit modo ſpacium in eodem tempore in h. propor-
<
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tione minus quam tunc / vt patet ex ſecunda propo-
<
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/>
ſitione, et ex conſequenti ſequitur / medo pertran
<
lb
/>
ſit b. ſpacium in h. proportione minus quam a. qm̄
<
lb
/>
a. pertranſit tantum ſicut tūc pertranſibat b. / quod
<
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/>
fuit probandum. </
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>
<
s
xml:id
="
N1EB13
"
xml:space
="
preserve
">Sed iam probo illam minorem:
<
lb
/>
videlicet b. modo mouetur velocitate in h. ꝓpor-
<
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/>
tione minori quam tunc, per hanc maximã. </
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>
<
s
xml:id
="
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xml:space
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">Quan
<
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/>
docun duo numeri inequales habent duas pro-
<
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portiones ad vnum tertium: tunc in </
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