Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Secundi tractatus
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ram in proportione irrationali / et volo / in maio
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ri illarum moueatur a. mobile gradu octauo et in
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minori illarū moueatur idem mobile gradu quar
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to </
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<
s
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N1E213
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xml:space
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preserve
">(Semper in iſtis argumentis ſuppono / vni gra
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dui velocitatis in hora correſpondeat pedanea per
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tranſitio) quo poſito ſic argumentor talis motus
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eſt difformiter difformis: et tamen non poteſt redu-
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ci ad vniformitatem: </
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<
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N1E21E
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xml:space
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preserve
">Nec eius valet dari ſiue aſſi-
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gnari determinata intenſio: igitur. </
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>
<
s
xml:id
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xml:space
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preserve
">Maior eſt nota /
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et minor probatur ſupponēdo / quanto aliq̈ pars
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/>
motus totalis eſt tn minori parte temporis tãto mi
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/>
nus facit ad denominationem intenſionis totiꝰ mo
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tus ceteris aliis paribus: et tanto minus de ſpacio
<
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/>
per talem motum tranſitur: vt motus vt vnum par-
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tialis in vna quarta hore facit ad intenſionem to-
<
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/>
tius motus vt vna quarta, et per illum in illa quar-
<
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/>
ta pertranſitur quarta pars pedalis. </
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>
<
s
xml:id
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xml:space
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preserve
">Et generali-
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ter obſeruandum eſt / in quacun proportione ſe
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habet pars temporis ad totuꝫ tempus in eadem ſe
<
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/>
habet velocitas motus in llla parte ad velocitateꝫ
<
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totalis motus in toto tempore. </
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>
<
s
xml:id
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xml:space
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preserve
">Quo poſito argui-
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tur aſſumptum / quia motus vt .8. in illa parte tem-
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poris non ſe habet in aliqua proportione rationa
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/>
li ad totalem motum, nec etiam vt quatuor: et penes
<
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/>
tales proportiones debet inueſtigari eius intenſio
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/>
et reductio ad vniformitatem: igttur non poteſt da
<
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/>
ri eius determinata intenſio aut reductio ad vnifor
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mitatem. </
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>
<
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xml:space
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preserve
">Conſequentia patet cum minore: et argui
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tur maior / quia partes temporis in quibus ſunt illi
<
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/>
motus ſe habent ad totum tempus in proportione
<
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/>
irrationali / vt poſitum eſt: igitur etiam motus illa
<
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rum partium ad totalem motum. </
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>
<
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">Conſequentiã de
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clarat ſuppoſitio.
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xml:id
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xml:space
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">Dicitur.</
note
>
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<
s
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xml:space
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">¶ Dices forte et bene concedendo /
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talis motus non poteſt dari determinata inten-
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ſio et rationalis reductio ad vniformitatem: ita ī
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tenſio illius motus ſe habeat ad motum alicuius il
<
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larum partium in proportione aliqua rationali:
<
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nec hoc eſt inconueniens, nec contra tituluꝫ queſtio
<
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nis: quia intelligitur titulus queſtionis dūmodo ꝑ
<
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tes in quibus tales motus ponūtur ſe habeãt in ꝓ-
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portione rationali. </
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">Unum tamen eſt / quod poſtea
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oſtendetur / talis motus totalis eſt intenſior quã
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motus vt ſex.</
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<
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xml:space
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">Sed contra ſolutionem arguitur ſic /
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quia aliquis eſt motus difformis cuius partes ſūt
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in partibus temporis rationalē ꝓportionē haben
<
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tibus ad totū tempus: et tamē talis motꝰ nõ valet
<
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reduci ad vniformitatē, nec valet inueniri certa eiꝰ
<
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intenſio: igit̄̄ ſolutio nulla. </
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>
<
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xml:id
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xml:space
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preserve
">Arguitur antecedēs et
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pono caſum / diuidatur hora per partes ꝓportio
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nales proportione dupla: et in prima a. mobile mo
<
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ueatur aliquatulū velociter exempli gratia vt .2. et
<
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in ſecunda in duplo velocius quã in prima. et in ter
<
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tia in triplo: et ſic conſequenter aſcendendo per om
<
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nes numeros. </
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<
s
xml:id
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xml:space
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">quo poſito ſic arguitur / talis mo-
<
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tus eſt difformiter difformis cuius partes ſunt in
<
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partibus temporis habentibꝰ proportionē ratio-
<
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nalem in ordine ad totum: et tamē non inuenit̄̄ nec
<
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dabilis eſt certa intenſio eiꝰ nec reductio ad vnifor
<
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mitatem: igitur propoſitū: tota ratio patet dem-
<
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pta minore / que ſic arguit̄̄ / q2 ille motus videtur eſſe
<
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infinitus: igitur nõ valet dari determinata eiꝰ intē
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tio ſaltem finita de qua loquimur. </
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<
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">Probatur añs /
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quia in infinitū intēſus eſt ille motus in illa hora:
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igitur apparet / ſit īfinitus.
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">Dicitur.</
note
>
</
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>
<
s
xml:id
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xml:space
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">¶ Dices forte / tota-
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lis ille motus eſt ita intenſus ſicut motus qui fit in
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ſecunda parte ꝓportionali temporis: ita talis
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motus eſt ī duplo ītenſior motu facto ī prima par
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te ꝓportionali tēporis: et reduciter ad vniformita
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Capitulum tertium
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tem ſupponendo / per quamlibet partē illius ho
<
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/>
re eſt motus vt duo et per totū reſiduū a prima par
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te ꝓportionali eſt motꝰ vt .4. et per totū reſiduum
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a ſecunda eſt motꝰ vt .6. et per totū reſiduū a tertia
<
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eſt motus vt .8. / vt facile patet ex caſu: ita queli-
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bet pars ſequens alterã cū oībus ſequētibus eam
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excedit immediate precedentem per duos gradus.
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</
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<
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">Quo ſuppoſito arguitur reductio vniformitatis
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talis motus: et volo / capiãtur duo gradus extēſi
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per totū reſiduū a. prīa ꝑte ꝓportionali: et ponan
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tur in prima ſibi equali. </
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<
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xml:space
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">Diuidendo em̄ proportio
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ne dupla totū aggregatū ex oībus immediate ſe-
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quentibus aliquã eſt equalis illi / vt patet ex quinto
<
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capite prime partis) / deinde capiantur duo gradꝰ
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a toto a ſecunda / et ponãtur in ſecunda: et nichil po
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natur vlterius in prima: aut ſecunda: deinde a ſe-
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quentibus tertiam capiantur duo gradus / qui po
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nantur in tertia: et ſic cõſequenter. </
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>
<
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xml:id
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xml:space
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">quo poſito in fi
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ne totus ille motus erit vniformis vt .4. / igit̄̄ dabi-
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lis eſt eius intēſio et ad vniformitateꝫ reductio ha
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betur em̄ / velocitas totalis motus eſt dupla ad
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velocitatem eiꝰ que eſt in prima parte proportio-
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nali hore.</
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<
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xml:space
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">Sed contra / quia tunc ſequeretur /
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ſi hora diuidatur per partes ꝓportionales ꝓpor-
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tione tripla et per primã illarū moueat̄̄ aliquod
<
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mobile aliquantula velocitate: et ꝑ ſecundam du
<
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pla velocitate: et per tertiam tripla: et ſic in infini
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tuꝫ vt in priori caſu. </
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<
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xml:space
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">tale mobile etiã moueret̄̄ in to
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tali hora adequate dupla velocitate ad velocitatē
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qua mouetur in prima parte proportionali hore /
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ſed cõſequens eſt falſum / igitur illud ex quo ſequit̄̄
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</
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<
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">Sequela probatur / quia non videtur maior ratio
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ni iſto caſu quam in p̄cedenti: falſitas tamē conſe
<
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/>
quentis arguitur / quia talis motus eſt dūtaxat in
<
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ſexquialtero velocior motu prime partis propor-
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tionalis temporis: igitur non eſt ī duplo velocior.
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</
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<
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xml:space
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preserve
">Conſequentia patet: et arguitur añs: et volo gra-
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tia argumēti / motus prime partis proportiona
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lis ſit vt .2. / quo poſito ſic argumētor motus vt duo
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eſt per totam horã. </
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>
<
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xml:id
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N1E340
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xml:space
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">ergo talis motus denominat
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totū moueri vt duo in tota hora motꝰ vero vt duo
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ſuperadditus in ſecunda parte ꝓportionali et in
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oībus ſequentibus eſt in ſubtriplo tempore: et eſt
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equalis intenſionis cñ aliis duobꝰ gradibꝰ per to
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tum: igitur in triplo minus denominat. </
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>
<
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xml:space
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">Duo vero
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gradus extenſi per tertiã partē ꝓpottionalē et to
<
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tum reſiduū ſunt in triplo minori ſubiecto / ergo ad
<
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/>
huc in triplo minꝰ denominãt: et ſic conſequenter
<
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ꝓcedendo per ſubtriplam proportionē: ergo tota
<
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lis denominatio talis motꝰ facti in illa hora con-
<
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flatur ex infinitis cõtinuo ſe habentibꝰ in ꝓportio
<
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ne ſubtripla: igitur reſiduū a prima eſt ſubdupluꝫ
<
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/>
ad primū / vt patet ex correlario prīe ↄ̨cluſionis q̇nti
<
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/>
capitis prime partis et primū illoꝝ erat vt duo hoc
<
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/>
eſt prima denomīatio erat vt .2. / igitur oēs alie de
<
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nominatiões ſunt vt vnū: modo duo et vnū ſūt tria /
<
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igit̄̄ totalis motꝰ velocitas eſt vt .3. et velocitas in
<
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prima parte ꝓportionali eſt vt .2. / ergo velocitas to
<
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talis motus ſe habet in ꝓportiõe ſexquialtera ad
<
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velocitatem eiuſdē motꝰ in prima parte ꝓportio-
<
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nali temporis / quod fuit ꝓbandū: patet tamen con
<
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ſequentia / q2 triū ad duo eſt ꝓportio ſexquialtera.</
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<
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difformiter difformis quorū partes diuerſis con-
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tinuo ꝓportionibus ſe habent: arguitur ſic: q2 ali
<
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quis eſt motus difformiter difformis cuius nõ eſt
<
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dabilis vniformitas nec denoīationis intēſio: igit̄̄ </
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