Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Primi tractatus
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correlarii patet ex ſecūdo correlario ſecūde cõclu-
<
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ſionis huius capitis: et ſecūda breuiter ꝓbatur ſic /
<
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q2 vbicū aliqua potentia īuariata mediū īuaria
<
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tum tranſeūdo ↄ̨tinuo vniformiter remittit motū
<
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ſuū ad extremū intenſius deueniendo: oīs maior
<
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vel minor verſus idem extremū veniendo per ean-
<
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dem lineã cõtinuo difformiter remittit motū ſuum
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ipſa et medio continuo inuariatis / vt ptꝫ ex quarta
<
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concluſione huiꝰ: et oīs potentia inuariata mediū
<
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inuariatū tanſeundo ab extremo intenſiori rece-
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dendo per eandem lineam oīno eodē modo inten-
<
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dit motum ſuū ſicut remittit ab extremo remiſſiori
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ꝓcedendo per eandē lineam verſus extremū inten
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ſius: ergo oīs maior ab eodē puncto intenſiori ꝓ-
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cedendo per eandē lineã per quam ꝓcedit potētia
<
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intendens motum ſuū vniformiter: ipſo medio in-
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uariato: difformiter cõtinuo intendit motum ſuuꝫ
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et ſimiliter oīs minor habens ad extremū intēſius
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eiuſdem medii ꝓportionē maioris inequalitatis.
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<
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xml:space
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">Et ſi fortiorē demonſtrati-
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onē exoptas: vtaris demonſtratione adducta ad
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quartã concluſionē paucis mutatis: que ſeſe ṗma
<
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fronte intelligenti probationē illius concluſionis
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offerūt.
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xml:space
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">3. correĺ.</
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<
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xml:space
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">¶ Sequitur tertio / vbicū aliqua potē-
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tia īuariata vniformiter cõtinuo ſucceſſiue intēdit
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/>
motū ſuū vſ ad nõ gradum: mediū īuariatū trã-
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/>
ſeundo ab extremo intenſiori verſus remiſſius: oīs
<
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potentia maior ab eodem extremo intenſiori ꝓce-
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dens continuo per eandē lineã in infinitū velociter
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intendit motum ſuū. </
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<
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ipſa potentia maior mouetur verſus extremū in-
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tenſius cõtinuo remittendo motum ſuū .etc̈. in infi-
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nitum velociter remittit motū ſuū / vt patet ex quin
<
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ta cõcluſione huius capitis: et oīno eadem veloci-
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tate intendit motū ſuū retrogrado motu per ean-
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dem lineã mouēdo ſicut antea remittebat in eiſdeꝫ
<
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partibus eiuſdem linee: ergo oīs talis potentia
<
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maior que ſic mouetur motu retrogrado ab extre
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mo intenſiori verſus remiſſius per eandē lineam
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etc̈. in infinitū velociter intendit motum ſuū / quod
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fuit probandū. </
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xml:space
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">Et ſic patꝫ correlariū.
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<
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xml:space
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">¶ Sequitur
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quarto / vbicun aliqua potentia īuariata me-
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dium īuariatum tranſeundo cõtinuo ſucceſſiue in
<
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/>
tēdit motum ſuū ad nõ gradum ſiue vniformiter
<
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ſiue difformiter: oīs potentia minor habens pro-
<
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portionē maioris inequalitatis ad aliquã parteꝫ
<
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eiuſdē medii in infinitū tardius intendit motum
<
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ſuū a puncto ad quē habet proportionē equalita
<
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tis recedendo verſus remiſſius extremū: quã data
<
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potētia maior ab eodē puncto recedendo verſus
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extremū remiſſiꝰ. </
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">Capitulū octauū / in quo inquiritur an due
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potentie īequales idē mediū īuariatū tran-
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ſeūtes valeãt vniformiter remittere aut intē
<
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dere motum ſuum per ambarū vel alterius
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earum variationem.</
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">POſt̄ ſuperiori capite oſtēſū
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eſt nullas duas potētias īequales īua-
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riatas: id eſt quarum nulla variat̄̄ idem
<
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mediū īuariatū trãſeūtes poſſe vniformiter intē-
<
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dere aut remittere motū ſuū: iã īquirendū eſt an ꝑ
<
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alteriꝰ eaꝝ vel ambaꝝ variationē id fieri valeat.</
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">Cuiꝰ inq̇ſitiõi p̄mittat̄̄ ꝓ baſi fūda
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mēto talis ſuppoſitio. </
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">Si aliq̈ potētia vniformiṫ
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ↄ̨tinuo ſuū motū remittēs aut ītēdēs aliq̈ potētia
<
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in certa ꝓportione cõtinuo velocius mouetur: ne-
<
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ceſſe eſt potentiã ipſam tardius motã cõtinuo vni
<
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formiter motū ſuū remittere aut intendere. </
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<
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">Et ſi
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Capitulū octauū.
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aliqua potentia vniformiter cõtinuo ſuū motum
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remittens aut intendens aliqua alia potentia in
<
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certa ꝓportione cõtinuo tardius mouetur: neceſſe
<
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eſt potentiã velocius motã vniformiter itidē con-
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tinuo motū ſuū remittere aut intendere. </
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">Exemplū /
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vt data potētia que incipit a gradu octauo exclu-
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ſiue moueri cõtinuo vniformiter remittēdo motū
<
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ſuū: et in dupla ꝓportione cõtinuo velocius moue
<
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do quã vna alia potētia que incipit moueri a gra
<
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/>
du quarto excluſiue: tūc dico / neceſſe eſt / illa po
<
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tentia que incipit moueri a quarto gradu excluſi-
<
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ue cõtinuo vniformiter remittat motum ſuū: </
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<
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batur / et ſit a. potentia remittens continuo vnifor-
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miter motū ſuū: et ſit b. potentia que cõtinuo in f.
<
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ꝓportiõe tardius mouetur quã a. potentia: et ma-
<
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nifeſtū eſt / etiã b. potentia remittit motū ſuū: q2
<
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alias motus illarū potentiarū nõ cõtinuo mane-
<
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rent in eadē ꝓportione. </
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">Uolo igitur / potētia a.
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perdat in toto tēpore adequate in quo mouetur c.
<
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latitudinē motus: et b.d. latitudinē motus: et tunc
<
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dico / d. latitudo motus deperdenda a b. poten-
<
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tia tardius mota vniformiter cõtinuo remittetur
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</
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<
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">Probatur / q2 d. latitudo motus in qualibet me-
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dietate tēporis in quo deperdetur perdet vnã me-
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dietatē ſui, et in qualibet tertia vnã tertiam, et in
<
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/>
qualibet quarta, vnã quartã, et ſic conſequenter:
<
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/>
igitur d. latitudo deperdenda a b. potentia tar-
<
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dius mota vniformiter continuo remittetur. </
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tet conſequentia ex diffitione remiſſionis vnifor-
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mis alicuius latitudinis. </
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<
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">Probatur antecedens:
<
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quoniã quandocun aliqua pars aliquota c. la-
<
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titudinis ab a. potentia deperdende deperdetur
<
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adequate conſimilis pars aliquota et eiuſdem de
<
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/>
nominationis deperdet d. latitudo: ſed in quali-
<
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/>
bet medietate temporis in quo ille latitudines re
<
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/>
mittuntur c. latitudo perdit vnam medietateꝫ ſui:
<
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et in qualibet tertia vnam tertiam ſui, et in quali-
<
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bet quarta quartam, et ſic conſequenter: quia c. la
<
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/>
titudo vniformiter remittitur continuo / vt patet
<
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ex hypotheſi / igitur d. latitudo in qualibet medie-
<
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ta temporis in quo remittitur perdit vnã medie-
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tatem ſui, et in qualibet tertia tertiam, et in quali-
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bet quarta quartam, et ſic cõſequenter. </
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ſequentia cum minore: et probatur maior: quoniã
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continuo latitudo motus quo mouetur a. ad lati-
<
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tudinem motus quo mouetur b. eſt proportio f. ex
<
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hypotheſi: et continuo motus quo mouetur a. et
<
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/>
etiam latitudo motus quo mouetur b. remittūtur /
<
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/>
ergo inter latitudinem deperditam a. motu quo
<
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/>
mouetur a. maiore, et latitudinem deperditam a
<
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motu minori quo mouetur b. eſt continuo propor
<
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tio f. / vt patet ex primo correlario quinte concluſi-
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onis ſecūdi capitis ſecunde partis: et latitudo de-
<
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perdenda a motu quo mouet̄̄ a. eſt c. et latitudo de
<
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ꝑdēda a motu quo mouet̄̄ b. eſt d. / igit̄̄ inter c. et d.
<
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eſt ꝓportio f. / et ex cõſequēti ſequit̄̄ / inter partes
<
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aliquotas eiuſdē denoīatiõis ipſiꝰ c. et ipſiꝰ d. pu-
<
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ta īter medietatatē c. et medietatē d, et īter tertias
<
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et īter quartas, et ſic cõſequēter eſt etiã ꝓportio f.
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p̄allegati: et vltra īter ꝑtes aliq̊tas eiuſdē denoīa
<
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tionis c. latitudīs eſt ꝓportio f. et ↄ̨tinuo īter ꝑteꝫ
<
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deꝑditã ab ipſo c. et deꝑditã a d. eſt f. ꝓportio / vt ꝓ
<
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batū eſt / g̊ quãdocū aliq̈ pars aliq̊ta c. latitudīs
<
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/>
ab a. potētia deꝑdēde deꝑdet̄̄: adeq̈te ↄ̨ſimilis ꝑs
<
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aliq̊ta et eiuſdē denoīatiõis deꝑdet d. latitudo / qḋ
<
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fuit probandum. </
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<
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xml:space
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preserve
">Et eodem modo probabis cum
<
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vtra potentia iutendit motum ſuum altera illa-
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rum que cotinuo in certa ꝓportione velocius mo- </
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