Alvarus, Thomas, Liber de triplici motu, 1509

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231 ꝓportiõi quã in eodē tꝑe acq̇rit poña, mīorē tñ ̄
reſiſtētia ↄ̨tinuo velociꝰ creſcēs / vt pꝫ aſpiciēti.
Qui­
bus īſpectis facile ptꝫ correlariū. 113. correĺ.
¶ Seq̇t̄̄ tertio / 
creſcētibꝰ a nõ gradu reſiſtētia alicuiꝰ paſſi et ponã
alterãtis ip̄m īcipiēdo ī eodē īſtãti: reſiſtētia ↄ̨tinuo
tardius et tardiꝰ, et cõtinuo tardiꝰ ꝙ̄ ponã data cõ­
tinuo vniformiṫ creſcēs: ip̄m alterãs ↄ̨tinuo intēdit
motū ſuū.
Probat̄̄ hoc correlariū ſicut ṗmū.
Decima ↄ̨̨cluſio Creſcētibꝰ a nõ gra-
du reſiſtētia alicuiꝰ paſſi et ponã alterãtis ip̄m inci­
piēdo ī eodē inſtãti et ponã et reſiſtētia ↄ̨tinuo velo-
cius et velociꝰ creſcētibꝰ: aut vtra ↄ̨tinuo creſcēte
tardius et tardiꝰ: ſtat alterãs ↄ̨tinuo vniformiter al­
terare: ſtat etiã ip̄m ↄ̨tinuo velociꝰ et velociꝰ altera-
re: ſtat ſiĺr ip̄3 alterare cõtinuo tardiꝰ et tardiꝰ: ſtat
etiã etc̈. miſceas mēbra.
Ptꝫ ↄ̨° facile. ¶ Inferas tua
induſtria concluſioues his ſiĺes a certis gradibus
ponã et reſiſtentia creſcere incipientibus.
Undecima cõcluſio materiã ſexti ar-
gumēti tangēs.
Diuiſa hora ꝑ partes ꝓportiona-
les ꝓportiõe ſexq̇altera ↄ̨ſtitutiſ tribꝰ ordinibꝰ
ꝑtiū ꝓportionaliū īterſcalariṫ ſe hñtiū ꝑ ṗmo ordīe
capiēdo ṗmã .4.7.10. / et ſic ↄ̨ñr omiſſis ↄ̨tinuo dua-
bus ꝑ 2° o capiēdo ſcḋam .5.8.11. / et ſic ↄ̨ñter omiſ­
ſis duabꝰ: ꝓ tertio o capiēdo tertiã .6.9.12. / et ſic
ↄ̨ñter omiſſis ſiĺr ↄ̨tinuo duabꝰ: et in ṗmo illoꝝ or­
dinū aliqḋ alterãs alteret aliqḋ paſſuꝫ certa veloci­
tate: et in ſcḋo tãta: et in tertio tãta adeq̈te: tūc qua­
litas ꝓducta mediãte totali velocitate in illis tribꝰ
ordinibꝰ ſe hꝫ ad q̈litatē ꝓductã in prīo illoꝝ ordi-
nū ī ꝓportiõe dupla ſexq̇nona: q̈lis eſt .19. ad 9.
pꝫ
ↄ̨cluſio eſto gr̄a argumēti /  ī prīo illoꝝ ordinū ꝓ-
duxerit nouē gradus q̈litatꝪ.
Tūc eī mãifeſtū ē /  in
ſcḋo ꝓduxit ſex et in tertio q̈tuor: ꝰ ſic oēs gradus ꝓ­
ducti in tribꝰ orbinibꝰ ſūt decē et nouē.
Mõ. ig. ad
6. eſt dctã ꝓportio dupla ſexq̇noua.
pꝫ igr̄ ꝓbatio
ↄ̨°nis additis his / q̄ dctã ſunt in ſeptīo capitis ṗme
partis.
¶ Inducas ſiĺes ↄ̨°nes īnitēdo doctrine ca-
pitis p̄allegati quot volueris.
Duodecima ↄ̨̨cluſio. diuiſa hora qua­
uis ꝓportiõe: et ī prīa parte ꝓportionali cuiꝰ aliqḋ
alteras alteret aliqḋ paſſuꝫ ab aliq̈ ꝓportiõe ade-
quate: et in ſcḋa a ꝓportiõe ī duplo maiori: et ī ṫtia
in triplo maiori ꝙ̄ in prīa: et ſic ↄ̨ñter: q̈litas ꝓdu-
cta mediãte totali velocitate ī illa hora ſe hꝫ ad q̈li­
tatē ꝓductã ī prīa ꝑte ꝓportionali in ꝓportiõe du-
pla ad ꝓportionē q̈ totū ſic diuiſū ſe hꝫ ad ṗmã ſui
ꝑtem ꝓportionalē.
pꝫ hec ↄ̨cluſio ex ꝓbatiõe q̈rte
ↄ̨°nis tertii capitis ſcḋi tractatꝰ.
¶ Addas his oēs
cõcluſiões ꝓbatas tertio capite p̄allegato mutatꝪ
mutandis. 223. articu-
lꝰ. q̄ſtionis
¶ Ad tertiū huius q̄ſtionis articulū ac-
cedēdo.
¶ Dubitatur prīo. Utrū luminoſū ꝓducat
in oē mediū in qḋ agit totã latitudinē luīs quã na-
tū eſt ꝓducere a gradu vcꝫ ſue lucis vſ ad nõ gra-
dū: dūmõ nõ ſit reflixio.
¶ Dubitat̄̄ ſcḋo. Penes q̇d
hēat attēdi difficultas actionis.
¶ Dubitat̄̄ tertio.
Utrū alterãs aliqḋ paſſū reſiſtēs valeat eq̄ velociter
alterare ꝑtē ꝓpinquã et remotã.
¶ Ad ṗmū dubium
argr̄ ꝓbãdo /  luīoſū nõ agit totã latitudinē ſui lu­
minis ī qḋcū mediū q̈litercū diſpoſitū: ſꝑ ītelli­
go dūmõ ſit luīs ſuſceptiuū: q2 tūc ſeq̄ret̄̄ /  luīoſuꝫ
vt .8. tãtã latitudinē luīs ꝓduceret ī mediū bñ diſpo­
ſitū ̄tã ī mediū ñ ita bñ diſpoſitū ad luīs ſuſceptio­
nē: ſꝫ ↄ̨ñs ē flm̄: igr̄ illḋ ex q̊ ſeq̇t̄̄.
Seq̄la ꝓbat̄̄ / q2 ſꝑ
ꝑ te ꝓducit ī qḋlꝫ mediū ī qḋ agit latitudinē ab .8.
vſ ad nõ g̈dū dūmõ nõ ſit reflexio īpediēs
(Impe­
diēs inquã ne fiat ꝓductio vſ ad nõ g̈du) / igr̄ tãtã
latitudinē luīs ꝓducit ī medio bñ diſpoſitio ̄tã in
medio non eq̄ bñ diſpoſito.
Fĺitas ↄ̨ñtis ꝓbat̄̄ qm̄
qḋlibet agēs naturale ſuapte natura velociꝰ agit ī
paſſum meliꝰ diſpoſitū ꝙ̄ in paſſuꝫ nõ eque bñ di-
ſpoſitū: igr̄ luīnoſū velociꝰ agit ī mediū meliꝰ diſpo-
ſitū ꝙ̄ in mediū nõ eq̄ bñ diſpoſitū: et ſic in eodē tꝑe
maiorē latitudinē luīs ꝓducit ī mediū meliꝰ diſpo-
ſitū ꝙ̄ minꝰ bñ diſpoſitū
Et ↄ̨fir̄at̄̄ / q2 aĺs ſeq̄ret̄̄ / 
diſpõ medii nullo pacto ad īductionē luīs cõferret /
qḋ irrõnabĺr ē dctm̄. 33Cal. de
acti. luīo.
¶ Dices forte cū calculatore
ↄ̨cedēdo illatū et negãdo fĺitatē ↄ̨ñtis: et ad ꝓbatio­
nē dr̄ /  illḋ verū ē de agēte cū reſiſtētia.
Nichil em̄
luī reſiſtit / q2 nulla q̈litas ei ↄ̈ria.
Et ſi tñ diſpõ me­
dii nichil ↄ̨ferat ad maiorē latitudinē luīs ītrodu-
cēdã: nichilominꝰ vt inq̇t idē calculator ↄ̨fert ad ꝓ-
ductionē luīs ꝑ maiorē diſtãtiã.
In ea eī ꝓportione
in q̈ mediū efficit̄̄ rariꝰ ī ea luīoſuꝫ ꝑ maiorē diſtan­
tiã ſui luīs latitudinē ꝓducit vt īq̇t.
¶ Sꝫ ↄ̨tra / q2 tūc
ſeq̄ret̄̄ /  qḋlꝫ luīoſuꝫ ̄tūcū paruū ſue naturali
diſpõi relictã poſſet ꝑ ̄tūcū diſtãtiã agere: ſed
ↄ̨ñs ē flm̄: igr̄ etc̈.
Seq̄la ꝓbat̄̄: et volo /  luīoſuꝫ a.
agat latitudinē ſui luīs ꝑ mediū pedalis ̄titatis
deiñ rarefiat mediū ad raritatē ī millecuplo maio­
iorē.
Quo poſito ſeq̇t̄̄ a. luīoſuꝫ agė latitudinē ſui
luīs ad diſtãtiã ī millecuplo maiorē ex ſolu°ne: et ſi
iterū rarefiat ad duplū adhuc aget ꝑ ī duplo maio­
rē diſtãtiã: et ſic in īfinitū.
Sꝫ ar̄ fĺitas ↄ̨ñtꝪ: q2 tūc ſe­
q̄ret̄̄ qḋlꝫ lūioſū / qḋ p̄t videri ī ꝓpinq̊ a certa poña
finita poſſe ab eadē poña a ̄tacū diſtãtiã videri /
qḋ eſt mãifeſte falſū: cū poña ſit finita: et ſiĺr luīoſum
pꝫ ſeq̄la / q2 ̄tã latitudinē luīs ꝓducit ī ꝓpīquū tã­
tã v3 ꝓducē ī ̄tãcū diſtãtiã / et ꝑ ↄ̨ñs videri cū lumē
ſit ſpēs lucis ſiue luīoſi vĺ eã ſꝑ ↄ̨comitet̄̄.
¶ Dices
forte ↄ̨cedēdo id qñ īfert̄̄: et negãdo fĺitatē ↄ̨ñtis et
ad ꝓbatiõeꝫ ↄ̨cedēdo qḋ iteꝝ īfert̄̄: et negãdo fĺitatē
ↄ̨ñtis.
¶ Sꝫ ↄ̈ / quaꝫ tūc ſeq̄ret̄̄ /  luīoſū vt .8. ꝓducens
lum̄ vniformiṫ diffor̄e ab .8. vſ ad nõ g̈dū nõ varia­
tū ī poña: īfinitã formã luīs poſſꝫ ꝓducē ſꝫ ↄ̨ñs ē fĺ3 /
igr̄ illḋ ex q̊ ſeq̇t̄̄.
Fĺitas ↄ̨ñtis ꝓbat̄̄: q2 tūc ſeq̄retur
qḋlꝫ luīoſū eē īfinite poñe: cū īfinitã mĺtitudinē for̄e
valeat ꝓducē.
Seq̄la tñ ꝓbat̄̄ et pono /  luīoſuꝫ vt .8.
agat latitudinē ſui luīs vniformiṫ difforme ab .8.
ad nõ g̈dū ꝑ aliquã ꝑtã alicuiꝰ medii īfiniti puta bi­
pedalē.
Deīde rarefiat totū illḋ mediū īfinitū vni-
formiṫ ꝑ totū et hoc ſine acq̇ſitiõe ̄titatꝪ: ſꝫ ꝑ ſolam
deꝑditionē maṫie (vt corr̄ ī hac mä opꝫ imaginari)
ad cētuplū: et mãifeſtū ē ex ſolutõe luīoſū vt .8. ꝓdu­
cere totã latitudinē ſui luīs ꝑ ducēta pedalia: ſigno
igr̄ / g̈dū mediū puta vt .4. ī fīe cēteſimi pedaĺ (vt oꝫ)
tūc uotū ē ī q̊lꝫ illoꝝ cētū pedaliū eē .4. g̈dꝰ luīs vni-
formis.
et cū hoc alcq̇d vltra: g̊ iã illḋ luīoſū vt .8. in
cãu dato ꝓducit latitudinē luīſ vuiformē vt .4. ꝑ .100
pedalia: et ſi iteꝝ rarefiat illḋ mediū infinitū ad du­
plū iã ꝓducet ī duplo maiorē mĺtitudinē for̄e: q2 la­
titudinē luīs vniformē vt .4. ꝑ ducēta pedalia: et ſic
in īfinitū: ſeq̇t̄̄ g̊ /  luīoſū vt .8. ꝓducēs lumē vnifor-
miṫ diffor̄e etc̈. nõ variatū ī poña īfinitã formã luīs
p̄t ꝓducē: qḋ fuit ꝓbãdū.
¶ Dices negãdo ſeq̄lã et ad
ꝓbationē admiſſo cãu ↄ̨cedēdo /  fcã tĺi rarefactõe
dat̄̄ ibi lumē cētipedaĺ ̄titatꝪ vnifor̄e vt .4. ſꝫ illud
nõ plꝰ ↄ̨tinet de for̄a ꝙ̄ ↄ̨tinebat lumē pedale vnifor­
me vt .4. qḋ ꝓducebat̄̄ añ medii rarefactionē ꝑ ṗmū
pedale illiꝰ ꝑtis bipedalis in quã ꝑtē bipedalē lu-
minoſū agebat añ rarefactionē quēadmodum de-
claratū eſt in ſecundo notabili.
Sed ↄ̨̨tra / q2 tūc ſequeretur /  in lati-
tudinē luīs vniformiter intēſi vt .4. eſſet in infini-
tū parū de forma adequate: ſꝫ ↄ̨ñs īplicat: igit̄̄ il-
lud ex quo ſequit̄̄.
Sequela ꝓbat̄̄: et volo /  illud me­
diū infinitū rarefiat in infinitū.
Quo poſito ibi re-
perietur infinita latitudo luīs quãtitatiue vnifor-

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