Alvarus, Thomas
,
Liber de triplici motu
,
1509
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De motu locali mixto difformi tꝑe ſubiecto quo ad effectū
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0172
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172
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Patet ↄ̨ña cū minore et ꝓbatur maior: q2 tota ꝑs
<
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citra centrum mundi continet b. partem equalem
<
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parti citra centrū mūdi ex hypotheſi: et inſuꝑ cõti-
<
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net d. et c. / igr̄ ꝑ d. et c. pars citra centrū mūdi exce-
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dit partē vltra centrū mundi / qḋ fuit ꝓbandū. </
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<
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ↄ̨ña intelligenti / quid ſit vnū excedere alterum per
<
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aliquid: et ſic patet ſuppoſitio .</
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</
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<
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<
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xml:space
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>
<
s
xml:id
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N20B84
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xml:space
="
preserve
">Qñ inter aliquos
<
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/>
terminos eſt ꝓportio maioris īequalitatis et ma-
<
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iore quartã exceſſus quo minorē excedit deꝑdente
<
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/>
adequate: minore eandē dūtaxat quartã acq̇ren-
<
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/>
te que a minori deperdit̄̄: ꝓportio inter datos ter-
<
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/>
minos pluſ̄ ad ſubduplum ſui diminuit̄̄ et ex ↄ̨ñti
<
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/>
data ꝓportio vltra ſuã medietatē deꝑdit. </
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>
<
s
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xml:space
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">Probat̄̄
<
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ſit ꝓportio f. īter a. terminū maiorem et e. terminū
<
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minorē: diuidat̄̄ exceſſus quo a. excedit e: in q̈tuor
<
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partes equales adequate hoc eſt in quatuor q̈rtas
<
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/>
et ſignētur ibi īter a. et e. ãnumeratis extremis q̇n
<
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/>
termini cõtinuo arithmetice ꝓportionabiles quoꝝ
<
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/>
primꝰ ſit a. ſecūdus b. qui excedit̄̄ ab a. ꝑ vnã quar-
<
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/>
tã illiꝰ exceſſus quo a. excedit e. adequate, et tertius
<
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/>
ſit c. qui excedat̄̄ a b. ꝑ aliã quartã illius exceſſus, et
<
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/>
quartꝰ ſit d. que excedat̄̄ a c. ꝑ vnã aliã quartã ex-
<
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/>
ceſſus, et quītus ſit e. terminꝰ minor ꝓportiõis date
<
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/>
qui excedit̄̄ ab ipſo d. ꝑ vltimam quartã exceſſus: et
<
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/>
manifeſtū eſt illos quī termīos cõtinuo eſſe arith
<
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/>
metice ꝓportionabiles cū equali exceſſu exupe
<
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/>
rent. </
s
>
<
s
xml:id
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N20BB2
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xml:space
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">deꝑdat igr̄ a. terminꝰ maior vnã quartã exceſ-
<
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ſus illã vcꝫ ꝑ quã b. terminū excedit: et illã adequate
<
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acq̇rat e. terminꝰ minor. </
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>
<
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">Tūc dico / data ꝓportio
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diminuit̄̄ et plus quã ſuã medietatē deꝑdit et ex hoc
<
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/>
plus quã ad ſubduplū diminuit̄̄. </
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>
<
s
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xml:space
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">Quod ſic oſtendi
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tur / q2 ꝓportio f. diminuit̄̄ et plus quã ſui medieta-
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tem deꝑdit ꝓpoſitū. </
s
>
<
s
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="
N20BC7
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xml:space
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">Maior ptꝫ manifeſte ex ſe
<
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cūdo correlario tertie concluſionis octaui capitis
<
lb
/>
ſecūde partis auxiliãte hypotheſi: et minor ꝓbatur /
<
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/>
q2 illa ꝓportio f. q̄ eſt inter a. et e. cõponit̄̄ adequate
<
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/>
ex quatuor proportionibꝰ puta ex ꝓportiõe d. ad e.
<
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/>
et ex ꝓportiõe c. ad d. et ex ꝓportiõe b. ad c. et ex q̈rta
<
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/>
ꝓportione ipſiꝰ a. ad b. / vt cõſtat cõſideranti hypo-
<
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theſim: et ille ꝓportiones ſunt cõtinuo minores et
<
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/>
minores et minori exceſſu continuo ſeſe excedunt:
<
lb
/>
igitur aggregatum ex duabus extremis proporti-
<
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/>
onibus puta ex ꝓportione d. ad e. et ex ꝓportione a.
<
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/>
ad b. eſt maiꝰ quã medietas aggregati ex illis qua
<
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/>
tuor ꝓportionibꝰ: et ꝑ ↄ̨ñs eſt maius quã medietas
<
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ipſiꝰ f. ꝓportionis adequate ex illis quatuor ꝓpor
<
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tionibꝰ cõpoſite. </
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<
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">Ptꝫ hec ↄ̨ña ex quarto correlario
<
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ſecūde cõcluſionis ſecūdi capitis ſecunde partis: et
<
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/>
aggregatū ex illis extremis ꝓportiõibꝰ ꝑdit ꝓpor
<
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/>
tio f. / vt ptꝫ ex hypotheſi auxiliãte primo correlario
<
lb
/>
ſexte concluſiõis octaui capitis ſecūde partis. </
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>
<
s
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xml:space
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">(Ter-
<
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minꝰ em̄ maior puta a. cū deꝑdit exceſſum quo exce
<
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dit b. deꝑdit ꝓportionē q̄ eſt ipſiꝰ a. ad b. et terminꝰ
<
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/>
minor puta e. cū acq̇rit illū exceſſum quo excedit̄̄ a
<
lb
/>
d. acq̇rit illã ꝓportionē adequate q̄ eſt ipſiꝰ d. ad e.) /
<
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/>
igr̄ ꝓportio f. plus quã ſui medietatē deꝑdit / qḋ fuit
<
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ꝓbandū. </
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>
<
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">Prima pars mīoris vcꝫ ille ꝓportiões
<
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ſunt cõtinuo minores et mīoris ꝓbat̄̄ / q2 qñ īter ali-
<
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quos termīos eſt aliqua ꝓportio maioris inequa-
<
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/>
litatis: et maiores equali exceſſu excedūt ſuos mīo-
<
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/>
res ſemꝑ inter maiores eſt minor ꝓportio quã inter
<
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mīores / vt ptꝫ ex octaua ſuppoſitiõe quarti capitis
<
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/>
ſecūde partis: ſed oēs illi termini .a. b.c.d. excedūt
<
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ſuos minores eq̈li exceſſu et d. et e. ſunt minores quã
<
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d. et c. et d. et c. mīores quã c. et b. et c. et b. minores quã
<
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b. et a. / igr̄ ꝓportio ipſiꝰ d. ad e. eſt maior ꝓportiõe
<
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c. ad d. et ꝓportio c. ad d. maior eſt ꝓportionē b. ad
<
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c. et ꝓportio b. ad c. maior ꝓportiõe a. ad b. et ſic ille
<
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De motu locali mixto difformi tꝑe ſubiecto quo ad effectū
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ꝓportiones ſunt ↄ̨tinuo minores et mīores / qḋ fuit
<
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ꝓbandū. </
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>
<
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xml:space
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">Sed iã ꝓbo aliã partē minoris vcꝫ cõti
<
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/>
nuo minori exceſſu ſe excedant: q2 ꝓportio ipſiꝰ d.
<
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/>
ad e. ꝑ maiorē ꝓportionē excedit ꝓportionē ipſiꝰ c.
<
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ad d. quã ꝓportio ipſius c. ad d. excedit ꝓportionē
<
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ipſiꝰ b. ad c. et ꝓportio ipſiꝰ c. ad d. ꝑ maiorē ꝓpor-
<
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tionē excedit ꝓportionē b. ad. c. quã ꝓportio b. ad c.
<
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/>
excedat ꝓportionē a. ad b. / igr̄ ille ꝓportiões conti-
<
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nuo minori exceſſu ſe excedūt. </
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>
<
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">Maior ptꝫ ex quinto
<
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correlario quīte cõcluſionis octaui capitis ſecūde
<
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/>
partis qm̄ .b.c.d.e. ſunt quatuor termini continuo
<
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/>
arithmetice ꝓportionabiles ex hypotheſi: igr̄ pro
<
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portio q̄ eſt inter duos termīos mīores puta inter
<
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/>
d. et e. ꝑ plus excedit ſecūdã ꝓportionē q̄ eſt inter c.
<
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/>
et d. quã illa ſcḋa excedat tertia q̄ eſt ipſiꝰ b. ad c. / vt
<
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ptꝫ ex correlario allegato. </
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>
<
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xml:space
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">Et ſic ꝓbabis minorem
<
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capiendo iſtos quatuor terminos cõtinuo arithme
<
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tice ꝓportionabiles puta .a. b.c.d. </
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>
<
s
xml:id
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N20C47
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xml:space
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">Et ſic ptꝫ corre-
<
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larium. </
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>
<
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xml:space
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">¶ Cõſimiliter ꝓbares / diuiſo exceſſu quo
<
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maior terminꝰ excedit minorē in qñ partes eq̈les
<
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/>
maiore termino deꝑdente vnã illaꝝ quītaꝝ minore
<
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/>
acq̇rente eandē tūc ꝓportio inter datos termīos
<
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/>
perdit plus quã duas quītas ſui et ſi exceſſus diui-
<
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/>
datur in ſex partes equales maiore deꝑdente vnã
<
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illaꝝ et minore acq̇rente eandē: ꝓportio īter datos
<
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/>
terminos perdit plus quam vnã tertiã: et ſi diuidat̄̄
<
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/>
exceſſus in ſeptē maiore deꝑdente vnã illaꝝ et mīore
<
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/>
acq̇rente eandē: ꝓportio inter datos termīos ꝑdit
<
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/>
plus quã duas ſeptimas / et ſic ↄ̨ñter. </
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>
<
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xml:id
="
N20C63
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xml:space
="
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">Oīa iſta patēt
<
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ex deductionibꝰ quīti correlarii prime cõcluſionis
<
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et quīti correlarii ſecūde cõcluſionis ſecūdi capitis
<
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ſecūde partis. </
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>
<
s
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xml:space
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preserve
">¶ Ex his inducit̄̄ et demõſtratur ꝓpo
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ſitū vcꝫ illud quadratū terreū ꝑpetuo moueret̄̄
<
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in tali caſu. </
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>
<
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="
N20C73
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xml:space
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">Sit vna pars illiꝰ q̈drati vltra centruꝫ
<
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mūdi minor medietate: et diuidat̄̄ pars intercepta
<
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/>
inter centrū illiꝰ quadrati et centrū mūdi q̄ eſt me-
<
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/>
dietas totiꝰ exceſſus partis citra centrū mundi ad
<
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/>
partē vltra centrū mūdi ex prima ſuppoſitione et
<
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/>
hoc ꝑ partes ꝓportionales ꝓportione dupla ma-
<
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/>
ioribꝰ ſus centrū mundi terminatis: q̄ pars ſit d.
<
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/>
ſit totū illud quadratū vniforme in grauitate: ſit
<
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/>
etiã ꝓportio totiꝰ partis citra centrū mūdi ad par
<
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/>
tē vltra centrū mūdi f. </
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>
<
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xml:id
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N20C88
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xml:space
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">Quo poſito ſic argr̄ q̈dratū
<
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/>
illud tamdiu mouebit̄̄ quãdiu aliqua pars ipſius
<
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/>
d. partis intercepte inter centrū q̈drati et centrum
<
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/>
mundi fuerit citra centrū mūdi qm̄ tamdiu excedet
<
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/>
pars citra centrū partē vltra centrū q2 tūc cõtinuo
<
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/>
erit maior: ſed ꝑpetuo aliqua pars ipſiꝰ d. partis
<
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/>
erit citra centrū mūdi: g̊ ꝑpetuo tale q̈dratū moue
<
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bitur / qḋ fuit ꝓbandū. </
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>
<
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xml:id
="
N20C99
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xml:space
="
preserve
">Cõſequētia ptꝫ cū maiore et
<
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/>
ꝓbat̄̄ minor / q2 ꝑpetuo aliqua pars aggregati ex
<
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/>
oībus partibꝰ ꝓportionalibꝰ ipſiꝰ d. partis deſcē
<
lb
/>
det: g̊ ꝑpetuo aliqua pars ipſiꝰ d. partis erit citra
<
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/>
centrū mūdi / qḋ fuit ꝓbandū, </
s
>
<
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xml:id
="
N20CA4
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xml:space
="
preserve
">Cõſequētia ptꝫ et pro
<
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/>
batur añs / q2 prima pars ꝓportionalis ipſius d.
<
lb
/>
partis incipit deſcēdere a ꝓportiõe f. vt habet̄̄ hy-
<
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/>
potheſi: et ſecūda pars ꝓportiõalis ipſiꝰ d. partis
<
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/>
incipit deſcēdere a ꝓportiõe ſubdupla ad ꝓportio
<
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/>
nē f. vel a minori: et tertia īcipit deſcēdere a ſubdu-
<
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/>
pla vel minori ſubdupla ad ꝓportionē a q̈ incipit
<
lb
/>
deſcēdere ſcḋa / et ſic ↄ̨ñter q̄libet pars ꝓportiõalis
<
lb
/>
ipſiꝰ d. ſequēs īcipiet deſcēdere a ꝓportione ſubdu
<
lb
/>
pla vel minori ad ꝓportionē a qua īcipit deſcēde-
<
lb
/>
re pars īmediate p̄cedēſupra: et q̄libet pars quãdiu ali-
<
lb
/>
q̇d eiꝰ deſcēdit cõtinuo deſcēdit ſiue mouet̄̄ a mīori
<
lb
/>
ꝓportione ꝙ̄ ſit illa a qua incipit illa eadem pars
<
lb
/>
deſcēdere (cū cõtinuo partis citra centrū mūdi ad
<
lb
/>
partē vltra centrū mūdi ꝓportio a qua partes ille
<
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/>
deſcendūt cõtinuo diminuatur: continuo em̄ pars </
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>
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