274 ditas ſit vt .4. et tota frigiditas vt .2. q̄ ſunt in ſcḋa
ꝑte ꝓportionali a. corꝑis. Uolo igr̄ / prima pars
ꝓportiõalĺ a. corꝑis acq̇rat in hõ aliquã quãtitatē
ꝑ rarefactiõeꝫ acq̇rēdo et ꝑs hñs duplã caliditatē
ad caliditatē ṗme partꝪ in eadē hora acq̇rat ſubdu
pla quãtitatē, et pars hñs q̈druplã caliditatem ad
caliditatē ṗme ꝑtis in eadē hora acq̇rat ſubq̈dru-
plã quãtitatē etc̈. Quo poſito argr̄ ſic / a. in fine ra-
refactiõis nec eſt calidū nec frigidū: et aña erat ca-
lidū: et nullã caliditatē aut frigiditatē deperdidit
aut acq̇ſiuit etc̈. / igr̄ ꝓpoſitū. Q, in fine nec eſt cali-
dū nec frigidū ꝓbat̄̄: q2 in fine hꝫ caliditatē ſuffici-
entē ip̄m denoīare īfinite calidū, et frigiditatē ſuffi
entē ipſuꝫ denoīare īfinite frigidū puta illã quã hꝫ
in quãtitate acq̇ſita ꝑ rarefactionē: igr̄ caliditas et
frigiditas totalr̄ et adeq̈te ſe īpediūt: et ꝑ ↄ̨ñs illud
nec eſt calidū nec frigidū / qḋ fuit ꝓbandū. Q, autē
caliditas exñs in quãtitate acq̇ſita ꝑ rarefactionē
et ſiĺr frigiditas exñs in eadē quãtitatē ſufficiat de
noīare a. infinite ſatis / ptꝫ ex his que dicta ſunt cir
ca ſextam concluſionem queſtionis.
ꝑte ꝓportionali a. corꝑis. Uolo igr̄ / prima pars
ꝓportiõalĺ a. corꝑis acq̇rat in hõ aliquã quãtitatē
ꝑ rarefactiõeꝫ acq̇rēdo et ꝑs hñs duplã caliditatē
ad caliditatē ṗme partꝪ in eadē hora acq̇rat ſubdu
pla quãtitatē, et pars hñs q̈druplã caliditatem ad
caliditatē ṗme ꝑtis in eadē hora acq̇rat ſubq̈dru-
plã quãtitatē etc̈. Quo poſito argr̄ ſic / a. in fine ra-
refactiõis nec eſt calidū nec frigidū: et aña erat ca-
lidū: et nullã caliditatē aut frigiditatē deperdidit
aut acq̇ſiuit etc̈. / igr̄ ꝓpoſitū. Q, in fine nec eſt cali-
dū nec frigidū ꝓbat̄̄: q2 in fine hꝫ caliditatē ſuffici-
entē ip̄m denoīare īfinite calidū, et frigiditatē ſuffi
entē ipſuꝫ denoīare īfinite frigidū puta illã quã hꝫ
in quãtitate acq̇ſita ꝑ rarefactionē: igr̄ caliditas et
frigiditas totalr̄ et adeq̈te ſe īpediūt: et ꝑ ↄ̨ñs illud
nec eſt calidū nec frigidū / qḋ fuit ꝓbandū. Q, autē
caliditas exñs in quãtitate acq̇ſita ꝑ rarefactionē
et ſiĺr frigiditas exñs in eadē quãtitatē ſufficiat de
noīare a. infinite ſatis / ptꝫ ex his que dicta ſunt cir
ca ſextam concluſionem queſtionis.
Scḋo ad idē argr̄ ſic.
Si ꝑs affirma
tiua dubii eēt a: ſeq̄ret̄̄ alicuiꝰ corꝑis certa diuiſi
one quãlꝫ partē ꝓportiõalē ꝓportiõe dupla eē ca-
lidã: et tñ totū nõ eē calidū: ↄ̨ñs videt̄̄ īpoſſibile: igr̄
illud ex quo ſequit̄̄. Seq̄la ꝓbat̄̄, et ſit a. diuiſū per
ꝑtes ꝓportiõales ꝓportiõe dupla, et in ṗma ꝑte ſit
caliditas vt .2. et frigiditas vt vnū, et in ſcḋa parte
ſit in duplo maior caliditas et ſiĺr frigiditas ꝙ̄ in
ṗma, et in tertia in duplo maior caliditas et frigi-
ditas ꝙ̄ in ſcḋa, et ſic deinceps ita in qualꝫ parte
proportionali caliditas ſit dupla ad frigiditatē.
Quo poſito manifeſtū eſt quãlꝫ partē ꝓportiõalē
ſcḋm illã diuiſionē eſſe calidã: Sed totū nõ ſit ca
lidū ꝓbat̄̄ / q2 caliditas īpedit totalr̄ frigiditatē: et
eocõtra: igr̄ neutra illaꝝ denoīat. Añs ꝓbat̄̄ / quia
vtra illaꝝ ſufficit denoīare īfinite vt ſatis ptꝫ ex
ſcḋa ↄ̨cluſiõe q̄ſtiõis: igr̄ ſe totalr̄ īpediūt. ¶ Itē ſe-
queret̄̄ alicuiꝰ corꝑis certa diuiſiõe ̄lꝫ partē ꝓpor
tionalē ꝓportiõe dupla eſſe īfinite calidã: et tñ totū
nõ eſſe calidū / qḋ īplicat. Seq̄la ꝓbat̄̄ retēto caſu ſu
periori: hoc addito / ꝑ totū a. ſit caliditas vnifor-
mis īfinite intenſiõis. Sed hoc ſit flm̄ ꝓbat̄̄ / q2 bñ
ſequit̄̄ ſcḋm hãc diuiſionē q̄lꝫ pars ꝓportiõalis
eiꝰ eſt calida: igr̄ ſcḋm hãc diuiſionē oēs ſunt calide
et oēs ſunt ip̄m totū: igr̄ totū eſt calidū / qḋ eſt nega
tū. 11ↄ̨fir̄tio. ¶ Et ↄ̨firmat̄̄ / q2 ſi intenſio mixti hñtis q̈litates
ↄ̈rias coextēſas ꝑ totū attendit̄̄ penes exceſſū q̈lita
tis excedētis ſupra exceſſam: ſequit̄̄ / intēſio mixti
hñtis q̈litates ↄ̈rias nõ coextēſas: ſed extēſas in di
uerſis partibꝰ ſubiecti itidē attendit̄̄ penes exceſſū
q̈litatis excedētis ſupra exceſſã: ſed hoc eſt flm̄: igr̄
illud ex quo ſequit̄̄. Seq̄la videt̄̄ nota: ſed falſitas
ↄ̨ñtis ꝓbat̄̄: q2 tūc ſeq̄ret̄̄ / frigiditas nullo pacto
īpediret caliditatē / qḋ eſt ↄ̈ fundamentū opinionis.
Seq̄la ꝓbat̄̄: et pono / ſit a. pedale in cuiꝰ vna me-
dietate ſic caliditas vt .8. et in alia frigiditas vt .4.
et b. in cuiꝰ vna medietate ſit caliditas vt .8. et alia
nec habeat caliditatē nec frigiditatē. Quo poſito
a. per te eſt calidū vt .4. cū .8. excedãt .4. per .4. et b.
ſimiltr eſt calidum vt .4. / igr̄ frigiditas in a. nullo
pacto īpedit caliditatem cum oīno habeãt eandem
caliditatem per eandem partem.
tiua dubii eēt a: ſeq̄ret̄̄ alicuiꝰ corꝑis certa diuiſi
one quãlꝫ partē ꝓportiõalē ꝓportiõe dupla eē ca-
lidã: et tñ totū nõ eē calidū: ↄ̨ñs videt̄̄ īpoſſibile: igr̄
illud ex quo ſequit̄̄. Seq̄la ꝓbat̄̄, et ſit a. diuiſū per
ꝑtes ꝓportiõales ꝓportiõe dupla, et in ṗma ꝑte ſit
caliditas vt .2. et frigiditas vt vnū, et in ſcḋa parte
ſit in duplo maior caliditas et ſiĺr frigiditas ꝙ̄ in
ṗma, et in tertia in duplo maior caliditas et frigi-
ditas ꝙ̄ in ſcḋa, et ſic deinceps ita in qualꝫ parte
proportionali caliditas ſit dupla ad frigiditatē.
Quo poſito manifeſtū eſt quãlꝫ partē ꝓportiõalē
ſcḋm illã diuiſionē eſſe calidã: Sed totū nõ ſit ca
lidū ꝓbat̄̄ / q2 caliditas īpedit totalr̄ frigiditatē: et
eocõtra: igr̄ neutra illaꝝ denoīat. Añs ꝓbat̄̄ / quia
vtra illaꝝ ſufficit denoīare īfinite vt ſatis ptꝫ ex
ſcḋa ↄ̨cluſiõe q̄ſtiõis: igr̄ ſe totalr̄ īpediūt. ¶ Itē ſe-
queret̄̄ alicuiꝰ corꝑis certa diuiſiõe ̄lꝫ partē ꝓpor
tionalē ꝓportiõe dupla eſſe īfinite calidã: et tñ totū
nõ eſſe calidū / qḋ īplicat. Seq̄la ꝓbat̄̄ retēto caſu ſu
periori: hoc addito / ꝑ totū a. ſit caliditas vnifor-
mis īfinite intenſiõis. Sed hoc ſit flm̄ ꝓbat̄̄ / q2 bñ
ſequit̄̄ ſcḋm hãc diuiſionē q̄lꝫ pars ꝓportiõalis
eiꝰ eſt calida: igr̄ ſcḋm hãc diuiſionē oēs ſunt calide
et oēs ſunt ip̄m totū: igr̄ totū eſt calidū / qḋ eſt nega
tū. 11ↄ̨fir̄tio. ¶ Et ↄ̨firmat̄̄ / q2 ſi intenſio mixti hñtis q̈litates
ↄ̈rias coextēſas ꝑ totū attendit̄̄ penes exceſſū q̈lita
tis excedētis ſupra exceſſam: ſequit̄̄ / intēſio mixti
hñtis q̈litates ↄ̈rias nõ coextēſas: ſed extēſas in di
uerſis partibꝰ ſubiecti itidē attendit̄̄ penes exceſſū
q̈litatis excedētis ſupra exceſſã: ſed hoc eſt flm̄: igr̄
illud ex quo ſequit̄̄. Seq̄la videt̄̄ nota: ſed falſitas
ↄ̨ñtis ꝓbat̄̄: q2 tūc ſeq̄ret̄̄ / frigiditas nullo pacto
īpediret caliditatē / qḋ eſt ↄ̈ fundamentū opinionis.
Seq̄la ꝓbat̄̄: et pono / ſit a. pedale in cuiꝰ vna me-
dietate ſic caliditas vt .8. et in alia frigiditas vt .4.
et b. in cuiꝰ vna medietate ſit caliditas vt .8. et alia
nec habeat caliditatē nec frigiditatē. Quo poſito
a. per te eſt calidū vt .4. cū .8. excedãt .4. per .4. et b.
ſimiltr eſt calidum vt .4. / igr̄ frigiditas in a. nullo
pacto īpedit caliditatem cum oīno habeãt eandem
caliditatem per eandem partem.
In oppoſitū tñ argit̄̄ ſic / q2 intenſio
mixti hñtis q̈litates ↄ̈rias coextēſas ꝑ totū nõ attē
dit̄̄ penes intēſionē q̈litatis intenſioris: cū tūc ↄ̈rie
q̈litates nullo mõ ſe īpedirēt in denoīationibꝰ ſuis
nec penes ꝓportionē q̈litatis excedētis ad q̈litatē
exceſſū: igr̄ d3 attendi penes exceſſū q̈litatis excedē
tis ſupra exceſſū cū nõ ſit aliꝰ modꝰ quo talis inten-
ſio poſſet mēſurari. Coña ptꝫ cū maiore: et ꝓbatur
mīor / q2 alias ſeq̄ret̄̄ albedinē vt .4. denoīare īfini-
te. Seq̄la ꝓbat̄̄ / et ſit in a. pedali albedo vt .4. ꝑ totū
coextēſa nigredini vt .2. et remittat̄̄ vniformiṫ ni-
gredo vſ ad nõ gradū in hora ſtãte albedīe. Quo
poſito argr̄ ſic / in infinitū augebit̄̄ ꝓportio albedi
nis ſupra nigredinē: igr̄ ꝑ te in īfinitū intēdet̄̄ deno
minatio albedinis: et per conſequens in infinitum
denominabit illa albedo / quod fuit probandum.
mixti hñtis q̈litates ↄ̈rias coextēſas ꝑ totū nõ attē
dit̄̄ penes intēſionē q̈litatis intenſioris: cū tūc ↄ̈rie
q̈litates nullo mõ ſe īpedirēt in denoīationibꝰ ſuis
nec penes ꝓportionē q̈litatis excedētis ad q̈litatē
exceſſū: igr̄ d3 attendi penes exceſſū q̈litatis excedē
tis ſupra exceſſū cū nõ ſit aliꝰ modꝰ quo talis inten-
ſio poſſet mēſurari. Coña ptꝫ cū maiore: et ꝓbatur
mīor / q2 alias ſeq̄ret̄̄ albedinē vt .4. denoīare īfini-
te. Seq̄la ꝓbat̄̄ / et ſit in a. pedali albedo vt .4. ꝑ totū
coextēſa nigredini vt .2. et remittat̄̄ vniformiṫ ni-
gredo vſ ad nõ gradū in hora ſtãte albedīe. Quo
poſito argr̄ ſic / in infinitū augebit̄̄ ꝓportio albedi
nis ſupra nigredinē: igr̄ ꝑ te in īfinitū intēdet̄̄ deno
minatio albedinis: et per conſequens in infinitum
denominabit illa albedo / quod fuit probandum.
Pro ſolutione huiꝰ dubii.
Notandum
eſt / q̈litates ↄ̈rie exiſtētes in eodē ſubiecto ſe īpe-
diūt in ſuis denoīationibꝰ. Nõ em̄ eq̄ albū et cor-
pus in quo ſunt ꝑ totū .6. gradꝰ albedīs cū .2. gra-
dibus nigredīs ſicut corpꝰ in q̊ ſūt .6. gradꝰ albedīs
ſine admixtiõe ↄ̈rie q̈litatis. Et nõ ſolū qualitates
ↄ̈rie ſe īpediūt qñ coextēdunt̄̄: verū etiã qñ in diuer-
ſis partibꝰ ſubiecti ponunt̄̄. Nõ em̄ tm̄ denoīat al-
bedo vt .4. exñs in vna medietate corꝑis in cuiꝰ alia
medietate eſt vnꝰ gradꝰ nigredīs quantū denoīaret
ſi in ſubiecto nõ eſſet aliq̈ nigredo. Hoc ſuppoſito
aduertendū eſt / quadruplex eſt opinio penes qḋ
debeat attendi inteſio mixti hñtis ↄ̈rias q̈litates
coextēſas: q̈s recitat calcu. in capĺo de ītēſio mixto-
rū. ¶ Prima eſt / intēſio mixti d3 attēdi penes ꝓ-
portionē q̈litatis excedētis ad q̈litatē exceſſã. Scḋa
dicit / d3 attēdi penes q̈litatē excedentē. Tertia di
cit / penes medietatē exceſſus q̈litatis excedentis.
Quarta dicit / penes exceſſū. Sed ꝓ īpugnatiõe
3. ṗmaꝝ opinionū pono tres ꝓpõnes. ¶ Prima ꝓ-
poſitio Intēſio mixti nõ attendit̄̄ penes ꝓportionē
q̈litatis excedētis ad exceſſam. Probat̄̄ / q2 tūc ſeq̄-
ret̄̄ / albedo vt duo īfinite poſſet denoīare ſubie-
ctū albū ipſa ↄ̨tinuo manēte vt duo: ſed hoc eſt flm̄:
igr̄ illud ex q̊ ſequit̄̄. Seq̄la probat̄̄: et pono / in a.
pedali ſit albedo vt duo: et nigredo vt vnū coextēſe
et remittat̄̄ nigredo vſ ad nõ gradū: ipſa albedīe
ↄ̨tinuo manēte vt duo. Quo poſita manifeſtū eſt /
īfinita erit ꝓportio albedīs vt duo ad nigredinem /
igr̄ īfinite illa albedo ſubiectū ſuū denoīabit. ¶ Se
cūda ꝓpõ intēſio mixti nõ attendit̄̄ penes q̈litateꝫ
excedentē. Probat̄̄ / q2 tūc ſeq̄ret̄̄ / vna q̈litas ↄ̈ria
nõ īpediret alterã in ſua denoīatiõe: qḋ eſt ↄ̈ notatū
ptꝫ ſeq̄la: q2 albedo vt .6. ſcḋm iſtã poſitionē ad mi-
xta nigredini vt .2. denoīat vt .6: et tm̄ denoīaret nõ
admixta ↄ̈rio: igr̄. ¶ Tertia ꝓpõ. Intēſio mixti nõ
attendit̄̄ penes medietatē exceſſus q̈litatis excedē-
tis. Probat̄̄: q2 tūc ſeq̄ret̄̄ / albedo vt duo īpedi-
ret totalr̄ .4. g̈dus nigredīs ſecū extenſe: ſed ↄ̨ñs eſt
flm̄: igr̄ illud ex q̊ ſequit̄̄. Falſitas ↄ̨ñtis ꝓbat̄̄: et po
no / .6 g̈dus nigredīs coextēdant̄̄ duobꝰ albedīs:
Tūc ſcḋm iſtã poſitionē illa nigredo denoīat vt .2.
q2 g̈dus vt duo eſt medietas exceſſus quo .6. exce-
dūt .2. / igr̄ .4. g̈dus illiꝰ nigredīs vt .6. īpediūtur ab
illis .2. g̈dibꝰ albedīs: et ſic albedo vt .2. īpedit tota
liter .4. g̈dus nigredīs: qḋ fuit ꝓbãdū. Hiis p̄miſſis
eſt / q̈litates ↄ̈rie exiſtētes in eodē ſubiecto ſe īpe-
diūt in ſuis denoīationibꝰ. Nõ em̄ eq̄ albū et cor-
pus in quo ſunt ꝑ totū .6. gradꝰ albedīs cū .2. gra-
dibus nigredīs ſicut corpꝰ in q̊ ſūt .6. gradꝰ albedīs
ſine admixtiõe ↄ̈rie q̈litatis. Et nõ ſolū qualitates
ↄ̈rie ſe īpediūt qñ coextēdunt̄̄: verū etiã qñ in diuer-
ſis partibꝰ ſubiecti ponunt̄̄. Nõ em̄ tm̄ denoīat al-
bedo vt .4. exñs in vna medietate corꝑis in cuiꝰ alia
medietate eſt vnꝰ gradꝰ nigredīs quantū denoīaret
ſi in ſubiecto nõ eſſet aliq̈ nigredo. Hoc ſuppoſito
aduertendū eſt / quadruplex eſt opinio penes qḋ
debeat attendi inteſio mixti hñtis ↄ̈rias q̈litates
coextēſas: q̈s recitat calcu. in capĺo de ītēſio mixto-
rū. ¶ Prima eſt / intēſio mixti d3 attēdi penes ꝓ-
portionē q̈litatis excedētis ad q̈litatē exceſſã. Scḋa
dicit / d3 attēdi penes q̈litatē excedentē. Tertia di
cit / penes medietatē exceſſus q̈litatis excedentis.
Quarta dicit / penes exceſſū. Sed ꝓ īpugnatiõe
3. ṗmaꝝ opinionū pono tres ꝓpõnes. ¶ Prima ꝓ-
poſitio Intēſio mixti nõ attendit̄̄ penes ꝓportionē
q̈litatis excedētis ad exceſſam. Probat̄̄ / q2 tūc ſeq̄-
ret̄̄ / albedo vt duo īfinite poſſet denoīare ſubie-
ctū albū ipſa ↄ̨tinuo manēte vt duo: ſed hoc eſt flm̄:
igr̄ illud ex q̊ ſequit̄̄. Seq̄la probat̄̄: et pono / in a.
pedali ſit albedo vt duo: et nigredo vt vnū coextēſe
et remittat̄̄ nigredo vſ ad nõ gradū: ipſa albedīe
ↄ̨tinuo manēte vt duo. Quo poſita manifeſtū eſt /
īfinita erit ꝓportio albedīs vt duo ad nigredinem /
igr̄ īfinite illa albedo ſubiectū ſuū denoīabit. ¶ Se
cūda ꝓpõ intēſio mixti nõ attendit̄̄ penes q̈litateꝫ
excedentē. Probat̄̄ / q2 tūc ſeq̄ret̄̄ / vna q̈litas ↄ̈ria
nõ īpediret alterã in ſua denoīatiõe: qḋ eſt ↄ̈ notatū
ptꝫ ſeq̄la: q2 albedo vt .6. ſcḋm iſtã poſitionē ad mi-
xta nigredini vt .2. denoīat vt .6: et tm̄ denoīaret nõ
admixta ↄ̈rio: igr̄. ¶ Tertia ꝓpõ. Intēſio mixti nõ
attendit̄̄ penes medietatē exceſſus q̈litatis excedē-
tis. Probat̄̄: q2 tūc ſeq̄ret̄̄ / albedo vt duo īpedi-
ret totalr̄ .4. g̈dus nigredīs ſecū extenſe: ſed ↄ̨ñs eſt
flm̄: igr̄ illud ex q̊ ſequit̄̄. Falſitas ↄ̨ñtis ꝓbat̄̄: et po
no / .6 g̈dus nigredīs coextēdant̄̄ duobꝰ albedīs:
Tūc ſcḋm iſtã poſitionē illa nigredo denoīat vt .2.
q2 g̈dus vt duo eſt medietas exceſſus quo .6. exce-
dūt .2. / igr̄ .4. g̈dus illiꝰ nigredīs vt .6. īpediūtur ab
illis .2. g̈dibꝰ albedīs: et ſic albedo vt .2. īpedit tota
liter .4. g̈dus nigredīs: qḋ fuit ꝓbãdū. Hiis p̄miſſis
Sit prima ↄ̨̨cluſio.
Intenſio mixti in
quo ſunt qualitates ↄ̈rie ſiue coextēſe ſiue nõ: men-
ſurãda eſt penes exceſſū denoīatiõis qua vna illaꝝ
q̈litatū admixta ↄ̈rio nata eſt magis denoīare ſub
iectū ꝙ̄ alia: ceretis paribꝰ. Exēplū / vt coextēſa al-
bedini vt .6. nigredīe vt .2. per totū ſubiectū: qm̄ albe
do vt .6. toti coextēſa ſubiecto valet ſine ↄ̈rii admix
tione denoīare vt .6. et nigredo vt duo coextēſa etiã
ꝑ totū ſubiectū deducto īpedimēto denoīaret vt .2.
Et .6. excedūt duo ꝑ .4. / ↄ̨ñs eſt illud ſubiectū eſſe al-
bū vt .4. Siĺr accõmoda exēplū ↄ̈riis q̈litatibꝰ non
coextēſis: ſemꝑ ad denoīatiões, et nõ ad q̈litatū in-
tenſiões aſpiciēdo. Probat̄̄ / q2 totū reſiduū deno-
quo ſunt qualitates ↄ̈rie ſiue coextēſe ſiue nõ: men-
ſurãda eſt penes exceſſū denoīatiõis qua vna illaꝝ
q̈litatū admixta ↄ̈rio nata eſt magis denoīare ſub
iectū ꝙ̄ alia: ceretis paribꝰ. Exēplū / vt coextēſa al-
bedini vt .6. nigredīe vt .2. per totū ſubiectū: qm̄ albe
do vt .6. toti coextēſa ſubiecto valet ſine ↄ̈rii admix
tione denoīare vt .6. et nigredo vt duo coextēſa etiã
ꝑ totū ſubiectū deducto īpedimēto denoīaret vt .2.
Et .6. excedūt duo ꝑ .4. / ↄ̨ñs eſt illud ſubiectū eſſe al-
bū vt .4. Siĺr accõmoda exēplū ↄ̈riis q̈litatibꝰ non
coextēſis: ſemꝑ ad denoīatiões, et nõ ad q̈litatū in-
tenſiões aſpiciēdo. Probat̄̄ / q2 totū reſiduū deno-
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