211
Probat̄̄ tñ illa ↄ̨ña: iſtud q̈dratū ꝑfectuꝫ efficit̄̄ in
duplo minꝰ lõgū, et in duplo minꝰ latū, et in duplo
minꝰ ꝓfundū. igr̄ efficit̄̄ in octuplo minꝰ: qm̄ coſta
illiꝰ q̈drati in fine ad coſtã illiꝰ in plīcipio diminu-
tiõis ſe hꝫ in ꝓportiõe ſubdupla: ita coſte illiꝰ q̈-
drati in prīcipio et in fine ſe hñt in ꝓportiõe dupla
et illa ſunt ꝑfecta q̈drata: igr̄ illa q̈drata ſe hñt in
ꝓportiõe triplicata ad duplã: et illa ē octupla / vt cõ
ſtat ex ſexto capite ſcḋe ꝑtis: igr̄ ꝓpoſitū. Ptꝫ hec
ↄ̨ña / ꝑ quãdã ↄ̨cluſiõeꝫ ſuperiꝰ ꝓbatã in tractatu de
motu locali peues effectū capite ſcḋo q̄ ↄ̨cĺo talṫ eſt
Proportio q̊dratoꝝ ꝑfectoꝝ eſt ꝓpor° coſtaꝝ tri-
plicata. Siĺe argumētū poteris facere de ſuꝑficie
cuiꝰ latitudo et lõgitudo vnifor̄iṫ diminūt̄̄ ꝑ horã.
duplo minꝰ lõgū, et in duplo minꝰ latū, et in duplo
minꝰ ꝓfundū. igr̄ efficit̄̄ in octuplo minꝰ: qm̄ coſta
illiꝰ q̈drati in fine ad coſtã illiꝰ in plīcipio diminu-
tiõis ſe hꝫ in ꝓportiõe ſubdupla: ita coſte illiꝰ q̈-
drati in prīcipio et in fine ſe hñt in ꝓportiõe dupla
et illa ſunt ꝑfecta q̈drata: igr̄ illa q̈drata ſe hñt in
ꝓportiõe triplicata ad duplã: et illa ē octupla / vt cõ
ſtat ex ſexto capite ſcḋe ꝑtis: igr̄ ꝓpoſitū. Ptꝫ hec
ↄ̨ña / ꝑ quãdã ↄ̨cluſiõeꝫ ſuperiꝰ ꝓbatã in tractatu de
motu locali peues effectū capite ſcḋo q̄ ↄ̨cĺo talṫ eſt
Proportio q̊dratoꝝ ꝑfectoꝝ eſt ꝓpor° coſtaꝝ tri-
plicata. Siĺe argumētū poteris facere de ſuꝑficie
cuiꝰ latitudo et lõgitudo vnifor̄iṫ diminūt̄̄ ꝑ horã.
Nono prīcipalr̄ ar̄ ſic: ſi illa poſi° eſſet
vera ſeq̄ret̄̄: ſi hora diuidat̄̄ ꝑ partes ꝓportiõales
ꝓportiõe dupla: et in ṗma ꝑte ꝓportiõali īpari pe-
dale a. aliq̈liṫ velociṫ augeat̄̄: et in ſcḋa īpari in du
plo velociꝰ: et in tertia īpari in duplo velociꝰ quã ī
ſcḋa īpari: et ſic ↄ̨ñter ↄ̨tinuo in q̈lꝫ īpari ſeq̄nte in
duplo velociꝰ̄ in īpari īmediate p̄cedēte: tūc a. pe
dale īfinite velociter augeret̄̄. Cõſequēs eſt flm̄. igr̄
illud ex q̊ ſequit̄̄. Seq̄la ptꝫ / q2 ſi illud pedale in q̈lꝫ
ꝑte ꝓportiõali vniꝰ hore ꝓportiõe dupla ita aug-
mētaret̄̄ in q̈lꝫ ſeq̄nte in duplo velociꝰ augmēta
ret̄̄̄ in īmediate p̄cedēte: ip̄m in q̈lꝫ ꝑte ꝓportiõa
li tantã quãtitatē acq̇reret ſicut in ṗma / vt cõſtat: et
ſic in illa hora in īfinitū velociṫ augmētaret̄̄. igr̄ ſi
illud idē pedale in q̈lꝫ ꝑte ꝓportiõali ꝓportiõe du
pla īpari ſeq̄nte in duplo velociꝰ augeat̄̄̄ in īpari
īmediate p̄cedēte: ipſum in q̈lꝫ ꝑte tantã quãtitatē
acquirit quantã in prima. Ptꝫ ↄ̨ña / q2 nõ eſt maior rõ
de vno ꝙ̄ de alio. Falſitas tñ ↄ̨ñtis argr̄ ſic. qm̄ ille
ꝑtes īpares ↄ̨tinuo ſe hñt in ꝓportiõe q̈drupla. vt
ptꝫ: et velocitates augmētationis in illis ꝑtibꝰ ↄ̨ti-
nuo ſe hñt in ꝓportiõe dupla: g̊ quãtitates acq̇ſite
ↄ̨tiuuo ſe hñt in ꝓportiõe ſubdupla: et ꝑ ↄ̨ñs aggre
gatū ex oībꝰ illis eſt duplū ad primã illaꝝ. oīa iſta
ſatis patent intelligenti ea que dicta ſunt de velo-
citate motus localis penes effectum ſuperius.
vera ſeq̄ret̄̄: ſi hora diuidat̄̄ ꝑ partes ꝓportiõales
ꝓportiõe dupla: et in ṗma ꝑte ꝓportiõali īpari pe-
dale a. aliq̈liṫ velociṫ augeat̄̄: et in ſcḋa īpari in du
plo velociꝰ: et in tertia īpari in duplo velociꝰ quã ī
ſcḋa īpari: et ſic ↄ̨ñter ↄ̨tinuo in q̈lꝫ īpari ſeq̄nte in
duplo velociꝰ̄ in īpari īmediate p̄cedēte: tūc a. pe
dale īfinite velociter augeret̄̄. Cõſequēs eſt flm̄. igr̄
illud ex q̊ ſequit̄̄. Seq̄la ptꝫ / q2 ſi illud pedale in q̈lꝫ
ꝑte ꝓportiõali vniꝰ hore ꝓportiõe dupla ita aug-
mētaret̄̄ in q̈lꝫ ſeq̄nte in duplo velociꝰ augmēta
ret̄̄̄ in īmediate p̄cedēte: ip̄m in q̈lꝫ ꝑte ꝓportiõa
li tantã quãtitatē acq̇reret ſicut in ṗma / vt cõſtat: et
ſic in illa hora in īfinitū velociṫ augmētaret̄̄. igr̄ ſi
illud idē pedale in q̈lꝫ ꝑte ꝓportiõali ꝓportiõe du
pla īpari ſeq̄nte in duplo velociꝰ augeat̄̄̄ in īpari
īmediate p̄cedēte: ipſum in q̈lꝫ ꝑte tantã quãtitatē
acquirit quantã in prima. Ptꝫ ↄ̨ña / q2 nõ eſt maior rõ
de vno ꝙ̄ de alio. Falſitas tñ ↄ̨ñtis argr̄ ſic. qm̄ ille
ꝑtes īpares ↄ̨tinuo ſe hñt in ꝓportiõe q̈drupla. vt
ptꝫ: et velocitates augmētationis in illis ꝑtibꝰ ↄ̨ti-
nuo ſe hñt in ꝓportiõe dupla: g̊ quãtitates acq̇ſite
ↄ̨tiuuo ſe hñt in ꝓportiõe ſubdupla: et ꝑ ↄ̨ñs aggre
gatū ex oībꝰ illis eſt duplū ad primã illaꝝ. oīa iſta
ſatis patent intelligenti ea que dicta ſunt de velo-
citate motus localis penes effectum ſuperius.
In oppoſitū argr̄ ſic.
Q2 nõ videt̄̄ alṫ
modus velocitatꝪ augmētatiõis ab altero illoꝝ co
gnoſcende: igitur penes alterum illorum debet ve-
locitas motus augmentationis attendi.
modus velocitatꝪ augmētatiõis ab altero illoꝝ co
gnoſcende: igitur penes alterum illorum debet ve-
locitas motus augmentationis attendi.
Pro ſolutiõe huiꝰ q̄ſtiõis quatuor ſūt
ordine faciēda. Primo em̄ definitiones et declara-
tiões termīoꝝ ad hãc materiã ſpectãtiū ponētur et
notant̄̄. Scḋo aliq̈ inducent̄̄ ↄ̨cluſiões. Tertio po-
nent̄̄ dubitatiões. Et poſtremo rõnes ãte oppoſitū
diſſoluent̄̄. Aduertendū igr̄ / augmētatio ita diffi-
nit̄̄ a pḣo primo de gñatiõe. 11q̇d aug-
mētatio. Augmētatio eſt p̄exi-
ſtētis magnitudīs additamētū.
22q̇d dimi-
nutio. ¶ Diminutio vero
p̄exiſtētꝪ quãtitatꝪ mīoramētū. 33pḣs ṗmo
de gene. Ex q̊ ↄ̨cludit phūs:
ex materia ſine magnitudīe nõ p̄t eſſe augmēta°
44Tex. Cõ-
mēti .31. Textu cõmēti triceſimi ṗmi. Hec aūt augmentatio
duplr̄ fieri p̄t. Uno° ꝓut diſtīguit̄̄ ↄ̈ rarefactionē: et
ſic fit ꝑ additionē alicuiꝰ rei quãte p̄exñti
eiuſdē ſpeciè cū illa ex q̈ re cū p̄exñte fit vnū maiꝰ.
Et hec eſt ꝓṗe illa augmētatio de q̈ phūs loquit̄̄ lo
cõ p̄allegato. quãuis videat̄̄ ibi ꝓṗe de augmenta-
tiõe aīati loqui q̄ fit ꝑ intꝰ ſuſceptionē. Alio° capit̄̄
augmētatio ꝓut eſt idē cū rarefactione. Et iſto mõ
augmētatio p̄t fieri ſine additiõe alicuiꝰ alteriꝰ: ſꝫ
p̄ciſe ꝑ maiorē extēſionē p̄exiſtētꝪ. Et vtro iſtorū
modoꝝ loq̇mur in propoſito quãuis de ea ſcḋo mõ
peculiariṫ dictū ſit in p̄cedēti capite. Tu tñ aduer-
te ꝓp̄e capiēdo ṫmīos: rarefactio differt ab aug-
mētatiõe ſaltē diuerſa cõnotant illi duo ṫmini q̇rū
termīoꝝ ſignificãtias et ↄ̨notatiões facile ex his q̄
circa primū de gñatiõe dicunt̄̄ intelligere poteris.
55pḣs ṗmo
de gene. Utrū aūt augmētatio fiat ſcḋm ꝑtes formales aut
materiales et q̄ ſint ꝑtes for̄ales aut materiales et
q̊t ↄ̨ditiões req̇rant̄̄: habes ṗmo de gñatiõe capĺo
de augmetatiõe 66Textu cõ
mē. 36. et
32. Textu cõmēti triceſimi ſcḋi et trice
ſimi ſexti videas ibi. 77Duplex
opīo de
augmē-
tatione. Nunc autē ſufficiat ſcire quid
augmētatio: et q̊tuplex eſt augmētatio: vt ītelligat̄̄
penes qḋ velocitas motꝰ augmētatiõis attēdi ha-
beat. In q̈ materia due ſūt opiniões q̈s calculator
recitat in capĺo de augmētatiõe: quãuis alii tertiã
adiiciãt. 88Calcula.
Hētiſberi Uideas Hentiſberū cū cõmētatore ſuo in
tractatu de motu locali in capĺo de augmētatione
Nūc aūt ſufficiet dicere / ſcḋm vnã opinionē velo
citas motꝰ augmētatiõis attēdit̄̄ penes ꝓportiõa-
lē quãtitatꝪ acq̇ſitionē. Hoc eſt dicere. ſi duo aug
mētent̄̄ ſiue eq̈lia ſiue ineq̈lia: et eq̈lē ꝓportionē in
eodē tꝑe adeq̈te acq̇rãt: ipſa eq̄ velociṫ augmētant̄̄
et ſi minꝰ in duplo maiorē ꝓportionē acquirit quam
maiꝰ in eodē tꝑe: vt puta q2 minꝰ acq̇rit q̈druplã: et
maiꝰ duplã: minꝰ in duplo velociꝰ augmētat̄̄ quam
maiꝰ. Quare ↄ̨cedit hec poſitio / ſtat aliq̇d ī q̈̈dru
plo velociꝰ augmētari quã illud et in q̈druplo mīo
rē quãtitatē acq̇rere adeq̈te. 99Calcuĺ. ¶ Ex q̊ ſeq̇t̄̄ has ↄ̨ñas
ſcḋm hãc poſitionē nichil valere: iſta duo in eodem
tꝑe eq̈lē quãtitatē acq̇rūt: g̊ eq̄ velociṫ augent̄̄ a. in
duplo velociꝰ acq̇rit de quantitate ꝙ̄ b. / g̊ in duplo
velociꝰ augmētat̄̄: a. īfinite velociṫ acq̇rit de quãti-
tate: g̊ īfinite velociṫ augmētat̄̄. Scḋa autē poſitio
nullo pacto ↄ̨ſiderat ꝓportionē quã illud qḋ auge
tur acq̇rit: ſed ſolū quãtitatē. Uñ hec ↄ̨ña ſcḋ3 eã eſt
bona: iſta duo ſiue ſint eq̈lia ſiue inequalia equalē
quãtitatē acq̇rūt s̈̄titatē p̄habitã ī eodē tꝑe: g̊ eq̄
velociṫ augent̄̄. Hiis ãnotatiõibꝰ breuiṫ trãſcurſis:
reſtat aliq̈s ↄ̨cluſiões īducere. Et ṗmo eas īducemꝰ
q̄ ex ṗori opīiõe ſequūt̄̄: q̄o ex ſcḋa poſteriꝰ ſic / igr̄
ordine faciēda. Primo em̄ definitiones et declara-
tiões termīoꝝ ad hãc materiã ſpectãtiū ponētur et
notant̄̄. Scḋo aliq̈ inducent̄̄ ↄ̨cluſiões. Tertio po-
nent̄̄ dubitatiões. Et poſtremo rõnes ãte oppoſitū
diſſoluent̄̄. Aduertendū igr̄ / augmētatio ita diffi-
nit̄̄ a pḣo primo de gñatiõe. 11q̇d aug-
mētatio. Augmētatio eſt p̄exi-
ſtētis magnitudīs additamētū.
22q̇d dimi-
nutio. ¶ Diminutio vero
p̄exiſtētꝪ quãtitatꝪ mīoramētū. 33pḣs ṗmo
de gene. Ex q̊ ↄ̨cludit phūs:
ex materia ſine magnitudīe nõ p̄t eſſe augmēta°
44Tex. Cõ-
mēti .31. Textu cõmēti triceſimi ṗmi. Hec aūt augmentatio
duplr̄ fieri p̄t. Uno° ꝓut diſtīguit̄̄ ↄ̈ rarefactionē: et
ſic fit ꝑ additionē alicuiꝰ rei quãte p̄exñti
eiuſdē ſpeciè cū illa ex q̈ re cū p̄exñte fit vnū maiꝰ.
Et hec eſt ꝓṗe illa augmētatio de q̈ phūs loquit̄̄ lo
cõ p̄allegato. quãuis videat̄̄ ibi ꝓṗe de augmenta-
tiõe aīati loqui q̄ fit ꝑ intꝰ ſuſceptionē. Alio° capit̄̄
augmētatio ꝓut eſt idē cū rarefactione. Et iſto mõ
augmētatio p̄t fieri ſine additiõe alicuiꝰ alteriꝰ: ſꝫ
p̄ciſe ꝑ maiorē extēſionē p̄exiſtētꝪ. Et vtro iſtorū
modoꝝ loq̇mur in propoſito quãuis de ea ſcḋo mõ
peculiariṫ dictū ſit in p̄cedēti capite. Tu tñ aduer-
te ꝓp̄e capiēdo ṫmīos: rarefactio differt ab aug-
mētatiõe ſaltē diuerſa cõnotant illi duo ṫmini q̇rū
termīoꝝ ſignificãtias et ↄ̨notatiões facile ex his q̄
circa primū de gñatiõe dicunt̄̄ intelligere poteris.
55pḣs ṗmo
de gene. Utrū aūt augmētatio fiat ſcḋm ꝑtes formales aut
materiales et q̄ ſint ꝑtes for̄ales aut materiales et
q̊t ↄ̨ditiões req̇rant̄̄: habes ṗmo de gñatiõe capĺo
de augmetatiõe 66Textu cõ
mē. 36. et
32. Textu cõmēti triceſimi ſcḋi et trice
ſimi ſexti videas ibi. 77Duplex
opīo de
augmē-
tatione. Nunc autē ſufficiat ſcire quid
augmētatio: et q̊tuplex eſt augmētatio: vt ītelligat̄̄
penes qḋ velocitas motꝰ augmētatiõis attēdi ha-
beat. In q̈ materia due ſūt opiniões q̈s calculator
recitat in capĺo de augmētatiõe: quãuis alii tertiã
adiiciãt. 88Calcula.
Hētiſberi Uideas Hentiſberū cū cõmētatore ſuo in
tractatu de motu locali in capĺo de augmētatione
Nūc aūt ſufficiet dicere / ſcḋm vnã opinionē velo
citas motꝰ augmētatiõis attēdit̄̄ penes ꝓportiõa-
lē quãtitatꝪ acq̇ſitionē. Hoc eſt dicere. ſi duo aug
mētent̄̄ ſiue eq̈lia ſiue ineq̈lia: et eq̈lē ꝓportionē in
eodē tꝑe adeq̈te acq̇rãt: ipſa eq̄ velociṫ augmētant̄̄
et ſi minꝰ in duplo maiorē ꝓportionē acquirit quam
maiꝰ in eodē tꝑe: vt puta q2 minꝰ acq̇rit q̈druplã: et
maiꝰ duplã: minꝰ in duplo velociꝰ augmētat̄̄ quam
maiꝰ. Quare ↄ̨cedit hec poſitio / ſtat aliq̇d ī q̈̈dru
plo velociꝰ augmētari quã illud et in q̈druplo mīo
rē quãtitatē acq̇rere adeq̈te. 99Calcuĺ. ¶ Ex q̊ ſeq̇t̄̄ has ↄ̨ñas
ſcḋm hãc poſitionē nichil valere: iſta duo in eodem
tꝑe eq̈lē quãtitatē acq̇rūt: g̊ eq̄ velociṫ augent̄̄ a. in
duplo velociꝰ acq̇rit de quantitate ꝙ̄ b. / g̊ in duplo
velociꝰ augmētat̄̄: a. īfinite velociṫ acq̇rit de quãti-
tate: g̊ īfinite velociṫ augmētat̄̄. Scḋa autē poſitio
nullo pacto ↄ̨ſiderat ꝓportionē quã illud qḋ auge
tur acq̇rit: ſed ſolū quãtitatē. Uñ hec ↄ̨ña ſcḋ3 eã eſt
bona: iſta duo ſiue ſint eq̈lia ſiue inequalia equalē
quãtitatē acq̇rūt s̈̄titatē p̄habitã ī eodē tꝑe: g̊ eq̄
velociṫ augent̄̄. Hiis ãnotatiõibꝰ breuiṫ trãſcurſis:
reſtat aliq̈s ↄ̨cluſiões īducere. Et ṗmo eas īducemꝰ
q̄ ex ṗori opīiõe ſequūt̄̄: q̄o ex ſcḋa poſteriꝰ ſic / igr̄
Prima concluſio.
Diuiſo corpore per
ꝑtes ꝓportiõales q̈uis ꝓportiõe: et ṗma ꝑs ꝓpor-
tiõalis talis corꝑis aliq̈liṫ augmētet̄̄ acq̇rēdo talē
ꝓportionē q̈lis eſt inṫ ipſam et ſcḋam vel maiorē: et
ſcḋa in eodē tꝑe augmēter̄ in duplo velociꝰ: et ṫtia
in triplo velociꝰ quã ṗma: et q̈rta in q̈druplo velociꝰ
̄ prima in eodē tꝑe: tale corpꝰ efficiṫ īfinitū, et īfi-
nitã ꝓportionē acquirit, et ſic īfinite velociꝰ augmētat̄̄
Probar̄ ↄ̨cĺo. q2 ī tali caſu q̄lꝫ ꝑs ꝓportiõalis illiꝰ
corꝑis ſeq̄ns efficit̄̄ eq̈lis vel maior ꝙ̄ ṗma. g̊ ſequit̄̄ /
illud corpꝰ efficit̄̄ īfinite magnū. Probat̄̄ añs: et
volo / a. corpꝰ diuidat̄̄ ꝓportiõe h. et ṗma ꝑs ꝓpor
tiõalis eiꝰ in hora acq̇rit ꝓportionē h. et ſcḋa duas
h. et ṫtia tres. et q̈rta q̈tuor . / et ſic ↄ̨ñter. Quo poſito
argr̄ ſic. Prima pars diſtat a ſcḋa ꝑ h. ꝓportionē
adeq̈te in prīcipio augmētatiõis et ip̄a p̄ma acq̇rit
h. ꝓportionē: et ſcḋa acq̇rit vnã h. ꝓportionē in q̈
ṗma excedebat eã: et īſuꝑ tãtã ꝓportiõeꝫ quãtã prīa
puta vnã aliã ꝓportionē h. / igr̄ efficit̄̄ eq̈lis prime.
Ptꝫ hec ↄ̨ña ꝑ maximã ſuperiꝰ poſitã. Quãdo due
quãtitates īequales creſcūt, et mīor illaꝝ acquirit
illã ꝓportionē q̄ eſt inter maiorē et ipſam, et inſuꝑ
tantaꝫ proportionē adeq̈te quantã acq̇rit maior in
fine augmētatiõis tales quãtitates manent eq̈les:
ſed ſic eſt in ꝓpoſito: igr̄. et ſic ꝓbabis / ṫtia pars
effecta eſt eq̈lis ſcḋe q2 acq̇ſiuit duas ꝓportiões h.
ſicut ſcḋa, et inſuꝑ vnã aliã h. in qua ſcḋa excedebat
tertiã, et ſiĺr q̈rta acq̇ſiuit tres ꝓportiões h. ſicut et
tertia et īſuꝑ vnã h. in q̈ tertia excedebat illã: igr̄ ꝑ
illã maximã oēs ille ꝑtes manēt eq̈les qm̄ ſic ꝓba
bis de quibuſcū duabꝰ īmeditatis. Et eodē° ꝓba-
bis tale corpꝰ acq̇rit infinitã ꝓportionē: ſi prima
pars eiꝰ acq̇reret maiorē ꝓportionē ꝙ̄ ſit ꝓportio
ꝑtes ꝓportiõales q̈uis ꝓportiõe: et ṗma ꝑs ꝓpor-
tiõalis talis corꝑis aliq̈liṫ augmētet̄̄ acq̇rēdo talē
ꝓportionē q̈lis eſt inṫ ipſam et ſcḋam vel maiorē: et
ſcḋa in eodē tꝑe augmēter̄ in duplo velociꝰ: et ṫtia
in triplo velociꝰ quã ṗma: et q̈rta in q̈druplo velociꝰ
̄ prima in eodē tꝑe: tale corpꝰ efficiṫ īfinitū, et īfi-
nitã ꝓportionē acquirit, et ſic īfinite velociꝰ augmētat̄̄
Probar̄ ↄ̨cĺo. q2 ī tali caſu q̄lꝫ ꝑs ꝓportiõalis illiꝰ
corꝑis ſeq̄ns efficit̄̄ eq̈lis vel maior ꝙ̄ ṗma. g̊ ſequit̄̄ /
illud corpꝰ efficit̄̄ īfinite magnū. Probat̄̄ añs: et
volo / a. corpꝰ diuidat̄̄ ꝓportiõe h. et ṗma ꝑs ꝓpor
tiõalis eiꝰ in hora acq̇rit ꝓportionē h. et ſcḋa duas
h. et ṫtia tres. et q̈rta q̈tuor . / et ſic ↄ̨ñter. Quo poſito
argr̄ ſic. Prima pars diſtat a ſcḋa ꝑ h. ꝓportionē
adeq̈te in prīcipio augmētatiõis et ip̄a p̄ma acq̇rit
h. ꝓportionē: et ſcḋa acq̇rit vnã h. ꝓportionē in q̈
ṗma excedebat eã: et īſuꝑ tãtã ꝓportiõeꝫ quãtã prīa
puta vnã aliã ꝓportionē h. / igr̄ efficit̄̄ eq̈lis prime.
Ptꝫ hec ↄ̨ña ꝑ maximã ſuperiꝰ poſitã. Quãdo due
quãtitates īequales creſcūt, et mīor illaꝝ acquirit
illã ꝓportionē q̄ eſt inter maiorē et ipſam, et inſuꝑ
tantaꝫ proportionē adeq̈te quantã acq̇rit maior in
fine augmētatiõis tales quãtitates manent eq̈les:
ſed ſic eſt in ꝓpoſito: igr̄. et ſic ꝓbabis / ṫtia pars
effecta eſt eq̈lis ſcḋe q2 acq̇ſiuit duas ꝓportiões h.
ſicut ſcḋa, et inſuꝑ vnã aliã h. in qua ſcḋa excedebat
tertiã, et ſiĺr q̈rta acq̇ſiuit tres ꝓportiões h. ſicut et
tertia et īſuꝑ vnã h. in q̈ tertia excedebat illã: igr̄ ꝑ
illã maximã oēs ille ꝑtes manēt eq̈les qm̄ ſic ꝓba
bis de quibuſcū duabꝰ īmeditatis. Et eodē° ꝓba-
bis tale corpꝰ acq̇rit infinitã ꝓportionē: ſi prima
pars eiꝰ acq̇reret maiorē ꝓportionē ꝙ̄ ſit ꝓportio
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