210 falſum: igr̄ ex illud quo ſequit̄̄.
Seq̄la ptꝫ / q2 tantã
quãtitatē ſupra totã p̄habitã acq̇rit medietas: ſic
totū: igr̄ medietas, et totū eq̄ velociṫ augent̄̄. Ptꝫ
ↄ̨ña expoſitiõe. Sed ꝓbo falſitatē ↄ̨ñtis. Tū ṗmo
q2 tūc ſeq̄ret̄̄ / eq̄ velociṫ augeret̄̄ totū ſicut in īfi-
nitū modica eiꝰ pars. Sꝫ hoc vr̄ abſurdū: igr̄ illud
ex q̊ ſequit̄̄. Seq̄la ptꝫ / q2 qñ totū acq̇rit vnū ſemipe
dale, medietas eiꝰ acq̇rit tm̄, et octaua et ſexdecima
termīata ad illã quantitatē acq̇ſitã, et ſic ↄ̨ñter: igr̄.
Tū ſcḋo q2 ſtat / medietas alicuiꝰ intēdat̄̄ aliq̈liṫ
velociṫ acq̇rēdo aliquã intēſionē: tñ totū nõ acq̇rit
tantã. ergo eodē mõ ſtat in motu augmētatiõis
medietas aliqualiṫ velociṫ augeat̄̄, et totū nõ: et ꝑ
ↄ̨ñs illatū flm̄. ¶ Dices et bene ↄ̨cedēdo illatū in ta
li caſu: et ad ꝓbationē falſitatꝪ eiꝰ ↄ̨cedēdo illḋ ↄ̨ñs
vcꝫ / ita velociter auget̄̄ totū ſicut īfinite modica
eiꝰ pars ſignãter ſi hoc fiat ꝑ additionē quãtitatis
alicui medietati: ſicut ſit qñ aliq̇d addit̄̄ parti aīaĺ:
et augmētat̄̄ aīal. ¶ Ad ſcḋam īprobationē cõcedo
q2 ſtat medietas
alicꝰ ītēdat̄̄ et nõ totū: et ſtat totū ītēdat̄̄ et vna eiꝰ
medietas nõ intēdat̄̄. Nõ tñ ſtat pars augmētet̄̄
ſine diminutiõe aliq̈ quī totū augmētet̄̄. Cõtra tūc
ſeq̄ret̄̄ / ſēꝑ eq̄ velociter augmētaret̄̄ aliqua pars
ſicut totū. Sed ↄ̨ñs eſt flm̄: igr̄ illud ex q̊ ſequit̄̄. Fal
ſitas ↄ̨ñtis ꝓbat̄̄. Et volo / vtri medietati vnius
pedalis addat̄̄ ſemipedale in extremis oppoſitis:
tūc manifeſtū eſt totū acq̇rit pedalē quãtitatem
et nulla ꝑs eiꝰ acq̇rit pedalē quãtitatē: igr̄ nulla ꝑs
ibi auget̄̄ ita velociṫ ſicut totū: et ꝑ ↄ̨ñs nõ ſēꝑ eque
velociṫ etc̈. Seq̄la tñ ꝓbat̄̄: q2 ſi nõ ſēꝑ augmētaret̄̄
aliq̈ pars ita velociṫ ſicut totū: maxīe eſſet in caſu
in q̊ ꝓbat̄̄ falſitas ↄ̨ñtis: ſed in illo caſu eque velo-
citer augetur aliqua pars ſicut totum puta pars
que cõponitur ex duabꝰ quartis extremis cū parti-
bus extremalibꝰ q̄ ꝑtes extreme circūferētiales cõ-
ſtituūt vnū quadratū inṫ qḋ manet aliud vt ptꝫ in
12[Figure 12] figura iã ſequenti: igr̄.
¶ Dices et bñ
negãdo ſeq̄lã: et ad punctū ꝓbatiõis
dr̄ etiã in illo caſu eq̄ velociṫ au-
get̄̄ aliq̈ ꝑs ſicut totū / vt ꝓbat argu-
mētū: et ſic negat̄̄ / maxīe eſſet ī illo
caſu: ſed dico / eſt in caſu vbi totuꝫ
ꝑ totū rarefit: tūc em̄ nulla ꝑs ita velociṫ auget̄̄ ſi-
cut totū / vt ſatꝪ ptꝫ / quī ſi totū aliqḋ qḋ ꝑ totū rare-
fit rarefiat ad duplū: ipſū totū acq̇rit tantã quãti-
tatē ſicut ipſū eſt: et nulla ꝑs acq̇rit quãtitatē
ſicut illud totū eſt. ¶ Sed ↄ̈: q2 tūc ſeq̄ret̄̄ / qñ ali-
quid augmētaret̄̄ ꝑ rarefactionē q̄ rarefactio eſt ꝑ
totū ſubiectū quãtitas quã adeq̈te acq̇rit totū eſſet
mīma quã nõ acq̇rit aliq̄ ꝑs. Sed hoc vr̄ flm̄: igr̄ il-
lud ex quo ſequit̄̄. Seq̄la pꝫ. q2 dato / totū acq̇rat
pedalē quãtitatē: manifeſtū eſt / vna medietas eiꝰ
acq̇ſiuit aliquã partē illiꝰ: et aggregatū ex illa me-
dietate et ṗma ꝑte ꝓportiõali alteriꝰ medietatꝪ acq̇
ſiuit maiorē: et aggregatū ex illa et duabus primis
ꝑtibꝰ ꝓportiõabilibꝰ alteriꝰ adhuc acq̇ſiuit maiorē /
et ſic ↄ̨ñter calculando. Ptꝫ / quãtitas acq̇ſita ipſi
toti eſt minima quã nõ acquiſiuit aliqua pars.
quãtitatē ſupra totã p̄habitã acq̇rit medietas: ſic
totū: igr̄ medietas, et totū eq̄ velociṫ augent̄̄. Ptꝫ
ↄ̨ña expoſitiõe. Sed ꝓbo falſitatē ↄ̨ñtis. Tū ṗmo
q2 tūc ſeq̄ret̄̄ / eq̄ velociṫ augeret̄̄ totū ſicut in īfi-
nitū modica eiꝰ pars. Sꝫ hoc vr̄ abſurdū: igr̄ illud
ex q̊ ſequit̄̄. Seq̄la ptꝫ / q2 qñ totū acq̇rit vnū ſemipe
dale, medietas eiꝰ acq̇rit tm̄, et octaua et ſexdecima
termīata ad illã quantitatē acq̇ſitã, et ſic ↄ̨ñter: igr̄.
Tū ſcḋo q2 ſtat / medietas alicuiꝰ intēdat̄̄ aliq̈liṫ
velociṫ acq̇rēdo aliquã intēſionē: tñ totū nõ acq̇rit
tantã. ergo eodē mõ ſtat in motu augmētatiõis
medietas aliqualiṫ velociṫ augeat̄̄, et totū nõ: et ꝑ
ↄ̨ñs illatū flm̄. ¶ Dices et bene ↄ̨cedēdo illatū in ta
li caſu: et ad ꝓbationē falſitatꝪ eiꝰ ↄ̨cedēdo illḋ ↄ̨ñs
vcꝫ / ita velociter auget̄̄ totū ſicut īfinite modica
eiꝰ pars ſignãter ſi hoc fiat ꝑ additionē quãtitatis
alicui medietati: ſicut ſit qñ aliq̇d addit̄̄ parti aīaĺ:
et augmētat̄̄ aīal. ¶ Ad ſcḋam īprobationē cõcedo
q2 ſtat medietas
alicꝰ ītēdat̄̄ et nõ totū: et ſtat totū ītēdat̄̄ et vna eiꝰ
medietas nõ intēdat̄̄. Nõ tñ ſtat pars augmētet̄̄
ſine diminutiõe aliq̈ quī totū augmētet̄̄. Cõtra tūc
ſeq̄ret̄̄ / ſēꝑ eq̄ velociter augmētaret̄̄ aliqua pars
ſicut totū. Sed ↄ̨ñs eſt flm̄: igr̄ illud ex q̊ ſequit̄̄. Fal
ſitas ↄ̨ñtis ꝓbat̄̄. Et volo / vtri medietati vnius
pedalis addat̄̄ ſemipedale in extremis oppoſitis:
tūc manifeſtū eſt totū acq̇rit pedalē quãtitatem
et nulla ꝑs eiꝰ acq̇rit pedalē quãtitatē: igr̄ nulla ꝑs
ibi auget̄̄ ita velociṫ ſicut totū: et ꝑ ↄ̨ñs nõ ſēꝑ eque
velociṫ etc̈. Seq̄la tñ ꝓbat̄̄: q2 ſi nõ ſēꝑ augmētaret̄̄
aliq̈ pars ita velociṫ ſicut totū: maxīe eſſet in caſu
in q̊ ꝓbat̄̄ falſitas ↄ̨ñtis: ſed in illo caſu eque velo-
citer augetur aliqua pars ſicut totum puta pars
que cõponitur ex duabꝰ quartis extremis cū parti-
bus extremalibꝰ q̄ ꝑtes extreme circūferētiales cõ-
ſtituūt vnū quadratū inṫ qḋ manet aliud vt ptꝫ in
negãdo ſeq̄lã: et ad punctū ꝓbatiõis
dr̄ etiã in illo caſu eq̄ velociṫ au-
get̄̄ aliq̈ ꝑs ſicut totū / vt ꝓbat argu-
mētū: et ſic negat̄̄ / maxīe eſſet ī illo
caſu: ſed dico / eſt in caſu vbi totuꝫ
ꝑ totū rarefit: tūc em̄ nulla ꝑs ita velociṫ auget̄̄ ſi-
cut totū / vt ſatꝪ ptꝫ / quī ſi totū aliqḋ qḋ ꝑ totū rare-
fit rarefiat ad duplū: ipſū totū acq̇rit tantã quãti-
tatē ſicut ipſū eſt: et nulla ꝑs acq̇rit quãtitatē
ſicut illud totū eſt. ¶ Sed ↄ̈: q2 tūc ſeq̄ret̄̄ / qñ ali-
quid augmētaret̄̄ ꝑ rarefactionē q̄ rarefactio eſt ꝑ
totū ſubiectū quãtitas quã adeq̈te acq̇rit totū eſſet
mīma quã nõ acq̇rit aliq̄ ꝑs. Sed hoc vr̄ flm̄: igr̄ il-
lud ex quo ſequit̄̄. Seq̄la pꝫ. q2 dato / totū acq̇rat
pedalē quãtitatē: manifeſtū eſt / vna medietas eiꝰ
acq̇ſiuit aliquã partē illiꝰ: et aggregatū ex illa me-
dietate et ṗma ꝑte ꝓportiõali alteriꝰ medietatꝪ acq̇
ſiuit maiorē: et aggregatū ex illa et duabus primis
ꝑtibꝰ ꝓportiõabilibꝰ alteriꝰ adhuc acq̇ſiuit maiorē /
et ſic ↄ̨ñter calculando. Ptꝫ / quãtitas acq̇ſita ipſi
toti eſt minima quã nõ acquiſiuit aliqua pars.
Octauo contra eandē partē q̄ſtionis
argr̄ ſic. Qm̄ ſi velocitas augmētatiõis attēderet̄̄
penes abſolutã acq̇ſitionē quãtitatꝪ: ſeq̄ret̄̄ / qḋlꝫ
iſtoꝝ īciperet īfinite velociṫ augeri: et tñ īciperet in-
finitū tarde augeri aliqḋ iſtoꝝ: ſed ↄ̨ñs videt̄̄ re-
pugnare: igr̄ illud ex quo ſequit̄̄. Seq̄la ptꝫ et volo /
ſint īfinita ↄ̨tinuo ſe habētia in ꝓportiõe ſubdu
pla: ita primū ſit pedale, ſcḋ3 ſemipedale, tertiū
q̈rta pedalis / et ſic ↄ̨ñter: et diuidat̄̄ hora ꝑ ꝑtes ꝓ-
portiõales ꝓportione dupla qḋlibet o illoꝝ diu
dat̄̄ ꝑ partes ꝓportiõales ꝓportiõe ſexquialtera: et
qḋlꝫ illoꝝ in q̈libet ꝑte ꝓportiõali hore ꝑdat vnaꝫ
partē ꝓportionalē ſui ꝓportiõe ſexq̇altera quouſ
in fine hore deueniat ad nõ quantū: deinde īcipiant
illa a nõ quãto augeri oīno ſicut diminuebant̄̄ pu-
ta in q̈libet ꝑte ꝓportiõali hore ꝓportiõe dupla ac
quirēdo vna ꝑte ꝓportiõalē ſui ꝓportiõe ſexq̇alte-
ra q̊ poſito argr̄ ſic: qḋlꝫ illoꝝ īmediate poſt illud
inſtãs augmētatiõis a nõ quãto in īfinitū velociter
augmētabit̄̄: et īmediate poſt tale inſtãs in infinitū
tarde augebit̄̄ aliqḋ illoꝝ: et mõ nullum illoꝝ aug-
mentat̄̄ igr̄ ꝓpoſitū. Probat̄̄ maior: q2 qḋlꝫ illoꝝ
īcipit a nõ quãto in qualꝫ ꝑte ꝓportiõali ꝓportiõe
dupla acq̇rere ꝓportionē ſexq̇alterã: g̊ qḋlꝫ illoꝝ in
cipit in īfinitū velociṫ acq̇rere de quãtitate / vt ptꝫ ex
ſcḋa ↄ̨firmatiõe ſcḋi argumēti huiꝰ q̄ſtiõis et ꝑ ↄ̨ñs
qḋlꝫ illoꝝ īcipit in īfinitū velociṫ augeri qñ in īfini
tū velox augmētatio eſt in īfinitū velox acq̇ſitio quã
titatꝪ / vt ptꝫ ex hac poſitionē. Probat̄̄ minor vcꝫ /
īmediate poſt hoc in īfinitū tarde acq̇ret aliqḋ iſto
rū de quãtitate q2 ↄ̨tinuo in īfinitū minꝰ primo erit
aliqḋ illoꝝ: ſicut fuit in via diminutiõis: et incipiunt
oīa illa a nõ quãto in eodē inſtãti augeri: g̊ quocū
inſtãti dato poſt hoc īter hoc et illud īfinite modicū
quãtitatē acq̇ſiuit aliqḋ illoꝝ: et ꝑ ↄ̨ñs īfinite tarde
auget̄̄ aliqḋ illoꝝ. ¶ Dices et bñ ↄ̨cedēdo illatū nec
illud eſt incõueniēs: ſed ſequēs / vt ꝓbat argumentū.
Sed ↄ̈ / q2 pari rõne ↄ̨cedendū eſſet / qḋ vnū et idem a
nõ quãto īciperet in īfinitū velociṫ augmētari: et il-
lud idē īciperet a nõ quãto in īfinitū tarde augmē-
tari. ſed ↄ̨ñs eſt flm̄: igr̄ illud ex quo ſequit̄̄. Falſi-
tas ↄ̨ñtis ptꝫ / q2 detur illud et ſit a. / et argr̄ ſic / a. inci
pit in īfinitū velociṫ augmētari: g̊ īcipit in infinitū
velociter acq̇rere de quãtitate: et ꝑ ↄ̨ñs nõ īcipit in
infinitū velociṫ acq̇rere de quãtitate: et ſic habet̄̄
īcipit ī īfinitū velociṫ acq̇rere de quantitate: et nõ
īcipit ī īfinitū velociṫ acq̇rē de quãtitate / qḋ īplicat
Seq̄la tū ꝓbat̄̄ et volo / a. īcipiat augeri a nõ quã
to in aliqua hora diuiſa ꝑ partes ꝓportiõales ꝓ-
portiõe dupla ſiĺr vna medietas eiꝰ in qualꝫ ꝑte
ꝓportiõali pari acq̇rat ꝓportionē ſexq̇alterã: et al
tera medietas in q̈libet īpari acq̇rat octuplã quo
poſito argr̄ ſic / illud in tali caſu īcipit in īfinitū ve-
lociter augeri et etiã īcipit in īfinitū tarde augeri et
hoc a nõ quãto: igr̄ ꝓpoſitū. Argr̄ maior / q2 incipit
in ꝑtibꝰ ꝓportiõalibꝰ paribꝰ īfinite velociṫ acq̇rere
de quãtitate / vt ptꝫ ex ſcḋa ↄ̨firmatiõe ſcḋi argumē
ti p̄allegati: igr̄ incipit in īfinitū velociter augeri.
Probat̄̄ mīor: q2 illud īcipit in īfinitū tarde acq̇re
re de quantitate in partibꝰ īparibꝰ / vt ptꝫ ex dedu-
ctione ṗme ↄ̨firmatiõis ſcḋi argumēti preallegati:
igr̄ īcipit illud īfinite tarde augeri in ꝑtibꝰ īparibꝰ
11Confir-
matio. ¶ Confirmat̄̄. Q2 ſi illn poſito eſſet vera ſeq̇ret̄̄ /
nullū quadratū ꝑfectū poſſet vniformiṫ diminui
ad nõ quãtū qñ trina eiꝰ dimēſio puta lõgitudo la
titudo et ꝓfūditas vniformiṫ a nõ quãto diminuūt̄̄ /
ſed ↄ̨ñs eſt flm̄ / q2 nõ videt̄̄ repugnare tale quadra
tū vniformiter ſic diminui ad nõ quantū: igit̄̄ illud
ex quo ſequit̄̄. Sequela tñ ꝓbatur: quia ſi aliquod
ſic poteſt diminui detur aliquod quadratū pedalr̄
lõgū, pedaliṫ latū, pedaliṫ ꝓfūdū, qḋ ſit a. Tūc ar̄
ſic / ↄ̨tinuo lõgitudo latitudo et ēt ꝓfūditas huiꝰ q̈-
drati a. vniformiṫ ī hora diminuit̄̄ vſ ad nõ ̄tū:
igr̄ in ṗma ꝑte ꝓportiõali hore ꝓportiõe dupla il-
lud q̈dratū efficit̄̄ in duplo minꝰ logū ī duplo minꝰ
latū. in duplo minꝰ ꝓfundū: et ſic ꝑ ↄ̨ñs efficit̄̄ ī octu
plo minꝰ: et ꝑ ↄ̨ñs in ṗma medietate ꝑdit ſeptē octa
uas: et in ſcḋa medietate vnã tm̄: et ꝑ ↄ̨ñs in illa hõ
cõtinuo diminuit̄̄ vniformiṫ / qḋ fuit probandū
argr̄ ſic. Qm̄ ſi velocitas augmētatiõis attēderet̄̄
penes abſolutã acq̇ſitionē quãtitatꝪ: ſeq̄ret̄̄ / qḋlꝫ
iſtoꝝ īciperet īfinite velociṫ augeri: et tñ īciperet in-
finitū tarde augeri aliqḋ iſtoꝝ: ſed ↄ̨ñs videt̄̄ re-
pugnare: igr̄ illud ex quo ſequit̄̄. Seq̄la ptꝫ et volo /
ſint īfinita ↄ̨tinuo ſe habētia in ꝓportiõe ſubdu
pla: ita primū ſit pedale, ſcḋ3 ſemipedale, tertiū
q̈rta pedalis / et ſic ↄ̨ñter: et diuidat̄̄ hora ꝑ ꝑtes ꝓ-
portiõales ꝓportione dupla qḋlibet o illoꝝ diu
dat̄̄ ꝑ partes ꝓportiõales ꝓportiõe ſexquialtera: et
qḋlꝫ illoꝝ in q̈libet ꝑte ꝓportiõali hore ꝑdat vnaꝫ
partē ꝓportionalē ſui ꝓportiõe ſexq̇altera quouſ
in fine hore deueniat ad nõ quantū: deinde īcipiant
illa a nõ quãto augeri oīno ſicut diminuebant̄̄ pu-
ta in q̈libet ꝑte ꝓportiõali hore ꝓportiõe dupla ac
quirēdo vna ꝑte ꝓportiõalē ſui ꝓportiõe ſexq̇alte-
ra q̊ poſito argr̄ ſic: qḋlꝫ illoꝝ īmediate poſt illud
inſtãs augmētatiõis a nõ quãto in īfinitū velociter
augmētabit̄̄: et īmediate poſt tale inſtãs in infinitū
tarde augebit̄̄ aliqḋ illoꝝ: et mõ nullum illoꝝ aug-
mentat̄̄ igr̄ ꝓpoſitū. Probat̄̄ maior: q2 qḋlꝫ illoꝝ
īcipit a nõ quãto in qualꝫ ꝑte ꝓportiõali ꝓportiõe
dupla acq̇rere ꝓportionē ſexq̇alterã: g̊ qḋlꝫ illoꝝ in
cipit in īfinitū velociṫ acq̇rere de quãtitate / vt ptꝫ ex
ſcḋa ↄ̨firmatiõe ſcḋi argumēti huiꝰ q̄ſtiõis et ꝑ ↄ̨ñs
qḋlꝫ illoꝝ īcipit in īfinitū velociṫ augeri qñ in īfini
tū velox augmētatio eſt in īfinitū velox acq̇ſitio quã
titatꝪ / vt ptꝫ ex hac poſitionē. Probat̄̄ minor vcꝫ /
īmediate poſt hoc in īfinitū tarde acq̇ret aliqḋ iſto
rū de quãtitate q2 ↄ̨tinuo in īfinitū minꝰ primo erit
aliqḋ illoꝝ: ſicut fuit in via diminutiõis: et incipiunt
oīa illa a nõ quãto in eodē inſtãti augeri: g̊ quocū
inſtãti dato poſt hoc īter hoc et illud īfinite modicū
quãtitatē acq̇ſiuit aliqḋ illoꝝ: et ꝑ ↄ̨ñs īfinite tarde
auget̄̄ aliqḋ illoꝝ. ¶ Dices et bñ ↄ̨cedēdo illatū nec
illud eſt incõueniēs: ſed ſequēs / vt ꝓbat argumentū.
Sed ↄ̈ / q2 pari rõne ↄ̨cedendū eſſet / qḋ vnū et idem a
nõ quãto īciperet in īfinitū velociṫ augmētari: et il-
lud idē īciperet a nõ quãto in īfinitū tarde augmē-
tari. ſed ↄ̨ñs eſt flm̄: igr̄ illud ex quo ſequit̄̄. Falſi-
tas ↄ̨ñtis ptꝫ / q2 detur illud et ſit a. / et argr̄ ſic / a. inci
pit in īfinitū velociṫ augmētari: g̊ īcipit in infinitū
velociter acq̇rere de quãtitate: et ꝑ ↄ̨ñs nõ īcipit in
infinitū velociṫ acq̇rere de quãtitate: et ſic habet̄̄
īcipit ī īfinitū velociṫ acq̇rere de quantitate: et nõ
īcipit ī īfinitū velociṫ acq̇rē de quãtitate / qḋ īplicat
Seq̄la tū ꝓbat̄̄ et volo / a. īcipiat augeri a nõ quã
to in aliqua hora diuiſa ꝑ partes ꝓportiõales ꝓ-
portiõe dupla ſiĺr vna medietas eiꝰ in qualꝫ ꝑte
ꝓportiõali pari acq̇rat ꝓportionē ſexq̇alterã: et al
tera medietas in q̈libet īpari acq̇rat octuplã quo
poſito argr̄ ſic / illud in tali caſu īcipit in īfinitū ve-
lociter augeri et etiã īcipit in īfinitū tarde augeri et
hoc a nõ quãto: igr̄ ꝓpoſitū. Argr̄ maior / q2 incipit
in ꝑtibꝰ ꝓportiõalibꝰ paribꝰ īfinite velociṫ acq̇rere
de quãtitate / vt ptꝫ ex ſcḋa ↄ̨firmatiõe ſcḋi argumē
ti p̄allegati: igr̄ incipit in īfinitū velociter augeri.
Probat̄̄ mīor: q2 illud īcipit in īfinitū tarde acq̇re
re de quantitate in partibꝰ īparibꝰ / vt ptꝫ ex dedu-
ctione ṗme ↄ̨firmatiõis ſcḋi argumēti preallegati:
igr̄ īcipit illud īfinite tarde augeri in ꝑtibꝰ īparibꝰ
11Confir-
matio. ¶ Confirmat̄̄. Q2 ſi illn poſito eſſet vera ſeq̇ret̄̄ /
nullū quadratū ꝑfectū poſſet vniformiṫ diminui
ad nõ quãtū qñ trina eiꝰ dimēſio puta lõgitudo la
titudo et ꝓfūditas vniformiṫ a nõ quãto diminuūt̄̄ /
ſed ↄ̨ñs eſt flm̄ / q2 nõ videt̄̄ repugnare tale quadra
tū vniformiter ſic diminui ad nõ quantū: igit̄̄ illud
ex quo ſequit̄̄. Sequela tñ ꝓbatur: quia ſi aliquod
ſic poteſt diminui detur aliquod quadratū pedalr̄
lõgū, pedaliṫ latū, pedaliṫ ꝓfūdū, qḋ ſit a. Tūc ar̄
ſic / ↄ̨tinuo lõgitudo latitudo et ēt ꝓfūditas huiꝰ q̈-
drati a. vniformiṫ ī hora diminuit̄̄ vſ ad nõ ̄tū:
igr̄ in ṗma ꝑte ꝓportiõali hore ꝓportiõe dupla il-
lud q̈dratū efficit̄̄ in duplo minꝰ logū ī duplo minꝰ
latū. in duplo minꝰ ꝓfundū: et ſic ꝑ ↄ̨ñs efficit̄̄ ī octu
plo minꝰ: et ꝑ ↄ̨ñs in ṗma medietate ꝑdit ſeptē octa
uas: et in ſcḋa medietate vnã tm̄: et ꝑ ↄ̨ñs in illa hõ
cõtinuo diminuit̄̄ vniformiṫ / qḋ fuit probandū