Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Inductionis gradus ſūmi ↄ̨̨ſideratio.
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tū alteratū extrēo rēiſſiori taĺ latitudīs vni. dif. tūc
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dico / ī a. tardiꝰ īducet̄̄ g̈dꝰ ſū: ꝙ̄ in b. / qḋ ſic ꝓbr̄ / q2
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eq̄ cito erit g̈. ſū. īductꝰ ꝑ totū a. ſic ꝑ totū b. / q2 eq̄ ci
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to erit īductꝰ ad vtriuſ extrēa rēiſſiora q̄ a prīci
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pio ſū eq̈lia: et eq̄uelociṫ ↄ̨tinuo alterãt̄̄. </
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<
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xml:space
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ↄ̨tinuo citiꝰ deueīet ad qḋlꝫ pūctū a. ꝙ̄ ad ↄ̨ſimile
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ī b. q2 qḋlꝫ tale pūctū eſt eq̄ īteſū ī a: ſic in b. et in a
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ↄ̨tinuo velo. altera. / vt ↄ̨ſtat. </
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<
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">igr̄ ↄ̨tinuo mīor pars
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ipſiꝰ a. reſtabit ꝑtrãſeūda ab ipſo g̈. ſū. in a ꝙ̄ in b
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</
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<
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xml:space
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">Et eq̄ cito veīet ad finē g̈. ſū. ī vtro. </
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<
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ducet̄̄ g̈. ſū. ī a. ꝙ̄ in b. / qḋ fuit ꝓbãdū.
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">¶ Dices et bñ
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ↄ̨cedēdo ſeq̄lã vt bñ ꝓbat argu. </
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ↄ̨ñtis. </
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<
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xml:space
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">īmo q2 per
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totū ꝑ qḋ altera. </
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<
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<
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velociꝰ ꝙ̄ b. / iõ tardiꝰ inducet̄̄ in eo gra ſū. ̄. in b.</
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">Q2 tūc ſe
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q̄ret̄̄ / ſi a. alteret̄̄
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lati. vni. di. ab .8. vſ ad .4. tardiꝰ in q̊lꝫ totali tꝑe
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terīto ad finē tꝑis īduceret̄̄ ī a. g̈. ſū. ꝙ̄ īduceret̄̄ ī ta
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li tꝑe ſi a. alṫaret̄̄ lati. vni. di. ab: 6. vſ ad .4. </
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ↄ̨ñs ē flm̄ / igr̄ illḋ ex q̊ ſeq̇t̄̄ </
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">Seq̄la. </
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">ſatꝪ ptꝫ ex deducti
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one argumēti. </
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">q2 tūc ſeq̄ret̄̄ / ſi
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eſſēt īfinita oīo ↄ̨ſiĺr diſpoſita ſiċ a. </
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">Et ṗmū īciꝑet
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alṫari lati. vni. di. ab 8. vſ ad .4. </
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">Et .2. lati. ab: 16
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vſ ad 4. </
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">Et .3. lati. ab .32. vſ ad 4. / et ſic ↄ̨ñr dupli
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cãdo ſꝑ extremū ītēſiꝰ manēte ſꝑ eodē extrēo rēiſſi
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ore ſꝰ extremū rēiſſiꝰ ſubiecti. </
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">Infinitū tarde īdu
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cet̄̄ g̈. ſū. ī aliqḋ iſtoꝝ </
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</
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">Seq̈la ꝓbr̄ / q2 īmediate pꝰ h° īfinitū mīor erit ꝑs
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rēiſſa alicuiꝰ illoꝝ ꝙ̄ ipſiꝰ b. ꝑ qḋ vni. īducit̄̄ g̈. ſū:
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</
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">Et nõ citiꝰ deueniet g̈. ſū. ad finē alicuꝰ illaꝝ ꝙ̄ ad fi
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nē ipſiꝰ b. / g̊ infinitū tarde īducet̄̄ g̈. ſū. ī aliqḋ illoꝝ
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̄ ī b. / et ꝑ ↄ̨ñs īfinitū tarde īducet̄̄ ī aliqḋ illoꝝ </
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">(Cū ī
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b. īducat̄̄ vīfor̄ṫ) / qḋ fuit ꝓbãdū </
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tur / q2 tūc ſeq̄ret̄̄ / ītēſio alṫatiõis ꝑ partē remiſſã
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per quam debet induci gra. ſum. eſſet impedimēto
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inductioni gra. ſū. / quod apparet manifeſte falſuꝫ</
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">Tertio prīcipalr̄ ar̄ ſic </
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">Si q̄ſtio eſſet
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a ſeq̄ret̄̄ / mediãte īfinita lati. alṫa niſi diffor̄e
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ſubiectū finitū terīatū ad ſū. vni. ↄ̨tinuo īduceret̄̄ g̈
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ſū </
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a pedale diuiſū ꝑ ꝑtas ꝓportõales ꝓportõe dupla
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et ṗma ſit vni. di. a ſū. vſ ad 4. </
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">Et ita intēſa et oīo
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diſpoſita ſit q̄lꝫ ſeq̄ns </
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hore alṫret̄̄ ṗma ꝑs ꝓportiõalĺ a alṫa vni. q̈ vni. īdu
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cat̄̄ g̈. ſū. ꝑ illã adeq̈te et ī .2. ꝑte tꝑis alṫet̄̄ 2. ꝑs ꝓpor
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tiõaĺ ipſiꝰ a. ꝑ totū adeq̈te alṫa vni. ī duplo maiori
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et ī .3. ꝑte tꝑis alṫre. 3. ꝑs ipſiꝰ a. alṫa: ī duplo maiori
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̄ .2. ſꝑ vni. et totã ꝑtē extēſã: et ſic ↄ̨ñr, ſꝑ duplãdo
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alṫa°nē </
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ꝓportiõe dupla, ṗma ꝑs ꝓpor°aĺ ipſiꝰ a. edē pro-
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portõe vni. efficiet̄̄ ſūma </
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">Et ī .2. tꝑis .2. ipſiꝰ a ēt effi
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ciet̄̄ ſūma vni </
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">Et ī 3. tꝑis .3. ip̄iꝰ a. / et ſic ↄ̨des;ñr / igr̄ ꝑ ip̄m
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a. ↄ̨tinuo īducet̄̄ g̈. ſū ↄ̨ña pꝫ et ꝓbr̄ añs. </
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īducit̄̄ g̈. ſū. ī ṗma ꝑte tꝑis vt poīt caſꝰ et q2 ī 2. ꝑte
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tꝑis 2. ꝑs ꝓpor°aĺ ip̄iꝰ a. alṫat̄̄ alṫa°ne ī du. maio
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re ꝑ totū vni. iõ ip̄a ī .2. ꝑte tꝑis fiet ſū. vni </
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ciſe alṫet̄̄ g̈du q̊ ṗma ip̄a ī tãto tꝑe ī quãto ṗma effi
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ceret̄̄ ſū. / ſꝫ mõ alṫat̄̄ ī duplo maiori alṫa°ne. </
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<
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plo mīori tꝑe efficiet̄̄ ſū. / et ꝑ ↄ̨ñs ī .2. ꝑte ꝓportiõali
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tꝑis. </
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<
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fĺitatē ↄ̨ñtꝪ / q2 tūc ſeq̄ret̄̄ / b. ē oīo ↄ̨ſiĺr dipoſitū et
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ēt eq̈le ip̄i a. et a. īfinita alṫa°ne alṫabr̄ / vt iã dictū ē
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</
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īducet̄̄ g̈. ſū. et ī a. vni. / vt dictū &etilde; </
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alṫa°ē īfinita / g̊ ꝑ nullã illaꝝ d3 g̈. ſū. ī īfinitū tarḋ
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īduci </
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">Sꝫ ꝓbo ſeq̄lã et ſi a tale q̈le iã poſitū ē et eo° ī
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illḋ īducat̄̄ g̈. ſū. / vt iã dictū ē: et ſit b. oīo eq̈le ↄ̨ſiĺ. </
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<
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Inductionis gradus ſūmi ↄ̨̨ſideratio.
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ſpoſitū ſiċ a. et qñ ṗma ꝑs ꝓportõaĺ a. ꝓpor°ne du
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pla effict̄̄ ſūma. </
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<
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<
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">et ṗme ip̄iꝰ b. puta ṗma et .2
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ſõme et qñ .2. ip̄iꝰ a. due ſeq̄ntes īmediate .2. ip̄iꝰ b. / et
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ſic ↄ̨ñr ꝓcedēdo ↄ̨tīuo ī b. ꝑ ꝑtes ꝓpor°ales ꝓpor°ne
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q̈drupla ſꝑ em̄ .2. ꝑtes īmediate ꝓportõe dupla ſūt
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vna ꝑs ꝓportõe q̈drupla / vt pꝫ ex .2 ꝑte </
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auxilio eoꝝ q̄ dicta ſṫ .3.c.2. tractatꝰ ſeq̇t̄̄ qḋ īferre ī
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tēdebã. </
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tē ↄ̨ñtꝪ et cū ꝓbr̄ ↄ̨cedo qḋ īfert̄̄ nec illḋ ē īcõueniēs ſꝫ
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veꝝ. </
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<
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">Et cū ꝓbr̄ / nõ: q2 vtra illaꝝ alṫa°nū ē īfīta
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dico īſeq̄do Cal. ↄ̨cedo añs: et negãdo ↄ̨ñaꝫ q2 coex
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tēſio ꝑtibꝰ tꝑis variat effectū motꝰ / vt pꝫ ex 3.c p̄alle</
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</
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<
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">Q2 tūc ſeq̄ret̄̄ / in a. pedale
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vni. dif. terīatū ad ſū. īduceret̄̄ g̈. ſū. vni. mediãte īfini
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ta lati. alṫatõs ꝑ totū extēſa extrēo īfini° ſꝰ extre
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mū ip̄iꝰ a. terīto </
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<
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">Sꝫ ↄ̨ñs vr̄ flm̄ / igr̄ illḋ ex q̊ ſeq̇t̄̄ </
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<
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">Se
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q̄la ꝓbr̄ / et ſit ī a. vni. dif. ad ſū. terīatū et capio lati.
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q̈ q̇lꝫ pūctꝰ nõ ſūmꝰ excedit̄̄ a ſūmo et diuido q̈lꝫ il
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laꝝ ꝑ ſuas ꝑtes ꝓpor°ales ꝓportõe dupla / et pono /
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ī ea ꝓportõe q̇lꝫ pūctꝰ nõ ſūmꝰ acq̇rat lati. ꝑ quã di
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ſtat a ſūmo ī mīori tꝑe īq̈ taĺ pūctꝰ magꝪ duīuta ſū
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</
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lb
/>
drupla et ī q̈lꝫ tali ꝑte acq̇rat pūctꝰ de illi lati. vnã
<
lb
/>
ꝑtē corrñdētē. </
s
>
<
s
xml:id
="
N2CBB9
"
xml:space
="
preserve
">Quo poſito ſeq̇t̄̄ facile illḋ / qḋ fuit ī
<
lb
/>
ferēdū auxilio 3.c. p̄allegati. </
s
>
<
s
xml:id
="
N2CBBE
"
xml:space
="
preserve
">ↄ̨tīuo em̄ / vt pꝫ ex caſu
<
lb
/>
vniformiter inducet̄̄ gru. ſū. </
s
>
<
s
xml:id
="
N2CBC3
"
xml:space
="
preserve
">Et tñ ↄ̨tīuo alteratio
<
lb
/>
terminabr̄ ad extremū infinitū ꝓpo. gra. ſū. / igitur</
s
>
</
p
>
<
p
xml:id
="
N2CBC8
">
<
s
xml:id
="
N2CBC9
"
xml:space
="
preserve
">Quarto prīcipaliṫ ar̄ ſic </
s
>
<
s
xml:id
="
N2CBCC
"
xml:space
="
preserve
">Seq̄ret̄̄ / vt iã
<
lb
/>
dictū ē īductõeꝫ g̈ ſū. debē attēdi penes ſubcm̄ ꝑ qḋ
<
lb
/>
īducit̄̄ g̈: ſū. / ſꝫ ↄ̨ñs ē flm̄: igr̄ illḋ ex q̊ ſeq̇t̄̄ ſeq̄la pꝫ et
<
lb
/>
fĺitas ↄ̨ñtꝪ ꝓbr̄ et pono / ꝙ̄ ꝑ .a pedale vni. di. terīatū
<
lb
/>
ad ſū. īducat̄̄ lati. alṫatiõs vni. ꝑ totū: et cū h° rarefi
<
lb
/>
at a ad duplū ī gö ſꝰ g̈. ſū. q̇eſcēte extrēo eiꝰ rēiſſio
<
lb
/>
ri / qḋ fiat ſū. ī hõ. </
s
>
<
s
xml:id
="
N2CBDB
"
xml:space
="
preserve
">Quo poſito ar̄ ſic: ſi vĺocitas īdu
<
lb
/>
ctiõs g̈. ſū. dēret attēdi penes ſubiectū ī qḋ īducit̄̄ g̈.
<
lb
/>
ſū. / tūc ſeq̄ret̄̄ / ī a ī caſu poſito ī duplo vĺociꝰ īdu
<
lb
/>
ceret̄̄ g̈. ſū: ꝙ̄ ſi ñ rarefiēt / ſꝫ ↄ̨ña ē flm / igr̄ illḋ ex q̊ ſe
<
lb
/>
q̇t̄̄ ſeq̄la ꝓbr̄ / q2 a ī fine erit ꝑ totū ſū. / vt pꝫ ex caſu et
<
lb
/>
erit ī duplo maiꝰ ꝙ̄ ſi ñ fuiſſꝫ rarefa° ex caſu / igr̄ ꝑ ī
<
lb
/>
duplo maiꝰ ſbcm̄ ꝓgrediebat̄̄ g̈. ſū. ꝙ̄ ſi ñ fuiſſꝫ fctã
<
lb
/>
rarefa° et ꝑ ↄ̨ñs ī duplo vĺociꝰ īducit̄̄ g̈. ſū. ꝙ̄ ſi ñ ra
<
lb
/>
refiēt / qḋ fuit ꝓbãdū. </
s
>
<
s
xml:id
="
N2CBEE
"
xml:space
="
preserve
">iã ꝓbr̄ fĺitas ↄ̨ñtꝪ / q2 ſi h° eſſet
<
lb
/>
veꝝ ſeq̄ret̄̄ / ī caſu mõeret̄̄ g̈. ſū. ſiue eiꝰ ī dn° p̄ciſe ꝑ
<
lb
/>
pedale et tñ ī īfinitū vĺociṫ īduceret̄̄: ſꝫ ↄ̨ñs ē fĺ3. </
s
>
<
s
xml:id
="
N2CBF5
"
xml:space
="
preserve
">igr̄
<
lb
/>
illḋ q̊ ſeq̇t̄̄ </
s
>
<
s
xml:id
="
N2CBFA
"
xml:space
="
preserve
">Seq̄la ꝓbr̄: et pono / ī a. pedale vni. di.
<
lb
/>
terīato ad ſū. īducat̄̄ g̈. ſū. et nū̄ rarefiat ꝑs aliq̈ q̊
<
lb
/>
uſ fuerit ſū. ſꝫ. cū fuerit ſū. ī īfinitū rarefiat </
s
>
<
s
xml:id
="
N2CC01
"
xml:space
="
preserve
">Quo
<
lb
/>
põito mãifeſtū ē g̈. ſū. ñ mouet̄̄ niſi ad pedalē di-
<
lb
/>
ſtãtiã et tñ ī īfinitū velĺr īducit̄̄: qm̄ ī fine ſbm̄ eiꝰ qḋ
<
lb
/>
ē īductꝰ īfinitū vĺ ſaltē ī īfinitū magnū fuit ī hõ / igr̄
<
lb
/>
ī illa hõ ī īfinitū velĺr īducit̄̄ g̈. ſū </
s
>
<
s
xml:id
="
N2CC0C
"
xml:space
="
preserve
">Et tñ pedalē diſtã
<
lb
/>
tiã p̄ciſe ꝑtrãſit.
<
note
position
="
right
"
xlink:href
="
note-0278-02a
"
xlink:label
="
note-0278-02
"
xml:id
="
N2CC35
"
xml:space
="
preserve
">Dicitur.</
note
>
</
s
>
<
s
xml:id
="
N2CC16
"
xml:space
="
preserve
">¶ Dices et bñ ↄ̨cedēdo ſeq̄lã. </
s
>
<
s
xml:id
="
N2CC19
"
xml:space
="
preserve
">et ne-
<
lb
/>
gãdo falcitatē ↄ̨ñtꝪ: et ad ꝓbationē adīſſo caſu ne
<
lb
/>
gãdo ſeq̄lã et rõ ē: q2 velocitas īductiõis gra. ſum.
<
lb
/>
in ſubiecto q̇eſcēte motu rarefactionis et ↄ̨dēſatio
<
lb
/>
nis deb3 attēdi penes ſubiecttuꝫ ī quod īducit̄̄ ita
<
lb
/>
in ea ꝓportione in qua eſt maius ceteris paribꝰ
<
lb
/>
in ea in illud velociꝰ gra. ſum. īducit̄̄. </
s
>
<
s
xml:id
="
N2CC28
"
xml:space
="
preserve
">Sꝫ occurren
<
lb
/>
te aliq̊ motu deb3 attēdi penes ſpaciuꝫ fixus quod
<
lb
/>
deſcribit talis g̈. ſum. cū īducit̄̄ / vt dictū eſt ſuperiꝰ
<
lb
/>
2. tractatu. c.4. de velocitate motus mixti vide ibi.</
s
>
</
p
>
<
p
xml:id
="
N2CC3B
">
<
s
xml:id
="
N2CC3C
"
xml:space
="
preserve
">Sed cõtra </
s
>
<
s
xml:id
="
N2CC3F
"
xml:space
="
preserve
">Q2 ſi illa ſolutio eſſet bo-
<
lb
/>
na ſequeret̄̄ ꝙ̄ quãdocū ſubiectum rarefit ſus
<
lb
/>
gradum ſū. cõtinuo gradꝰ ſūmꝰ tardiꝰ inducitur
<
lb
/>
̄ ſi nõ rarefieret ſubiectū: ſed cõſequens eſt falſuꝫ /
<
lb
/>
igitur illud ex quo ſequit̄̄: ſequela probatur et po-
<
lb
/>
no / a. pedale vnifor. diffor. terminū ad ſūmū </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>