Vitruvius
,
De architectura libri decem
,
1567
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514.01.214
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214
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LIBER
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tus ſuauitatem: </
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<
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xml:id
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xml:space
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">uel ratione maioris, et abſolutæ conſonantiæ, quæ cæteras continet. </
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>
<
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xml:id
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xml:space
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">Veræ igitur cõſonantiæ, aut
<
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ſimplices ſunt, aut cõpoſitæ. </
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>
<
s
xml:id
="
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xml:space
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">Simplices ſunt tres, diateſſaron proportione ſeſquitertia conſtans, diapente quæ ſeſ-
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quialtera cõparatione eſſicitur, diapaſon dupla ratione confecta. </
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>
<
s
xml:id
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xml:space
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">Cõpoſitæ ſunt diapaſon diapente, diapaſon dia
<
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teſſaron, diſdiapaſon. </
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>
<
s
xml:id
="
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xml:space
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">Nunc ſingulæ declarabuntur. </
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>
<
s
xml:id
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xml:space
="
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">Diateſſaron concentus a noſtris quarta dicitur. </
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>
<
s
xml:id
="
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xml:space
="
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">Constat to
<
lb
/>
nis duob. </
s
>
<
s
xml:id
="
echoid-s13998
"
xml:space
="
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">et hemitonio minori, ſeſquitertia ſcilicet proportione conſtans. </
s
>
<
s
xml:id
="
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xml:space
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">Diapente dicitur quinta, quoniã quem-
<
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admodũ diateſſaron, ideſt quarta, ſcandit a linea ad ſecundum ſpatium, uel a ſpatio ad ſecundã lineã, quatuor uo
<
lb
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cis gradus amplectens. </
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>
<
s
xml:id
="
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xml:space
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">Ita diapente ſcandit a qualibet linea ad tertiã, & </
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">a quolibet ſpatio ad tertium per quin-
<
lb
/>
que uocis gradus, poniturq́; </
s
>
<
s
xml:id
="
echoid-s14002
"
xml:space
="
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">in proportione ſeſquialtera. </
s
>
<
s
xml:id
="
echoid-s14003
"
xml:space
="
preserve
">Ideo quemadmodum in monachordo diateſſaron po-
<
lb
/>
nitur in quatuor partibus diuiſo neruo, ita diapente ponitur tripartito. </
s
>
<
s
xml:id
="
echoid-s14004
"
xml:space
="
preserve
">atque ut in ſumma dicam, quicquid ſo-
<
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<
note
position
="
left
"
xlink:label
="
note-514.01.214-01
"
xlink:href
="
note-514.01.214-01a
"
xml:space
="
preserve
">10</
note
>
num emittere potest, ſiue nernus, ſiue calamus, ſiue aliud ex qua uis materia conſtans corpus, cum uelimus
<
lb
/>
concentum ab eo reddi, neceſſe est uel magnitudines, uel ſpatia proportione illa diſtinguere, quam concentus
<
lb
/>
requirit. </
s
>
<
s
xml:id
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echoid-s14005
"
xml:space
="
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">Ita ijs regulis organorum artifices utentes, non temere, nec caſu, ut plerique faciunt, ſed linearum
<
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& </
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>
<
s
xml:id
="
echoid-s14006
"
xml:space
="
preserve
">corporum proportiones inuenientes quàm primum rem ipſam conſequuntur, nec experiundo tentant, quæ
<
lb
/>
certitudine præcognoſcunt. </
s
>
<
s
xml:id
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echoid-s14007
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xml:space
="
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">Sed nos ad rem. </
s
>
<
s
xml:id
="
echoid-s14008
"
xml:space
="
preserve
">Quemadmodum diateſſaron non progreditur uſque ad tres tonos,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s14009
"
xml:space
="
preserve
">ditonum hemitonio minori excellit, & </
s
>
<
s
xml:id
="
echoid-s14010
"
xml:space
="
preserve
">eſt amplius ſeſquitono per interuallum toni, ſexq́; </
s
>
<
s
xml:id
="
echoid-s14011
"
xml:space
="
preserve
">dieſes, & </
s
>
<
s
xml:id
="
echoid-s14012
"
xml:space
="
preserve
">duo com
<
lb
/>
mata complectitur, ita diapente trium tonorum ſpatio, & </
s
>
<
s
xml:id
="
echoid-s14013
"
xml:space
="
preserve
">dieſi una conſtat, a qua ſi tonus auferatur, diateſſa-
<
lb
/>
ron relinquitur, & </
s
>
<
s
xml:id
="
echoid-s14014
"
xml:space
="
preserve
">quarta dempta relinquitur tonus. </
s
>
<
s
xml:id
="
echoid-s14015
"
xml:space
="
preserve
">his ſtantibus, eſt, quod etiam cognoſcamus diapente mi-
<
lb
/>
norem eße octo dieſibus, & </
s
>
<
s
xml:id
="
echoid-s14016
"
xml:space
="
preserve
">conſtare ditono, & </
s
>
<
s
xml:id
="
echoid-s14017
"
xml:space
="
preserve
">ſeſquitono, & </
s
>
<
s
xml:id
="
echoid-s14018
"
xml:space
="
preserve
">diſcrimen inter diateſſaron, & </
s
>
<
s
xml:id
="
echoid-s14019
"
xml:space
="
preserve
">diapente tonus
<
lb
/>
eſt, unde ſi diateſſaron tonus addatur, fit diapente, prædictæ hæ conſonantiæ ſupraparticularibus maiori-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.214-02
"
xlink:href
="
note-514.01.214-02a
"
xml:space
="
preserve
">20</
note
>
bus proportionibus constant, quoniam nulla proportio ſupraparticularis maior est ſeſquialtera, uel ſeſ-
<
lb
/>
quitertia, quod ex earum denominationibus haberi poteſt, quemadmodum in tertio libro dictum est.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s14020
"
xml:space
="
preserve
">Præterea neque duæ diateſſaron, neque duæ diapente conſonantiam efficere poſſunt, quoniam neque in
<
lb
/>
multiplici, neque in ſupraparticulari proportione reperiuntur, in quibus diximus concentus poni, ſed pro-
<
lb
/>
portione ſunt ſuprapartienti, ex qua nullus concentus fieri potest, cuius ratio eſt. </
s
>
<
s
xml:id
="
echoid-s14021
"
xml:space
="
preserve
">Quod ſymphoniæ, concen. </
s
>
<
s
xml:id
="
echoid-s14022
"
xml:space
="
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">
<
lb
/>
tusq́; </
s
>
<
s
xml:id
="
echoid-s14023
"
xml:space
="
preserve
">in ijs uocum, & </
s
>
<
s
xml:id
="
echoid-s14024
"
xml:space
="
preserve
">ſonituum comparationibus reperiuntur, in quibus manifesta, & </
s
>
<
s
xml:id
="
echoid-s14025
"
xml:space
="
preserve
">clara est earum com-
<
lb
/>
munis menſura, quemadmodum in multiplici proportione est dupla, cuius illa pars eſt menſura, quæ inter
<
lb
/>
duos terminos pro differentia collocatur, quemadmodum inter duo, & </
s
>
<
s
xml:id
="
echoid-s14026
"
xml:space
="
preserve
">quatuor, binarius eſt utriusq́; </
s
>
<
s
xml:id
="
echoid-s14027
"
xml:space
="
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">menſura. </
s
>
<
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xml:id
="
echoid-s14028
"
xml:space
="
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">
<
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/>
Inter nouem & </
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>
<
s
xml:id
="
echoid-s14029
"
xml:space
="
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">octo unitas, & </
s
>
<
s
xml:id
="
echoid-s14030
"
xml:space
="
preserve
">in ſupraparticularibus etiam ut in ſeſquialtera inter quatuor, & </
s
>
<
s
xml:id
="
echoid-s14031
"
xml:space
="
preserve
">ſex binarius
<
lb
/>
cadit, tanquam menſura cognita utriusq; </
s
>
<
s
xml:id
="
echoid-s14032
"
xml:space
="
preserve
">termini, ita etiam inter ſex, & </
s
>
<
s
xml:id
="
echoid-s14033
"
xml:space
="
preserve
">octo, quæ ſeſquitertia proportione
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.214-03
"
xlink:href
="
note-514.01.214-03a
"
xml:space
="
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">30</
note
>
comparantur, binarius quoque communis menſura eſt utriuſque numeri, quod in ſuprapartientibus non eſt repe
<
lb
/>
rire, quemadmodum inter tria, & </
s
>
<
s
xml:id
="
echoid-s14034
"
xml:space
="
preserve
">quinque binarius non eſt menſura, neque ternarius, quomam binarius non
<
lb
/>
æquat, ternarius excellit quinarium, ſimilis ratio est in reliquis ſuprapartientibus. </
s
>
<
s
xml:id
="
echoid-s14035
"
xml:space
="
preserve
">Diapaſon a noſtris octana
<
lb
/>
dicitur, ea ponitur in dupla comparatione. </
s
>
<
s
xml:id
="
echoid-s14036
"
xml:space
="
preserve
">ita integer neruus ad dimidium comparatus diapaſon reddit. </
s
>
<
s
xml:id
="
echoid-s14037
"
xml:space
="
preserve
">Ea
<
lb
/>
autem in ſcala ordinatur ab una linea ad quartum ſpatium, uel ab uno ſpatio ad quartam lineam. </
s
>
<
s
xml:id
="
echoid-s14038
"
xml:space
="
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">Dicitur
<
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/>
diapaſon, quod per omnes concentus eat, amplectitur enim diateſſaron, & </
s
>
<
s
xml:id
="
echoid-s14039
"
xml:space
="
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">diapente, & </
s
>
<
s
xml:id
="
echoid-s14040
"
xml:space
="
preserve
">eſt terminus omnium
<
lb
/>
ſimplicium concentuum, continetur aut em interuallo maiori, quàm quinque, & </
s
>
<
s
xml:id
="
echoid-s14041
"
xml:space
="
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">minori quàm tonis. </
s
>
<
s
xml:id
="
echoid-s14042
"
xml:space
="
preserve
">Oritur a
<
lb
/>
ſeſquialtera, & </
s
>
<
s
xml:id
="
echoid-s14043
"
xml:space
="
preserve
">ſeſquitertia proportione, quemadmodum tertio libro diximus. </
s
>
<
s
xml:id
="
echoid-s14044
"
xml:space
="
preserve
">conſtat igitur quinque tonis, & </
s
>
<
s
xml:id
="
echoid-s14045
"
xml:space
="
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">
<
lb
/>
duobus hemitonijs minoribus, caditq́; </
s
>
<
s
xml:id
="
echoid-s14046
"
xml:space
="
preserve
">a ſex integris tonis commate uno. </
s
>
<
s
xml:id
="
echoid-s14047
"
xml:space
="
preserve
">Eſt autem comma illud amplius quo
<
lb
/>
apotome dieſim excellit. </
s
>
<
s
xml:id
="
echoid-s14048
"
xml:space
="
preserve
">Quod ſi a diapaſon diateſſaron auferatur, relinquitur diapente, & </
s
>
<
s
xml:id
="
echoid-s14049
"
xml:space
="
preserve
">ſi diapente tol-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.214-04
"
xlink:href
="
note-514.01.214-04a
"
xml:space
="
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">40</
note
>
las diateſſaron reliqua erit, & </
s
>
<
s
xml:id
="
echoid-s14050
"
xml:space
="
preserve
">ablato tono, & </
s
>
<
s
xml:id
="
echoid-s14051
"
xml:space
="
preserve
">diapente restat ſeſquitonus. </
s
>
<
s
xml:id
="
echoid-s14052
"
xml:space
="
preserve
">Animaduertendum uero est nul-
<
lb
/>
lam è ſimplicibus conſonantijs poſſe æque partiri certo, & </
s
>
<
s
xml:id
="
echoid-s14053
"
xml:space
="
preserve
">integro numero. </
s
>
<
s
xml:id
="
echoid-s14054
"
xml:space
="
preserve
">hoc primum in concentu diateſſa-
<
lb
/>
ron, & </
s
>
<
s
xml:id
="
echoid-s14055
"
xml:space
="
preserve
">diapente manifeſtum eſt, quoniam utraque in comparatione ſuperparticulari ponitur. </
s
>
<
s
xml:id
="
echoid-s14056
"
xml:space
="
preserve
">Simile iudicium
<
lb
/>
diapaſon habetur, nam cum eius minimi termini ſit unitas, & </
s
>
<
s
xml:id
="
echoid-s14057
"
xml:space
="
preserve
">binarium, cumq́; </
s
>
<
s
xml:id
="
echoid-s14058
"
xml:space
="
preserve
">binarius non ſit è numeris qua-
<
lb
/>
dratis, continuo ſequitur diapaſon, quod comparatione constat unius ad duo non pofſe æque partiri, nec etiam
<
lb
/>
in plures partes, quoniam in arithmeticis probatum est, quod inter duos quadratos numeros proportione re-
<
lb
/>
ſpondens medium cadit, & </
s
>
<
s
xml:id
="
echoid-s14059
"
xml:space
="
preserve
">aliàs dictum eſt, ignotas, & </
s
>
<
s
xml:id
="
echoid-s14060
"
xml:space
="
preserve
">irregulares eas rationes haberi, quæ certo, & </
s
>
<
s
xml:id
="
echoid-s14061
"
xml:space
="
preserve
">deter-
<
lb
/>
minato numero deſignari non poſſunt. </
s
>
<
s
xml:id
="
echoid-s14062
"
xml:space
="
preserve
">Cum igitur ex arithmeticis habeatur ex multiplicatione non quadra-
<
lb
/>
ti numeri in quadratum, non effici quadratum, & </
s
>
<
s
xml:id
="
echoid-s14063
"
xml:space
="
preserve
">ubihoc non datur, ibi non reperiri medium inter eos duos
<
lb
/>
numeros proportione reſpondens: </
s
>
<
s
xml:id
="
echoid-s14064
"
xml:space
="
preserve
">Sequitur nullam comparationem mediam inter multiplices reperiri. </
s
>
<
s
xml:id
="
echoid-s14065
"
xml:space
="
preserve
">cum me-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.214-05
"
xlink:href
="
note-514.01.214-05a
"
xml:space
="
preserve
">50</
note
>
dietas arithmetica nil aliud ſit, quàm uinculum extremorum ex ea comparatione, quam utrunque habet ad
<
lb
/>
medium. </
s
>
<
s
xml:id
="
echoid-s14066
"
xml:space
="
preserve
">Diateſſaron diapente eſt compoſita conſonantia, una inquam non duæ, uocaturq́; </
s
>
<
s
xml:id
="
echoid-s14067
"
xml:space
="
preserve
">a nostris undecima.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s14068
"
xml:space
="
preserve
">Alij eam non admittunt, licet ſuauiſſime ad aures perueniat, quoniam ſuprapartienti comparatione constat. </
s
>
<
s
xml:id
="
echoid-s14069
"
xml:space
="
preserve
">
<
lb
/>
Eſto a 1, & </
s
>
<
s
xml:id
="
echoid-s14070
"
xml:space
="
preserve
">b 2. </
s
>
<
s
xml:id
="
echoid-s14071
"
xml:space
="
preserve
">minimi diapaſon numeri, ſit c 4. </
s
>
<
s
xml:id
="
echoid-s14072
"
xml:space
="
preserve
">d 3. </
s
>
<
s
xml:id
="
echoid-s14073
"
xml:space
="
preserve
">minimi diateſſaron. </
s
>
<
s
xml:id
="
echoid-s14074
"
xml:space
="
preserve
">T uco c. </
s
>
<
s
xml:id
="
echoid-s14075
"
xml:space
="
preserve
">in b 4, in
<
lb
/>
2, redduntur 8, & </
s
>
<
s
xml:id
="
echoid-s14076
"
xml:space
="
preserve
">ſic e 8, duco a. </
s
>
<
s
xml:id
="
echoid-s14077
"
xml:space
="
preserve
">in d. </
s
>
<
s
xml:id
="
echoid-s14078
"
xml:space
="
preserve
">i, unum in tria, redduntur, 3, quæ ſint f, certum eſt e,
<
lb
/>
ad f, ideſt octo ad tria continere duplam, & </
s
>
<
s
xml:id
="
echoid-s14079
"
xml:space
="
preserve
">ſeſquitertiam, quoniam ſi proportio una addit ad aliam tantũ,
<
lb
/>
quantum tertia eſt ſupra quartam, ſit ut quæ erit compoſita ex prima, & </
s
>
<
s
xml:id
="
echoid-s14080
"
xml:space
="
preserve
">quarta æqualis ſit ijs, quæ ex alijs
<
lb
/>
componentur. </
s
>
<
s
xml:id
="
echoid-s14081
"
xml:space
="
preserve
">Eſto igitur ut quantum proportio inter 1. </
s
>
<
s
xml:id
="
echoid-s14082
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s14083
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s14084
"
xml:space
="
preserve
">addit ſupra 3, & </
s
>
<
s
xml:id
="
echoid-s14085
"
xml:space
="
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">4. </
s
>
<
s
xml:id
="
echoid-s14086
"
xml:space
="
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">tantum addat
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lb
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proportio inter 2. </
s
>
<
s
xml:id
="
echoid-s14087
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s14088
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s14089
"
xml:space
="
preserve
">proportioni, quæ eſt inter 8, & </
s
>
<
s
xml:id
="
echoid-s14090
"
xml:space
="
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">ſex. </
s
>
<
s
xml:id
="
echoid-s14091
"
xml:space
="
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">Dico proportionem compoſita ex 1. </
s
>
<
s
xml:id
="
echoid-s14092
"
xml:space
="
preserve
">ad
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lb
/>
2, & </
s
>
<
s
xml:id
="
echoid-s14093
"
xml:space
="
preserve
">ex ſex, ad octo fore æqualem ex alijs compoſitæ, ſcilicet 3. </
s
>
<
s
xml:id
="
echoid-s14094
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s14095
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s14096
"
xml:space
="
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">2. </
s
>
<
s
xml:id
="
echoid-s14097
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s14098
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s14099
"
xml:space
="
preserve
">ut in Arithmeticis
<
lb
/>
probatur. </
s
>
<
s
xml:id
="
echoid-s14100
"
xml:space
="
preserve
">Dico igitur e 8, non eſſe multiplicem f 3, neque ſupraparticularem eſſe eorum comparationẽ. </
s
>
<
s
xml:id
="
echoid-s14101
"
xml:space
="
preserve
">
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.214-06
"
xlink:href
="
note-514.01.214-06a
"
xml:space
="
preserve
">60</
note
>
</
s
>
</
p
>
</
div
>
</
div
>
</
text
>
</
echo
>