Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

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                <pb o="400" rhead="IO. BAPT. BENED." n="412" file="0412" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0412"/>
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                  <s xml:id="echoid-s4727" xml:space="preserve">Hic
                    <reg norm="animaduertendum" type="context">animaduertendũ</reg>
                  eſt omnes interpretes falli, qui hoc loco Platonem de omni-
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                  bus proportionalitatibus continuis quæ ternario numero (alia enim Arithmetica,
                    <lb/>
                  alia geometrica, alia harmonica dicitur) continentur, intelligendum eſſe cenſent,
                    <lb/>
                  quia de numeris, magnitudinibus,
                    <reg norm="viribusque" type="simple">viribusq́;</reg>
                  , aut ut dici ſolet, virtutibus mentionem
                    <lb/>
                  fecerit. </s>
                  <s xml:id="echoid-s4728" xml:space="preserve">Plato enim nihil aliud inferre voluit, quam eandem paſſionem (ut ipſe reci-
                    <lb/>
                  tat) inter medium
                    <reg norm="extremaque" type="simple">extremaq́;</reg>
                  vnius proportionalitatis continuæ geometricæ, tam
                    <lb/>
                  in quantitate, quam in qualitate
                    <reg norm="reſultaturam" type="context">reſultaturã</reg>
                  , cum tres termini eiuſdem eſſent ſpe-
                    <lb/>
                  ciei, & quia quantitas in duas principes
                    <reg norm="primariasque" type="simple">primariasq́;</reg>
                  partes, ideſt in continuam, &
                    <lb/>
                  diſcretam diuiditur, hanc ob cauſam Plato hoc præcipuè ſignificat numerorum ma-
                    <lb/>
                    <reg norm="gnitudinisque" type="simple">gnitudinisq́;</reg>
                  vocabulis vtens, quibus vniuerſum quantitatis genus complectitur.</s>
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                <p>
                  <s xml:id="echoid-s4729" xml:space="preserve">Cum verò ait vires, uniuerſum qualitatis genus inferre uult. </s>
                  <s xml:id="echoid-s4730" xml:space="preserve">Quia proportio &
                    <lb/>
                  proportionalitas tam continua quam diſcreta, non ſolum interterminos quanti, ſed
                    <lb/>
                  inter eos etiam qui quali attribuuntur elucet.</s>
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                <p>
                  <s xml:id="echoid-s4731" xml:space="preserve">Sed quod eo loco de harmonica proportionalitate quæ
                    <reg norm="cum" type="context">cũ</reg>
                  geometrica magis ſim
                    <lb/>
                  bola eſt quam cum Arithmetica Plato minime intelligat, ex eiuſdem uerbis cum ita
                    <lb/>
                  ſcribit manifeſtè patet.</s>
                </p>
                <quote>
                  <s xml:id="echoid-s4732" xml:space="preserve">Quando enim medium ita ſe habet ad poſtremum ut primum ad medium,
                    <reg norm="uiciſ- ſimque" type="simple">uiciſ-
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                    ſimq́;</reg>
                  ut poſtremum cum medio ita medium cum primo congruit.</s>
                </quote>
                <p>
                  <s xml:id="echoid-s4733" xml:space="preserve">Id enim in harmonica proportionalitate non cernitur in qua primus terminus ad
                    <lb/>
                  poſtremum, & non ad medium, ita ſe habet geometricè ut differentia inter primum
                    <lb/>
                  & medium ad differentiam inter medium & ultimum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4734" xml:space="preserve">Quod ſi clarum eſt ipſum de harmonica proportionalitate nullo modo intellige-
                    <lb/>
                  re, quanto minus de Arithmetica, quæ cum geometrica nihil habet commune.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4735" xml:space="preserve">Cum uerò Plato ait.</s>
                </p>
                <quote>
                  <s xml:id="echoid-s4736" xml:space="preserve">Tunc quod medium eſt & primum fit & poſtremum, poſtremum quoque, & pri-
                    <lb/>
                  mum media fiunt,
                    <reg norm="&c." type="unresolved">&c.</reg>
                  </s>
                </quote>
                <p>
                  <s xml:id="echoid-s4737" xml:space="preserve">Nihil aliud oſtendere uult, quam ſimilitudinem quæ inter huiuſmodi medium &
                    <lb/>
                  extrema intercedit, cum ipſum medium ad poſtremum, quem primus ad ſeipſum,
                    <lb/>
                  eundem reſpectum habeat, in quo eſt ſimilis primo, & contra ad primum
                    <reg norm="terminum" type="context">terminũ</reg>
                  ,
                    <lb/>
                  eundem reſpectum, quem poſtremum ad ſeipſum habet, </s>
                  <s xml:id="echoid-s4738" xml:space="preserve">unde hac ratione ultimum
                    <lb/>
                  repręſentat, uolens Plato inferre de conuenientia quę inter media elementa, & ex-
                    <lb/>
                  trema intercedit, ut aquæ inter aerem, & terram, cum aqua, ratione ſuæ frigiditatis,
                    <lb/>
                  terrę, ratione uero ſuæ humiditatis aeri ſimilis euadat. </s>
                  <s xml:id="echoid-s4739" xml:space="preserve">Aer uero qui inter ignem,
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                  ponitur quod ad caliditatem attinet cum igne, quod uero ad humidita-
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                  tem ſpectat cum aqua communicet.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4740" xml:space="preserve">Sed quia Plato multis in rebus doctrinam Pythagoricam ſequutus eſt, Pythago-
                    <lb/>
                  rici aut em omnia numeris metiebantur, & de omnire ſecundum numerorum ratio
                    <lb/>
                  nem diſſerebant,
                    <reg norm="uidensque" type="simple">uidensq́;</reg>
                  Plato quod inter duos numeros ſuperficiales,
                    <reg norm="inuicemque" type="simple">inuicemq́;</reg>
                    <lb/>
                  ſimiles exiſtentes, unum tantum numerum medium in proportionalitate continua
                    <lb/>
                  geometrica cadere poteſt, ideo ſubiungit.</s>
                </p>
                <quote>
                  <s xml:id="echoid-s4741" xml:space="preserve">Quod ſi uniuerſi corpus latitudinem habere debuiſſet, nullam uerò profundita-
                    <lb/>
                  tem, unum ſanè, tum ad ſeipſum, tum ad extrema uincienda interiectum medium
                    <lb/>
                  ſuffeciſſet.</s>
                </quote>
                <p>
                  <s xml:id="echoid-s4742" xml:space="preserve">Sequitur poſtea ſic.</s>
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                <quote>
                  <s xml:id="echoid-s4743" xml:space="preserve">Sed cum ſoliditatem mundus requireret, ſolida uerò non uno, ſed duobus ſem-
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                  per modis copulentur, inter ignem, & terram, Deus, Aerem, Aquamq́ue loca-
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                  uit,
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                  </s>
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