Biancani, Giuseppe, Aristotelis loca mathematica, 1615

Table of figures

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              <s id="s.001000">
                <pb pagenum="55" xlink:href="009/01/055.jpg"/>
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              principijs huius)
                <emph.end type="italics"/>
              affert nunc exemplum alterius demonſtrationis, quæ non
                <lb/>
              ex communibus, vt præcedens Bryſonis, ſed ex proprijs principijs oſtendit
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              affectionem de ſubiecto proprio. </s>
              <s id="s.001001">Eſt autem illud exemplum toties decan­
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              tatum de triangulo habente tres angulos æquales duobus rectis angulis; id­
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              circo operæpretium eſſe puto explicare demonſtrationem, 32. primi Eucli­
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              dis, quæ iſtud ex proprijs principijs demonſtrat, & quam hoc loco Ariſto­
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              teles innuit, hoc enim modo ipſius Ariſt. mentem probè penetrare poteri­
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                <figure id="id.009.01.055.1.jpg" place="text" xlink:href="009/01/055/1.jpg" number="27"/>
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              mus. </s>
              <s id="s.001002">ſit ergo
                <expan abbr="triãgulum">triangulum</expan>
              A B C. </s>
              <s id="s.001003">Dico ag­
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              gregatum
                <expan abbr="triũ">trium</expan>
              ipſius angulorum A, B, C,
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              eſſe æquale aggregato ex duobus angu­
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              lis rectis (vt autem melius intelligas, quæ
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              ſequuntur, lege prius ea, quæ dicta ſunt
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              in lib. 1. Priorum ſecto 3. cap. 1.) produ­
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              catur latus B C,
                <expan abbr="vſq;">vſque</expan>
              in D, vt fiat angulus
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              externus A C D; Iam ſic, quoniam
                <expan abbr="pro-batũ">pro­
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                batum</expan>
              eſt in 13. primi, duos angulos, quos
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              facit linea A C, cum linea B D, ſcilicet angulos A C B, A C D, eſſe pares
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              duobus rectis: & quia pariter in prima parte huius propoſ. </s>
              <s id="s.001004">32. probatum
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              eſt ab Euclide duos angulos A B, eſſe æquales externo angulo A C D: ſi ter­
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              tius angulus reliquus A C B, ſumatur bis, ſemel cum duobus angulis A, B,
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              & ſemel cum externo A C D,
                <expan abbr="addẽtur">addentur</expan>
              æqualia æqualibus, & propterea tres
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              anguli A, B, A C B, ſimul ſumpti, erunt æquales duobus A C D, A C B, ſimul
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              ſumptis; ſed his duobus ſunt æquales duo recti, ergo cum quæ ſunt æqualia
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              vni tertio, ſint etiam æqualia inuicem, erit aggregatum trium angulorum
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              A, B, A C B, æquale aggregato duorum rectorum; quod erat demonſtran­
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              dum. </s>
              <s id="s.001005">Medium
                <expan abbr="itaq;">itaque</expan>
              huius demonſtrationis, ſi res ad trutinam Logicam ex­
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              pendatur, eſt, quod partes aggregati
                <expan abbr="triũ">trium</expan>
                <expan abbr="angulorũ">angulorum</expan>
              A, B, A C B, ſunt æqua­
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              les partibus aggregati
                <expan abbr="duorũ">duorum</expan>
              , & ideo
                <expan abbr="aggregatũ">aggregatum</expan>
              , aggregato æqua­
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              le eſt. </s>
              <s id="s.001006">quod medium eſt in genere cauſæ materialis. </s>
              <s id="s.001007">quod verò partes illius
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              ſint æquales partibus huius, probatur, per dignitatem
                <expan abbr="illã">illam</expan>
              , quæ ſunt æqualia
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              vni tertio, ſunt etiam inter ſe. </s>
              <s id="s.001008">partes porrò aggregati trium angulorum
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              erant hæ, anguli A, B, vna; altera verò angulus A C B; partes verò aggre­
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              gati duorum rectorum erant A C B, A C D, quibus partibus, illæ ſunt æqua­
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              les, & ideo totum toti æquale. </s>
              <s id="s.001009">quod medium eſt omnino intrinſecum, & ex
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              proprijs ipſius trianguli, ſiue ex proprijs angulorum ipſius, cum ſint ipſius
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              partes. </s>
              <s id="s.001010">quod pariter medium ex parte paſſionis, quæ demonſtratur, eſt ex
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              proprijs, cum ſint partes illius materiales. </s>
              <s id="s.001011">per materiam autem oportet
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              hoc loco intelligere materiam intelligibilem, ideſt quantitatem à qualita­
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              tibus abſtractam, & terminatam, de qua pluribus agemus infra in tractatu
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              de natura mathematicarum. </s>
              <s id="s.001012">Hinc videas eos magnopere decipi, qui pu­
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              tant, hanc demonſtrationem eſſe per extrinſeca, eò quod ad demonſtran­
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              dum producatur linea B C, in D, putantes lineam illam productam C D,
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              eſſe demonſtrationis medium; lineæ
                <expan abbr="namq;">namque</expan>
              huiuſmodi, quæ in demonſtra­
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              tionibus geometricis conſtruuntur, nunquam ſunt media propria demon­
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              ſtrationum, ſed tantummodo aſſumuntur ad probandum medium iam ex­
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              cogitatum eſſe veram cauſam concluſionis. </s>
              <s id="s.001013">Hinc etiam manifeſtè colligas </s>
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