Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.002071">
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              ctionem, quæ erit portio maximi circuli, per 6. Theodoſij, cum planum ſe­
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              cans hemiſphærium, tranſeat per
                <expan abbr="centrũ">centrum</expan>
              ipſius, quæ ſectio, ſiue circuli por­
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              tio repræſentatur in figura, per ſemicirculum in quo A, ſiue in quo G A M­
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              R O. nihil autem refert quodcunque intelligas planum ſuper axem G K O,
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              tranſiens ſiue per triangulum G K M, ſiue per aliud illi ſimile. </s>
              <s id="s.002072">Præmitten­
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              dum præterea non poſſe in ſemicirculo ſuperiori, quod eſt planum, & ſectio
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              trianguli G K M, poni alias duas lineas. </s>
              <s id="s.002073">v. g. G R, K R, ad aliud punctum,
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              vti eſt R, quæ habeant eandem inuicem proportionem, quam habent prio­
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              res duæ G M, K M, quod probatur, quia ſi ſint vt G M, ad K M, ita G R, ad
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              K R, cum G R, ſit centro K, propinquior quam G M, erit etiam eadem G R,
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              longior ipſa G M, per 15. 3. & tamen deberet eſſe æqualis illi; quemadmo­
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              dum K M, eſt æqualis alteri K R; nequeunt autem duæ lineæ inæquales inui­
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              cem, habere eandem rationem ad duas inuicem æquales: ergo non habent
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              eandem rationem G M, & K M, quam habent G R, & K R. quod ſi punctum
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              R, ſumatur ſupra M, erit ſimilis
                <expan abbr="demõſtratio">demonſtratio</expan>
              , ſi literæ M, & R, loca permu­
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              tent. </s>
              <s id="s.002074">his poſitis, ait
                <emph type="italics"/>
              (Quoniam enim G, K, puncta data ſunt, & c.)
                <emph.end type="italics"/>
              ideſt data
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              ſunt poſitione, cum notum ſit vbi ſint. </s>
              <s id="s.002075">G, enim eſt in ortu. </s>
              <s id="s.002076">K, verò in centro
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              horizontis, ſequitur, quod etiam linea G K, cuius ipſa ſunt extrema, data
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              ſit, & poſitione, & magnitudine, per 26. Datorum Euclidis. </s>
              <s id="s.002077">eadem quoque
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              ratione data erit K M, linea; ſiue quia eſt æqualis ipſi G K, ſiue quia per
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              aſtrolabium poſſumus ipſius longitudinem, & poſitionem inueſtigare; qua­
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              re & punctum M, datum erit per 27. Datorum, quare & linea G M, data
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              erit quoad ſitum, & magnitudinem per 26. Datorum. </s>
              <s id="s.002078">Quare per primam
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              Datorum erit data proportio linearum G M, M K, punctum
                <expan abbr="itaq;">itaque</expan>
              M, tanget
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              ambitum datum, qui baſis eſt coni, quem linea K M, deſcribit in reuolutio­
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              ne axis G K O, ſuper polis G, O. cum enim data ſit K M, poſitu, & magni­
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              tudine,
                <expan abbr="eaq́">eaque</expan>
              ; ſit latus prædicti coni, ſequitur periphæriam, vel ambitum ba­
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              ſis coni eſſe datum per ſimilem definitionem 5. definitioni Datorum. </s>
              <s id="s.002079">ſit
                <expan abbr="au-tẽ">au­
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                tem</expan>
              ambitus ille in figura ſequenti notatus literis L M N. qui ambitus L M N,
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              non eſt
                <expan abbr="concipiẽdus">concipiendus</expan>
              in eodem plano ſemicirculi G A N O, quemadmodum
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              falsò pingitur in figura; ſed debemus ipſum concipere tanquam erectum ad
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              angulos rectos cum prædicto ſemicirculo, necnon cum horizonte G K O.
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              </s>
              <s id="s.002080">Iam ſi
                <expan abbr="triãgulum">triangulum</expan>
              G M K, prioris figuræ circumuoluatur circa axem G K O,
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              punctum ipſius M, deſcribit prædictum ambitum L M N. hunc ambitum
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              inquit Ariſtot. linea K M, attinget,
                <expan abbr="eritq́">eritque</expan>
              ; hic ambitus datus, vt dictum eſt.
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                <figure id="id.009.01.118.1.jpg" place="text" xlink:href="009/01/118/1.jpg" number="60"/>
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              Erit præterea ſectio circunferentiarum ho­
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              rizontis, & huius ambitus data, cuius extre­
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              ma puncta eſſent L, & N. ſi enim
                <expan abbr="cõcipiamus">concipiamus</expan>
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              in figura non ſolum horizontis diametrum
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              G K O, ſed etiam circunferentiam (in qua
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              circunferentia eſſent duo illa puncta L, & N,
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              vt in præſenti deſcriptione melius intellige­
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              tur, in qua horizon G N O L, & ambitus
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              prædictus eſt L M N, qui debet intelligi ele­
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              uatus ſupra horizontem perpendiculariter)
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              tunc ſectio ipſius mutua cum horizonte eſſet </s>
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