Biancani, Giuseppe, Aristotelis loca mathematica, 1615
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              hanc formam, dimidium duorum rectorum eſt rectus, angulus in ſemicir­
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              culo eſt dimidium duorum
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              , ergo angulus in ſemicirculo eſt rectus.
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              <s id="s.001229">vides in minori propoſitione contineri definitionem ſubiecti materialem?
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              <s id="s.001230">adeò vt hæc ſit demonſtratio omnibus numeris abſoluta per cauſam mate­
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              rialem, vt benè ſentit Ariſt. </s>
              <s id="s.001231">Reliqua ad logicum pertinent, etiamſi per cha­
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              racteres more mathematicorum exponantur.</s>
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              72</s>
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              <s id="s.001234">Tex. 24.
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              (Vt propter quid reſonat? </s>
              <s id="s.001235">aut propter quid apparet? </s>
              <s id="s.001236">aut propter quid
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              Iris? </s>
              <s id="s.001237">omnia enim hæc idem problemata ſunt genere, omnia enim ſunt refractio, ſed
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              ſpecie altera)
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              propter quid reſonat? </s>
              <s id="s.001238">ſcilicet echo; propter quid apparet?
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              </s>
              <s id="s.001239">ſcilicet imago in ſpeculo. </s>
              <s id="s.001240">dicit cauſam echo, imaginis in ſpeculo, & iridis
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              in nubibus eſſe eandem; nimirum refractionem; quamuis tres illæ refractio­
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              nes, ſeu; vt melius loquamur, reflexiones differant ſpecie ab inuicem, illa
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              enim eſt repercuſſio vocis; hæc reflexio ſpeciei viſibilis ex corpore terſo;
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              iſta
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              radiorum Solis ex nube rorida in ſtato angulo repercuſſus. </s>
              <s id="s.001241">qua
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              ratione autem iſta omnia fiant, longum eſſet exponere, & ab intelligentia
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              huius loci fortè alienum. </s>
              <s id="s.001242">Illud tamen non prætereundum, quod ſi propriè
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              cum Perſpectiuis loqui velimus, dicendum eſſe, omnia illa eſſe reflexionem,
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              non refractionem. </s>
              <s id="s.001243">nam reflexio eſt, quando linea viſualis, per quam fertur
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              ſpecies in aliquod corpus terſum, impingit, ex quo deinde ad oculos refle­
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              ctitur. </s>
              <s id="s.001244">refractio tunc eſt, quando ſpecies obiecti viſibilis tranſit per media
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              diuerſæ craſſitiei., vt quando ſpecies lapilli per aquam primùm, deinde per
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              aerem means ad oculum peruenit; tunc enim linea, per quam ſpecies pro­
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              greditur, frangitur in confinio aquæ, & aeris, ita vt ſpecies non per vnicam
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              lineam rectam, ſed per fractam, ſeu refractam in confinio illo, oculis tan­
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              dem accidat.</s>
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              <s id="s.001245">In fine textus
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              (Quoniam Luna deficit)
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              non intelligit defectum illum, qui
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              eclypſis appellatur, ſed ilium, quo paulatim lumen Lunæ minus oculis no­
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              ſtris apparet: decreſcente enim Luna ſolent humida augeri.</s>
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              73</s>
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              <s id="s.001248">Tex. 25.
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              (Vt propter quid, & permutatim proportionale? </s>
              <s id="s.001249">& c.
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              ) quod quan­
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              titates, quæ ſunt proportionales, ſint etiam alternatim, ſeu permutatim
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              proportionales explicatum eſt ad tex. 13. primi Poſter. quæ etiam neceſſa­
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              ria ſunt ad hunc locum benè intelligendum. </s>
              <s id="s.001250">Illud autem commune propter
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              quod ea, quæ ſunt proportionalia, ſint etiam permutatim proportionalia,
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              eſt quoddam innominatum, de quo ibi dictum eſt, quod cum conueniat li­
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              neis, & numeris, & tamen ſeparatim de vtriſque illa paſſio demonſtretur,
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              quærit cuinam primò, & per ſe conueniat hæc paſſio, eſſe permutatim pro­
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              portionale; ſcilicet quidnam ſit illud innominatum; in quo deinde commu­
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              nicent lineæ, & numeri, vt inde habeant eſſe etiam permutatim propor­
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              tionalia.</s>
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              74</s>
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              <s id="s.001253">Ibidem (
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              Hic quidem fortaſſe proportionaliter habere latera, & angulos
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              ) vult
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              indicare, in quonam conſiſtat ſimilitudo inter duas figuras rectilineas geo­
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              metricas, quam ſimilitudinem Euclides definit. </s>
              <s id="s.001254">1. ſexti, ſic explicat: ſimi­
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              les figuræ rectilíneæ ſunt; quæ & angulos ſingulos, ſingulis angulis æquales
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              habent,
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              etiam latera, quæ circa angulos æquales ſunt proportionalia.
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              <s id="s.001255">vt ſi duo triangula appoſita habeant angulos æquales,
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              A, angulo D:
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              angulum B, angulo E. angulum C, angulo F. & præterea latera, quæ ſunt </s>
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