Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              lum requiratur idem angulus, ſed etiam tanta Iridis altitudo,
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              requi­
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              ritur vt angulus in orbem conſtituatur, ex quo Iris poſſit apparere. </s>
              <s id="s.002092">hæc à
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              nemine hactenus animaduerſa placuit addere, vt ex ijs demonſtratio Iridis
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              omnibus numeris aliquando abſolui poſſit, quod infra (ni fallor, fauente
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              Deo) præſtabimus.
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              165</s>
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              <s id="s.002094">Ibidem
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              (Extraponatur igitur quædam linea, quæ D B, & ſeindatur vt M G, ad
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              M K, ſic quæ D, ad B, maior autem quæ M G, ea quàm M K, quoniam ſuper ma­
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              iorem angulum reflexio coni, maiori enim angulo ſubtenditur trianguli M K G.
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              </s>
              <s id="s.002095">Maior igitur eſt & ipſa D, ipſa B. addatur igitur ad eam, quæ B, ea in qua F, vt
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              ſit quod D, ad B, quæ B F, ad D. </s>
              <s id="s.002096">Deinde quod F, ad K G, quæ B, ad aliam fiat,
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              quæ K P. & à P, ad M, copuletur quæ P M, erit igitur P. polus circuli, ad quem
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              lineæ, quæ à K, incidunt)
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                <expan abbr="hucuſq;">hucuſque</expan>
              oſtendit lineas viſuales cadere ad M, pun­
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              ctum in Iridis periphæriam, pergit deinceps inueſtigare polum, & poſtea
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              centrum eiuſdem ambitus, vtraque autem exiſtere in horizonte reperit, vt
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              hinc inferat Iridis portionem illam, quæ oriente Sole ſupra horizontem ap­
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              paret, eſſe ſemicirculum, vt propoſuerat. </s>
              <s id="s.002097">Differt autem polus circuli à cen­
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              tro eiuſdem circuli. </s>
              <s id="s.002098">polus eſt punctum extra planum circuli, ex quo tamen
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              vt
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              adhibito circino circuli periphæria deſcribi poteſt; ſic polus æqua­
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              toris eſt idem, qui polus mundi:
                <expan abbr="centrũ">centrum</expan>
              verò eſt in plano ſui cir culi, ſic cen­
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              trum æquatoris eſt idem cum centro mundi, cum æquator per illud incedat.</s>
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              <s id="s.002099">Dicit
                <expan abbr="itaq;">itaque</expan>
              Ariſt. cum data ſit proportio linearum K M, & M G, in ſupe­
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              riori ſecunda figura numeri 164. quam nunc iterum inſpicere opertet; ex­
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              ponatur alia linea recta B D. quæ diui­
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              datur in partes B, & D. proportionales
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              cum lineis K M, G M, per 10. 6. cum
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              ergo K M, ſit minor quàm G M, per 19.
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              primi, quia in triangulo G M K, oppo­
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              nitur minori angulo, erit
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              B, minor quàm D, addatur iam ipſi B. linea
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              nea F, ita vt ſit tota F B, tertia proportionalis ad duas B, & D, per 11. 6.
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              hoc ordine, vt F B, ad D. ita D, ad B. </s>
              <s id="s.002100">Deinde vt ſe habet F, ad K G. ita ſit
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              B, ad aliam, quæ ſit K P, in eadem figura per 12. 6. & à puncto P, ad M, iun­
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              gatur recta P M. </s>
              <s id="s.002101">Dico P, eſſe polum circuli, quem dixi Iridis, & in quem li­
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              neæ à K, procedentes turbinis formam effingunt, probatur autem ab Ariſt.
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              in ſequentibus.</s>
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              166</s>
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              <s id="s.002104">Ibidem
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              (Erit etiam, quod quæ F, ad K G. & quæ B, ad K P. & quæ D, ad P M.
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              non enim ſit, ſed aut ad minorem, aut ad maiorem ea, quæ P M, nihil enim differet.
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              </s>
              <s id="s.002105">ſit enim ad P R. eandem ergo rationem G K, & K P, & P R, inuicem habebunt,
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              quam quæ F, B, D: quæ autem F, B, D, proportionales crant, quod quidem D, ad
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              B. quæ F B, ad D: quare quod quæ P G, ad P R, quæ P R, ad eam, quæ P K. ſi igi­
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              tur ab ijs, quæ K G, quæ G R, & K R, ad R, coniungantur, coniunctæ hæ eandem
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              habebunt rationem, quam quæ G P, ad eam, quæ P R, circa eundem enim angulum
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              P, proportion aliter, & quæ trianguli G P R, & eius, qui K R P. quare & quæ G R,
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              ad eam quæ K R, eandem rationem habebit, quam & quæ G P, ad eam quæ P R,
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              habet autem & quæ M G, ad M K, eam rationem, quam quæ D, ad eam quæ B,
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              quare ambæ à punctis G K, non ſolum ad circunferentiam M N, conſtituentur ean­
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              dem habentes rationem, ſed & alibi, quod quidem impoſſibile)
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              incipit, vt </s>
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