Biancani, Giuseppe, Aristotelis loca mathematica, 1615

Table of figures

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            <p type="main">
              <s id="s.002620">
                <pb pagenum="151" xlink:href="009/01/151.jpg"/>
                <figure id="id.009.01.151.1.jpg" place="text" xlink:href="009/01/151/1.jpg" number="79"/>
                <lb/>
              ipſi æquidiſtanter, dum punctum A, mouetur
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              ad B. his duabus lationibus A, latum. </s>
              <s id="s.002621">neceſſa­
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              riò motu mixto progredietur per diametrum
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              A M, quod ſic probari poteſt; ſit iam A, mo­
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              tum primo motu
                <expan abbr="vſq;">vſque</expan>
              ad D, linea verò ex ſe­
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              cundo motu ſit in G F E, quo motu punctum
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              A, quod erat in D,
                <expan abbr="tractũ">tractum</expan>
              erit in F. quod pun­
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              ctum eſt in diametro A M, quoniam enim mo­
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              uetur duobus motibus, cum lineis A B, A C, proportionalibus, motus au­
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              tem
                <expan abbr="hucuſq;">hucuſque</expan>
              ſunt A D, A E, quæ debent eſſe proportionales, cum A B, A C
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              compleatur rectangulum A D F E, erunt ſimiliter proportionalia F E, D E,
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              cum ſint æqualia duobus D A, A E, quare per 26. 6. cum quadrilaterum
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              paruum A D F E, ſit ſimile toti A B M C, erit A M,
                <expan abbr="vtriuſq;">vtriuſque</expan>
              diameter, ergò
                <lb/>
              punctum F, in quo eſt A, eſt in diametro A M. eodem modo, de quouis pun­
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              cto in linea A B, ad quod A, perueniat, probabitur ab altero motu deſcen­
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              diſſe vſque ad diametrum. </s>
              <s id="s.002622">ſemper ergò latum A, per rectam A M, diame­
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              trum quadrilateri, cum illis motibus proportionalibus progreditur, quod
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              probandum erat. </s>
              <s id="s.002623">è conuersò manifeſtum etiam eſt, quod ſi quid ſecundum
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              diametrum duabus fertur lationibus, eas lationes eſſe proportionales late­
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              ribus quadrilateri, cuius eſt illa diameter, ſi enim illæ lationes non ſunt la­
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              teribus proportionales, latum illud non feretur ſecundum diametrum il­
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              lam, ſed ſecundum aliam alterius quadrilateri.</s>
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            <p type="main">
              <s id="s.002624">Quod ſi quid duabus lationibus nullam habentibus proportionem per­
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              petuò ferratur, impoſſibile eſt ipſum motu mixto lineam rectam deſcribere.
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              </s>
              <s id="s.002625">ſi enim dixeris illud poſſe deſcribere rectam lineam, tunc circa rectam il­
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              lam tanquam diametrum deſcribam quadrilaterum, & poſtea oſtendam, vt
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              proximè oſtenſum eſt, illud latum eſſe ſecundum laterum illius proportio­
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              nem, quare impoſſibile eſt id, quod mouetur duabus lationibus nullam in­
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              uicem rationem habentibus, ferri per lineam rectam: quapropter
                <expan abbr="dicẽdum">dicendum</expan>
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              eſt hoc modo
                <expan abbr="latũ">latum</expan>
              , neceſſariò ferri circulariter, ſiue per lineam circularem.
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              </s>
              <s id="s.002626">Quod autem ea, quæ deſcribit circulum linea, dum altero eius manente
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              extremo circumagitur, duabus ſimul feratur lationibus, ex quibus motus
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              orbicularis oriatur, manifeſtum eſt ex ſuperioribus, quia & antrorſum, &
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              retrorſum impellitur; tùm etiam, quia ſi rectà tenderet recta
                <expan abbr="deſcribẽs">deſcribens</expan>
              cir­
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                <figure id="id.009.01.151.2.jpg" place="text" xlink:href="009/01/151/2.jpg" number="80"/>
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              culum, nunquam ad diametri perpendiculum
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              perueniret, ſed tamen peruenit, ita vt ſit ipſa
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              à centro perpendicularis diametro. </s>
              <s id="s.002627">ſit circuli
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              figura A B C D, in qua extremum diametri
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              B, feratur ad alterum extremum vbi D, per
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              ipſius diametri B D, circumuolutionem circa
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              centrum F, neceſſe eſt aliquando B, perueniat
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              ad C. ſi igitur B, feretur duabus lationibus
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              aliquo modo proportionatis, v. g. vt eſt pro­
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              portio lateris B E, ad E C, latus, ſequeretur
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              ex demonſtratis ipſum B, ferri per
                <expan abbr="rectã">rectam</expan>
              B C,
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              quæ diameter eſſet quadrilateri B E C G. ſed </s>
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