Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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            <p type="main">
              <s id="s.002254">
                <pb pagenum="133" xlink:href="009/01/133.jpg"/>
              ſed figuræ rectilineæ illius, quæ dicitur Altera parte longior, qualis eſt præ­
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              ſens figura A B C D, cuius quadrandæ ratio eſt huiuſmodi. </s>
              <s id="s.002255">per 13. 6. inue­
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                <figure id="id.009.01.133.1.jpg" place="text" xlink:href="009/01/133/1.jpg" number="70"/>
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              niatur recta linea media proportionalis inter
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              duo latera figuræ A B, B C,
                <expan abbr="eaq́">eaque</expan>
              ; ſit B D, in ſe­
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              quenti figura. </s>
              <s id="s.002256">eſſe autem mediam proportio­
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              nalem nihil aliud eſt quam ita eſſe A B, ad B D,
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              ſicut B D, ad B C.
                <expan abbr="diciturq́">diciturque</expan>
              ; media proportio­
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              nalis, quia in hac habitudine medium locum obtinet. </s>
              <s id="s.002257">quadratum autem li­
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              neæ B D, æquale eſt rectangulo dato A B C D, per 17.6. Inuentio porrò hu­
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              ius mediæ proportionalis, quia facilis eſt, & ſcitu iucunda, eam ſic habeto.
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                <figure id="id.009.01.133.2.jpg" place="text" xlink:href="009/01/133/2.jpg" number="71"/>
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              accipe duo latera A B, & B C,
                <expan abbr="quadrãdi">quadrandi</expan>
              rectan­
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              guli,
                <expan abbr="eaq́">eaque</expan>
              ; in directum conſtitue, vt vnicam re­
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              ctam conſtituant A C, vt apparet in figura; de­
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              inde diuiſa tota A C, bifariam in E, facto cen­
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              tro in E, deſcribe ſemicirculum ſuper lineam
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              A C, demum à puncto B, in quo duo latera con­
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              iunguntur, erigatur linea perpendicularis
                <expan abbr="vſq;">vſque</expan>
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              ad periphæriam, quæ ſit B D. hæc enim B D, eſt media proportionalis inter
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              latera A B, B D, quam nimirum habitudinem habet A B, ad B D, eam quo­
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              que obtinet B D, ad B C. </s>
              <s id="s.002258">Quadratum igitur huius B D, hoc eſt quadratum,
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              cuius quatuor latera ſint æqualia lineæ B D, quale eſt præſens, æquale erit
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                <figure id="id.009.01.133.3.jpg" place="text" xlink:href="009/01/133/3.jpg" number="72"/>
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              dato ſuperiori rectangulo A B C D,
                <expan abbr="atq;">atque</expan>
              hoc modo per­
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              acta erit quadratio, ſeu tetragoniſmus dati quadrilateri
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              A B C D. </s>
              <s id="s.002259">Vides igitur, qua ratione quadratum conſti­
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              tuatur æquale dato quadrilatero; & qua rationem inuen­
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              tio illius mediæ proportionalis ſit cauſa quadraturæ re­
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              ctanguli, & proinde ſi quis dicat quadrationem hanc eſſe
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              effectionem rectanguli æquilateri, ideſt quadrati, æqualis dato quadrilate­
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              ro, hic definitionem formalem ſolum afferet: quæ definitio, vt dixit in Lo­
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              gicis, eſt inſtar concluſionis. </s>
              <s id="s.002260">ſi quis verò dicat tetragoniſmum hunc quadri­
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              lateri dati eſſe mediæ prædictæ inuentionem cauſalem afferet definitionem,
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              cum rei cauſam dicat. </s>
              <s id="s.002261">Aduerte 10. Grammaticum immeritò accuſare Ale­
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              xandrum, quod dicat quadrationem hanc per inuentionem mediæ propor­
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              tionalis tradi in 2. Elem. nam verè in 14. 2. traditur talis inuentio, quam­
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              uis enim ibi nulla fiat expreſſa mentio huiuſmodi mediæ, in ipſa tamen ea
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              reperitur, ac per eam figuræ rectilineæ quadrantur: quod patet ex figura
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              14. prædictæ, quæ eadem eſt cum figura 13. 6. qua docemur prædictam in­
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              uentionem.</s>
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            <p type="main">
              <s id="s.002262">
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              <s id="s.002263">
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              186</s>
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            <p type="main">
              <s id="s.002264">Tex. 86.
                <emph type="italics"/>
              (Acutum mouet ſenſum in tempore pauco multùm: graue autem in
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              multo parùm; non igitur velox eſt acutum, graue autem tardum, ed ſit illius qui­
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              dem propter velocitatem motus huiuſmodi, huius autem propter tarditatem)
                <emph.end type="italics"/>
              vide
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              quæ de hac re primo topic. </s>
              <s id="s.002265">cap. 13. dicta ſunt, illa enim omnia in hunc lo­
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              cum quadrant. </s>
              <s id="s.002266">Verum occurrit illa dubitatio; quod cum Ariſt. ibi dicat
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                <emph type="italics"/>
              (Vox acuta quidem velox)
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              hic autem
                <emph type="italics"/>
              (Non igitur velox eſt acutum
                <emph.end type="italics"/>
              ) repugnan­
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              tia dicere videtur. </s>
              <s id="s.002267">cui dubitationi ſic occurrendum; vt dicamus ibi Philo­
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              ſophum dicere vocem acutam eſſe velocem, quatenus acumen vocis oritur </s>
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