Biancani, Giuseppe, Aristotelis loca mathematica, 1615

Table of figures

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              <s id="s.003879">
                <pb pagenum="228" xlink:href="009/01/228.jpg"/>
                <emph type="italics"/>
              figuram non deſtruit, quamuis diuidat. </s>
              <s id="s.003880">quemadmodum faciunt; qui vaſa militaria
                <lb/>
              partiuntur. </s>
              <s id="s.003881">At cæteræ lineæ, quæ per lineas compoſitam figuram ſecant, eam cor­
                <lb/>
              rumpunt: committitur enim rectilinea figura in angulis, vel ſecundum angulos)
                <emph.end type="italics"/>
                <lb/>
              Vt rectè problema hoc percipiamus, proponenda eſt figura rectilinea, &
                <lb/>
              vna ex ijs, quæ parallelogramma dicuntur, vt ſunt Quadratum, Quadrila­
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                <figure id="id.009.01.228.1.jpg" place="text" xlink:href="009/01/228/1.jpg" number="141"/>
                <lb/>
              terum, Rhombus, Rhomboides, cuiuſmo­
                <lb/>
              di eſt præſens, aliter verba Ariſt. illi non
                <lb/>
              ſemper quadrarent, quia illarum diameter
                <lb/>
              illas ſemper bifariam non ſe caret. </s>
              <s id="s.003882">quemad­
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              modum videre eſt in trapezio. </s>
              <s id="s.003883">& pentagono
                <lb/>
              etiam æquilatero. </s>
              <s id="s.003884">Quærit igitur, cur ex om­
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              nibus lineis, quæ quadrilaterum A B C D,
                <lb/>
              bifariam diuidunt, quales ſunt E F, G H, &
                <lb/>
              D B. ſola D B, quæ ab angulo ad angulum
                <lb/>
              ducta eſt, mœruit appellari diameter. </s>
              <s id="s.003885">Reſpondet autem, eam fortè appel­
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              lationem hanc præ cæteris inde promeruiſſe, quòd, quamuis aliæ omnes
                <lb/>
              æquè parallelogrammum dimetiantur, ſola tamen ipſa D B, ipſum non de­
                <lb/>
              ſtruit, nec ſcindit, cùm ei nouam aliquam diuiſionem non inferat, ſed id per
                <lb/>
              angulos ſecet, vbi prius laterum commiſſuræ
                <expan abbr="erãt">erant</expan>
              : reliquæ verò omnes no­
                <lb/>
              uas figuræ ſectiones inferunt, cùm eius latera in punctis E, F, G, H,
                <expan abbr="diuidãt">diuidant</expan>
              ,
                <lb/>
              vbi nulla prius erat diuiſio; quapropter ipſam quodammodo deſtruunt,
                <lb/>
                <expan abbr="atq;">atque</expan>
              corrumpunt. </s>
              <s id="s.003886">Aduertè vulgatam verſionem latinam hanc
                <emph type="italics"/>
              (Angulis enim
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              constant, quæ rectis lineis continentur)
                <emph.end type="italics"/>
              malè græco textui
                <foreign lang="grc">συγκεινται γαρ τὸ
                  <lb/>
                ευθυγραμμον κατὰ τας γωνίας,</foreign>
              reſpondere, qui ſic latinè reddendus eſt: com­
                <lb/>
              ponitur enim rectilineum iuxta angulos; quæ interpretatio vera eſt, quia
                <lb/>
              anguli ſunt laterum commiſſuræ, vt dictum eſt.</s>
            </p>
            <p type="main">
              <s id="s.003887">
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            <p type="margin">
              <s id="s.003888">
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              338</s>
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            <p type="main">
              <s id="s.003889">Eadem ſect. </s>
              <s id="s.003890">num. </s>
              <s id="s.003891">2.
                <emph type="italics"/>
              (cur diameter ita eſt appellata? </s>
              <s id="s.003892">Vtrum quoniam ſola bi­
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              partitò figuram diuidat? </s>
              <s id="s.003893">An quod ſola figuram ſecat per partes, ſiue membra, qui­
                <lb/>
              bus in flexa coarctatur, cùm cæteræ per latera diuidant?)
                <emph.end type="italics"/>
              præſentis problematis
                <lb/>
              expoſitio petatur ex præcedentis expoſitione.</s>
            </p>
            <p type="main">
              <s id="s.003894">
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            <p type="margin">
              <s id="s.003895">
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              339</s>
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            <p type="main">
              <s id="s.003896">In problemate 3.
                <emph type="italics"/>
              (Cur homines omnes tam Græci, quàm Barbari ad decem
                <lb/>
                <expan abbr="vſq;">vſque</expan>
              numerare conſueuere, & c. </s>
              <s id="s.003897">Vtrum quod denarius numerus perfectus ſit: con­
                <lb/>
              tinet enim omnia numerorum genera. </s>
              <s id="s.003898">vt par, impar, quadratum, quadrantale, lon­
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              gum, planum, primum, compoſitum)
                <emph.end type="italics"/>
              Cur omnes nationes miro quodam con­
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              ſenſu ſuos numeros in denas, veluti in gradus quoſdam diuidant, Ariſtoteles
                <lb/>
              cauſam indagaturus, reſpondet primò id fortè accidiſſe ob denarij numeri
                <lb/>
              perfectionem: cuius perfectionis hoc eſt indicium, quod denarius contineat
                <lb/>
              omnes numerorum ſpecies. </s>
              <s id="s.003899">quæ quidem omnes numerorum ſpecies in defi­
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              nitionibus 7. Elem. exponuntur, quas conſulere debes. </s>
              <s id="s.003900">in denario numero
                <lb/>
              contineri numeros pares, ac impares, per ſe patet. </s>
              <s id="s.003901">continetur etiam in eo
                <lb/>
              quadratus numerus, imò duo quadrati numeri, nam, & quaternarius eſt
                <lb/>
              numerus quadratus, quippe qui ex ductu binarij in binarium producatur:
                <lb/>
              item nouenarius eſt quadratus, quippe qui ex multiplicatione ternarij in
                <lb/>
              ternarium gignitur. </s>
              <s id="s.003902">Porrò pro quadrantali numero intelligendus eſt nume­
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              rus cubus, erat. </s>
              <s id="s.003903">n. </s>
              <s id="s.003904">quadratal apud Romanos vas cubicæ figuræ: imò in græ­
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              co textu voci huic quadrantali, reſpondet
                <foreign lang="grc">κυβος,</foreign>
              ideſt, cubus. </s>
              <s id="s.003905">vnde apud la­</s>
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