Biancani, Giuseppe, Aristotelis loca mathematica, 1615

Page concordance

< >
Scan Original
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
< >
page |< < of 355 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000785">
                <pb pagenum="41" xlink:href="009/01/041.jpg"/>
              æqualitas nullum diſcrimen, quantumuis minimum admittat, quod ſenſui
                <lb/>
              vitare ob ſui imperfectionem non licet: vnde inter eæ, quæ mathematicè
                <lb/>
              ſunt æqualia, nullus intellectus aliquam valeat reperire differentiam) ſumat
                <lb/>
              inquam triangulum quodpiam materiale, vt ex charta, quantum fieri po­
                <lb/>
              teſt perfectum, deinde ducat lineam vnam perpendicularem ſuper aliam,
                <lb/>
              quæ ſcilicet faciat, cum illa duos angulos rectos. </s>
              <s id="s.000786">poſtea abſcindat tres an­
                <lb/>
              gulos trianguli materialis,
                <expan abbr="eosq́">eosque</expan>
              ; ita ſimul componat, vt mucrones illorum
                <lb/>
              ſint vniti, & contigui ad punctum lineæ perpendicularis cum altera, vti eſt
                <lb/>
              in ſuperiori figura punctum E; & illicò apparebit tres illos angulos mate­
                <lb/>
              riales obtegere adæquatè totum illud ſpatium duorum rectorum, quos per­
                <lb/>
              pendicularis conſtituit. </s>
              <s id="s.000787">Hoc autem experiri poteris in diuerſis admodum
                <lb/>
              triangulis Scalenis, Rectangulis, Iſoſcelibus, Aequilateris, &c. </s>
              <s id="s.000788">non ſine de­
                <lb/>
              lectatione, atque hic eſt ſenſus illorum verborum, omnis triangulus habet
                <lb/>
              tres ęquales duobus rectis. </s>
              <s id="s.000789">Abſtineo à demonſtrationibus geometricis, quo­
                <lb/>
              niam ij, qui Mathematicis ſunt imbuti, noſtra hac opera parum indigent.
                <lb/>
              </s>
              <s id="s.000790">ſi quis tamen volet, conſulat 32. primi Elem. </s>
              <s id="s.000791">Ex hac igitur declaratione
                <lb/>
              licet cognoſcere nonnullos ageometretos locum hunc, & ſimiles ſubſequen­
                <lb/>
              tes non ſatis intelligere, dicentes, nihil aliud verba illa Ariſt. velle ſignifi­
                <lb/>
              care, quàm omnem triangulum habere tres angulos, quod inquiunt, notiſ­
                <lb/>
              ſimum eſt. </s>
              <s id="s.000792">Sed ſi incidant in ſequentia; æquales duobus rectis, tunc, cum
                <lb/>
              hæc non intelligant, abſtinent etiam à priorum declaratione, quibus præ­
                <lb/>
              miſſis facile eſt Ariſt. textum percipere. </s>
              <s id="s.000793">ſit A, duo recti, ideſt, duo anguli
                <lb/>
              recti ſint paſſio demonſtranda, in quo B, triangulus, in quo C, æquicrus. </s>
              <s id="s.000794">ipſi
                <lb/>
              itaque C, ideſt triangulo æquicruſi, ineſt A, ſcilicet duo recti, hoc eſt, ineſt
                <lb/>
              æquicruſi hæc, paſſio habere tres angulos æquales duobus rectis per B, ideſt
                <lb/>
              per
                <expan abbr="triangulũ">triangulum</expan>
              vniuerſale, quia hæc proprietas eſt trianguli propria, &
                <expan abbr="cõpe-tit">compe­
                  <lb/>
                tit</expan>
              æquicruſi, non vt æquicrus eſt, ſed, vt triangulum eſt; quare B, non erit
                <lb/>
              medium ipſius A, quia prædicta paſſio. </s>
              <s id="s.000795">A, non competit triangulo B, per
                <lb/>
              aliud, ſed per ſe, de eo enim primo, & per ſe demonſtratur in 32. primi Elem.
                <lb/>
              optimè Aegydius, & Niphus in hunc locum.</s>
            </p>
            <p type="main">
              <s id="s.000796">
                <arrow.to.target n="marg11"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.000797">
                <margin.target id="marg11"/>
              11</s>
            </p>
            <p type="main">
              <s id="s.000798">Ex eodem cap.
                <emph type="italics"/>
              (Non oportet autem exiſtimare penes id, quod exponimus, ali­
                <lb/>
              quid accidere abſurdum, nihil enim vtimur eo, quod eſt hoc aliquid eſſe. </s>
              <s id="s.000799">ſed ſicut
                <lb/>
              Geometra pedalem, & rectam hanc, & ſine latitudine dicit, quæ non ſunt. </s>
              <s id="s.000800">verum
                <lb/>
              non ſic vtitur, tanquam ex his ratiocinans)
                <emph.end type="italics"/>
              Quoniam Ariſt. in exemplis affert
                <lb/>
              pro rebus characteres, A, B, C, poſſet quiſpiam ſuſpicari aliquod propterea
                <lb/>
              abſurdum accidere: cui ſuſpicioni Ariſt. reſpondet, dicens, nihil inde abſur­
                <lb/>
              di accidere poſſe, quoniam ipſe vtitur hiſce literis,
                <expan abbr="nõ">non</expan>
              quatenus literæ ſunt,
                <lb/>
              ſed quatenus rerum vicem, pro quibus exponuntur, gerunt: quemadmodum
                <lb/>
              etiam Geometræ faciunt, qui lineam, quæ pedalis non eſt, pedalem, & quæ
                <lb/>
              non eſt recta, rectam; & quæ lata eſt, non latam, ſupponunt, & tamen nihil
                <lb/>
              inde abſurdi contingit. </s>
              <s id="s.000801">Ex quibus intelligimus per lineas illas ſenſibiles, &
                <lb/>
              phyſicas, quas Geometræ in ſuis figuris ducunt, intelligendas eſſe lineas ve­
                <lb/>
              rè Mathematicas omni latitudine carentes; vtitur enim inquit Ariſt. Geo­
                <lb/>
              metra lineis phyſicis, non tanquam phyſicis, nec de eis tanquam de phyſicis
                <lb/>
              lineis ratiocinatur, ſed ijs vtitur tanquam verè mathematicis. </s>
              <s id="s.000802">idem dicen­
                <lb/>
              dum eſt de ſuperficiebus, necnon de corporibus, quæ ijdem Geometræ de­
                <lb/>
              ſcribunt, vt per ea, de verè mathematicis diſcurrant.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum