Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

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            <div xml:id="echoid-div291" type="math:theorem" level="3" n="153">
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            <div xml:id="echoid-div293" type="appendix" level="3" n="1">
              <head xml:id="echoid-head173" xml:space="preserve">APPENDIX</head>
              <head xml:id="echoid-head174" xml:space="preserve">DE SPECVLATIONE
                <lb/>
              REGVLAE FALSI.</head>
              <p>
                <s xml:id="echoid-s1332" xml:space="preserve">
                  <emph style="sc">Nvnc</emph>
                idem ferè mihi accidit, quod & Michaeli Stifelio, à quo
                  <lb/>
                cum Petreius Tipographus nuper totam ſuam Arithmeticam re
                  <lb/>
                cepiſſet, mox poſteà per literas petijt
                  <reg norm="explicationem" type="context">explicationẽ</reg>
                regulæ falſi.</s>
              </p>
              <p>
                <s xml:id="echoid-s1333" xml:space="preserve">Similiter poſt inciſas omnes ſuperiorum Theorematum figu-
                  <lb/>
                ras,
                  <reg norm="opereque" type="simple">opereq́;</reg>
                Typographo commiſſo, amicus quidam omnium
                  <lb/>
                ſcientiarum ornatiſſimus maxima neceſſitudine mecum coniun-
                  <lb/>
                ctus monuit me, vt aliquid de regula falſi ſcribere vellem, cuius
                  <lb/>
                ſuaſu hæc, quæ ſequuntur appendicis vice ponere libuit, nelector, quidpiam quod
                  <lb/>
                ad hancrem pertinet iure merito à nobis deſiderare poſſet; </s>
                <s xml:id="echoid-s1334" xml:space="preserve">vt autem ad ipſam
                  <reg norm="re- gulam" type="context">re-
                    <lb/>
                  gulã</reg>
                accedamus Ego ſicut, & in alijs multis, ita & in huiuſcæ regulę inuentione cum
                  <lb/>
                ipſo Stifelio maximè conuenio, putans regulam falſi, ſeu falſarum poſitionum in-
                  <lb/>
                uentam fuiſſe per paruos numeros in quæſtionibus facillimis & cognitis, eodem fer
                  <lb/>
                mè modo, quo ipſe monſtrat illis duobus exemplis, quæ quamuis ipſe appellet theo
                  <lb/>
                remata, nihilominus the oremata ego illa non vocarem, niſi adiuncta fuerit ſpecu-
                  <lb/>
                latio ab ipſo præterita, & non experientia tantummodo, vt ipſe fecit. </s>
                <s xml:id="echoid-s1335" xml:space="preserve">Primum eius
                  <lb/>
                exemplum eſt, quòd.</s>
              </p>
              <p>
                <s xml:id="echoid-s1336" xml:space="preserve">Quorumcumque
                  <reg norm="duorum" type="context">duorũ</reg>
                numerorum differentia, ſi fuerit multiplicata in aggre
                  <lb/>
                gatum eorum, producit ipſam differentiam, quæ eſt inter quadrata eorum.</s>
              </p>
              <p>
                <s xml:id="echoid-s1337" xml:space="preserve">Secundum verò exemplum eſt, quod.</s>
              </p>
              <p>
                <s xml:id="echoid-s1338" xml:space="preserve">Datis tribus numeris ſecundum progreſſionem arithmeticam diſpoſitis, facit mul
                  <lb/>
                tiplicatio medij in ſe,
                  <reg norm="quantum" type="context">quãtum</reg>
                multiplicatio extremorum inter ſe cum multiplicatio
                  <lb/>
                ne differentiarum inter ſe.</s>
              </p>
              <p>
                <s xml:id="echoid-s1339" xml:space="preserve">Talia enim exempla ipſe aliter non probat niſi experientia in aliquibus numeris,
                  <lb/>
                arbitratus ex eo inuentam eſſe regulam falſi, experientia tantummodo confirma-
                  <lb/>
                tam, quod quidem etiam & ego credo. </s>
                <s xml:id="echoid-s1340" xml:space="preserve">At experientia in philoſophia mathema-
                  <lb/>
                tica, aut
                  <reg norm="nullam" type="context">nullã</reg>
                prorſus facit
                  <reg norm="ſcientiam" type="context">ſcientiã</reg>
                , aut omnino ſuperfluus fuit Euclides in multis
                  <lb/>
                ſuis propoſitionibus, & præcipuè in eius ſecundo libro, ſi ſufficeret experientia. </s>
                <s xml:id="echoid-s1341" xml:space="preserve">Id-
                  <lb/>
                circo quo magis ad euidentiam ipſius veritatis, quam profiteor, deuenire poſſim,
                  <lb/>
                  <reg norm="accipiam" type="context">accipiã</reg>
                primò primum exemplum
                  <lb/>
                ipſius Stifelij hic ſuperius citatum,
                  <lb/>
                & pro numero maiori, in prima hic
                  <lb/>
                  <figure xlink:label="fig-0115-01" xlink:href="fig-0115-01a" number="158">
                    <image file="0115-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0115-01"/>
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                ſubſcripta figura .AE. accipio
                  <var>.a.i.</var>
                  <lb/>
                cuius quadratum ſit
                  <var>.a.c</var>
                : pro minori
                  <lb/>
                vero numero capio
                  <var>.a.e.</var>
                  <reg norm="partem" type="context">partẽ</reg>
                ipſius
                  <lb/>
                  <var>a.i.</var>
                cuius quadratum fit
                  <var>.a.t.</var>
                differen
                  <lb/>
                tia autem horum numerorum erit
                  <var>.
                    <lb/>
                  e.i.</var>
                reliqua pars ipſius
                  <var>.a.i</var>
                : & differen
                  <lb/>
                tia ipſorum quadratorum erit gno-
                  <lb/>
                mon
                  <var>.e.c.o</var>
                : Nunc autem protraho
                  <var>.
                    <lb/>
                  i.c.</var>
                latus quadrati maioris quouſque
                  <lb/>
                  <var>c.n.</var>
                æqualis ſit
                  <var>.a.e.</var>
                numero minori,
                  <lb/>
                  <reg norm="perficioque" type="simple">perficioq́;</reg>
                rectangulum
                  <var>.e.n.</var>
                quod </s>
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