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]

Page concordance

< >
Scan Original
61 49
62 50
63 51
64 52
65 53
66 54
67 55
68 56
69 57
70 58
71 59
72 60
73 61
74 62
75 63
76 64
77 65
78 66
79 67
80 70
81 71
82 70
83 71
84 72
85 73
86 74
87 75
88 76
89 77
90 78
< >
page |< < (28) of 445 > >|
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div7" type="chapter" level="2" n="1">
            <div xml:id="echoid-div92" type="math:theorem" level="3" n="43">
              <p>
                <s xml:id="echoid-s375" xml:space="preserve">
                  <pb o="28" rhead="IO. BAPT. BENED." n="40" file="0040" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0040"/>
                quadrato dimidij, prout ex ſpeculatione huiuſmodi operis cognoſcetur,
                  <reg norm="cuiæquanda" type="context">cuiæquãda</reg>
                  <lb/>
                eſt
                  <reg norm="differentia" type="context">differẽtia</reg>
                inter
                  <reg norm="ſummam" type="context">ſummã</reg>
                  <reg norm="quadratorum" type="context">quadratorũ</reg>
                  <reg norm="duorum" type="context">duorũ</reg>
                qui
                  <reg norm="quæruntur" type="context">quærũtur</reg>
                  <reg norm="numerorum" type="context">numerorũ</reg>
                , ſimul
                  <reg norm="cum" type="context">cũ</reg>
                pro
                  <lb/>
                ducto
                  <reg norm="eorum" type="context">eorũ</reg>
                radicum. </s>
                <s xml:id="echoid-s376" xml:space="preserve">Dimidium numeri .20. in ſeipſum multiplicandum eſſet, qua-
                  <lb/>
                  <reg norm="dratumque" type="simple">dratumq́;</reg>
                detrahendum ex .208. vtremanerent .108. quorum .108. tertiæ partis qua
                  <lb/>
                drata radix eſſet .6. quæ ſi iuncta fuerit dimidio .20. nempe .10. daretur maior nu-
                  <lb/>
                merus quæſitus .16. quo detracto è .20. darentur .4.</s>
              </p>
              <p>
                <s xml:id="echoid-s377" xml:space="preserve">Cuius ſpeculationis cauſa, datus primus numerus ſignificetur linea
                  <var>.g.h.</var>
                in qua
                  <lb/>
                maior numerus incognitus ſit
                  <var>.g.h.</var>
                minor verò
                  <var>.b.h.</var>
                quorum quadrata ſint
                  <var>.y.t.</var>
                et
                  <var>.
                    <lb/>
                  b.l.</var>
                in quadrato maximo
                  <var>.g.p.</var>
                tum productum
                  <var>.g.b.</var>
                in
                  <var>.b.h.</var>
                ſit
                  <var>.g.c.</var>
                  <reg norm="cogitenturque" type="simple">cogitenturq́;</reg>
                duo
                  <lb/>
                diametri
                  <var>.q.h.</var>
                et
                  <var>.g.p.</var>
                diuiſi per medium in puncto
                  <var>.o.</var>
                per quod duę lineæ ducan-
                  <lb/>
                tur
                  <var>.f.d.</var>
                et
                  <var>.k.m.</var>
                parallelæ lateribus maximi quadrati. </s>
                <s xml:id="echoid-s378" xml:space="preserve">Hæ dictum quadratum in
                  <lb/>
                quatuor quadrata æqualia diuident, quorum
                  <reg norm="vnumquodque" type="simple">vnumquodq́;</reg>
                , æquale erit quadrato
                  <var>.
                    <lb/>
                  g.f.</var>
                dimidij ipſius
                  <var>.g.h.</var>
                datę, </s>
                <s xml:id="echoid-s379" xml:space="preserve">quare eorum
                  <reg norm="vnumquodque" type="simple">vnumquodq́;</reg>
                cognitum erit. </s>
                <s xml:id="echoid-s380" xml:space="preserve">Iterum co
                  <lb/>
                gitemus
                  <var>.s.x.</var>
                per
                  <var>.e.</var>
                  <reg norm="parallelam" type="context">parallelã</reg>
                  <var>.g.k.</var>
                tantum diſtan-
                  <lb/>
                tem à
                  <var>.g.k.</var>
                quantum
                  <var>.y.l.</var>
                ab
                  <var>.g.h.</var>
                diſtare inueni-
                  <lb/>
                  <figure xlink:label="fig-0040-01" xlink:href="fig-0040-01a" number="55">
                    <image file="0040-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0040-01"/>
                  </figure>
                tur. </s>
                <s xml:id="echoid-s381" xml:space="preserve">Cogitetur pariter
                  <var>.z.i.a.</var>
                per punctum
                  <var>.i.</var>
                  <lb/>
                parallela
                  <var>.d.p.</var>
                </s>
                <s xml:id="echoid-s382" xml:space="preserve">quare
                  <var>.a.t.</var>
                æqualis erit
                  <var>.f.c.</var>
                et
                  <var>.y.x.</var>
                  <lb/>
                æqualis
                  <var>.f.e.</var>
                et
                  <var>.y.s</var>
                :
                  <var>b.l.</var>
                æqualis. </s>
                <s xml:id="echoid-s383" xml:space="preserve">Ita ſubtractis è
                  <lb/>
                duobus quadratis ſuperius dictis
                  <var>.a.t.y.x.</var>
                et
                  <var>.b.l.</var>
                  <lb/>
                producto
                  <var>.y.b.</var>
                æqualibus, ſupererunt
                  <var>.k.d.</var>
                et
                  <var>.a.c.
                    <lb/>
                  x.</var>
                cognita, tanquam æqualia dato ſecundo nu-
                  <lb/>
                mero, ſed
                  <var>.k.d.</var>
                quadratum eſt medietatis
                  <var>.g.f.</var>
                  <lb/>
                cognitæ, cognoſcetur igitur reſiduum
                  <var>.a.c.x.</var>
                vnà
                  <lb/>
                etiam ſingulæ tertiæ partes nempe quadrata
                  <var>.o.
                    <lb/>
                  i.o.c.</var>
                et
                  <var>.o.e.</var>
                & radix
                  <var>.b.f.</var>
                vel
                  <var>.f.s.</var>
                ſingularum,
                  <lb/>
                qua coniuncta dimidio
                  <var>.g.f.</var>
                  <reg norm="rurfusque" type="simple">rurfusq́;</reg>
                ab
                  <reg norm="eodem" type="context">eodẽ</reg>
                de-
                  <lb/>
                tracta, propoſitum conſequemur.</s>
              </p>
            </div>
            <div xml:id="echoid-div94" type="math:theorem" level="3" n="44">
              <head xml:id="echoid-head60" xml:space="preserve">THEOREMA
                <num value="44">XLIIII</num>
              .</head>
              <p>
                <s xml:id="echoid-s384" xml:space="preserve">CVR ſi quis cupiat numerum propoſitum in duas eiuſmodi partes diuidere, vt
                  <lb/>
                quadratum maioris, quadratum minoris ſuperet quantitate alterius numeri
                  <lb/>
                propoſiti, rectè primum numerum in ſeipſum multiplicabit, & ab eodem ſecun-
                  <lb/>
                dum numerum detrahet, reſiduum verò per duplum primi diuidet, ex quo proue-
                  <lb/>
                niens primi pars minor erit, quæ ex illo primo detracta, partem maiorem
                  <lb/>
                proferet.</s>
              </p>
              <p>
                <s xml:id="echoid-s385" xml:space="preserve">Exempli gratia, ſi proponantur .20. diuiſa in duas eiuſmodi partes, vt
                  <reg norm="quadratum" type="context">quadratũ</reg>
                  <lb/>
                maioris ſuperet quadratum minoris numero æquali ipſi .240. oportebit primum
                  <lb/>
                numerum, qui quadratus cum fuerit, erit .400. in ſeipſum multiplicare, & ex hoc
                  <lb/>
                quadrato ſecundum numerum nempe .240. detrahere, </s>
                <s xml:id="echoid-s386" xml:space="preserve">tunc remanebunt .160. quę
                  <lb/>
                diuiſa per .40.
                  <reg norm="numerum" type="context">numerũ</reg>
                  <reg norm="duplum" type="context">duplũ</reg>
                primo, dabuntur quatuor pro minori numero, à reſi-
                  <lb/>
                duo verò .20. detractis quatuor, erunt .16. pro maiorinumero.</s>
              </p>
              <p>
                <s xml:id="echoid-s387" xml:space="preserve">Quod vt exactè conſideremus, primus numerus propoſitus ſignificetur linea
                  <var>.q.
                    <lb/>
                  h.</var>
                diuidendus in duas partes
                  <var>.q.p.</var>
                et
                  <var>.p.h.</var>
                tales quales quærimus. </s>
                <s xml:id="echoid-s388" xml:space="preserve">Poſtmodum eriga
                  <lb/>
                  <gap extent="2"/>
                r quadratum
                  <var>.q.e.</var>
                diuiſum diametro
                  <var>.f.h.</var>
                  <reg norm="ductisque" type="simple">ductisq́;</reg>
                  <var>.p.o.t.</var>
                et
                  <var>.a.o.c.</var>
                parallelis lateri-
                  <lb/>
                bus quadrati, dabuntur imaginaria quadrata
                  <var>.c.t.</var>
                et
                  <var>.p.a.</var>
                duarum partium
                  <var>.q.p.</var>
                et
                  <var>.p.
                    <lb/>
                  h.</var>
                incognitarum. </s>
                <s xml:id="echoid-s389" xml:space="preserve">Ad hæc cogitemus quadratum
                  <var>.u.n.</var>
                æquale quadrato
                  <var>.p.a.</var>
                è quadra­ </s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum