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
31 19
32 20
33 21
34 22
35 23
36 24
37 25
38 26
39 27
40 28
41 29
42 30
43 31
44 32
45 33
46 34
47 35
48 36
49 37
50 38
51 39
52 40
53 41
54 42
55 43
56 44
57 45
58 46
59 47
60 48
< >
page |< < (23) 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-div79" type="math:theorem" level="3" n="36">
              <p>
                <s xml:id="echoid-s324" xml:space="preserve">
                  <pb o="23" rhead="THEOR. ARITH." n="35" file="0035" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0035"/>
                ipſius
                  <var>.a.x.</var>
                tam ſit multiplex ad vnitatem, quam cupimus numerum
                  <var>.a.e.</var>
                numero
                  <var>.
                    <lb/>
                  e.o.</var>
                multiplicem eſſe.</s>
              </p>
            </div>
            <div xml:id="echoid-div81" type="math:theorem" level="3" n="37">
              <head xml:id="echoid-head53" xml:space="preserve">THEOREMA
                <num value="37">XXXVII</num>
              .</head>
              <p>
                <s xml:id="echoid-s325" xml:space="preserve">CVR inuenire cupientes duos numeros, quorum quadrata in ſummam colle-
                  <lb/>
                cta, æqualia ſint numero propoſito, & ijſdem numeris multiplicatis ad-
                  <lb/>
                inuicem, productum alteri numero propoſito ſit æquale, rectè ſumant dimidium
                  <lb/>
                primi numeri propoſiti, cui ſumma quadratorum æquari debet,
                  <reg norm="hocque" type="simple">hocq́;</reg>
                dimidium
                  <lb/>
                in ſeipſum multiplicent, vnà etiam alterum numerum propoſitum in ſeipſum
                  <lb/>
                multiplicent, quod quadratum detrahunt de primo, & reſidui quadratam radicem,
                  <lb/>
                dimidio primi numeri propoſiti coniungunt, ex qua ſumma, quadratam radicem
                  <lb/>
                  <reg norm="eruunt" type="context">eruũt</reg>
                , quæ duobus quæſitis numeris maior erit, cuius quadrato de primo numero
                  <lb/>
                detracto, & exreliquo erutaradice quadrata, detur minor numerus, duorum
                  <reg norm="quae- ſitorum" type="simple">quę-
                    <lb/>
                  ſitorum</reg>
                .</s>
              </p>
              <p>
                <s xml:id="echoid-s326" xml:space="preserve">Exempli gratia, ſi proponerentur .34. pro primo numero cui æquari de-
                  <lb/>
                beret ſumma duorum quadratorum, quorum radicum productum æquale eſſe de-
                  <lb/>
                beret alteri numero, verbi gratia .15. iubet antiquorum regula, dimidium primi
                  <lb/>
                numeri in ſeipſum multiplicari, cuius dimidij quadratum erit .289. è quo ſi detra-
                  <lb/>
                has quadratum ſecundi numeri, nempe .225. remanebit .64.
                  <reg norm="atque" type="simple">atq;</reg>
                huius ſi quadra-
                  <lb/>
                tam radicem ſumas nempe .8. quam dimidio primi numeri, nempe .17. coniun-
                  <lb/>
                gas, dabitur duorum quadratorum numerorum quęſitorum maior numerus .25. hac
                  <lb/>
                deinde radice è dimidio detracta, minus quadratum dabitur .9. ſcilicet, quorum
                  <lb/>
                radices .5. et .3. eſſent ij numeri, qui quæruntur.</s>
              </p>
              <p>
                <s xml:id="echoid-s327" xml:space="preserve">Cuius ſpeculationis gratia, cogitemus primum numerum, cui quadratorum fum
                  <lb/>
                ma æquari debet, ſignificari linea
                  <var>.a.n.</var>
                tum concipiamus quæſita quadrata ſignifi-
                  <lb/>
                cari,
                  <reg norm="coniungique" type="simple">coniungiq́</reg>
                modo ſubſcripto
                  <var>.t.b.k.</var>
                ſecundum porrò numerum propoſitum,
                  <lb/>
                ſignificari producto
                  <var>.d.b</var>
                . </s>
                <s xml:id="echoid-s328" xml:space="preserve">Iam nil ſupereſt aliud quam vt quantitates
                  <var>.d.p.</var>
                et
                  <var>.b.p.</var>
                  <lb/>
                quæramus.</s>
              </p>
              <p>
                <s xml:id="echoid-s329" xml:space="preserve">Itaque cum in linea
                  <var>.a.n.</var>
                ſummæ quadratorum numerus detur, quadratum di-
                  <lb/>
                midij
                  <var>.o.a.</var>
                ſit
                  <var>.s.a.</var>
                quod nobis erit cognitum; </s>
                <s xml:id="echoid-s330" xml:space="preserve">ſit etiam
                  <var>.a.u.</var>
                numerus quadrati ma
                  <lb/>
                ioris, et
                  <var>.u.n.</var>
                minoris, et
                  <var>.a.z.</var>
                productum vnius in alterum; </s>
                <s xml:id="echoid-s331" xml:space="preserve">qui quidem numerus
                  <var>.a.
                    <lb/>
                  z.</var>
                æqualis erit
                  <lb/>
                quadrato nume
                  <lb/>
                  <figure xlink:label="fig-0035-01" xlink:href="fig-0035-01a" number="49">
                    <image file="0035-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0035-01"/>
                  </figure>
                ri
                  <var>.d.b.</var>
                ex .19.
                  <lb/>
                theoremate hu-
                  <lb/>
                ius libri. </s>
                <s xml:id="echoid-s332" xml:space="preserve">
                  <reg norm="Itaque" type="simple">Itaq;</reg>
                  <lb/>
                  <var>a.z.</var>
                cognitum
                  <lb/>
                erit, cum eius
                  <lb/>
                radix
                  <var>.d.b.</var>
                ſit
                  <reg norm="ſe- cundus" type="context">ſe-
                    <lb/>
                  cũdus</reg>
                numerus
                  <lb/>
                propoſitus, quæ
                  <lb/>
                minor erit
                  <var>.a.s.</var>
                ex quinta ſecundi, aut ſeptima conſequentia poſt .16. noni Eucli-
                  <lb/>
                dis. </s>
                <s xml:id="echoid-s333" xml:space="preserve">Iam ſubtracta quantitate
                  <var>.z.a.</var>
                è quadrato
                  <var>.a.s.</var>
                cognoſcetur quadratum
                  <var>.t.x.</var>
                  <lb/>
                cuius radix æqualis erit
                  <var>.o.u.</var>
                ex poſtremo adductis, Itaque cognoſcemus
                  <var>.o.u.</var>
                qui
                  <lb/>
                numerus coniunctus dimidio
                  <var>.o.a.</var>
                cognito, dabit quadratum
                  <var>.a.u.</var>
                cognitum, at-
                  <lb/>
                queita
                  <var>.u.n.</var>
                pariter cognoſcetur, & eorum radices conſequenter.</s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum