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
51 39
52 40
53 41
54 42
55 43
56 44
57 45
58 46
59 47
60 48
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
< >
page |< < (17) 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-div59" type="math:theorem" level="3" n="26">
              <p>
                <s xml:id="echoid-s250" xml:space="preserve">
                  <pb o="17" rhead="THEOREM. ARITH." n="29" file="0029" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0029"/>
                numerorum, proueniat numerus æqualis numero producti duorum primorum nu-
                  <lb/>
                m erorum ſimul.</s>
              </p>
              <p>
                <s xml:id="echoid-s251" xml:space="preserve">Sint exempli gratia propoſiti numeri .2. et .8. qui mutuo diuiſi in primis dent pro
                  <lb/>
                uenientia quatuor integra, tum quartam partem pro altero proueniente, hæc colle-
                  <lb/>
                cta dabunt ſummam quatuor integrorum et quartæ partis vnius, ſumma autem qua
                  <lb/>
                dratorum binarij & octonarij erit .68. qui quidem numerus per quatuor & quar
                  <lb/>
                tam partem vnius diuiſus dabit .16. pro proueniente, quæ .16. æqualia erunt pro
                  <lb/>
                ducto binarii in octonarium.</s>
              </p>
              <p>
                <s xml:id="echoid-s252" xml:space="preserve">Cuius rei hæc erit ſpeculatio, ſint duæ lineæ
                  <var>.o.e.</var>
                et
                  <var>.o.n.</var>
                quæ duos numeros pro-
                  <lb/>
                poſitos ſignificent, inuicem ad angulum rectum
                  <var>.o.</var>
                coniunctæ, quarum quadrata
                  <lb/>
                ſint
                  <var>.o.a.</var>
                et
                  <var>.o.p.</var>
                ipſorum productum ſit
                  <var>.n.e.</var>
                tum
                  <var>.o.t.</var>
                ſit proueniens ex diuiſione
                  <var>.o.e.</var>
                  <lb/>
                per
                  <var>.o.n</var>
                . </s>
                <s xml:id="echoid-s253" xml:space="preserve">Hęc ſingulatim conſideremus (
                  <reg norm="nam" type="context">nã</reg>
                ſi in partibus ſimplicibus quod dicimus ac
                  <lb/>
                ciderit, id ipſum in compoſitis conſequenter eueniet) quamobrem ex definitione di
                  <lb/>
                uiſionis dabitur eadem proportio
                  <var>.o.e.</var>
                ad
                  <var>.o.t.</var>
                quæ eft
                  <var>.o.n.</var>
                ad vnitatem, quæ ſit
                  <var>.o.
                    <lb/>
                  x</var>
                . </s>
                <s xml:id="echoid-s254" xml:space="preserve">Nunc cogitemus
                  <reg norm="ſuperficiem" type="context">ſuperficiẽ</reg>
                  <reg norm="rectangulam" type="context">rectangulã</reg>
                  <var>.o.c.</var>
                  <reg norm="æqualem" type="context">æqualẽ</reg>
                quadrato
                  <var>.o.a</var>
                . </s>
                <s xml:id="echoid-s255" xml:space="preserve">tunc numerus
                  <var>.
                    <lb/>
                  c.t.</var>
                proueniens erit, ut patet, ex diuiſione numeri quadrati
                  <var>.o.a.</var>
                per
                  <reg norm="numerum" type="context">numerũ</reg>
                  <var>.o.t.</var>
                  <reg norm="eritque" type="simple">eritq́</reg>
                  <lb/>
                  <reg norm="eadem" type="context">eadẽ</reg>
                proportio
                  <var>.c.t.</var>
                ad
                  <var>.o.e.</var>
                quæ eſt
                  <var>.o.e.</var>
                ad
                  <var>.o.t.</var>
                ex ſecunda parte quintæ decimæ ſexti,
                  <lb/>
                aut .20. ſeptimi. </s>
                <s xml:id="echoid-s256" xml:space="preserve">
                  <reg norm="Iam" type="context">Iã</reg>
                  <reg norm="autem" type="context">autẽ</reg>
                dictum eſt
                  <var>.o.e.</var>
                ad
                  <var>.o.t.</var>
                ſic ſe habere ſicut
                  <var>.o.n.</var>
                ad
                  <var>.o.x</var>
                . </s>
                <s xml:id="echoid-s257" xml:space="preserve">
                  <reg norm="Itaque" type="simple">Itaq;</reg>
                ex .
                  <lb/>
                11. quinti ſic ſe habebit
                  <var>.c.t.</var>
                ad
                  <var>.o.e.</var>
                ſicut
                  <var>.o.n.</var>
                ad
                  <var>.o.x</var>
                . </s>
                <s xml:id="echoid-s258" xml:space="preserve">Sed ex prima ſexti, aut .18. vel .
                  <lb/>
                19. ſeptimi, ſic ſe habet
                  <reg norm="productum" type="simple">ꝓductum</reg>
                  <var>.n.e.</var>
                ad
                  <var>.e.x.</var>
                ſicut
                  <var>.o.n.</var>
                ad
                  <var>.o.x</var>
                . </s>
                <s xml:id="echoid-s259" xml:space="preserve">quare denuo ſic ſe ha-
                  <lb/>
                bebit numerus
                  <var>.c.t.</var>
                ad numerum
                  <var>.o.e.</var>
                ſicut nume-
                  <lb/>
                rus
                  <var>.n.e.</var>
                ad numerum
                  <var>.x.e</var>
                . </s>
                <s xml:id="echoid-s260" xml:space="preserve">Sed numerus
                  <var>.o.e.</var>
                cum
                  <lb/>
                  <figure xlink:label="fig-0029-01" xlink:href="fig-0029-01a" number="38">
                    <image file="0029-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0029-01"/>
                  </figure>
                numero
                  <var>.x.e.</var>
                ſpecie idem eſt, igitur ex .9. quinti nu
                  <lb/>
                merus
                  <var>.c.t.</var>
                numero
                  <var>.n.e.</var>
                æqualis erit.</s>
              </p>
              <p>
                <s xml:id="echoid-s261" xml:space="preserve">Id ipſum de quadrato ipſius
                  <var>.o.n.</var>
                videlicet
                  <var>.p.o.</var>
                  <lb/>
                dico. </s>
                <s xml:id="echoid-s262" xml:space="preserve">Nam ſi proueniens
                  <var>.o.n.</var>
                diuiſo per
                  <var>.o.e.</var>
                ideſt
                  <var>.
                    <lb/>
                  o.i.</var>
                proportionale reſpondens ad
                  <var>.o.t.</var>
                cum
                  <var>.o.t.</var>
                  <lb/>
                  <reg norm="coniunctum" type="context">coniunctũ</reg>
                fuerit, et per
                  <reg norm="hanc" type="context">hãc</reg>
                ſummam diuiſa ſumma
                  <lb/>
                quadratorum
                  <var>.o.a.</var>
                et
                  <var>.o.p.</var>
                patet per ſe proueniens
                  <lb/>
                futurum eiuſdem numeri
                  <var>.c.t.</var>
                  <reg norm="ipſumque" type="simple">ipſumq́</reg>
                  <var>.c.t.</var>
                proue-
                  <lb/>
                niens ſemper ſuturum.</s>
              </p>
              <p>
                <s xml:id="echoid-s263" xml:space="preserve">Quo autem lucidius res hæc innoteſcat. </s>
                <s xml:id="echoid-s264" xml:space="preserve">Cogi
                  <lb/>
                temus proueniens quadrati
                  <var>.o.p.</var>
                diuiſi ab
                  <var>.o.i.</var>
                re-
                  <lb/>
                  <reg norm="ſpondentisque" type="simple">ſpondentisq;</reg>
                  <var>.o.t.</var>
                eſſe
                  <var>.i.u.</var>
                quod via prædicta inue-
                  <lb/>
                nitur æqualis eſſe numero
                  <var>.n.e.</var>
                ex quo conſe-
                  <lb/>
                quenter æquale
                  <var>.c.t</var>
                : cogitato deinde rectangu-
                  <lb/>
                lo
                  <var>.o.u.</var>
                æquali
                  <var>.o.p.</var>
                coniuncto
                  <var>.o.c</var>
                :totum
                  <var>.t.u.</var>
                æqua-
                  <lb/>
                le erit compoſito duorum quadratorum
                  <var>.o.a.</var>
                et
                  <var>.o.
                    <lb/>
                  p.</var>
                cum in nullo numerus
                  <var>.c.t.</var>
                mutetur, tam ex com-
                  <lb/>
                poſito
                  <var>.t.u.</var>
                  <reg norm="quam" type="context">quã</reg>
                ex ſimplici
                  <var>.o.c.</var>
                ex quo propoſiti ſe
                  <lb/>
                ſe ueritas profert.</s>
              </p>
            </div>
            <div xml:id="echoid-div61" type="math:theorem" level="3" n="27">
              <head xml:id="echoid-head43" xml:space="preserve">THEOREMA
                <num value="27">XXVII</num>
              .</head>
              <p>
                <s xml:id="echoid-s265" xml:space="preserve">
                  <emph style="sc">PRoposvervnt</emph>
                veteres nobile quidem problema, ſed quod tamen citra al-
                  <lb/>
                gebraticam effectionem, aut neſcierunt, aut noluerunt diſſoluere, quod nihi-
                  <lb/>
                lominus facillimum eſt.</s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>