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 |< < (198) 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-div387" type="chapter" level="2" n="4">
            <div xml:id="echoid-div439" type="section" level="3" n="39">
              <pb o="198" n="210" file="0210" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0210"/>
            </div>
          </div>
          <div xml:id="echoid-div441" type="chapter" level="2" n="5">
            <head xml:id="echoid-head321" xml:space="preserve">IN QVINTVM
              <lb/>
            EVCLIDIS LIBRVM</head>
            <p type="title" style="it">
              <s xml:id="echoid-s2404" xml:space="preserve">QVamuis omnia libri quinti Euclid. uerißima ſint.
                <lb/>
              </s>
              <s xml:id="echoid-s2405" xml:space="preserve">Animaduertimus tamen permultos ſumma
                <reg norm="cum" type="context">cũ</reg>
                <lb/>
              difficultate
                <reg norm="eorum" type="context">eorũ</reg>
              demonstr ationes percipere. </s>
              <s xml:id="echoid-s2406" xml:space="preserve">Prœ
                <unsure/>
              -
                <lb/>
              cipuè ubi quint a, aut ſeptima deffinitiones eiuſ-
                <lb/>
              dem libri neceſſariœ
                <unsure/>
              ſunt. </s>
              <s xml:id="echoid-s2407" xml:space="preserve">Illœ enim adeo obſcurœ
                <lb/>
              uidentur, ut longè facilius admißuri ſint hœc no-
                <lb/>
              ſtra poſtulat at anquam clarior a. </s>
              <s xml:id="echoid-s2408" xml:space="preserve">At que etiam tanquam intellectui
                <lb/>
              commodiora, quam ſit illud quintum
                <reg norm="idemque" type="simple">idemq́ꝫ</reg>
              ultimum postulatum
                <lb/>
              eiuſdem in primo libro poſitum, de line a duas alias ſecante. </s>
              <s xml:id="echoid-s2409" xml:space="preserve">Quan-
                <lb/>
              doquidem
                <reg norm="ijs" type="lig">ijs</reg>
              noſtris postulatis admißis, ſequentia Theoremata per
                <lb/>
              facillima reddentur.</s>
            </p>
            <div xml:id="echoid-div441" type="section" level="3" n="1">
              <div xml:id="echoid-div441" type="section" level="4" n="1">
                <head xml:id="echoid-head322" style="it" xml:space="preserve">Horum autem primum est.</head>
                <p>
                  <s xml:id="echoid-s2410" xml:space="preserve">
                    <emph style="sc">Qvod</emph>
                  tota compoſita ex æquali numero partium æqualium, ſunt inuicem
                    <lb/>
                  æqualia.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2411" xml:space="preserve">Vtſi quis diceret omnes proportiones quæ
                    <reg norm="compoſitæ" type="context">cõpoſitæ</reg>
                  ſunt ex æquali numero alia-
                    <lb/>
                  rum proportionum inuicem æqualium, ſunt etiam inuicem æquales, quod Eucli-
                    <lb/>
                  des conatur demonſtrare in .22. et .23. quinti libri.</s>
                </p>
              </div>
              <div xml:id="echoid-div442" type="section" level="4" n="2">
                <head xml:id="echoid-head323" xml:space="preserve">SECVNDVM.</head>
                <p>
                  <s xml:id="echoid-s2412" xml:space="preserve">
                    <emph style="sc">Qvod</emph>
                  ſi à totis æqualibus detractæ fuerint æquales partes, quæ remanent erunt
                    <lb/>
                  partes inuicem æquales.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2413" xml:space="preserve">Et è conuerſo ſi æqualibus æqualia addas compoſita erunt inuicem æqualia.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2414" xml:space="preserve">Quod in ipſis proportionibus hoc loco ſemper intelligendum eſt.</s>
                </p>
              </div>
              <div xml:id="echoid-div443" type="section" level="4" n="3">
                <head xml:id="echoid-head324" xml:space="preserve">TERTIVM.</head>
                <head xml:id="echoid-head325" style="it" xml:space="preserve">Quę est εuclidis ſeptima propoſitio.</head>
                <p>
                  <s xml:id="echoid-s2415" xml:space="preserve">
                    <emph style="sc">Qvod</emph>
                  ſi fuerint plures termini æquales inuicem, ratio ſeu proportio vnius ip-
                    <lb/>
                  ſorum ad alium tertium terminum maiorem, minoremúe, ſed eiuſdem generis, erit
                    <lb/>
                  cadem quæ cuiuſuis alterius termini ad eundem tertium. </s>
                  <s xml:id="echoid-s2416" xml:space="preserve">Et è conuerſo, quæ fuerit
                    <lb/>
                  proportio tertij termini ad vnum prædictorum æqualium, eadem erit, ſpecie, cum
                    <lb/>
                  alio eorundem terminorum.</s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum