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
91 79
92 80
93 81
94 82
95 89
96 84
97 85
98 96
99 87
100 88
101 89
102 90
103 91
104 92
105 93
106 94
107 95
108 96
109 97
110 98
111 99
112 100
113 101
114 102
115 103
116 104
117 105
118 106
119 107
120 108
< >
page |< < (200) 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-div441" type="chapter" level="2" n="5">
            <div xml:id="echoid-div441" type="section" level="3" n="1">
              <div xml:id="echoid-div448" type="section" level="4" n="8">
                <pb o="200" rhead="IO. BAPT. BENED." n="212" file="0212" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0212"/>
              </div>
              <div xml:id="echoid-div449" type="section" level="4" n="9">
                <head xml:id="echoid-head336" xml:space="preserve">NONVM.</head>
                <head xml:id="echoid-head337" style="it" xml:space="preserve">Euclidis uero tertiadecima propoſitio.</head>
                <p>
                  <s xml:id="echoid-s2424" xml:space="preserve">
                    <emph style="sc">Qvotiescvnqve</emph>
                  aliqua proportio plurium proportionum inuicem æqua-
                    <lb/>
                  lium, tertia aliqua proportione, maior aut minor fuerit, quælibet prædictarum æqua
                    <lb/>
                  lium inter ſe, tertia illa proportione maior aut minor pariter erit.</s>
                </p>
              </div>
              <div xml:id="echoid-div450" type="section" level="4" n="10">
                <head xml:id="echoid-head338" xml:space="preserve">DECIMVM.</head>
                <p>
                  <s xml:id="echoid-s2425" xml:space="preserve">
                    <emph style="sc">Qvotiescvnqve</emph>
                  fuerint ex vna parte plurestermini (ſiue coniuncti ſiue di-
                    <lb/>
                  ſiuncti ſint) æquales ſinguli vni tertio termino; </s>
                  <s xml:id="echoid-s2426" xml:space="preserve">ex altera verò parte totidem fuerint
                    <lb/>
                  alteri tertio termino æquales, proportio aggregati priorum terminorum ad
                    <reg norm="ſuum" type="context">ſuũ</reg>
                  ter-
                    <lb/>
                  tium, æqualis erit proportioni aggregati reliquorum terminorum ad ſuum tertium,
                    <lb/>
                  & è conuerſo, ita ſe habebit primus tertius terminus ad ſuos multos terminos, ſicut
                    <lb/>
                  ſe habet ſecundus tertius terminus ad ſuos ſimul ſumptos.</s>
                </p>
              </div>
              <div xml:id="echoid-div451" type="section" level="4" n="11">
                <head xml:id="echoid-head339" xml:space="preserve">VNDECIMVM.</head>
                <p>
                  <s xml:id="echoid-s2427" xml:space="preserve">Aggregatum ex partibus proportiona litatis continuæ, quod inter maximum, &
                    <lb/>
                  minimum terminum omnium terminorum proportionalium compræhenditur, ſem
                    <lb/>
                  per multiplex eſt ad ſingulas partiales proportiones, ex quibus ipſum componitur.</s>
                </p>
              </div>
              <div xml:id="echoid-div452" type="section" level="4" n="12">
                <head xml:id="echoid-head340" xml:space="preserve">DVODECIMVM.</head>
                <p>
                  <s xml:id="echoid-s2428" xml:space="preserve">Quæuis proportio quocunque modo diuiſa fuerit, ex iis partibus componitur, in
                    <lb/>
                  quas diuiditur.</s>
                </p>
                <p style="it">
                  <s xml:id="echoid-s2429" xml:space="preserve">Cum enim bæ præpoſitiones ſint ita conſpicuæ ipſi intellectui, ut
                    <reg norm="abſque" type="simple">abſq;</reg>
                  dubio inter obie
                    <lb/>
                  ct a ipſius intellectus connumerari poſſint, nullus ſanæ mentis eas negabit.</s>
                </p>
              </div>
            </div>
            <div xml:id="echoid-div454" type="section" level="3" n="2">
              <div xml:id="echoid-div454" type="section" level="4" n="1">
                <head xml:id="echoid-head341" xml:space="preserve">THEOR.I. II. ET III.</head>
                <p>
                  <s xml:id="echoid-s2430" xml:space="preserve">PRimum, ſecundum, & tertium theorema quinti Euclidis ab ipſo ſatis exactè de
                    <lb/>
                  monſtratur, ſtudioſus itaque autorem conſulat.</s>
                </p>
              </div>
              <div xml:id="echoid-div455" type="section" level="4" n="2">
                <head xml:id="echoid-head342" xml:space="preserve">THEOREM. IIII.</head>
                <p>
                  <s xml:id="echoid-s2431" xml:space="preserve">QVartum vero Theorema Eu-
                    <lb/>
                    <figure xlink:label="fig-0212-01" xlink:href="fig-0212-01a" number="262">
                      <image file="0212-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0212-01"/>
                    </figure>
                  clidis ego ſic
                    <reg norm="demonſtrarem" type="context">demonſtrarẽ</reg>
                  .
                    <lb/>
                  </s>
                  <s xml:id="echoid-s2432" xml:space="preserve">ſit, verbi gratia, proportio
                    <var>.a.</var>
                  ad
                    <var>.b.</var>
                    <lb/>
                  quæ eſt
                    <var>.c.</var>
                  ad
                    <var>.d.</var>
                  ſumptis multiplici-
                    <lb/>
                  bus
                    <var>.e.</var>
                  et
                    <var>.f.</var>
                  ad
                    <var>.a.</var>
                  et
                    <var>.c.</var>
                  æqualiter, item
                    <lb/>
                  multiplicibus
                    <var>.g.</var>
                  et
                    <var>.h.</var>
                  ad
                    <var>.b.</var>
                  et
                    <var>.d.</var>
                  dico
                    <lb/>
                  proportionem
                    <var>.e.</var>
                  ad
                    <var>.g.</var>
                  eſſe eandem
                    <lb/>
                  quæ eſt
                    <var>.f.</var>
                  ad
                    <var>.h</var>
                  . </s>
                  <s xml:id="echoid-s2433" xml:space="preserve">Habemus enim ex .10
                    <lb/>
                  poſtulato præmiſſo, eandem futuram
                    <lb/>
                  proportionem
                    <var>.e.</var>
                  ad
                    <var>.a.</var>
                  quæ eſt
                    <var>.f.</var>
                  ad
                    <var>.c.</var>
                    <lb/>
                  & ita
                    <var>.b.</var>
                  ad
                    <var>.g.</var>
                  quæ eſt
                    <var>.d.</var>
                  ad
                    <var>.h.</var>
                  ex præ-
                    <lb/>
                  ſuppoſito verò
                    <reg norm="cum" type="context">cũ</reg>
                  ſic ſe habeat
                    <var>.a.</var>
                  ad
                    <lb/>
                  b. ſicut
                    <var>.c.</var>
                  ad
                    <var>.d.</var>
                  erit ex primo poſtula-
                    <lb/>
                  to
                    <reg norm="eadem" type="context">eadẽ</reg>
                  proportio
                    <var>.e.</var>
                  ad
                    <var>.g.</var>
                  quæ eſt
                    <var>.f.</var>
                    <lb/>
                  ad
                    <var>.h</var>
                  . </s>
                  <s xml:id="echoid-s2434" xml:space="preserve">Nam proportio
                    <var>.e.</var>
                  ad
                    <var>.g.</var>
                  compo
                    <lb/>
                  nitur ex eis quæ ſunt
                    <var>.e.</var>
                  ad .a: et
                    <var>.a.</var>
                  ad
                    <var>. </var>
                  </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum