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
111 99
112 100
113 101
114 102
115 103
116 104
117 105
118 106
119 107
120 108
121 109
122 110
123 111
124 112
125 113
126 114
127 115
128 116
129 117
130 118
131 119
132 120
133 121
134 122
135 123
136 124
137 125
138 126
139 127
140 128
< >
page |< < (82) 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-div230" type="math:theorem" level="3" n="120">
              <pb o="82" rhead="IO. BAPT. BENED." n="94" file="0094" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0094"/>
              <p>
                <s xml:id="echoid-s1083" xml:space="preserve">Pro cuius ratione conſideremus triangulum hic ſubnotatum
                  <var>.a.b.c.</var>
                cuius
                  <lb/>
                unumquodque latus ſignificet ſummam duorum ſociorum, vtputa latus
                  <var>.a.b.</var>
                ſignifi-
                  <lb/>
                cet ſummam primi cum ſecundo, latus verò
                  <var>.b.c.</var>
                ſummam ſecundi cum tertio, la-
                  <lb/>
                rus autem
                  <var>.a.c.</var>
                ſummam primi cum tertio, et
                  <var>.a.e.</var>
                ſeu
                  <var>.a.o.</var>
                ſit numerus primi ſocij, et
                  <var>.
                    <lb/>
                  e.b.</var>
                vel
                  <var>.b.u.</var>
                ſit ſecundi ſocij, et
                  <var>.c.u.</var>
                ſeu
                  <var>.c.o.</var>
                ſit tertij, cum autem
                  <var>.a.e.</var>
                æqualis ſit
                  <var>.a.o.</var>
                  <lb/>
                  <figure xlink:label="fig-0094-01" xlink:href="fig-0094-01a" number="128">
                    <image file="0094-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0094-01"/>
                  </figure>
                et
                  <var>.b.e</var>
                :æ qualis
                  <var>.b.u.</var>
                et
                  <var>.c.u.</var>
                æqualis
                  <var>.c.o.</var>
                  <lb/>
                ex ſuppoſito ſi
                  <reg norm="dempta" type="context">dẽpta</reg>
                fuerit ſumma ſeu
                  <lb/>
                latus
                  <var>.a.c.</var>
                datum ex aggregato laterum
                  <var>.
                    <lb/>
                  a.b.</var>
                cum
                  <var>.b.c.</var>
                reliquarum ſummarum, re
                  <lb/>
                linquet nobis cognitum aggregatum
                  <lb/>
                ex
                  <var>.b.e.</var>
                cum
                  <var>.b.u</var>
                . </s>
                <s xml:id="echoid-s1084" xml:space="preserve">Quare & eius medic-
                  <lb/>
                tas
                  <var>.b.e.</var>
                ſiue
                  <var>.b.u.</var>
                nobis cognita erit, qua
                  <lb/>
                detracta exſumma
                  <var>.b.a.</var>
                relinquetur no
                  <lb/>
                bis cognitus numerus
                  <var>.a.e.</var>
                detracto ve-
                  <lb/>
                ro numero
                  <var>.a.e.</var>
                hoc eſt
                  <var>.a.o.</var>
                ex
                  <var>.a.c.</var>
                ſum-
                  <lb/>
                ma, ſeu latus, aut
                  <var>.b.u.</var>
                ex
                  <var>.b.c.</var>
                remanebit
                  <lb/>
                  <var>o.c.</var>
                ſeu
                  <var>.c.u.</var>
                cognitus.</s>
              </p>
            </div>
            <div xml:id="echoid-div232" type="math:theorem" level="3" n="121">
              <head xml:id="echoid-head139" xml:space="preserve">THEOREMA
                <num value="121">CXXI</num>
              .</head>
              <p>
                <s xml:id="echoid-s1085" xml:space="preserve">HAC etiam methodo hoc facere poſſumus non
                  <reg norm="ſolum" type="context">ſolũ</reg>
                de tribus ſocijs, ſed
                  <reg norm="etiam" type="context">etiã</reg>
                  <lb/>
                de omnibus quotquot volueris, vt exempli gratia,
                  <lb/>
                  <figure xlink:label="fig-0094-02" xlink:href="fig-0094-02a" number="129">
                    <image file="0094-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0094-02"/>
                  </figure>
                ſint ſex ſocij
                  <var>.a.b.c.d.e.f.</var>
                quorum ſumma per binos co-
                  <lb/>
                gnita, vtputà ſumma numeri
                  <var>.a.</var>
                cum
                  <var>.b.</var>
                cognita nobis ſit,
                  <lb/>
                & ſumma numeri
                  <var>.b.</var>
                cum
                  <var>.c.</var>
                & ſumma
                  <var>.c.</var>
                cum
                  <var>.d.</var>
                & ſum-
                  <lb/>
                ma
                  <var>.d.</var>
                cum
                  <var>.e.</var>
                & ſumma
                  <var>.e.</var>
                cum
                  <var>.f.</var>
                neceſle eft etiam ſcire
                  <lb/>
                ſummam duorum vno relicto, vtputa ſummam
                  <var>.a.</var>
                cum
                  <lb/>
                c. vt poſſimus triangulum
                  <var>.a.b.c.</var>
                conſtituere. </s>
                <s xml:id="echoid-s1086" xml:space="preserve">Vnde ex
                  <lb/>
                præmiffa, cognitus numerus nobis erit vniuſcuiuſque
                  <var>.a.
                    <lb/>
                  b.c</var>
                . </s>
                <s xml:id="echoid-s1087" xml:space="preserve">Quapropter dempto numero
                  <var>.c.</var>
                ex ſumma
                  <var>.c.</var>
                cum
                  <lb/>
                d. & numero
                  <var>.d.</var>
                ex ſumma
                  <var>.d.</var>
                cum
                  <var>.e.</var>
                & numero
                  <var>.e.</var>
                ex ſum
                  <lb/>
                ma
                  <var>.e.</var>
                cum
                  <var>.f.</var>
                habebimus intentum.</s>
              </p>
            </div>
            <div xml:id="echoid-div234" type="math:theorem" level="3" n="122">
              <head xml:id="echoid-head140" xml:space="preserve">THEOREMA
                <num value="122">CXXII</num>
              ,</head>
              <p>
                <s xml:id="echoid-s1088" xml:space="preserve">CVM aliquando, illud quod Archimedes inuenit, vt furtum Regiab aurifa-
                  <lb/>
                bro in regia corona factum, quemadmodum ſcribit Vitruuius, proderet, con-
                  <lb/>
                templarer, mihi etiam viſum eſt, vt aliquem modum ſcientiſicum inueſtigarem, quo
                  <lb/>
                proportio auri ad argentum, quod in aliquo propoſito corpore exipſis miſto cogni
                  <lb/>
                ti ponderis cognoſci poſſet. </s>
                <s xml:id="echoid-s1089" xml:space="preserve">Et cum multos diuerſis temporibus excogitarim offi-
                  <lb/>
                cio meo deeſſe nolui in ijſdem literarum monumentis mandandis, quorum hic
                  <lb/>
                vnus erit: </s>
                <s xml:id="echoid-s1090" xml:space="preserve">propoſita nobis ſint tria corpora
                  <var>.A.M.V.</var>
                æqualia inter ſe, ſed diuer-
                  <lb/>
                ſarum ſpecierum materiei, vtputa quod
                  <var>.A.</var>
                ſit argenteum, & omogeneum
                  <var>.V.</var>
                ve-
                  <lb/>
                rò aureum omogeneum, & M. mixtum exauro, & argento, ideſt heterogeneum,
                  <lb/>
                cupimusergo ſcire
                  <reg norm="iuſtam" type="context">iuſtã</reg>
                quantitatem auri & argenti, quæ eſt in ipſo corpore
                  <var>.M.</var>
                  <lb/>
                miſto. </s>
                <s xml:id="echoid-s1091" xml:space="preserve">Ita igitur faciamus. </s>
                <s xml:id="echoid-s1092" xml:space="preserve">Videamus primum quantum ſit pondus vniuſcuiuſque
                  <lb/>
                ipſorum corporum, ponamus autem pondus corporis
                  <var>.V.</var>
                auri eſſe vt .234. pondus </s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum