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
81 71
82 70
83 71
84 72
85 73
86 74
87 75
88 76
89 77
90 78
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
< >
page |< < (87) 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-div244" type="math:theorem" level="3" n="128">
              <p>
                <s xml:id="echoid-s1134" xml:space="preserve">
                  <pb o="87" rhead="THEOREM. ARITH." n="99" file="0099" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0099"/>
                tionatus .216. ad .156. vt .18. ad .13. maniteſtum eſt exijſdem, nam tam .18. quam
                  <num value="13">.
                    <lb/>
                  13.</num>
                multiplicatus fuit per .12.</s>
              </p>
            </div>
            <div xml:id="echoid-div245" type="math:theorem" level="3" n="129">
              <head xml:id="echoid-head147" xml:space="preserve">THEOREMA
                <num value="129">CXXIX</num>
              .</head>
              <p>
                <s xml:id="echoid-s1135" xml:space="preserve">ALIVD proponitur problema hoc modo: </s>
                <s xml:id="echoid-s1136" xml:space="preserve">ſupponitur obſidio alicuius loci, vbi
                  <lb/>
                alimento ad nutriendos .10000. homines ſufficiunt pro quinque menſibus tan-
                  <lb/>
                tum, ſed quia eum locum obſidione non liberari putatur niſi .18. menſibus exactis,
                  <lb/>
                quæritur, quot homines eo tempore illis alimentis nutriri poſſint, hoc eſt .18.
                  <lb/>
                menſibus.</s>
              </p>
              <p>
                <s xml:id="echoid-s1137" xml:space="preserve">Præcipitregula, vt multiplicetur primus numerus, hoc eſt hominum .10000. cum
                  <lb/>
                ſecundo, hoc eſt menſium quinque, productum verò diuidatur per .18. hoc eſt men-
                  <lb/>
                ſium, </s>
                <s xml:id="echoid-s1138" xml:space="preserve">tunc proueniet .2777. cum .7. nonis.</s>
              </p>
              <p>
                <s xml:id="echoid-s1139" xml:space="preserve">Cuius operationis ratio eſt hæc, ſint exempli gratia duo hic ſubſcripta producta
                  <lb/>
                ſuperficialia
                  <var>.a.n.</var>
                et
                  <var>.o.u.</var>
                inuicem æqualia, ſed tal@ figura delineata, vt proportio
                  <var>.u.
                    <lb/>
                  x.</var>
                ad
                  <var>.x.o.</var>
                ſit, vt .10000. ad quinque, & proportio
                  <var>a.x.</var>
                ad
                  <var>.x.o.</var>
                ſit vt .18. ad quinque,
                  <lb/>
                ct
                  <var>.x.n.</var>
                ſit nobis ignota, quæ quidem eſt illa, quæ indagatur, ita
                  <reg norm="quod" type="simple">ꝙ</reg>
                vnumquodque
                  <lb/>
                iſtorum productorum ſignificabit alimentum, et
                  <var>.u.x.</var>
                ſignificabit numerum homi-
                  <lb/>
                num .10000. qui quidem homines comederent totum alimentum
                  <var>.u.o.</var>
                ſpacio tem-
                  <lb/>
                poris
                  <var>.x.o.</var>
                quinque menſium, proptereà quòd
                  <var>u.o.</var>
                ſupponitur productum eſſe ab
                  <var>.
                    <lb/>
                  u.x.</var>
                in
                  <var>.x.o</var>
                . </s>
                <s xml:id="echoid-s1140" xml:space="preserve">Deinde
                  <reg norm="ſupponendo" type="context">ſupponẽdo</reg>
                  <var>.a.x.</var>
                tem
                  <lb/>
                  <figure xlink:label="fig-0099-01" xlink:href="fig-0099-01a" number="134">
                    <image file="0099-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0099-01"/>
                  </figure>
                pus eſſe .18. menſium, ergo
                  <var>.x.n.</var>
                ſignifi-
                  <lb/>
                cabit numerum hominum, qui eo tem-
                  <lb/>
                poris ſpacio ali poſſunt, hoc eſt
                  <var>.x.a.</var>
                ali-
                  <lb/>
                mento
                  <var>.n.a.</var>
                eo quòd
                  <var>.a.n.</var>
                producitur ex
                  <var>.
                    <lb/>
                  n.x.</var>
                in
                  <var>.a.x.</var>
                vnde ex .15. ſexti, ſeu ex, 20.
                  <lb/>
                ſeptimi proportio
                  <var>.x.u.</var>
                ad
                  <var>.x.n.</var>
                  <reg norm="eadem" type="context">eadẽ</reg>
                erit,
                  <lb/>
                quę
                  <var>.a.x.</var>
                ad
                  <var>.x.o.</var>
                quapropter rectè factum
                  <lb/>
                erit accipere
                  <reg norm="productum" type="context">productũ</reg>
                  <var>.u.o.</var>
                quodidem
                  <lb/>
                eſt in quantitate, quod productum .2. n. & ipſum diuidere per
                  <var>.a.x.</var>
                vnde nobis
                  <lb/>
                proueniat
                  <var>.n.x</var>
                .</s>
              </p>
            </div>
            <div xml:id="echoid-div247" type="math:theorem" level="3" n="130">
              <head xml:id="echoid-head148" xml:space="preserve">THEOREMA
                <num value="130">CXXX</num>
              .</head>
              <p>
                <s xml:id="echoid-s1141" xml:space="preserve">QVotieſcunque nobis propoſitum fuerit inuenire tertium terminum, trium ter
                  <lb/>
                minorum continuè proportionalium armonicæ proportionalitatis, quo-
                  <lb/>
                tum duo nobis cogniti ſint, ita agemus.</s>
              </p>
              <p>
                <s xml:id="echoid-s1142" xml:space="preserve">Sint, exempli gratia, tres termini
                  <var>.q.p</var>
                :
                  <var>a.g.</var>
                et
                  <var>.e.c.</var>
                continuæ proportionalium at
                  <lb/>
                monicæ proportionalitatis, quorum
                  <var>.q.p.</var>
                maior et
                  <var>.a.g.</var>
                medius ſint nobis cogniti,
                  <lb/>
                cum ergo voluerimus tertium
                  <var>.e.
                    <lb/>
                  c.</var>
                cognitum nobis eſſe: </s>
                <s xml:id="echoid-s1143" xml:space="preserve">a.g. detra-
                  <lb/>
                  <figure xlink:label="fig-0099-02" xlink:href="fig-0099-02a" number="135">
                    <image file="0099-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0099-02"/>
                  </figure>
                hatur ex
                  <var>.q.p.</var>
                differentia verò
                  <var>.d.
                    <lb/>
                  p.</var>
                addatur
                  <var>.q.p.</var>
                quorum ſumma
                  <lb/>
                erit
                  <var>.q.o.</var>
                cognita, qua mediante
                  <lb/>
                diuidatur productum, quod ex
                  <var>.a.
                    <lb/>
                  g.</var>
                in
                  <var>.d.p.</var>
                exurgit, & proueniet no
                  <lb/>
                bis
                  <var>.n.g.</var>
                hoc e@t minor differentia, eo quòd productum
                  <var>.q.o.</var>
                in
                  <var>.n.g.</var>
                æquale eſt pro- </s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>