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 |< < (91) 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-div258" type="math:theorem" level="3" n="135">
              <p>
                <s xml:id="echoid-s1187" xml:space="preserve">
                  <pb o="91" rhead="THEOREM. ARIT." n="103" file="0103" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0103"/>
                propoſiti
                  <var>.a.e.</var>
                maior, et
                  <var>.e.o.</var>
                minor,
                  <reg norm="Sitque" type="simple">Sitq́;</reg>
                  <var>.o.k.</var>
                medius arithmeticus inter dictos, vn-
                  <lb/>
                de clarè patebit
                  <var>.o.k.</var>
                eſſe dimidium ſummæ dictorum terminorum ex .75. theorema
                  <lb/>
                te huius libri. </s>
                <s xml:id="echoid-s1188" xml:space="preserve">Sit ergo productum
                  <var>a.t.</var>
                id quod fit ex
                  <var>.a.e.</var>
                in
                  <var>.o.k.</var>
                et
                  <var>.o.t.</var>
                ſit
                  <reg norm="productum" type="context">productũ</reg>
                  <lb/>
                quod fit ex
                  <var>.e.o.</var>
                in
                  <var>.o.k.</var>
                et
                  <var>.n.m.</var>
                ſit productum quod ſit ex
                  <var>.a.e.</var>
                in
                  <var>.e.o.</var>
                quorum vnum-
                  <lb/>
                quodque erit dimid ium vniuſcuiuſque producti præcedentis theorematis,
                  <lb/>
                ex .18. et .19. ſeptimi Eucli. vnumquodque ſui relatiui. </s>
                <s xml:id="echoid-s1189" xml:space="preserve">Quare argumentando per
                  <lb/>
                mutando à concluſionibus præcedentis theorematis ad has præſentis, habebimus
                  <lb/>
                productum.</s>
              </p>
            </div>
            <div xml:id="echoid-div260" type="math:theorem" level="3" n="136">
              <head xml:id="echoid-head154" xml:space="preserve">THEOREMA
                <num value="136">CXXXVI</num>
              .</head>
              <p>
                <s xml:id="echoid-s1190" xml:space="preserve">MEDIVM autem contra
                  <reg norm="harmonicum" type="context">harmonicũ</reg>
                inuenire cum quis voluesit inter duos
                  <lb/>
                propoſitos terminos, ita faciendum erit, hoc eſt per ſummam datorum ex
                  <lb/>
                tremorum diuidatur productum quod fit ex minimo termino in
                  <reg norm="differentiam" type="context">differẽtiam</reg>
                dato-
                  <lb/>
                rum, prouentus poſtea erit differentia inter maximum & med
                  <unsure/>
                um quæſitum.</s>
              </p>
              <p>
                <s xml:id="echoid-s1191" xml:space="preserve">Vt exempli gratia, ſi nobis propoſiti fuerint hi duo termini .3. et .2. ſumma eo-
                  <lb/>
                rum erit quinque, per quam cum diuiſerimus productum, quod naſcitur ex mini-
                  <lb/>
                mo .2. in differentiam eorum, quæ eſt vnum, quod quidem erit .2. </s>
                <s xml:id="echoid-s1192" xml:space="preserve">tunc duæ quintæ
                  <lb/>
                partes prouenient, quæ ſi demptæ fuerint ex maximo termino, reliquum erit .2.
                  <reg norm="cum" type="context">cũ</reg>
                  <lb/>
                3. quintis, hoc eſt medius terminus contta harmonicus.</s>
              </p>
              <p>
                <s xml:id="echoid-s1193" xml:space="preserve">Pro cuius ratione cogitemus
                  <var>.u.d.</var>
                et
                  <var>.x.c.</var>
                eſſe duosterminosnobis propoſitos, in-
                  <lb/>
                ter quos deſideremus inuenire
                  <var>.o.s.</var>
                medium ita illis
                  <reg norm="relatum" type="context">relatũ</reg>
                , vt proportio exceſſus ip-
                  <lb/>
                ſius ſupra
                  <var>.x.c.</var>
                (qui ſit
                  <var>.e.n.</var>
                ) ad exceſ-
                  <lb/>
                ſum
                  <var>.u.d.</var>
                ſupra
                  <var>.o.s.</var>
                (qui ſit
                  <var>.n.d.</var>
                ) ea-
                  <lb/>
                  <figure xlink:label="fig-0103-01" xlink:href="fig-0103-01a" number="142">
                    <image file="0103-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0103-01"/>
                  </figure>
                dem ſit quæ
                  <var>.u.d.</var>
                ad
                  <var>.x.c</var>
                .</s>
              </p>
              <p>
                <s xml:id="echoid-s1194" xml:space="preserve">Cogitemus igitur
                  <var>.x.c.</var>
                coniunctum
                  <lb/>
                eſſe cum
                  <var>.u.d.</var>
                & hæcſumma vocetur
                  <var>.
                    <lb/>
                  b.d.</var>
                vnde habebimus proportionem
                  <var>.
                    <lb/>
                  u.d.</var>
                ad
                  <var>.u.b.</var>
                vt
                  <var>.e.n.</var>
                ad
                  <var>.n.d</var>
                . </s>
                <s xml:id="echoid-s1195" xml:space="preserve">Quare
                  <reg norm="com- ponendo" type="context">cõ-
                    <lb/>
                  ponendo</reg>
                ita erit
                  <var>.d.b.</var>
                ad
                  <var>.u.b.</var>
                ut
                  <var>.e.d.</var>
                3d.n.d. ſed quia
                  <var>.d.b</var>
                :
                  <var>u.b.</var>
                et
                  <var>.e.d.</var>
                quantitates no-
                  <lb/>
                bis cognitę ſunt, ideò
                  <var>.d.n.</var>
                ex .20. ſeptimi cognita nobis erit.</s>
              </p>
            </div>
            <div xml:id="echoid-div262" type="math:theorem" level="3" n="137">
              <head xml:id="echoid-head155" xml:space="preserve">THEOREMA
                <num value="137">CXXXVII</num>
              .</head>
              <p>
                <s xml:id="echoid-s1196" xml:space="preserve">SVpponunt antiqui aliquot mercatores dantes pecunias lucro in diuerſis vnius
                  <lb/>
                anni temporibus, </s>
                <s xml:id="echoid-s1197" xml:space="preserve">tunc in fine anni ſumma torius lucri datur cognita, ſed quæ-
                  <lb/>
                ritur quantuni
                  <unsure/>
                vnicuique illorum exipſa ſumma debeatur.</s>
              </p>
              <p>
                <s xml:id="echoid-s1198" xml:space="preserve">Exempli gratia, primus in principio anni poſuit .100. aurcos, ſecundus verò .100
                  <lb/>
                diebus poſt primum poſuit .50. aureos tertius autem .200. diebus poſt primum po-
                  <lb/>
                ſuit .25. aureos ſumma lucri poſtea in fine anni fuit aureorum .60.</s>
              </p>
              <p>
                <s xml:id="echoid-s1199" xml:space="preserve">Nunc vt ſciamus quantum huius ſummæ vniduique illorum proueniat, præcipit
                  <lb/>
                regula, vt faciamus tria producta, quorum primum ſit ex numero dierum totius an-
                  <lb/>
                ni in numerum aureorum primi, vnde tale productum in præſenti caſu erit .36500.
                  <lb/>
                ſecundum verò ſit ex numero dierum à primo die in quo ipſe ſecundus poſuit uſque
                  <lb/>
                ad finem anni, in numerum ipſorum nummorum, quod erit .13250. tertium autem
                  <lb/>
                productum ex diebus tertij in numerum ſuorum aureorum, quod
                  <reg norm="quidem" type="context">quidẽ</reg>
                erit .4125.
                  <lb/>
                quæ producta ſimul collecta faciunt .53875. deinde multiplicetur vnumquodque </s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum