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
141 129
142 130
143 131
144 132
145 133
146 134
147 135
148 136
149 137
150 138
151 139
152 140
153 141
154 142
155 143
156 144
157 145
158 146
159 147
160 148
161 149
162 150
163 151
164 152
165 153
166 154
167 155
168 156
169 157
170 158
< >
page |< < (366) of 445 > >|
IO. BAPT. BENED.
    <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-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div708" type="section" level="3" n="36">
              <div xml:id="echoid-div710" type="letter" level="4" n="2">
                <p>
                  <s xml:id="echoid-s4369" xml:space="preserve">
                    <pb o="366" rhead="IO. BAPT. BENED." n="378" file="0378" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0378"/>
                  proportionalis inter
                    <var>.g.</var>
                  et
                    <var>.h</var>
                  . </s>
                  <s xml:id="echoid-s4370" xml:space="preserve">quare
                    <var>.g.</var>
                  et
                    <var>.h.</var>
                  non erunt minimi in ea proportione, quia
                    <lb/>
                  vnitas diuiſibilis eſſet ſi
                    <var>.g.h.</var>
                  minimi fuiſſent, quod non conceditur, ſint igitur mini
                    <lb/>
                  mi in dicta proportione
                    <var>.a.</var>
                  et
                    <var>.b.</var>
                  quorum differentia erit vnitas, vt ſcis,
                    <reg norm="ſitque" type="simple">ſitq́;</reg>
                    <var>.c.</var>
                  quadra
                    <lb/>
                  tum ipſius
                    <var>.g.</var>
                  et
                    <var>.d.</var>
                  quadratum ipſius
                    <var>.K</var>
                  . </s>
                  <s xml:id="echoid-s4371" xml:space="preserve">tunc clarum erit ex .11. octaui, quod propor-
                    <lb/>
                  tio ipſius c. ad
                    <var>.d.</var>
                  eadem erit quæ
                    <var>.g.</var>
                  ad
                    <var>.h.</var>
                  hoc eſt vt ipſius
                    <var>.a.</var>
                  ad
                    <var>.b.</var>
                  vnde ſi vnus termi.
                    <lb/>
                  norum
                    <var>.a.</var>
                  vel
                    <var>.b.</var>
                  eſſet quadratus, reliquus etiam quadratus eſſet ex .22. octaui, & ex
                    <lb/>
                  16. eiuſdem, inter
                    <var>.a.</var>
                  et
                    <var>.b.</var>
                  reperiretur aliquis medius numerus proportionalis, quod
                    <lb/>
                  fieri non poteſt ex hypotheſi, cum inter
                    <var>.a.</var>
                  et
                    <var>.b.</var>
                  nullus ſit numerus, quia differunt in
                    <lb/>
                  ter ſe per vnitatem tantummodo. </s>
                  <s xml:id="echoid-s4372" xml:space="preserve">Nunc autem cum nullus numerorum
                    <var>.a.</var>
                  vel
                    <var>.b.</var>
                  qua
                    <lb/>
                  dratus ſit, ponatur quod
                    <var>.f.</var>
                  quadratus ſit ipſius
                    <var>.b.</var>
                  et
                    <var>.e.</var>
                  ſit productum ipſius
                    <var>.a.</var>
                  in
                    <var>.b.</var>
                  vn
                    <lb/>
                  de ex .18. ſeptimi, proportio ipſius
                    <var>.e.</var>
                  ad
                    <var>.f.</var>
                  erit vt. ipſius
                    <var>.a.</var>
                  ad
                    <var>.b.</var>
                  hoc eſt vt ipſius
                    <var>.c.</var>
                  ad
                    <lb/>
                  d. quapropter
                    <var>.e.</var>
                  erit quadratus ex .22. octaui, cuius latus tetragonicum eſſet
                    <reg norm="medium" type="context">mediũ</reg>
                    <lb/>
                  proportionale inter
                    <var>.a.</var>
                  et
                    <var>.b.</var>
                  ex .20. ſeptimi, quod eſt impoſſibile, vt iam dixi, cum
                    <var>.a.</var>
                    <lb/>
                  et
                    <var>.b.</var>
                  ſint inui cem conſequentes, vnus poſt alium immediatè.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4373" xml:space="preserve">Superius enim dixi hunc modum eſſe vniuerſalem,
                    <lb/>
                  hoc eſt quod hac methodo poſſumus in cognitionem
                    <lb/>
                  vcnire, quod non ſolum in duas æquales partes diui-
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0378-01a" xlink:href="fig-0378-01"/>
                  di non poſſit, ſed nec in tres, nec quatuor nec quot vo
                    <lb/>
                  lueris. </s>
                  <s xml:id="echoid-s4374" xml:space="preserve">Primum enim quod non in tres diuidatur à te
                    <lb/>
                  ipſo cognoſces ope
                    <reg norm="cuborum" type="context">cuborũ</reg>
                  vice
                    <reg norm="quadratorum" type="context">quadratorũ</reg>
                  , opevero
                    <lb/>
                    <reg norm="cenſuum" type="context">cenſuũ</reg>
                    <reg norm="cenſuum" type="context context">cẽſuũ</reg>
                  , ve
                    <unsure/>
                  l qui cognouerit eam
                    <reg norm="proportionem" type="context">proportionẽ</reg>
                    <lb/>
                  eſſe indiuiſibilem per æqualia, illicò etiam cognoſcet
                    <lb/>
                  indiuiſibilem eſſe per quatuor partes, ope verò pri-
                    <lb/>
                  morum relatorum, cognoſcet non eſſe diuiſibilem per
                    <lb/>
                    <reg norm="quinque" type="simple">quinq;</reg>
                  partes, & ſic de cęteris, ſed mediantibus ijs
                    <lb/>
                  quas ſcripſi de iſtis dignitatibus in libro
                    <reg norm="Thęorematum" type="context">Thęorematũ</reg>
                    <lb/>
                  arithmeticorum.</s>
                </p>
                <div xml:id="echoid-div710" type="float" level="5" n="1">
                  <figure xlink:label="fig-0378-01" xlink:href="fig-0378-01a">
                    <image file="0378-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0378-01"/>
                  </figure>
                </div>
                <p>
                  <s xml:id="echoid-s4375" xml:space="preserve">Id autem quod Illuſtriſſimus Daniel Barbarus ſcri
                    <lb/>
                  bit in quinta parte ſuæ perſpectiuæ, ſi ſupra aliquo im
                    <lb/>
                  mobili, atque magno pariete facere volueris, te opor
                    <lb/>
                  tebit hoc ex reflexione radij ſolaris à ſpeculo plano
                    <lb/>
                  perficere.</s>
                </p>
              </div>
            </div>
            <div xml:id="echoid-div713" type="section" level="3" n="37">
              <div xml:id="echoid-div713" type="letter" level="4" n="1">
                <head xml:id="echoid-head540" xml:space="preserve">DE INVENTIONE DIAMETRI
                  <lb/>
                circuli circunſcribentis triangulum.</head>
                <head xml:id="echoid-head541" style="it" xml:space="preserve">Francbino Triuultio.</head>
                <p>
                  <s xml:id="echoid-s4376" xml:space="preserve">
                    <emph style="sc">QVod</emph>
                  mihi nunc proponis eſt triangulum, cuius baſis cum angulo ſibi op
                    <lb/>
                  poſito dantur. </s>
                  <s xml:id="echoid-s4377" xml:space="preserve">
                    <reg norm="Vellesque" type="simple">Vellesq́;</reg>
                  diametrum circuli apti eum triangulum circnn-
                    <lb/>
                  ſcribere inuenire in diſcreto.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4378" xml:space="preserve">Sit igitur triangulum
                    <var>.a.b.g.</var>
                  cuius baſis
                    <var>.b.g.</var>
                  ſimul cum angulo
                    <var>.a.</var>
                  ei op-
                    <lb/>
                  poſito data ſit in numeris. </s>
                  <s xml:id="echoid-s4379" xml:space="preserve">Imaginetur ergo circulas circunſeribens ipſum triangu-
                    <lb/>
                  lum
                    <var>.b.p.g.q.</var>
                  cuius diameter ſit
                    <var>.q.p.</var>
                  perpendicularis eius baſi
                    <var>.b.g.</var>
                  vnde
                    <var>.b.g.</var>
                  diuiſa
                    <lb/>
                  erit per æqualia ab ipſo diametro in puncto
                    <var>.m.</var>
                  per tertiam tertij, protrahatur etiam </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>