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
161 149
162 150
163 151
164 152
165 153
166 154
167 155
168 156
169 157
170 158
171 159
172 160
173 161
174 162
175 163
176 164
177 165
178 166
179 167
180 168
181 169
182 170
183 171
184 172
185 173
186 174
187 175
188 176
189 177
190 178
< >
page |< < (178) 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-div387" type="chapter" level="2" n="4">
            <div xml:id="echoid-div411" type="section" level="3" n="15">
              <p>
                <s xml:id="echoid-s2110" xml:space="preserve">
                  <pb o="178" rhead="IO. BAPT. BENED." n="190" file="0190" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0190"/>
                cies, & quæ inter corpor a
                  <reg norm="reperitur" type="simple">reperit̃</reg>
                : </s>
                <s xml:id="echoid-s2111" xml:space="preserve">Ariſtoteles igitur in eo defecit. </s>
                <s xml:id="echoid-s2112" xml:space="preserve">Quòd
                  <reg norm="autem" type="context">autẽ</reg>
                inter
                  <lb/>
                ſuperficies non eadem ſit proportio, quæ inter corpora extat, ſi primo ad ſphęricas
                  <lb/>
                mentem verterimus, intelligemus proportionem eam, quæ inter duas ſphæras repe
                  <lb/>
                ritur triplam ſemper exiſtere ei, quæ eſt inter ipſarum diametros ex vltima .12. libr.
                  <lb/>
                Euclid. </s>
                <s xml:id="echoid-s2113" xml:space="preserve">Eſt autem proportio, quæ eſt inter ſuperficies ſphęricas ęqualis ei, quæ eſt
                  <lb/>
                ipſorum circulorum maiorum ex .16. lib. quinti, cum ex .31. primi de ſphæra & cy-
                  <lb/>
                lindro Archimedis, omnis ſphærica ſuperficies quadrupla, ſit maiori circulo ipſius
                  <lb/>
                ſphęræ, ſed proportio, quæ eſt inter dictos circulos, eſt dupla ei, quæ eſt inter
                  <reg norm="eorun- dem" type="context context">eorũ-
                    <lb/>
                  dẽ</reg>
                diametros ex .2. lib. 12. Euc. </s>
                <s xml:id="echoid-s2114" xml:space="preserve">ergo
                  <reg norm="proportio" type="simple">ꝓportio</reg>
                , quæ eſt inter corpora, ſeſquialtera erit
                  <lb/>
                ei, quæ eſt ſuperficierum, & non æqualis, ut Ariſtoteles putauit. </s>
                <s xml:id="echoid-s2115" xml:space="preserve">Idem de corporibus
                  <lb/>
                ſimilibus à ſuperficiebus planis terminatis dico, ratiocinando mediante .36. lib. 11.
                  <lb/>
                et .18. ſexti, vnde cognoſcemus proportionem corporum, proportioni laterum, tri-
                  <lb/>
                plam futuram, & ſuperficierum proportionem, laterum proportioni duplam. </s>
                <s xml:id="echoid-s2116" xml:space="preserve">Quare
                  <lb/>
                corporum proportio, ei, quæ ſuperficierum eſt, ſeſquialtera erit, ita ut ſi velocitates
                  <lb/>
                extitiſſent ad inuicem proportionatæ, vt ſuperficies, proportio velocitatis corporis
                  <var>.
                    <lb/>
                  B.</var>
                ei, quæ eſt corporis
                  <var>.C.</var>
                fuiſſet ſubſeſquialtera proportioni corporum, & non æqua
                  <lb/>
                lis eidem.</s>
              </p>
            </div>
            <div xml:id="echoid-div412" type="section" level="3" n="16">
              <head xml:id="echoid-head273" style="it" xml:space="preserve">Fdipſum aliter demonſtr atur.</head>
              <head xml:id="echoid-head274" xml:space="preserve">CAP. XVI.</head>
              <p>
                <s xml:id="echoid-s2117" xml:space="preserve">ALio quoque modo probari poteſt non eſſe in vniuerſum verum id, quod Ari-
                  <lb/>
                ſtoteles in prima parte capitis vltimi lib. 7. phyſicorum ait, ſic ſcribens.</s>
              </p>
              <p>
                <s xml:id="echoid-s2118" xml:space="preserve">Si
                  <var>.A.</var>
                quidem ſit id quod mouet
                  <var>.B.</var>
                verò id quod mouetur, et
                  <var>.C.</var>
                ſit longitudo per
                  <lb/>
                quam, et
                  <var>.D.</var>
                tempus in quo eſt motum, in tempore nimirum ęquali, potentia æqua-
                  <lb/>
                lis
                  <var>.A.</var>
                dimidium ipſius
                  <var>.B.</var>
                per duplum mouebit ipſius
                  <var>.C.</var>
                per ipſum autem
                  <var>.C.</var>
                in dimi
                  <lb/>
                dio temporis
                  <var>.D.</var>
                ſic enim erit rationis ſimilitudo.</s>
              </p>
              <p>
                <s xml:id="echoid-s2119" xml:space="preserve">Sit ergo corpus
                  <var>.o.</var>
                ſeptimi capitis pondere æquali corpori
                  <var>.u.</var>
                eiuſdem capitis, ſed
                  <lb/>
                area corporea minusipſo
                  <var>.u.</var>
                pro medietate. </s>
                <s xml:id="echoid-s2120" xml:space="preserve">Simile tamen figura. </s>
                <s xml:id="echoid-s2121" xml:space="preserve">Imaginemur
                  <reg norm="nunc" type="context">nũc</reg>
                  <lb/>
                tertium aliud corpus omogeneum ipſi
                  <var>.u.</var>
                quod ſit
                  <var>.i.</var>
                magnitudine & figura ſimile ipſi
                  <lb/>
                o. vnde minor erit ipſo
                  <var>.u.</var>
                pro media parte, & hanc ob cauſam ipſum
                  <var>.u.</var>
                erit duplo ma
                  <lb/>
                gis graue, quàm ipſum
                  <var>.i.</var>
                & per conſequens ipſum quoque
                  <var>.o.</var>
                duplo grauius erit
                  <reg norm="quam" type="context">quã</reg>
                  <lb/>
                ſit ipſum
                  <var>.i.</var>
                ex .7. libr. quinti Euclidis. </s>
                <s xml:id="echoid-s2122" xml:space="preserve">Ipſum ergo corpus
                  <var>.o.</var>
                duplo velocius erit,
                  <lb/>
                quàm ipſum
                  <var>.i.</var>
                ex primo ſuppoſito cap .2. huius lib. </s>
                <s xml:id="echoid-s2123" xml:space="preserve">Vnde ex .9. quinti, velocitas ipſius
                  <lb/>
                i. æqualis eſſet ei, quæ eſt ipſius u. cum Ariſtoteles ſcribat
                  <var>.o.</var>
                quoque futurum duplo
                  <lb/>
                velocius ipſo
                  <var>.u.</var>
                  <reg norm="quod" type="simple">ꝙ</reg>
                cap .7. huius lib. falſum eſſe demonſtraui.</s>
              </p>
            </div>
            <div xml:id="echoid-div413" type="section" level="3" n="17">
              <head xml:id="echoid-head275" style="it" xml:space="preserve">De alio Aristo. lapſu.</head>
              <head xml:id="echoid-head276" xml:space="preserve">CAP. XVII.</head>
              <p>
                <s xml:id="echoid-s2124" xml:space="preserve">SCribit Ariſtoteles in ultimo cap. lib. 7. phyſicorum in hunc modum.
                  <lb/>
                </s>
                <s xml:id="echoid-s2125" xml:space="preserve">Si duo quædam ſeorſum per tantum ſpatium tanto tempore duo ſeorſum pon
                  <lb/>
                dera mouent, & compoſita per longitudinem æqualem,
                  <reg norm="ęqualiuem" type="context">ęqualiuẽ</reg>
                in tempore, com-
                  <lb/>
                poſitum ex ponderibus
                  <reg norm="vtriſque" type="simple">vtriſq;</reg>
                mouebunt, eſt enim in eis eadem ratio.</s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>