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
181 169
182 170
183 171
184 172
185 173
186 174
187 175
188 176
189 177
190 178
191 179
192 180
193 181
194 182
195 183
196 184
197 185
198 186
199 187
200 188
201 189
202 190
203 191
204 192
205 193
206 194
207 195
208 196
209 197
210 198
< >
page |< < (357) 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-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div680" type="section" level="3" n="31">
              <div xml:id="echoid-div686" type="letter" level="4" n="3">
                <p>
                  <s xml:id="echoid-s4283" xml:space="preserve">
                    <pb o="357" rhead="EPISTOL AE." n="369" file="0369" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0369"/>
                  gulus
                    <var>.p.n.q.</var>
                  vnde ex methodo .56.
                    <lb/>
                    <figure xlink:label="fig-0369-01" xlink:href="fig-0369-01a" number="407">
                      <image file="0369-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0369-01"/>
                    </figure>
                  primi triangulorum Monteregij,
                    <lb/>
                  cognoſcemus reliqua trianguli
                    <var>.
                      <lb/>
                    q.p.n</var>
                  . </s>
                  <s xml:id="echoid-s4284" xml:space="preserve">Conſtituendo poſtea angu-
                    <lb/>
                  lum
                    <var>.q.n.u.</var>
                  æqualem angulo
                    <var>.n.q.p.</var>
                    <lb/>
                  propoſitum habebimus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4285" xml:space="preserve">Si etiam puncta
                    <var>.q.p.</var>
                  lineæ
                    <var>.q.p.</var>
                    <lb/>
                  orizontali in eodem plano non exi
                    <lb/>
                  ſterent cum puncto
                    <var>.n.</var>
                  nihil refer-
                    <lb/>
                  ret, dummodo in pauimento
                    <reg norm="notem" type="context">notẽ</reg>
                    <lb/>
                  tur
                    <reg norm="puncta" type="context">pũcta</reg>
                    <var>.c.e.</var>
                  proxima
                    <var>.n.</var>
                  in ijſdem
                    <lb/>
                  ſuperficiebus triangulorum
                    <var>.n.o.p.</var>
                    <lb/>
                  et
                    <var>.n.o.q.</var>
                  vnde
                    <var>.n.c.</var>
                  et
                    <var>.n.e.</var>
                  erunt
                    <reg norm="com- munes" type="context">cõ-
                      <lb/>
                    munes</reg>
                  ſectiones dictarum ſuperficierum cum ſuperficie pauimenti ſupra quam fit
                    <lb/>
                  ſtatio.</s>
                </p>
              </div>
            </div>
            <div xml:id="echoid-div690" type="section" level="3" n="32">
              <div xml:id="echoid-div690" type="letter" level="4" n="1">
                <head xml:id="echoid-head524" xml:space="preserve">CONI RECTI DIVISIO A PLANO
                  <lb/>
                parallelo baſi ſecundum datam proportionem.</head>
                <head xml:id="echoid-head525" style="it" xml:space="preserve">Rapbaeli de Auria.</head>
                <p>
                  <s xml:id="echoid-s4286" xml:space="preserve">
                    <emph style="sc">QVotiescvnqve</emph>
                  volueris conum rectum diuidere à plano parallelo ba-
                    <lb/>
                  ſi ſecundum vnam datam proportionem, nullius tibi erit difficultatis, con
                    <lb/>
                  ceſſa
                    <reg norm="tamen" type="wordlist">tamẽ</reg>
                  pro inuenta diuiſione cuiuſuis propoſitę proportionis per tres
                    <lb/>
                  æquales partes.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4287" xml:space="preserve">Sit exempli gratia conus rectus
                    <var>.a.b.c.</var>
                  ſecandus vt dictum eſt, accipiatur latus
                    <lb/>
                  ipſius, quod ſit
                    <var>.a.c.</var>
                    <reg norm="ipſumque" type="simple">ipſumq́;</reg>
                  diuidatur in puncto
                    <var>.d.</var>
                  ſecundum illam proportionem
                    <lb/>
                  quam deſideras, hoc eſt ipſius
                    <var>.a.c.</var>
                  ad
                    <var>.a.d.</var>
                  quo facto, inter totum
                    <var>.a.c.</var>
                  et
                    <var>.a.d.</var>
                  inuenian
                    <lb/>
                  tur duæ lineæ proportionales, quarum maior ſit
                    <var>.a.i.</var>
                  </s>
                  <s xml:id="echoid-s4288" xml:space="preserve">tunc ſi conus
                    <var>.a.b.c.</var>
                  ſectus fue-
                    <lb/>
                  rit à plano per punctum
                    <var>.i.</var>
                  parallelo baſi, habebimus quod quærebamus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4289" xml:space="preserve">Cuius rei ratio, primò eſt, quia quotieſcunque conus aliquis ſectus fuerit ab ali-
                    <lb/>
                  quo plano parallelo baſi ipſius, pars ſuperior ſimilis ſemper erit totali cono, quod
                    <lb/>
                  ita probo, cogitemus conum ſectum eſſe
                    <lb/>
                  à plano per axem
                    <var>.a.l.</var>
                  vnde ex .3. primi
                    <lb/>
                    <figure xlink:label="fig-0369-02" xlink:href="fig-0369-02a" number="408">
                      <image file="0369-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0369-02"/>
                    </figure>
                  Pergei, talis ſectio triangularis erit, quæ
                    <lb/>
                  ſit
                    <var>.a.b.c.</var>
                  et
                    <var>.b.c.</var>
                  diameter erit baſis.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4290" xml:space="preserve">Imaginemur deinde
                    <var>.K.i.</var>
                  communem
                    <lb/>
                  eſſe ſectionem huiuſmodi trianguli cum
                    <lb/>
                  plano parallelo ipſi baſi, </s>
                  <s xml:id="echoid-s4291" xml:space="preserve">tunc tale
                    <reg norm="planum" type="context">planũ</reg>
                  ,
                    <lb/>
                  circulare erit ex .4. primi ipſius Pergei
                    <var>.K.
                      <lb/>
                    i.</var>
                  verò, eius diameter erit, et
                    <var>.a.m.</var>
                    <reg norm="ſuus" type="simple">ſuꝰ</reg>
                  axis.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4292" xml:space="preserve">Cum verò
                    <var>.a.l.</var>
                  ſit perpendicularis ipſi
                    <lb/>
                  baſi conitotalis, eo quod rectus ſupponi-
                    <lb/>
                  tur, ideo eadem
                    <var>.a.m.l.</var>
                  erit perpendicula
                    <lb/>
                  ris eriam ipſi ſecundo plano circulari, ex
                    <lb/>
                  conuerſa .14. vndecimi Euclid. </s>
                  <s xml:id="echoid-s4293" xml:space="preserve">vnde ex </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum