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
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
171 159
172 160
173 161
174 162
175 163
176 164
177 165
178 166
179 167
180 168
< >
page |< < (351) 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-div670" type="section" level="3" n="29">
              <div xml:id="echoid-div673" type="letter" level="4" n="2">
                <pb o="351" rhead="EPISTOL AE." n="363" file="0363" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0363"/>
                <p>
                  <s xml:id="echoid-s4222" xml:space="preserve">Volo etiam quod ad partem
                    <var>.c.l.s.</var>
                  quadrilateri conſtituta ſit alia parallela ad
                    <var>.z.
                      <lb/>
                    r.</var>
                  & in æquali diſtantia ab ipſa quemadmodum
                    <var>.u.n.</var>
                  diſtat ad eademmet
                    <var>.z.r.</var>
                  ad ean
                    <lb/>
                  dem operationem faciendam. </s>
                  <s xml:id="echoid-s4223" xml:space="preserve">Vnde in vno tantummodo itinere puncti
                    <var>.s.</var>
                  ab
                    <var>.r.</var>
                    <reg norm="vſque" type="simple">vſq;</reg>
                    <lb/>
                  ad
                    <var>.c.</var>
                  deſignabimus quartam partem ſectionis, conuerſo poſtea inſtrumento, hoc eſt
                    <lb/>
                  poſito puncto
                    <var>.r.</var>
                  vbi prius erat
                    <var>.z.</var>
                  et
                    <var>.z.</var>
                  vbi erat
                    <var>.r.</var>
                  aliam delineabimus quartam, &
                    <lb/>
                  ſic ad oppoſitam partem ipſius
                    <var>.z.r.</var>
                  faciendum erit. </s>
                  <s xml:id="echoid-s4224" xml:space="preserve">Hoc inſtrumentum poſſumus
                    <lb/>
                  etiam ita conſtruere, vt puncta
                    <var>.o.</var>
                  et
                    <var>.K.</var>
                  poſſint collocari in laterihus
                    <var>.c.e.</var>
                  et
                    <var>.e.s.</var>
                  vbi no
                    <lb/>
                  bis magis libuerit, ita vt licebit in qualibet proportione
                    <reg norm="axium" type="context">axiũ</reg>
                  propoſita, oxygoniam
                    <lb/>
                  deſignare. </s>
                  <s xml:id="echoid-s4225" xml:space="preserve">Nam
                    <var>.c.o.</var>
                  erit longitudo dimidij axis minoris, et
                    <var>.c.e.</var>
                  dimidij maioris.</s>
                </p>
              </div>
            </div>
            <div xml:id="echoid-div676" type="section" level="3" n="30">
              <div xml:id="echoid-div676" type="letter" level="4" n="1">
                <head xml:id="echoid-head515" xml:space="preserve">DE CONSTITVTIONE TRIANGVLI
                  <lb/>
                orthogonij conditionati.</head>
                <head xml:id="echoid-head516" style="it" xml:space="preserve">Domino Ludouico de Rocchaforte.</head>
                <p>
                  <s xml:id="echoid-s4226" xml:space="preserve">
                    <emph style="sc">QVod</emph>
                  à me poſtulas, non eſt admodum difficile, cupis enim triangulum
                    <lb/>
                  orthogonium, exempli gratia
                    <var>.o.i.e.</var>
                  in figura
                    <var>.A.</var>
                  ita conſtituere, vt di-
                    <lb/>
                  uiſum ſit à perpendiculari
                    <var>.a.i.</var>
                  & quod proportio
                    <var>.o.e.</var>
                  ad
                    <var>.o.i.</var>
                  ſit vt
                    <var>.o.i.</var>
                  ad
                    <lb/>
                    <var>i.e.</var>
                  & quod quadrati
                    <var>.o.i.</var>
                  ad quadratum
                    <var>.o.a.</var>
                  ſit vt
                    <var>.e.i.</var>
                  ad
                    <var>.e.a.</var>
                  & quadra
                    <lb/>
                  tum
                    <var>.o.i.</var>
                  ad quadratum
                    <var>.e.i.</var>
                  ſit .ut
                    <var>.o.a.</var>
                  ad
                    <var>.e.a</var>
                  . </s>
                  <s xml:id="echoid-s4227" xml:space="preserve">Quæ omnia in promptu veniunt, quo
                    <lb/>
                  tieſcunque
                    <var>.o.e.</var>
                  fuerit diameter alicuius circuli,
                    <reg norm="diuiſaque" type="simple">diuiſaq́;</reg>
                  in puncto
                    <var>.a.</var>
                  ſecundum pro
                    <lb/>
                  portionem habentem medium
                    <reg norm="duoque" type="simple">duoq́;</reg>
                  extrema, protracta deinde perpendiculari
                    <var>.a.
                      <lb/>
                    i.</var>
                  ad
                    <var>o.e.</var>
                  uſque ad circunferentiam,
                    <reg norm="coniunctæque" type="simple">coniunctæq́;</reg>
                    <var>.o.i.</var>
                  et
                    <var>.i.e</var>
                  : tale triangulum, omnia
                    <lb/>
                  ſupradicta in ſe continebit.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4228" xml:space="preserve">Nam ex .30. tertij angulus
                    <var>.i.</var>
                  rectus erit, & ex .8. ſexti
                    <var>.o.i.</var>
                  erit media proportio-
                    <lb/>
                  nalis inter
                    <var>.o.e.</var>
                  et
                    <var>.o.a.</var>
                  et
                    <var>.e.i.</var>
                  inter
                    <var>.o.e.</var>
                    <lb/>
                    <figure xlink:label="fig-0363-01" xlink:href="fig-0363-01a" number="400">
                      <image file="0363-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0363-01"/>
                    </figure>
                  et
                    <var>.a.e.</var>
                  ſed quia ex diuiſione facta in
                    <reg norm="pum" type="context">pũ</reg>
                    <lb/>
                  cto
                    <var>.a.</var>
                  etiam
                    <var>.o.a.</var>
                  erit media proportio-
                    <lb/>
                  nalis inter totum & reſiduum, ideo ex
                    <num value="11">.
                      <lb/>
                    11.</num>
                  quinti ita erit
                    <var>.o.e.</var>
                  ad
                    <var>.e.i.</var>
                  vt
                    <var>.o.e.</var>
                  ad
                    <var>.
                      <lb/>
                    o.a.</var>
                  vnde ex .9. eiuſdem
                    <var>.a.o.</var>
                  erit æqua-
                    <lb/>
                  lis
                    <var>.e.i.</var>
                  & ideo
                    <var>.o.i.</var>
                  erit media proportio
                    <lb/>
                  nalis inter
                    <var>.o.e.</var>
                  et
                    <var>.e.i</var>
                  . </s>
                  <s xml:id="echoid-s4229" xml:space="preserve">Sed quia propor-
                    <lb/>
                  tio
                    <var>.e.i.</var>
                  ad
                    <var>.a.e.</var>
                    <reg norm="eadem" type="context">eadẽ</reg>
                  eſt, quę ipſius
                    <var>.o.e.</var>
                  ad
                    <lb/>
                    <var>o.a</var>
                  . </s>
                  <s xml:id="echoid-s4230" xml:space="preserve">tunc videbis ex .18. ſexti, quod pro
                    <lb/>
                  portio quadrati
                    <var>.o.i.</var>
                  ad quadratum
                    <var>.o.a.</var>
                    <lb/>
                  erit vt
                    <var>.e.i.</var>
                  ad
                    <var>.e.a.</var>
                  cum vero duo trian-
                    <lb/>
                  guli
                    <var>.o.i.a.</var>
                  et
                    <var>.a.i.e.</var>
                  ſint inuicem ſimiles
                    <lb/>
                  ex ſupradicta .8. ſexti, </s>
                  <s xml:id="echoid-s4231" xml:space="preserve">tunc videbis ex
                    <lb/>
                  18. et .17. eiuſdem dictos
                    <reg norm="triangulos" type="context">triãgulos</reg>
                  ean
                    <lb/>
                  dem habere inter ſe proportionem, quę
                    <lb/>
                  eſt inrer quadrata ipſius
                    <var>.o.i.</var>
                  et
                    <var>.i.e.</var>
                  vnde
                    <lb/>
                  ex prima ſexti ita ſe inuicem habebunt
                    <var>.
                      <lb/>
                    a.o.</var>
                  et
                    <var>.a.e</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4232" xml:space="preserve">Circa eam verò difficultatem quam </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>