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
131 119
132 120
133 121
134 122
135 123
136 124
137 125
138 126
139 127
140 128
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
< >
page |< < (316) 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-div614" type="section" level="3" n="24">
              <div xml:id="echoid-div615" type="letter" level="4" n="2">
                <p>
                  <s xml:id="echoid-s3872" xml:space="preserve">
                    <pb o="316" rhead="IO. BAPT. BENED." n="328" file="0328" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0328"/>
                  lum, cuius data ſit b aſis tantummodo ſimul cum angulo, qui ipſi baſi opponitur.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3873" xml:space="preserve">Imagineris igitur triangulum datum eſſe obtuſiangulum
                    <var>.a.b.g.</var>
                  cuius baſi
                    <var>.b.
                      <lb/>
                    g.</var>
                  ſit nobis data ſimul cum angulo
                    <var>.a.</var>
                  ei oppoſito, obtuſoq́ue; </s>
                  <s xml:id="echoid-s3874" xml:space="preserve">Conſidera etiam cir-
                    <lb/>
                  culum
                    <var>.a.b.g.q.</var>
                  ipſum trian gulum circunſcribentem, cuius diameter
                    <var>.q.e.p.</var>
                  tranſeat
                    <lb/>
                  per
                    <var>.m.</var>
                  punctum medium ipſius
                    <var>.b.g.</var>
                    <reg norm="tunc" type="context">tũc</reg>
                  protractis imaginatione
                    <var>.e.g.</var>
                  et
                    <var>.g.p.</var>
                  certi eri-
                    <lb/>
                  mus angulos. circa
                    <var>.m.</var>
                  rectos eſſe ex .3 tertij Eucli.
                    <reg norm="angulumque" type="simple">angulumq́</reg>
                    <var>.q.e.g.</var>
                  duplum eſſe an
                    <lb/>
                  gulo
                    <var>.q.p.g.</var>
                  ex .19. eiuſdem, vnde æqualem angulo
                    <var>.a.</var>
                  qui etiam duplus eſt angulo
                    <var>.q.
                      <lb/>
                    p.g.</var>
                  quapropter proportio arcus
                    <var>.q.g.</var>
                  ad arcum
                    <lb/>
                    <figure xlink:label="fig-0328-01" xlink:href="fig-0328-01a" number="350">
                      <image file="0328-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0328-01"/>
                    </figure>
                    <var>g.p.</var>
                  tibi cognita erit, & proportio etiam chor-
                    <lb/>
                  de
                    <var>.p.g.</var>
                  ad ſinum
                    <var>.m.g.</var>
                  arcus
                    <var>.g.p.</var>
                  & quia
                    <var>.m.g.</var>
                  vt
                    <lb/>
                  dimidium ipſius
                    <var>.b.g.</var>
                  tibi data eſt, cognoſces
                    <lb/>
                  etiam
                    <var>.p.g.</var>
                  vt
                    <var>.m.g.</var>
                  & ſic tertium latus
                    <var>.m.p.</var>
                  trian-
                    <lb/>
                  guli orthogonij
                    <var>.p.m.g.</var>
                  & q
                    <unsure/>
                  a ex .34. tertij quod
                    <lb/>
                  fit ex
                    <var>.p.m.</var>
                  in
                    <var>.m.q.</var>
                  eſt æquale ei quod fit ex
                    <var>.b.m.</var>
                    <lb/>
                  in
                    <var>.m.g.</var>
                  ideo cum diuiſum fuerit productum
                    <var>.b.</var>
                    <lb/>
                  m in
                    <var>.m.g.</var>
                  per
                    <var>.p.m.</var>
                  proueniet
                    <var>.m.q.</var>
                  quapropter
                    <lb/>
                  habebis totum
                    <var>.q.p</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s3875" xml:space="preserve">Idem efficies, ſi
                    <reg norm="cum" type="context">cũ</reg>
                  angulus
                    <var>.a.</var>
                  acutus fuiſſet.</s>
                </p>
              </div>
              <div xml:id="echoid-div617" type="letter" level="4" n="3">
                <head xml:id="echoid-head479" style="it" xml:space="preserve">Modus inueniendi puncta elliptica via Pergei.</head>
                <head xml:id="echoid-head480" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3876" xml:space="preserve">MOdus inueniendi puncta elliptica, via .21. primi lib. Pergei ex datis axibus,
                    <lb/>
                  vt vbi alias ſignificati, talis eſt.
                    <lb/>
                    <figure xlink:label="fig-0328-02" xlink:href="fig-0328-02a" number="351">
                      <image file="0328-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0328-02"/>
                    </figure>
                  </s>
                  <s xml:id="echoid-s3877" xml:space="preserve">Sit exempli gratia maior axis propo-
                    <lb/>
                  ſitus
                    <var>.a.c.</var>
                  minor autem
                    <var>.b.d.</var>
                  cum ergo
                    <lb/>
                  volueris inuenire punctum circunfe-
                    <lb/>
                  rentiæ correſpondentem puncto
                    <var>.e.</var>
                    <lb/>
                  maioris axis, inueniemus primò la-
                    <lb/>
                  tus tetragonicum producti
                    <var>.a.g.</var>
                  in
                    <var>.g.
                      <lb/>
                    c.</var>
                  quod ſit
                    <var>.h.</var>
                    <reg norm="latusque" type="simple">latusq́</reg>
                    <reg norm="tetragonicum" type="context">tetragonicũ</reg>
                  pro-
                    <lb/>
                  ducti
                    <var>.a.e.</var>
                  in
                    <var>.e.c.</var>
                  quod ſit
                    <var>.i</var>
                  . </s>
                  <s xml:id="echoid-s3878" xml:space="preserve">deinde in-
                    <lb/>
                  ueniemus lineam
                    <var>.K.</var>
                  tertiam in con-
                    <lb/>
                  tinua proportionalitate cum
                    <var>.h.</var>
                  et
                    <var>.i.</var>
                    <lb/>
                  vnde
                    <var>.i.</var>
                  erit media proportionalis in-
                    <lb/>
                  ter
                    <var>.h.</var>
                  et
                    <var>.K.</var>
                  & vt
                    <var>.h.</var>
                  proportionalis erit
                    <lb/>
                  ad
                    <var>.K.</var>
                  inueniemus
                    <var>.e.f.</var>
                  cui
                    <var>.g.d.</var>
                  medie-
                    <lb/>
                  tas ſecundi axis ita ſe habeat, quæ po
                    <lb/>
                  ſtea iuncta axi maiori, ad angulosrectos in puncto
                    <var>.e.</var>
                  dabit ſitum puncti
                    <var>.f.</var>
                  quæſiti ex
                    <lb/>
                  dicta .21. primi lib. Pergei, ſed talis modus prolixus eſt.</s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum