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 |< < (104) 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-div7" type="chapter" level="2" n="1">
            <div xml:id="echoid-div293" type="appendix" level="3" n="1">
              <p>
                <s xml:id="echoid-s1341" xml:space="preserve">
                  <pb o="104" rhead="IO. BAPT. BENED." n="116" file="0116" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0116"/>
                producitur ex
                  <var>.i.e.</var>
                differentia in
                  <var>.i.n.</var>
                aggregatum amborum numerorum, ſed hoc pro
                  <lb/>
                ductum excedit productum
                  <var>e.c</var>
                : partem gnomonis dicti per
                  <var>.u.n.</var>
                quod quidem
                  <var>.u.
                    <lb/>
                  n.</var>
                æquatur ipſi
                  <var>.u.o.</var>
                reliquæ ſcilicet parti ipſius gnomonis,
                  <reg norm="nam" type="context">nã</reg>
                  <var>.e.u.</var>
                æqualis eft
                  <var>.i.c.</var>
                qua
                  <lb/>
                re et
                  <var>.a.i.</var>
                ſed
                  <var>.e.t.</var>
                ęquatur
                  <var>.e.a.</var>
                vnde
                  <var>.t.u.</var>
                æqualis erit
                  <var>.e.i.</var>
                </s>
                <s xml:id="echoid-s1342" xml:space="preserve">quare et
                  <var>.u.c</var>
                : at cum
                  <var>.c.n.</var>
                æqua
                  <lb/>
                lis ſit ipſi
                  <var>.a.e.</var>
                erit etiam æqualis ipſi
                  <var>.
                    <lb/>
                  o.t</var>
                . </s>
                <s xml:id="echoid-s1343" xml:space="preserve">quare
                  <var>.u.n.</var>
                æqualis erit ipſi
                  <var>.u.o.</var>
                  <lb/>
                & tunc intellectus quieſcit, &
                  <reg norm="abſque" type="simple">abſq;</reg>
                  <lb/>
                  <figure xlink:label="fig-0116-01" xlink:href="fig-0116-01a" number="159">
                    <image file="0116-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0116-01"/>
                  </figure>
                aliqua alia experientia verè ſcientifi
                  <lb/>
                  <reg norm="ceque" type="simple">ceq́;</reg>
                dicere poteft, quòd.</s>
              </p>
              <p>
                <s xml:id="echoid-s1344" xml:space="preserve">Quorumcumque duorum nume-
                  <lb/>
                rorum differentia, fi fuerit multipli-
                  <lb/>
                cata in aggregatum eorum, producit
                  <lb/>
                ipſam
                  <reg norm="differentiam" type="context">differentiã</reg>
                , quæ eftinter qua-
                  <lb/>
                drata eorum.</s>
              </p>
              <p>
                <s xml:id="echoid-s1345" xml:space="preserve">Hæcautem propoſitio à me ipſo
                  <lb/>
                etiam in .60. </s>
                <s xml:id="echoid-s1346" xml:space="preserve">Theoremate huius libri
                  <lb/>
                aliter demonftrata fuit.</s>
              </p>
              <p>
                <s xml:id="echoid-s1347" xml:space="preserve">DE ſpeculatione autem, etſcientia ſecundi exempli, in ſecunda hic ſubſcripta
                  <lb/>
                figura
                  <var>.ω.</var>
                cogitemus lineam
                  <var>.u.a.</var>
                tribusin partibus arithmeticè diuiſam, qua
                  <lb/>
                rum maxima ſit
                  <var>.u.o.</var>
                media. ſit
                  <var>.o.e.</var>
                minima verò ſit
                  <var>.e.a.</var>
                multiplicatio autem mediæ
                  <var>.
                    <lb/>
                  o.e.</var>
                in ſe ſit quadratum
                  <var>.o.t.</var>
                abſcindatur deinde ex
                  <var>.o.e</var>
                :
                  <var>e.i.</var>
                æqualis
                  <var>.e.a.</var>
                </s>
                <s xml:id="echoid-s1348" xml:space="preserve">tunc
                  <var>.o.i.</var>
                erit
                  <lb/>
                differentia inter
                  <var>.o.e.</var>
                et
                  <var>.e.a.</var>
                & æqualis differentiæ inter
                  <var>.o.e.</var>
                et
                  <var>.o.u.</var>
                ex hypotefi, quæ
                  <lb/>
                quidem
                  <var>.o.i.</var>
                in ſe ducta procreabit quadratum
                  <var>.o.c.</var>
                quod erit productum ex differen
                  <lb/>
                tijs ipſarum partium, & erit pars quadrati
                  <var>.o.t.</var>
                ſuperius dicti, vt exſe patet. </s>
                <s xml:id="echoid-s1349" xml:space="preserve">Nunc
                  <lb/>
                autem dico gnomonem
                  <var>.i.t.n.</var>
                æqualem eſſe ei quod fit ex
                  <var>.a.e.</var>
                in
                  <var>.o.u</var>
                . </s>
                <s xml:id="echoid-s1350" xml:space="preserve">Producatur igi
                  <lb/>
                tur
                  <var>.e.t.</var>
                quouſque
                  <var>.t.r.</var>
                æqualis ſit ipſi
                  <var>.o.i</var>
                . </s>
                <s xml:id="echoid-s1351" xml:space="preserve">tunc
                  <var>.e.r.</var>
                erit æqualis
                  <var>.o.u.</var>
                quod etiam clarum
                  <lb/>
                eſt. </s>
                <s xml:id="echoid-s1352" xml:space="preserve">Claudatur ergo rectangulum
                  <var>.i.r.</var>
                quod erit æquale producto ipſius
                  <var>.e.a.</var>
                in
                  <var>.o.u.</var>
                  <lb/>
                Nam
                  <var>.e.i.</var>
                ſumpta fuit
                  <lb/>
                æqualis
                  <var>.e.a.</var>
                ſed ex ra
                  <lb/>
                  <figure xlink:label="fig-0116-02" xlink:href="fig-0116-02a" number="160">
                    <image file="0116-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0116-02"/>
                  </figure>
                tionibus in priori
                  <reg norm="exem" type="context">exẽ</reg>
                  <lb/>
                plo allatis,
                  <reg norm="productum" type="simple">ꝓductum</reg>
                  <var>.
                    <lb/>
                  i.r.</var>
                æquale erit gno-
                  <lb/>
                moni
                  <var>.i.t.n</var>
                . </s>
                <s xml:id="echoid-s1353" xml:space="preserve">Nuncau
                  <lb/>
                tem verè, ſcientifice-
                  <lb/>
                q́ue poſſumus affirma
                  <lb/>
                re, quòd. </s>
                <s xml:id="echoid-s1354" xml:space="preserve">Datis tribus
                  <lb/>
                numeris
                  <reg norm="ſecundum" type="context">ſecundũ</reg>
                pro
                  <lb/>
                greffionem arithme-
                  <lb/>
                ticam diſpofitis, fa-
                  <lb/>
                cit multiplicatio me-
                  <lb/>
                dij in ſe quantum mul
                  <lb/>
                tiplicatio extremorum inter ſe, cum multiplicatione differentiarum inter ſe.</s>
              </p>
              <p>
                <s xml:id="echoid-s1355" xml:space="preserve">Et ſic de alijs huiuſmodi inuentionibus infero.</s>
              </p>
              <p>
                <s xml:id="echoid-s1356" xml:space="preserve">DIcturus igitur aliquid circa
                  <reg norm="regulam" type="context">regulã</reg>
                falſi, videtur mihi nullam oportere facere
                  <lb/>
                mentionem de origine huiuſcæ regulæ, cum in hoc Stifelius ſatisfecerit, ſed </s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum