Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Page concordance

< >
Scan Original
141 117
142 118
143 119
144 120
145 121
146 122
147 123
148 124
149 125
150 126
151 127
152 128
153 129
154 130
155 131
156 132
157 133
158 134
159 135
160 136
161 137
162 138
163 139
164 140
165 141
166 142
167 143
168 144
169 145
170 146
< >
page |< < (5) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div536" type="section" level="1" n="223">
          <p>
            <s xml:id="echoid-s5261" xml:space="preserve">
              <pb o="5" file="0187" n="187" rhead=""/>
            D M (cum latus rectum B F, vel duplum ſit, vel plus quàm duplum ad
              <lb/>
            B D) ergo M N ipſo aggregato B D cum D M adhuc maior erit, vnde
              <lb/>
            rectangulum ſub N M in M B, ſiue quadratum L M, maius erit
              <note symbol="a" position="right" xlink:label="note-0187-01" xlink:href="note-0187-01a" xml:space="preserve">Coroll.
                <lb/>
              primæ pri
                <lb/>
              mi huius.</note>
            gulo ſub aggregato B D cum D M, in eadem M B, quibus communi ad-
              <lb/>
            dito quadrato M D, erit quadratum L M cum M D, ſiue vnicum qua-
              <lb/>
            dratum D L, maius rectangulo ſub B D cum D M in M B, vna cum qua-
              <lb/>
            drato D M, ſiue maius vnico quadrato D B, quod prædicto
              <note symbol="b" position="right" xlink:label="note-0187-02" xlink:href="note-0187-02a" xml:space="preserve">1. huius.</note>
            æquale eſt, ſiue linea D L maior D B. </s>
            <s xml:id="echoid-s5262" xml:space="preserve">Quare ſegmentum axis D B, non
              <lb/>
            excedens dimidium recti lateris B F, eſt _MINIMA_ linearum ducibilium
              <lb/>
            ex D ad Hyperbolæ peripheriam. </s>
            <s xml:id="echoid-s5263" xml:space="preserve">Quod primò oſtendere oportebat.</s>
            <s xml:id="echoid-s5264" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5265" xml:space="preserve">Præterea, quadratum A D ſuperat quadratum L M, eo exceſſu quo re-
              <lb/>
            ctangulum B D G ſuperat rectangulum B M N, (ſunt enim ſingula
              <note symbol="c" position="right" xlink:label="note-0187-03" xlink:href="note-0187-03a" xml:space="preserve">Coroll.
                <lb/>
              primæ pri
                <lb/>
              mi huius.</note>
            lis æqualia) ſed exceſſus rectanguli B D G ſupra rectangulum B M N ma-
              <lb/>
            ius eſt rectangulo M D G, ergo quadratum A D ſuperat
              <note symbol="d" position="right" xlink:label="note-0187-04" xlink:href="note-0187-04a" xml:space="preserve">4. huius.</note>
            L M maiori rectangulo quàm M D G; </s>
            <s xml:id="echoid-s5266" xml:space="preserve">ſed quadratum D L ſuperat idem
              <lb/>
            quadratum L M quadrato D M, quod minus eſt rectangulo MDG (nam
              <lb/>
            eſt D G maior D M, cum ſuperiùs demonſtrata ſit maior ipſa D B) ergo
              <lb/>
            quadratum D A maius eſt quadrato D L, ſiue linea D A maior quacun-
              <lb/>
            que D L, intercepta inter applicatam D A, & </s>
            <s xml:id="echoid-s5267" xml:space="preserve">axem D B.</s>
            <s xml:id="echoid-s5268" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5269" xml:space="preserve">Ampliùs, ducatur alia quæpiam D O ſupra D A, ſed remotior à ſe-
              <lb/>
            gmento DB quàm D L, applicataque O P, producatur donec regulatrici
              <lb/>
            E F occurrat in Q. </s>
            <s xml:id="echoid-s5270" xml:space="preserve">Erit exceſſus quadrati O P ſupra quadratum L M,
              <lb/>
            idem ac exceſſus rectanguli B P Q ſupra B M N (nam ſunt
              <note symbol="e" position="right" xlink:label="note-0187-05" xlink:href="note-0187-05a" xml:space="preserve">Coroll.
                <lb/>
              primæ pri
                <lb/>
              mi huius.</note>
            quadratis æqualia, vtrumque vtrique) ſed exceſſus rectanguli B P Q ſu-
              <lb/>
            pra B M N maior eſt rectangulo M P Q, ergo exceſſus quadrati O P,
              <note symbol="f" position="right" xlink:label="note-0187-06" xlink:href="note-0187-06a" xml:space="preserve">4. huius.</note>
            pra quadratum L M, maior eſt rectangulo ſub M P, & </s>
            <s xml:id="echoid-s5271" xml:space="preserve">P Q; </s>
            <s xml:id="echoid-s5272" xml:space="preserve">at exceſſus
              <lb/>
            quadrati M D ſupra quadratum D P, minor eſt prædicto rectangulo (nam
              <lb/>
            quadratum M D ſuperat quadratum D P, rectangulo ſub M D cum
              <note symbol="g" position="right" xlink:label="note-0187-07" xlink:href="note-0187-07a" xml:space="preserve">1. huius.</note>
            in M P, quod eſt minus rectangulo ſub Q P in eadem M P, quoniam
              <lb/>
            M D cum D P minor eſt recto latere B F, & </s>
            <s xml:id="echoid-s5273" xml:space="preserve">eò minor ipſa QP,
              <lb/>
            quę maior eſt B F) quare exceſſus quadrati O P ſupra L M,
              <lb/>
            maior eſt exceſſu quadrati M D ſupra D P: </s>
            <s xml:id="echoid-s5274" xml:space="preserve">duo igi-
              <lb/>
              <handwritten xlink:label="hd-0187-1" xlink:href="hd-0187-1a" number="12"/>
            tur extrema ſimul quadrata O P, P D, ſiue vni-
              <lb/>
            cum quadratum D O, maius eſt duobus ſi-
              <lb/>
            mul quadratis medijs L M, M D, hoc
              <lb/>
            eſt vnico quadrato D L, ſiue li-
              <lb/>
            nea DO maior eſt linea DL.
              <lb/>
            </s>
            <s xml:id="echoid-s5275" xml:space="preserve">Vnde quæ minorem
              <lb/>
            efficit angulum
              <lb/>
            cum _MINI_-
              <lb/>
            _M A_
              <lb/>
            D B, minor eſt, &</s>
            <s xml:id="echoid-s5276" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5277" xml:space="preserve">Quod
              <lb/>
            fuit vltimò demon-
              <lb/>
            ſtrandum. </s>
            <s xml:id="echoid-s5278" xml:space="preserve">
              <lb/>
            * * *
              <lb/>
            * *
              <lb/>
            *</s>
          </p>
        </div>
      </text>
    </echo>
Impressum