Vitruvius, De architectura libri decem, 1567

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        <div xml:id="echoid-div1" type="section" level="1" n="1">
          <div xml:id="echoid-div718" type="section" level="2" n="135">
            <p style="it">
              <s xml:id="echoid-s21058" xml:space="preserve">
                <pb o="278" file="514.01.310" n="310" rhead="LIBER"/>
              cunda proprietaseſt: </s>
              <s xml:id="echoid-s21059" xml:space="preserve">Quod ſi inter regulam a b. </s>
              <s xml:id="echoid-s21060" xml:space="preserve">& </s>
              <s xml:id="echoid-s21061" xml:space="preserve">flexam lineam ducetur linea, illa tandem flexam ſeca-
                <lb/>
              bit. </s>
              <s xml:id="echoid-s21062" xml:space="preserve">Eſto ergo regula a b. </s>
              <s xml:id="echoid-s21063" xml:space="preserve">polus c. </s>
              <s xml:id="echoid-s21064" xml:space="preserve">atque in interuallo d e.</s>
              <s xml:id="echoid-s21065" xml:space="preserve">deſcribatur flexa,quæ conchoides dicitur. </s>
              <s xml:id="echoid-s21066" xml:space="preserve">& </s>
              <s xml:id="echoid-s21067" xml:space="preserve">
                <lb/>
              inter hanc & </s>
              <s xml:id="echoid-s21068" xml:space="preserve">regulam a b. </s>
              <s xml:id="echoid-s21069" xml:space="preserve">ducatur recta f g h. </s>
              <s xml:id="echoid-s21070" xml:space="preserve">dico f g h. </s>
              <s xml:id="echoid-s21071" xml:space="preserve">flexam lineam ſecaturam. </s>
              <s xml:id="echoid-s21072" xml:space="preserve">ſit f g h.
                <lb/>
              </s>
              <s xml:id="echoid-s21073" xml:space="preserve">æque diſtans lineæ a b. </s>
              <s xml:id="echoid-s21074" xml:space="preserve">aut non ſit. </s>
              <s xml:id="echoid-s21075" xml:space="preserve">poſito ergo prius quod ſit & </s>
              <s xml:id="echoid-s21076" xml:space="preserve">fiat, ut ſicut ſe habet d g. </s>
              <s xml:id="echoid-s21077" xml:space="preserve">ad g c. </s>
              <s xml:id="echoid-s21078" xml:space="preserve">ita
                <lb/>
              ſe habeat d e. </s>
              <s xml:id="echoid-s21079" xml:space="preserve">ad alium, puta k. </s>
              <s xml:id="echoid-s21080" xml:space="preserve">& </s>
              <s xml:id="echoid-s21081" xml:space="preserve">constituto centro c. </s>
              <s xml:id="echoid-s21082" xml:space="preserve">interuallo k. </s>
              <s xml:id="echoid-s21083" xml:space="preserve">ſecet circunferentiam deſcriptã
                <lb/>
              in f. </s>
              <s xml:id="echoid-s21084" xml:space="preserve">atque iungatur c f. </s>
              <s xml:id="echoid-s21085" xml:space="preserve">quæ ſecet ab in l. </s>
              <s xml:id="echoid-s21086" xml:space="preserve">erit ergo ut ſicut d g. </s>
              <s xml:id="echoid-s21087" xml:space="preserve">ſe habet ad g c. </s>
              <s xml:id="echoid-s21088" xml:space="preserve">ita ſe habent l
                <lb/>
              f. </s>
              <s xml:id="echoid-s21089" xml:space="preserve">ad f c. </s>
              <s xml:id="echoid-s21090" xml:space="preserve">Sedſicut eſt d g. </s>
              <s xml:id="echoid-s21091" xml:space="preserve">ad g c. </s>
              <s xml:id="echoid-s21092" xml:space="preserve">ita ſe habebat d e. </s>
              <s xml:id="echoid-s21093" xml:space="preserve">ad k. </s>
              <s xml:id="echoid-s21094" xml:space="preserve">ideſt ad c f. </s>
              <s xml:id="echoid-s21095" xml:space="preserve">ergo d e. </s>
              <s xml:id="echoid-s21096" xml:space="preserve">inuenietur
                <lb/>
              æ qualis ipſi l f. </s>
              <s xml:id="echoid-s21097" xml:space="preserve">quod fieri non potest, ita enim pars æqualis toti eſſet, quod manifeſtum fit producta linea
                <lb/>
              c f. </s>
              <s xml:id="echoid-s21098" xml:space="preserve">donec ſecet flexam lineam per e in o. </s>
              <s xml:id="echoid-s21099" xml:space="preserve">quoniam l f o. </s>
              <s xml:id="echoid-s21100" xml:space="preserve">recta æ qualis est ipſi de ex diſſinitione con-
                <lb/>
              choidis. </s>
              <s xml:id="echoid-s21101" xml:space="preserve">Reliquum igitur est, quod recta f g h. </s>
              <s xml:id="echoid-s21102" xml:space="preserve">ſecet flexam lineam modo ad eaſdem partes ducatur. </s>
              <s xml:id="echoid-s21103" xml:space="preserve">Ve-
                <lb/>
                <note position="left" xlink:label="note-514.01.310-01" xlink:href="note-514.01.310-01a" xml:space="preserve">10</note>
              rum æ quediſtet linea illa, quæ inter a b. </s>
              <s xml:id="echoid-s21104" xml:space="preserve">& </s>
              <s xml:id="echoid-s21105" xml:space="preserve">flexam producetur, & </s>
              <s xml:id="echoid-s21106" xml:space="preserve">ſit ea m g n, ducaturq́; </s>
              <s xml:id="echoid-s21107" xml:space="preserve">per g. </s>
              <s xml:id="echoid-s21108" xml:space="preserve">æ que-
                <lb/>
              diſtans f g. </s>
              <s xml:id="echoid-s21109" xml:space="preserve">regulæ a b. </s>
              <s xml:id="echoid-s21110" xml:space="preserve">ergo f g. </s>
              <s xml:id="echoid-s21111" xml:space="preserve">concurret cum flexa, & </s>
              <s xml:id="echoid-s21112" xml:space="preserve">ideo multo magis concurret m n. </s>
              <s xml:id="echoid-s21113" xml:space="preserve">Cum
                <lb/>
              ergo huiuſmodi proprietates organo collectæ fuerint, uſus eius ad propoſitũ oſtẽdendus erit modo terti a proprie
                <lb/>
              tas adducatur, quæ est huiuſmodi. </s>
              <s xml:id="echoid-s21114" xml:space="preserve">Recta a b. </s>
              <s xml:id="echoid-s21115" xml:space="preserve">& </s>
              <s xml:id="echoid-s21116" xml:space="preserve">prima flexa conchoides cum deſcripta illa nunquam con-
                <lb/>
              current, etiam ſi in infinitum protrahantur, hoc facile innoteſcet, ſi ad formam organi attendatur, quoniam in
                <lb/>
              eadem forma, linea media regulæ e f. </s>
              <s xml:id="echoid-s21117" xml:space="preserve">in deſcribenda flexa ſecat ſemper lineam a b. </s>
              <s xml:id="echoid-s21118" xml:space="preserve">in e. </s>
              <s xml:id="echoid-s21119" xml:space="preserve">quo fit ut nota
                <lb/>
              k. </s>
              <s xml:id="echoid-s21120" xml:space="preserve">nunquam perueniet ad ab. </s>
              <s xml:id="echoid-s21121" xml:space="preserve">licet ad eam continenter accedat, per primam prædictam proprietatem.
                <lb/>
              </s>
              <s xml:id="echoid-s21122" xml:space="preserve">Hoc Nicomedis aſſumptum utile es̃t demonſtrationi ſequenti. </s>
              <s xml:id="echoid-s21123" xml:space="preserve">Si angulus fiet ad rectam quæ altera par-
                <lb/>
              te in infinitum tendat, & </s>
              <s xml:id="echoid-s21124" xml:space="preserve">ſi a puncto extra dato ducatur linea, quæ circa eundem angulum ſecet duas
                <lb/>
              rectas, cuius rectæ lineæ particula inter duas, quæ rectum continent datum angulum, equalis ſit da-
                <lb/>
              tæ lineæ quod hoc modo facies. </s>
              <s xml:id="echoid-s21125" xml:space="preserve">Eſto data linea a b. </s>
              <s xml:id="echoid-s21126" xml:space="preserve">ex parte b, infinita, ſupra quam datus an--
                <lb/>
                <note position="left" xlink:label="note-514.01.310-02" xlink:href="note-514.01.310-02a" xml:space="preserve">20</note>
              gulus b a g. </s>
              <s xml:id="echoid-s21127" xml:space="preserve">nota extra ſit c. </s>
              <s xml:id="echoid-s21128" xml:space="preserve">recta autem data ſic d. </s>
              <s xml:id="echoid-s21129" xml:space="preserve">ab c, ad a b. </s>
              <s xml:id="echoid-s21130" xml:space="preserve">ducatur perpendicula-
                <lb/>
              ris c e. </s>
              <s xml:id="echoid-s21131" xml:space="preserve">cui addatur e f. </s>
              <s xml:id="echoid-s21132" xml:space="preserve">æ qualis ipſi d. </s>
              <s xml:id="echoid-s21133" xml:space="preserve">& </s>
              <s xml:id="echoid-s21134" xml:space="preserve">ex organo a polo c. </s>
              <s xml:id="echoid-s21135" xml:space="preserve">& </s>
              <s xml:id="echoid-s21136" xml:space="preserve">interuallo e f, ad regulam a
                <lb/>
              b deſcribatur linea flexa conchoides prima. </s>
              <s xml:id="echoid-s21137" xml:space="preserve">Ergo ex ſecunda proprietate a g, primæ conchoidis produ-
                <lb/>
              cta eoincidet cum conchoidi f g. </s>
              <s xml:id="echoid-s21138" xml:space="preserve">coincidet ergo in g, & </s>
              <s xml:id="echoid-s21139" xml:space="preserve">linea c g, producta, ſecabit a b. </s>
              <s xml:id="echoid-s21140" xml:space="preserve">in h. </s>
              <s xml:id="echoid-s21141" xml:space="preserve">aio li-
                <lb/>
              neam g h. </s>
              <s xml:id="echoid-s21142" xml:space="preserve">eſſe æqualem ipſi d. </s>
              <s xml:id="echoid-s21143" xml:space="preserve">quod inde patet, quoniam ex conchoidis primæ diffinitione, g h, eſt æ-
                <lb/>
              qualis ipſi e f, ſed ex præ ſumpto e f eſt æ qualis ipſi d. </s>
              <s xml:id="echoid-s21144" xml:space="preserve">ergo ex communi ſententia quæ æ qualia tertio,
                <lb/>
              æ qualia inuicem dicuntur, recta g h, eſt æ qualis ipſi d. </s>
              <s xml:id="echoid-s21145" xml:space="preserve">propoſitum ergo habemus. </s>
              <s xml:id="echoid-s21146" xml:space="preserve">Ex Nicomede igitur duæ
                <lb/>
              mediæ comparabiles hoc modo inuenientur. </s>
              <s xml:id="echoid-s21147" xml:space="preserve">Sint duæ rectæ a b, & </s>
              <s xml:id="echoid-s21148" xml:space="preserve">b c, ad angulos rectos poſitæ, inter
                <lb/>
              quas comparabiles duas medias inuenire oporteat: </s>
              <s xml:id="echoid-s21149" xml:space="preserve">perficiatur parallelogrammum a b c d. </s>
              <s xml:id="echoid-s21150" xml:space="preserve">ſecetur utra-
                <lb/>
              que in duas partes, c d, quidem in e. </s>
              <s xml:id="echoid-s21151" xml:space="preserve">d a. </s>
              <s xml:id="echoid-s21152" xml:space="preserve">uero in f. </s>
              <s xml:id="echoid-s21153" xml:space="preserve">coniungaturq́; </s>
              <s xml:id="echoid-s21154" xml:space="preserve">b e, &</s>
              <s xml:id="echoid-s21155" xml:space="preserve">tranſeat uſque ad a d.
                <lb/>
              </s>
              <s xml:id="echoid-s21156" xml:space="preserve">
                <note position="left" xlink:label="note-514.01.310-03" xlink:href="note-514.01.310-03a" xml:space="preserve">30</note>
              productam in punctum g. </s>
              <s xml:id="echoid-s21157" xml:space="preserve">ſed in linea a d. </s>
              <s xml:id="echoid-s21158" xml:space="preserve">cadat ad rectos angulos linea f h. </s>
              <s xml:id="echoid-s21159" xml:space="preserve">& </s>
              <s xml:id="echoid-s21160" xml:space="preserve">producatur a h. </s>
              <s xml:id="echoid-s21161" xml:space="preserve">quæ
                <lb/>
              ſit & </s>
              <s xml:id="echoid-s21162" xml:space="preserve">qualis ipſi c e. </s>
              <s xml:id="echoid-s21163" xml:space="preserve">& </s>
              <s xml:id="echoid-s21164" xml:space="preserve">iungatur g h. </s>
              <s xml:id="echoid-s21165" xml:space="preserve">cui æque diſtet, a i. </s>
              <s xml:id="echoid-s21166" xml:space="preserve">ita ut angulus k a i, ſit æqualis angulo
                <lb/>
              f g h. </s>
              <s xml:id="echoid-s21167" xml:space="preserve">& </s>
              <s xml:id="echoid-s21168" xml:space="preserve">expræcedenti aſſumpto ducatur recta g i k. </s>
              <s xml:id="echoid-s21169" xml:space="preserve">quæ ſecet a i.</s>
              <s xml:id="echoid-s21170" xml:space="preserve">in i. </s>
              <s xml:id="echoid-s21171" xml:space="preserve">& </s>
              <s xml:id="echoid-s21172" xml:space="preserve">d a. </s>
              <s xml:id="echoid-s21173" xml:space="preserve">in parte a. </s>
              <s xml:id="echoid-s21174" xml:space="preserve">pro-
                <lb/>
              ducta ſupra k. </s>
              <s xml:id="echoid-s21175" xml:space="preserve">ita ut. </s>
              <s xml:id="echoid-s21176" xml:space="preserve">i k. </s>
              <s xml:id="echoid-s21177" xml:space="preserve">ſit æqualis ipſi. </s>
              <s xml:id="echoid-s21178" xml:space="preserve">a h. </s>
              <s xml:id="echoid-s21179" xml:space="preserve">& </s>
              <s xml:id="echoid-s21180" xml:space="preserve">iuncta k b, producatur in l, donec cadat in d c.
                <lb/>
              </s>
              <s xml:id="echoid-s21181" xml:space="preserve">productum. </s>
              <s xml:id="echoid-s21182" xml:space="preserve">Dico iam quod ſicut ſe habet a b. </s>
              <s xml:id="echoid-s21183" xml:space="preserve">ad a k. </s>
              <s xml:id="echoid-s21184" xml:space="preserve">ita a k. </s>
              <s xml:id="echoid-s21185" xml:space="preserve">ad l c. </s>
              <s xml:id="echoid-s21186" xml:space="preserve">& </s>
              <s xml:id="echoid-s21187" xml:space="preserve">l c. </s>
              <s xml:id="echoid-s21188" xml:space="preserve">ad c b. </s>
              <s xml:id="echoid-s21189" xml:space="preserve">quoniam
                <lb/>
              c d. </s>
              <s xml:id="echoid-s21190" xml:space="preserve">est in duas partes diuiſa in e. </s>
              <s xml:id="echoid-s21191" xml:space="preserve">& </s>
              <s xml:id="echoid-s21192" xml:space="preserve">huic apponitur k a. </s>
              <s xml:id="echoid-s21193" xml:space="preserve">ergo ex eadem ſexta ſecundi elementorum,
                <lb/>
              quod eſt ſub d k a. </s>
              <s xml:id="echoid-s21194" xml:space="preserve">cum eo, quod fit ex a f æquale est illi, quod fit ex f k. </s>
              <s xml:id="echoid-s21195" xml:space="preserve">Apponatur commune, quod
                <lb/>
              eſtinter f h. </s>
              <s xml:id="echoid-s21196" xml:space="preserve">ergo quod est ſub d k a cum eo, quod fit ex a f & </s>
              <s xml:id="echoid-s21197" xml:space="preserve">ex f h. </s>
              <s xml:id="echoid-s21198" xml:space="preserve">hoc eſt cum eo, quod fit ex
                <lb/>
              a g. </s>
              <s xml:id="echoid-s21199" xml:space="preserve">æquale est illi, quod fit ex k f. </s>
              <s xml:id="echoid-s21200" xml:space="preserve">& </s>
              <s xml:id="echoid-s21201" xml:space="preserve">ex f h. </s>
              <s xml:id="echoid-s21202" xml:space="preserve">ideſt illi, quod fit ex k h. </s>
              <s xml:id="echoid-s21203" xml:space="preserve">& </s>
              <s xml:id="echoid-s21204" xml:space="preserve">quoniam ſicuti ſe habet
                <lb/>
              l c, ad c d. </s>
              <s xml:id="echoid-s21205" xml:space="preserve">ita ſe habet d a. </s>
              <s xml:id="echoid-s21206" xml:space="preserve">ad a k. </s>
              <s xml:id="echoid-s21207" xml:space="preserve">ſed c e. </s>
              <s xml:id="echoid-s21208" xml:space="preserve">eſt dimidium ipſius c d. </s>
              <s xml:id="echoid-s21209" xml:space="preserve">& </s>
              <s xml:id="echoid-s21210" xml:space="preserve">a g. </s>
              <s xml:id="echoid-s21211" xml:space="preserve">est dupla ipſi d a. </s>
              <s xml:id="echoid-s21212" xml:space="preserve">
                <lb/>
                <note position="left" xlink:label="note-514.01.310-04" xlink:href="note-514.01.310-04a" xml:space="preserve">40</note>
              quoniam ex quarta ſexti elementorum ut ſe habet a b. </s>
              <s xml:id="echoid-s21213" xml:space="preserve">ad d e. </s>
              <s xml:id="echoid-s21214" xml:space="preserve">ita ſe habet g a. </s>
              <s xml:id="echoid-s21215" xml:space="preserve">ad a d. </s>
              <s xml:id="echoid-s21216" xml:space="preserve">ex ſuppoſi-
                <lb/>
              tis b a, eſt dupla ipſi d e. </s>
              <s xml:id="echoid-s21217" xml:space="preserve">ergo g a. </s>
              <s xml:id="echoid-s21218" xml:space="preserve">est dupla ipſi a d. </s>
              <s xml:id="echoid-s21219" xml:space="preserve">ſequetur ergo, ut ſicuti l c. </s>
              <s xml:id="echoid-s21220" xml:space="preserve">ſe habet ad c e.
                <lb/>
              </s>
              <s xml:id="echoid-s21221" xml:space="preserve">ita g a. </s>
              <s xml:id="echoid-s21222" xml:space="preserve">ad a k. </s>
              <s xml:id="echoid-s21223" xml:space="preserve">exæquali & </s>
              <s xml:id="echoid-s21224" xml:space="preserve">permutata proportione,ex uigeſima tertia quinti elementorum. </s>
              <s xml:id="echoid-s21225" xml:space="preserve">ſed ut g a. </s>
              <s xml:id="echoid-s21226" xml:space="preserve">
                <lb/>
              ad a k. </s>
              <s xml:id="echoid-s21227" xml:space="preserve">ita h i. </s>
              <s xml:id="echoid-s21228" xml:space="preserve">ad i k. </s>
              <s xml:id="echoid-s21229" xml:space="preserve">exſecunda ſexti elementorum. </s>
              <s xml:id="echoid-s21230" xml:space="preserve">quoniam ex ſubiectis g h. </s>
              <s xml:id="echoid-s21231" xml:space="preserve">& </s>
              <s xml:id="echoid-s21232" xml:space="preserve">a i. </s>
              <s xml:id="echoid-s21233" xml:space="preserve">ſunt æ qui-
                <lb/>
              distantes, & </s>
              <s xml:id="echoid-s21234" xml:space="preserve">ex decima octaua quinti elementorum componendo ſequitur, quod ſicut ſe habet l e ad c e,
                <lb/>
              ita ſe habeat h k. </s>
              <s xml:id="echoid-s21235" xml:space="preserve">ad k i. </s>
              <s xml:id="echoid-s21236" xml:space="preserve">ſed poſita eſt i k. </s>
              <s xml:id="echoid-s21237" xml:space="preserve">æ qualis c e. </s>
              <s xml:id="echoid-s21238" xml:space="preserve">quoniam i k. </s>
              <s xml:id="echoid-s21239" xml:space="preserve">eſt æqualis ipſi a h. </s>
              <s xml:id="echoid-s21240" xml:space="preserve">& </s>
              <s xml:id="echoid-s21241" xml:space="preserve">a h. </s>
              <s xml:id="echoid-s21242" xml:space="preserve">ipſi
                <lb/>
              c e. </s>
              <s xml:id="echoid-s21243" xml:space="preserve">ergo e l. </s>
              <s xml:id="echoid-s21244" xml:space="preserve">eſt æqualis ipſi h k. </s>
              <s xml:id="echoid-s21245" xml:space="preserve">& </s>
              <s xml:id="echoid-s21246" xml:space="preserve">conſequenter æquale est illud, quod fit e x l e, illi quod fit, ex h
                <lb/>
              k. </s>
              <s xml:id="echoid-s21247" xml:space="preserve">& </s>
              <s xml:id="echoid-s21248" xml:space="preserve">quod fit ex l e, æquale eſt illi, quod fit ſub d l c. </s>
              <s xml:id="echoid-s21249" xml:space="preserve">cum eo quod fit ex c e, per ſextam ſecundi ele-
                <lb/>
              mentorum. </s>
              <s xml:id="echoid-s21250" xml:space="preserve">Eiautem quod est ex h k. </s>
              <s xml:id="echoid-s21251" xml:space="preserve">demonſtratum est æquale eſſe id, quod fit ſub d k a. </s>
              <s xml:id="echoid-s21252" xml:space="preserve">cum eo, quod
                <lb/>
              ex a h. </s>
              <s xml:id="echoid-s21253" xml:space="preserve">Quorumid, quod eſt ex c e, æquale eſt ei, quod ex a h. </s>
              <s xml:id="echoid-s21254" xml:space="preserve">Aequalis nanque poſitaes̃t a h. </s>
              <s xml:id="echoid-s21255" xml:space="preserve">ipſi
                <lb/>
                <note position="left" xlink:label="note-514.01.310-05" xlink:href="note-514.01.310-05a" xml:space="preserve">50</note>
              c e. </s>
              <s xml:id="echoid-s21256" xml:space="preserve">Sed ex communi ſententia, ſi ab æqualibus auferantur æqualia, æqualia ſunt reliqua, igitur quod fit ſub
                <lb/>
              d l c, æquale eſt ei, quod fit ſub d k a atuqui per decimam quartam ſexti æqualium, & </s>
              <s xml:id="echoid-s21257" xml:space="preserve">æquiangulorum pa-
                <lb/>
              rallelogrammorum latera mutua ſe proportione conſequuntur. </s>
              <s xml:id="echoid-s21258" xml:space="preserve">ergo ut ipſa l d. </s>
              <s xml:id="echoid-s21259" xml:space="preserve">ad d k. </s>
              <s xml:id="echoid-s21260" xml:space="preserve">& </s>
              <s xml:id="echoid-s21261" xml:space="preserve">k a. </s>
              <s xml:id="echoid-s21262" xml:space="preserve">ad c l.
                <lb/>
              </s>
              <s xml:id="echoid-s21263" xml:space="preserve">verũ ut d l. </s>
              <s xml:id="echoid-s21264" xml:space="preserve">ad d k. </s>
              <s xml:id="echoid-s21265" xml:space="preserve">et a b ad a k & </s>
              <s xml:id="echoid-s21266" xml:space="preserve">l c. </s>
              <s xml:id="echoid-s21267" xml:space="preserve">ad c b. </s>
              <s xml:id="echoid-s21268" xml:space="preserve">& </s>
              <s xml:id="echoid-s21269" xml:space="preserve">l c. </s>
              <s xml:id="echoid-s21270" xml:space="preserve">ad c b. </s>
              <s xml:id="echoid-s21271" xml:space="preserve">& </s>
              <s xml:id="echoid-s21272" xml:space="preserve">a b, ad a k. </s>
              <s xml:id="echoid-s21273" xml:space="preserve">& </s>
              <s xml:id="echoid-s21274" xml:space="preserve">a k. </s>
              <s xml:id="echoid-s21275" xml:space="preserve">ad a k. </s>
              <s xml:id="echoid-s21276" xml:space="preserve">ad l c.</s>
              <s xml:id="echoid-s21277" xml:space="preserve">& </s>
              <s xml:id="echoid-s21278" xml:space="preserve">ipſa l c, ad c b. </s>
              <s xml:id="echoid-s21279" xml:space="preserve">
                <lb/>
              Duabus igitur datis rectis lineis a b. </s>
              <s xml:id="echoid-s21280" xml:space="preserve">& </s>
              <s xml:id="echoid-s21281" xml:space="preserve">b c. </s>
              <s xml:id="echoid-s21282" xml:space="preserve">mediæ duæ inuentæ ſunt comparabiles, & </s>
              <s xml:id="echoid-s21283" xml:space="preserve">reſpondentes a k. </s>
              <s xml:id="echoid-s21284" xml:space="preserve">
                <lb/>
              & </s>
              <s xml:id="echoid-s21285" xml:space="preserve">l c. </s>
              <s xml:id="echoid-s21286" xml:space="preserve">quod facere propoſitum fuit. </s>
              <s xml:id="echoid-s21287" xml:space="preserve">Cæ terum modi alij ſunt antiquor um inueniendi duas medias compara-
                <lb/>
              biles, quos ne moleſtus ſim, omittam, præſertim cum eos in commentarijs Archimedis uidere poſſis, & </s>
              <s xml:id="echoid-s21288" xml:space="preserve">a Ver
                <lb/>
              Hero diligenter explicati ſint. </s>
              <s xml:id="echoid-s21289" xml:space="preserve">nam Philoponus, Dion Bizantius, Diocles, Pappus in mechanicis, Porus, & </s>
              <s xml:id="echoid-s21290" xml:space="preserve">
                <lb/>
              Menechmus de ijs multa. </s>
              <s xml:id="echoid-s21291" xml:space="preserve">dixere. </s>
              <s xml:id="echoid-s21292" xml:space="preserve">V eniam igitur ad id, quod quinto libro pollicitus ſum, & </s>
              <s xml:id="echoid-s21293" xml:space="preserve">modum ponam,
                <lb/>
                <note position="left" xlink:label="note-514.01.310-06" xlink:href="note-514.01.310-06a" xml:space="preserve">60</note>
              </s>
            </p>
          </div>
        </div>
      </text>
    </echo>
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