Vitruvius, I Dieci Libri dell' Architettvra di M. Vitrvvio, 1556

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      <text xml:lang="it" type="free">
        <div xml:id="echoid-div607" type="section" level="1" n="110">
          <p style="it">
            <s xml:id="echoid-s17784" xml:space="preserve">
              <pb o="206" file="0216" n="225" rhead="LIBRO"/>
            quanto e dal g. </s>
            <s xml:id="echoid-s17785" xml:space="preserve">all’i, & </s>
            <s xml:id="echoid-s17786" xml:space="preserve">ſia quello ſpacio b. </s>
            <s xml:id="echoid-s17787" xml:space="preserve">K. </s>
            <s xml:id="echoid-s17788" xml:space="preserve">& </s>
            <s xml:id="echoid-s17789" xml:space="preserve">dallo i. </s>
            <s xml:id="echoid-s17790" xml:space="preserve">al K. </s>
            <s xml:id="echoid-s17791" xml:space="preserve">ſi tire una linea ſin al toccamento della linea g d. </s>
            <s xml:id="echoid-s17792" xml:space="preserve">& </s>
            <s xml:id="echoid-s17793" xml:space="preserve">ſia iui ſegnato l. </s>
            <s xml:id="echoid-s17794" xml:space="preserve">& </s>
            <s xml:id="echoid-s17795" xml:space="preserve">perche
              <lb/>
            per la 33. </s>
            <s xml:id="echoid-s17796" xml:space="preserve">del primo di Euclide la linea a b, e paralella alla linea g i b, & </s>
            <s xml:id="echoid-s17797" xml:space="preserve">per lo preſuppoſto noſtro le linee g i, & </s>
            <s xml:id="echoid-s17798" xml:space="preserve">b K. </s>
            <s xml:id="echoid-s17799" xml:space="preserve">ſono eguali, ne ſegue an-
              <lb/>
            cho, che la linea b g. </s>
            <s xml:id="echoid-s17800" xml:space="preserve">ſia paralella alla linea i l. </s>
            <s xml:id="echoid-s17801" xml:space="preserve">Oltra di queſto delle linee g c, & </s>
            <s xml:id="echoid-s17802" xml:space="preserve">h e. </s>
            <s xml:id="echoid-s17803" xml:space="preserve">ſi leuino due parti eguali alla parte i l. </s>
            <s xml:id="echoid-s17804" xml:space="preserve">& </s>
            <s xml:id="echoid-s17805" xml:space="preserve">ſiano qutlle g m.
              <lb/>
            </s>
            <s xml:id="echoid-s17806" xml:space="preserve">& </s>
            <s xml:id="echoid-s17807" xml:space="preserve">h n. </s>
            <s xml:id="echoid-s17808" xml:space="preserve">& </s>
            <s xml:id="echoid-s17809" xml:space="preserve">ſiano congiunte inſieme i m. </s>
            <s xml:id="echoid-s17810" xml:space="preserve">& </s>
            <s xml:id="echoid-s17811" xml:space="preserve">m n. </s>
            <s xml:id="echoid-s17812" xml:space="preserve">per la allegata propoſitione paralelle ſeranno g l, & </s>
            <s xml:id="echoid-s17813" xml:space="preserve">m i, & </s>
            <s xml:id="echoid-s17814" xml:space="preserve">ſimilmente g h, & </s>
            <s xml:id="echoid-s17815" xml:space="preserve">m n. </s>
            <s xml:id="echoid-s17816" xml:space="preserve">Tagli an-
              <lb/>
            cho la linea m n. </s>
            <s xml:id="echoid-s17817" xml:space="preserve">la a d nel punto o, & </s>
            <s xml:id="echoid-s17818" xml:space="preserve">della linea b K. </s>
            <s xml:id="echoid-s17819" xml:space="preserve">ſia pre ſo tanto quanto è la m @. </s>
            <s xml:id="echoid-s17820" xml:space="preserve">& </s>
            <s xml:id="echoid-s17821" xml:space="preserve">ſia quella parte b p, & </s>
            <s xml:id="echoid-s17822" xml:space="preserve">dal punto o uer ſo il punto p. </s>
            <s xml:id="echoid-s17823" xml:space="preserve">
              <lb/>
            ſia tirata una linea, fin che ella tocchi la linea i m. </s>
            <s xml:id="echoid-s17824" xml:space="preserve">nel punto q. </s>
            <s xml:id="echoid-s17825" xml:space="preserve">ſe adunque la linea m ſera eguale alla o q. </s>
            <s xml:id="echoid-s17826" xml:space="preserve">egli ſtara bene. </s>
            <s xml:id="echoid-s17827" xml:space="preserve">Ma ſe la m c. </s>
            <s xml:id="echoid-s17828" xml:space="preserve">ſer a
              <lb/>
            minore ne ſegue che la b g, ſera ſtata pr eſa, maggiore di quello, che biſognaua, e pero da capo ſi deue tornare, e tanto eſperimentare, che la
              <lb/>
            parte o q, ſia eguale alla m c. </s>
            <s xml:id="echoid-s17829" xml:space="preserve">Sia adunque m c eguale alla o q. </s>
            <s xml:id="echoid-s17830" xml:space="preserve">ne ſeguir à per la allegata propoſitione 23. </s>
            <s xml:id="echoid-s17831" xml:space="preserve">del primo, & </s>
            <s xml:id="echoid-s17832" xml:space="preserve">per lo preſuppoſto
              <lb/>
            noſtro che la c o, & </s>
            <s xml:id="echoid-s17833" xml:space="preserve">la m q. </s>
            <s xml:id="echoid-s17834" xml:space="preserve">ſiano paralelle, & </s>
            <s xml:id="echoid-s17835" xml:space="preserve">ſinalmente (come detto hauemo) nella prima dimoſtratione a b. </s>
            <s xml:id="echoid-s17836" xml:space="preserve">g i. </s>
            <s xml:id="echoid-s17837" xml:space="preserve">m o d c. </s>
            <s xml:id="echoid-s17838" xml:space="preserve">ſi chiameràno le pri
              <lb/>
            me paralelle, & </s>
            <s xml:id="echoid-s17839" xml:space="preserve">a g. </s>
            <s xml:id="echoid-s17840" xml:space="preserve">m i. </s>
            <s xml:id="echoid-s17841" xml:space="preserve">c o. </s>
            <s xml:id="echoid-s17842" xml:space="preserve">le ſeconde. </s>
            <s xml:id="echoid-s17843" xml:space="preserve">Dico adunque che, g i, & </s>
            <s xml:id="echoid-s17844" xml:space="preserve">m o, ſono le due di mezzo proportionali, tra la a b, & </s>
            <s xml:id="echoid-s17845" xml:space="preserve">c d. </s>
            <s xml:id="echoid-s17846" xml:space="preserve">Fac ciaſi adun
              <lb/>
              <note position="left" xlink:label="note-0216-01" xlink:href="note-0216-01a" xml:space="preserve">10</note>
            que. </s>
            <s xml:id="echoid-s17847" xml:space="preserve">che la a d. </s>
            <s xml:id="echoid-s17848" xml:space="preserve">& </s>
            <s xml:id="echoid-s17849" xml:space="preserve">la a b. </s>
            <s xml:id="echoid-s17850" xml:space="preserve">concorrino nel puntor. </s>
            <s xml:id="echoid-s17851" xml:space="preserve">ne ſeguira quello, che ancho di ſopra detto hauemo per la ſimiglianza de i triangoli ſecondo
              <lb/>
            la preallegata propoſitione di Euclide, che nelle prime par alelle, che ſi come è proportionata la a r alla r i. </s>
            <s xml:id="echoid-s17852" xml:space="preserve">coſi ſera la b r alla r g. </s>
            <s xml:id="echoid-s17853" xml:space="preserve">& </s>
            <s xml:id="echoid-s17854" xml:space="preserve">nelle ſe-
              <lb/>
            conde paralelle quello riſpetto di comparatione che hauera la ar alla r i coſi ſara la g r. </s>
            <s xml:id="echoid-s17855" xml:space="preserve">all’a r m. </s>
            <s xml:id="echoid-s17856" xml:space="preserve">& </s>
            <s xml:id="echoid-s17857" xml:space="preserve">ſeguitando ancho ſi come nelle prune ſi
              <lb/>
            hauera la g r. </s>
            <s xml:id="echoid-s17858" xml:space="preserve">alla r m. </s>
            <s xml:id="echoid-s17859" xml:space="preserve">coſi la i r alla r o, & </s>
            <s xml:id="echoid-s17860" xml:space="preserve">nelle ſeconde ſi come ſi hauera la i r alla r o. </s>
            <s xml:id="echoid-s17861" xml:space="preserve">coſi la m r. </s>
            <s xml:id="echoid-s17862" xml:space="preserve">alla r c. </s>
            <s xml:id="echoid-s17863" xml:space="preserve">Ne ſegue adunque, che la b r.
              <lb/>
            </s>
            <s xml:id="echoid-s17864" xml:space="preserve">r g. </s>
            <s xml:id="echoid-s17865" xml:space="preserve">m r. </s>
            <s xml:id="echoid-s17866" xml:space="preserve">m c. </s>
            <s xml:id="echoid-s17867" xml:space="preserve">ſiano in continua proportione, & </s>
            <s xml:id="echoid-s17868" xml:space="preserve">ſotto la isteſſa ragione per la quarta del ſeſto ſeranno come la a b, alla g i. </s>
            <s xml:id="echoid-s17869" xml:space="preserve">la g i. </s>
            <s xml:id="echoid-s17870" xml:space="preserve">alla m o, et la
              <lb/>
            m o. </s>
            <s xml:id="echoid-s17871" xml:space="preserve">alla c d. </s>
            <s xml:id="echoid-s17872" xml:space="preserve">propoſte adunque due linee dritte a b, & </s>
            <s xml:id="echoid-s17873" xml:space="preserve">c d. </s>
            <s xml:id="echoid-s17874" xml:space="preserve">tra quelle trouato ne hauemo due continue proportionali, che ſono ſtate la g i, & </s>
            <s xml:id="echoid-s17875" xml:space="preserve">
              <lb/>
            la m o. </s>
            <s xml:id="echoid-s17876" xml:space="preserve">ilche fare uoleuamo. </s>
            <s xml:id="echoid-s17877" xml:space="preserve">Et con ſimili ragioni potremo ritrouarne quante ci ſera in piacere. </s>
            <s xml:id="echoid-s17878" xml:space="preserve">Et pero per trouarne due di mczzo pro-
              <lb/>
            portionali la b f. </s>
            <s xml:id="echoid-s17879" xml:space="preserve">ſer a un terzo della b o. </s>
            <s xml:id="echoid-s17880" xml:space="preserve">parche la b g. </s>
            <s xml:id="echoid-s17881" xml:space="preserve">è alquanto piu del terzo della b c. </s>
            <s xml:id="echoid-s17882" xml:space="preserve">& </s>
            <s xml:id="echoid-s17883" xml:space="preserve">non mai minore, ne eguale alla b f. </s>
            <s xml:id="echoid-s17884" xml:space="preserve">& </s>
            <s xml:id="echoid-s17885" xml:space="preserve">per ti ouar
              <lb/>
            ne tre di mezzo proportionali la b f. </s>
            <s xml:id="echoid-s17886" xml:space="preserve">ſera un quarto della b c. </s>
            <s xml:id="echoid-s17887" xml:space="preserve">et la b g. </s>
            <s xml:id="echoid-s17888" xml:space="preserve">alquãto maggiore della b f. </s>
            <s xml:id="echoid-s17889" xml:space="preserve">& </s>
            <s xml:id="echoid-s17890" xml:space="preserve">per trouarne quattro la b f. </s>
            <s xml:id="echoid-s17891" xml:space="preserve">ſera un qu n
              <lb/>
            to della b c. </s>
            <s xml:id="echoid-s17892" xml:space="preserve">& </s>
            <s xml:id="echoid-s17893" xml:space="preserve">la b g. </s>
            <s xml:id="echoid-s17894" xml:space="preserve">ſera alquanto maggiore della b f. </s>
            <s xml:id="echoid-s17895" xml:space="preserve">cioe un qumio di eſſa b c. </s>
            <s xml:id="echoid-s17896" xml:space="preserve">& </s>
            <s xml:id="echoid-s17897" xml:space="preserve">coſi ſempre la b c. </s>
            <s xml:id="echoid-s17898" xml:space="preserve">ſera partita in una parte di piu di quel,
              <lb/>
              <note position="left" xlink:label="note-0216-02" xlink:href="note-0216-02a" xml:space="preserve">20</note>
            che ſono le linee mezzane proportionali, che trouar uorremo, & </s>
            <s xml:id="echoid-s17899" xml:space="preserve">ſempre lab f. </s>
            <s xml:id="echoid-s17900" xml:space="preserve">ſer a una di quelle parti, & </s>
            <s xml:id="echoid-s17901" xml:space="preserve">la b g. </s>
            <s xml:id="echoid-s17902" xml:space="preserve">alquanto magg ore ſi pren
              <lb/>
            dera che la b f. </s>
            <s xml:id="echoid-s17903" xml:space="preserve">et però la parte b f. </s>
            <s xml:id="echoid-s17904" xml:space="preserve">ſi piglia, che tante ſiate à punto ſia della b c. </s>
            <s xml:id="echoid-s17905" xml:space="preserve">accioche la grandezza della b f. </s>
            <s xml:id="echoid-s17906" xml:space="preserve">ſi poſſa coniettur are piu preſto.</s>
            <s xml:id="echoid-s17907" xml:space="preserve"/>
          </p>
          <figure number="112">
            <variables xml:id="echoid-variables42" xml:space="preserve">a b n e k p b l i q o d f g w c r</variables>
          </figure>
          <p style="it">
            <s xml:id="echoid-s17908" xml:space="preserve">Quanto appartiene ad Archita dico la inuentione eſſer difficile, & </s>
            <s xml:id="echoid-s17909" xml:space="preserve">la dimoſtra
              <lb/>
            tione molto ſottile in modo, che à porla in opera, non ſi troua instrumen-
              <lb/>
            to alcuno ſatto ſecondo quella dimostratione. </s>
            <s xml:id="echoid-s17910" xml:space="preserve">Noi con quella facilità, che
              <lb/>
            ſi può dimoſtreremo tal coſa, i ſond onenti dellaquale ſono diſperſi in molte
              <lb/>
            propoſitioni di Euclide, lequali é neceſſario hauerle per certe perche trop
              <lb/>
            po ſarebbe il ſcioglier ogni anello de ſi gran catena. </s>
            <s xml:id="echoid-s17911" xml:space="preserve">Date ci ſian due linee
              <lb/>
            a d. </s>
            <s xml:id="echoid-s17912" xml:space="preserve">maggiore, l’altra ſia c. </s>
            <s xml:id="echoid-s17913" xml:space="preserve">Tra queste biſogna trouarne due di mezzo
              <lb/>
              <note position="left" xlink:label="note-0216-03" xlink:href="note-0216-03a" xml:space="preserve">30</note>
            proportionali. </s>
            <s xml:id="echoid-s17914" xml:space="preserve">Prendiamo adunque la maggiore a d. </s>
            <s xml:id="echoid-s17915" xml:space="preserve">d’intorno laquale ſi
              <lb/>
            faccia un circolo di modo, che la ne diuenti il diametro di eſſa, & </s>
            <s xml:id="echoid-s17916" xml:space="preserve">ſia il det-
              <lb/>
            to circolo a b d f. </s>
            <s xml:id="echoid-s17917" xml:space="preserve">nel qual circolo per la prima delterzo di Euclide ſi fara
              <lb/>
            una linea eguale alla linea c. </s>
            <s xml:id="echoid-s17918" xml:space="preserve">& </s>
            <s xml:id="echoid-s17919" xml:space="preserve">ſi quella a b. </s>
            <s xml:id="echoid-s17920" xml:space="preserve">laquale tanto ſi stenda oltra il
              <lb/>
            circolo, che tocchi il punto p. </s>
            <s xml:id="echoid-s17921" xml:space="preserve">ilquale ſia lo eſtremo d’una linea, & </s>
            <s xml:id="echoid-s17922" xml:space="preserve">tocchi
              <lb/>
            il circolo nel punto d. </s>
            <s xml:id="echoid-s17923" xml:space="preserve">& </s>
            <s xml:id="echoid-s17924" xml:space="preserve">ſcende fin al punto o, & </s>
            <s xml:id="echoid-s17925" xml:space="preserve">ſia tutta p d o, & </s>
            <s xml:id="echoid-s17926" xml:space="preserve">à que
              <lb/>
            sta ne ſia tratta una egualmente diſtante, che tagli la linea a d. </s>
            <s xml:id="echoid-s17927" xml:space="preserve">nel punto e. </s>
            <s xml:id="echoid-s17928" xml:space="preserve">intendiſi poi una metà di colonna ritonda, che ſemicilindro ſi chia-
              <lb/>
            ma, dritto ſopra il ſemicircolo a b d. </s>
            <s xml:id="echoid-s17929" xml:space="preserve">& </s>
            <s xml:id="echoid-s17930" xml:space="preserve">oltra di queſto imaguiamoci nel taglio equidistante, che paralellogrammo è, detto del ſemcilindro ſo-
              <lb/>
            pra a d. </s>
            <s xml:id="echoid-s17931" xml:space="preserve">diſſegnato un ſemicircolo ilquale è come un par alellogrammo del ſemicilindro ad anguli giuſti nel piano del circolo A
              <unsure/>
            b d f. </s>
            <s xml:id="echoid-s17932" xml:space="preserve">Queſto ſe
              <lb/>
            micircolo girato dal punto d nel punto b, stando fermo il punto a, che è termine del Diametro a d. </s>
            <s xml:id="echoid-s17933" xml:space="preserve">nel ſuo girare tagliera quella ſoperficie co-
              <lb/>
              <note position="left" xlink:label="note-0216-04" xlink:href="note-0216-04a" xml:space="preserve">40</note>
            lonnare, ò cilindrica, & </s>
            <s xml:id="echoid-s17934" xml:space="preserve">deſcriuera in eſſa una certa linea, dapoi ſe ſtando ſerma la a d. </s>
            <s xml:id="echoid-s17935" xml:space="preserve">il triangolo a p d gir ando ſi fara un mouimento contra
              <lb/>
            rio al ſemicircolo ſenza dubbio eg’i deſcriuera una ſoperficie conica della linea dritta a p. </s>
            <s xml:id="echoid-s17936" xml:space="preserve">laquale nel girarſi ſi congiugne in qualche punto di
              <lb/>
            quella linea, che poco auanti ſu deſcritta mediante il mouimento del ſemicircolo nella ſoperficie del cilindro. </s>
            <s xml:id="echoid-s17937" xml:space="preserve">Similmente ancho il b. </s>
            <s xml:id="echoid-s17938" xml:space="preserve">circonſcri-
              <lb/>
            uera un ſemicircolo nella ſoperficie del cono. </s>
            <s xml:id="echoid-s17939" xml:space="preserve">Et finalmenie il ſemicircolo a d e. </s>
            <s xml:id="echoid-s17940" xml:space="preserve">habbia il ſuo ſito dapoi che ſera moſſo la doue le linee caden-
              <lb/>
            do concorrono, & </s>
            <s xml:id="echoid-s17941" xml:space="preserve">il triangolo che al contrario ſi moua, habbia queſto ſito d l a. </s>
            <s xml:id="echoid-s17942" xml:space="preserve">& </s>
            <s xml:id="echoid-s17943" xml:space="preserve">il punto doue concadono ſia K. </s>
            <s xml:id="echoid-s17944" xml:space="preserve">ſia ancho per b. </s>
            <s xml:id="echoid-s17945" xml:space="preserve">deſcritto
              <lb/>
            un ſemicircolo b m f. </s>
            <s xml:id="echoid-s17946" xml:space="preserve">& </s>
            <s xml:id="echoid-s17947" xml:space="preserve">la doue ſi taglia col circolo b d f a. </s>
            <s xml:id="echoid-s17948" xml:space="preserve">ſia b f. </s>
            <s xml:id="echoid-s17949" xml:space="preserve">indi da punto K. </s>
            <s xml:id="echoid-s17950" xml:space="preserve">à quel piano, che è del ſemicircolo b d a. </s>
            <s xml:id="echoid-s17951" xml:space="preserve">cada una perpen-
              <lb/>
            dicolare, certo è che cadera nella cir conferenza del circolo, perche nel piano dello iſteßo circolo fu drizzato il cilindro. </s>
            <s xml:id="echoid-s17952" xml:space="preserve">Cada adnnque,
              <lb/>
            & </s>
            <s xml:id="echoid-s17953" xml:space="preserve">ſia K i & </s>
            <s xml:id="echoid-s17954" xml:space="preserve">quella linea, che uiene dallo i. </s>
            <s xml:id="echoid-s17955" xml:space="preserve">nello a congiunta ſia con b f. </s>
            <s xml:id="echoid-s17956" xml:space="preserve">nel punto h. </s>
            <s xml:id="echoid-s17957" xml:space="preserve">Ma perche luno, & </s>
            <s xml:id="echoid-s17958" xml:space="preserve">l’altro ſimicircolo cioe il d a, & </s>
            <s xml:id="echoid-s17959" xml:space="preserve">il
              <lb/>
            b m f. </s>
            <s xml:id="echoid-s17960" xml:space="preserve">è drizzato ſopra il ſottopoſto piano del circolo a b d f. </s>
            <s xml:id="echoid-s17961" xml:space="preserve">& </s>
            <s xml:id="echoid-s17962" xml:space="preserve">pero il lor taglio commune m h. </s>
            <s xml:id="echoid-s17963" xml:space="preserve">sta con anguli giuſti ſopra il piano del circo
              <lb/>
            lo a b d f. </s>
            <s xml:id="echoid-s17964" xml:space="preserve">perilche ancho ſopra eſſa b f. </s>
            <s xml:id="echoid-s17965" xml:space="preserve">è drizzata la m h. </s>
            <s xml:id="echoid-s17966" xml:space="preserve">A dunque cio che è contenuto ſotto la b h f. </s>
            <s xml:id="echoid-s17967" xml:space="preserve">& </s>
            <s xml:id="echoid-s17968" xml:space="preserve">lo h f. </s>
            <s xml:id="echoid-s17969" xml:space="preserve">& </s>
            <s xml:id="echoid-s17970" xml:space="preserve">ſotto lo h a, & </s>
            <s xml:id="echoid-s17971" xml:space="preserve">lo h i ſi tro-
              <lb/>
              <note position="left" xlink:label="note-0216-05" xlink:href="note-0216-05a" xml:space="preserve">50</note>
            ua eguale à quello che è ſotto la h m. </s>
            <s xml:id="echoid-s17972" xml:space="preserve">Adunque lo angulo a m i, è giuſto, per la conuerſione del corolario della ottaua del ſesto. </s>
            <s xml:id="echoid-s17973" xml:space="preserve">& </s>
            <s xml:id="echoid-s17974" xml:space="preserve">il triangolo
              <lb/>
            a m i, ſi troua ſimile all’uno, & </s>
            <s xml:id="echoid-s17975" xml:space="preserve">all’altro de i due trianguli m a h. </s>
            <s xml:id="echoid-s17976" xml:space="preserve">& </s>
            <s xml:id="echoid-s17977" xml:space="preserve">a K d. </s>
            <s xml:id="echoid-s17978" xml:space="preserve">& </s>
            <s xml:id="echoid-s17979" xml:space="preserve">perche lo angulo d K a. </s>
            <s xml:id="echoid-s17980" xml:space="preserve">è giusto per la trenteſima del trenteſimo.
              <lb/>
            </s>
            <s xml:id="echoid-s17981" xml:space="preserve">
              <figure xlink:label="fig-0216-02" xlink:href="fig-0216-02a" number="113">
                <variables xml:id="echoid-variables43" xml:space="preserve">c p l k b m i o b a e d f o</variables>
              </figure>
            A dunque per la uinteſimanona del primo d K m, ſono egualmente distanti, impe-
              <lb/>
            roche per le coſe dimoſtrate h i m h. </s>
            <s xml:id="echoid-s17982" xml:space="preserve">ſono perpendicolari al piano del circolo a b d
              <lb/>
            f. </s>
            <s xml:id="echoid-s17983" xml:space="preserve">A dunque egli è proportionale, che come ſi ha d a. </s>
            <s xml:id="echoid-s17984" xml:space="preserve">ad a K coſi ſi habbia K a. </s>
            <s xml:id="echoid-s17985" xml:space="preserve">ad a i.
              <lb/>
            </s>
            <s xml:id="echoid-s17986" xml:space="preserve">& </s>
            <s xml:id="echoid-s17987" xml:space="preserve">i a ad a m. </s>
            <s xml:id="echoid-s17988" xml:space="preserve">percioche i triangoli d a K. </s>
            <s xml:id="echoid-s17989" xml:space="preserve">K a i. </s>
            <s xml:id="echoid-s17990" xml:space="preserve">i m a. </s>
            <s xml:id="echoid-s17991" xml:space="preserve">ſono ſimili per la quarta del
              <lb/>
            ſeſto, & </s>
            <s xml:id="echoid-s17992" xml:space="preserve">coſi ſeguita che quattro dritte linee d a. </s>
            <s xml:id="echoid-s17993" xml:space="preserve">a K. </s>
            <s xml:id="echoid-s17994" xml:space="preserve">a i. </s>
            <s xml:id="echoid-s17995" xml:space="preserve">a m ſiano continue propor
              <lb/>
            tionali, ma la a m. </s>
            <s xml:id="echoid-s17996" xml:space="preserve">ſi troua eguale alla c, & </s>
            <s xml:id="echoid-s17997" xml:space="preserve">per la commune ſententia, quelle coſe
              <lb/>
            che ſono eguale ad una, ſono tra ſe eguali, perche la a m ſi troua eguale alla a b. </s>
            <s xml:id="echoid-s17998" xml:space="preserve">
              <lb/>
            A dunque proposte due linee ad. </s>
            <s xml:id="echoid-s17999" xml:space="preserve">c. </s>
            <s xml:id="echoid-s18000" xml:space="preserve">ne hauemo trouate due di mezzo proportiona-
              <lb/>
              <note position="left" xlink:label="note-0216-06" xlink:href="note-0216-06a" xml:space="preserve">60</note>
            li, che ſono a K. </s>
            <s xml:id="echoid-s18001" xml:space="preserve">a i. </s>
            <s xml:id="echoid-s18002" xml:space="preserve">come doueuamo fare. </s>
            <s xml:id="echoid-s18003" xml:space="preserve">Platone ſimilmente ne fece, & </s>
            <s xml:id="echoid-s18004" xml:space="preserve">la dimo
              <lb/>
            ſtratione, & </s>
            <s xml:id="echoid-s18005" xml:space="preserve">lo inſlrumento, come qui ſotto poneremo. </s>
            <s xml:id="echoid-s18006" xml:space="preserve">Lega le due dritte linee,
              <lb/>
            tra lequali uuoi trouarne due proportionali, legale dico in un angulo dritto nel purt
              <lb/>
            to b. </s>
            <s xml:id="echoid-s18007" xml:space="preserve">& </s>
            <s xml:id="echoid-s18008" xml:space="preserve">ſia la maggiore b g. </s>
            <s xml:id="echoid-s18009" xml:space="preserve">& </s>
            <s xml:id="echoid-s18010" xml:space="preserve">la minore e b. </s>
            <s xml:id="echoid-s18011" xml:space="preserve">allonga poi l’una, & </s>
            <s xml:id="echoid-s18012" xml:space="preserve">l’altra fuori del
              <lb/>
            l’angulo b. </s>
            <s xml:id="echoid-s18013" xml:space="preserve">la maggiore uerſo il d. </s>
            <s xml:id="echoid-s18014" xml:space="preserve">& </s>
            <s xml:id="echoid-s18015" xml:space="preserve">la minore uerſo il c, & </s>
            <s xml:id="echoid-s18016" xml:space="preserve">fa due anguli dritti
              <lb/>
            trouando il punto c, & </s>
            <s xml:id="echoid-s18017" xml:space="preserve">il punto d. </s>
            <s xml:id="echoid-s18018" xml:space="preserve">nelle loro linee conueniente, & </s>
            <s xml:id="echoid-s18019" xml:space="preserve">ſia l’uno angulo
              <lb/>
            g c d. </s>
            <s xml:id="echoid-s18020" xml:space="preserve">& </s>
            <s xml:id="echoid-s18021" xml:space="preserve">l’altro c d e. </s>
            <s xml:id="echoid-s18022" xml:space="preserve">ſi dico, che tra le due linee dritte e b. </s>
            <s xml:id="echoid-s18023" xml:space="preserve">& </s>
            <s xml:id="echoid-s18024" xml:space="preserve">b g. </s>
            <s xml:id="echoid-s18025" xml:space="preserve">proportionato ha
              <lb/>
            uerai due altre linee, che ſono b d. </s>
            <s xml:id="echoid-s18026" xml:space="preserve">& </s>
            <s xml:id="echoid-s18027" xml:space="preserve">b c. </s>
            <s xml:id="echoid-s18028" xml:space="preserve">perche preſuppoſto hauemo lo angulo e d
              <lb/>
            c.</s>
            <s xml:id="echoid-s18029" xml:space="preserve">eſſer dritto, & </s>
            <s xml:id="echoid-s18030" xml:space="preserve">la e d. </s>
            <s xml:id="echoid-s18031" xml:space="preserve">eſſer par alella alla c g. </s>
            <s xml:id="echoid-s18032" xml:space="preserve">pero ne ſegue per la 29 del primo,
              <lb/>
            che lo angulo g c d. </s>
            <s xml:id="echoid-s18033" xml:space="preserve">ſia giuſto, & </s>
            <s xml:id="echoid-s18034" xml:space="preserve">eguale allo angulo c d e. </s>
            <s xml:id="echoid-s18035" xml:space="preserve">ilquale ſimilmente eſſer
              <lb/>
              <note position="left" xlink:label="note-0216-07" xlink:href="note-0216-07a" xml:space="preserve">70</note>
            giuſto preſupponemo, ma la d b per lo nostro componimento cade porpendicolare
              <lb/>
            ſopra la g b d. </s>
            <s xml:id="echoid-s18036" xml:space="preserve">adunqae per lo corolario della ottaua del ſesto la b d. </s>
            <s xml:id="echoid-s18037" xml:space="preserve">è quella linea
              <lb/>
            proportionata, che cade tra la e b, & </s>
            <s xml:id="echoid-s18038" xml:space="preserve">la b c. </s>
            <s xml:id="echoid-s18039" xml:space="preserve">& </s>
            <s xml:id="echoid-s18040" xml:space="preserve">ſunilmente la linea b c, è la mezza
              <lb/>
            na proportionale tra la b d. </s>
            <s xml:id="echoid-s18041" xml:space="preserve">& </s>
            <s xml:id="echoid-s18042" xml:space="preserve">la b g. </s>
            <s xml:id="echoid-s18043" xml:space="preserve">poſta adunque la ragione, & </s>
            <s xml:id="echoid-s18044" xml:space="preserve">la proportione
              <lb/>
            commune della linea b d alla linea b c. </s>
            <s xml:id="echoid-s18045" xml:space="preserve">ne ſeguita che la e b h iuera quello r ſpet o di
              <lb/>
            comparatione alla linea b d. </s>
            <s xml:id="echoid-s18046" xml:space="preserve">che hauer a la c b. </s>
            <s xml:id="echoid-s18047" xml:space="preserve">alla linea b c. </s>
            <s xml:id="echoid-s18048" xml:space="preserve">percioche l’una, et </s>
          </p>
        </div>
      </text>
    </echo>
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