Vitruvius Pollio, I dieci libri dell?architettura, 1567

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                <p type="main">
                  <s id="s.002477">
                    <pb pagenum="112" xlink:href="045/01/120.jpg"/>
                    <emph type="italics"/>
                  re ſono ſtati da i corpi humani, nelle compoſitioni de i Tempij transſerite: dice anche le miſure
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                  iſteſſe eſſere ſtate pigliate.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s id="s.002478">Similmente gli antichi raccolſero da i membri del corpo le ragioni delle miſure, che in
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                  tutte l'opere pareno eſſer neceſſarie, come il dito, il palmo, il piede, il cubito; & quelle
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                  diſtribuirono nel numero perfetto, che da i Greci Telion è detto. </s>
                </p>
                <p type="main">
                  <s id="s.002479">
                    <emph type="italics"/>
                  Coſa perfetta è quella, a cui nulla manca, & niente ſe le puo aggiugnere, & che di tutte ſue
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                  parti è compoſta, nè altro le ſopr'auanza: per queſta ragione il mondo è perfetto aſſolutamente.
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                  </s>
                  <s id="s.002480">& molte altre coſe nel loro genere ſono perfette. </s>
                  <s id="s.002481">Ma uedianio noi con che ragione ſi chiamino i
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                  numeri perfetti, & quali ſieno.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s id="s.002482">Perfetto numero da gli antichi fu poſto il dieci, perche dalle mani ſi caua il numero de
                    <lb/>
                  nario delle dita; dalle dita il palmo; & dal palmo il piede, & ſi come nell'una, & l'altra
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                  mano dalle dita naturalmente è proceduto il dieci, coſi piacque a Platone, che quel nume
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                  ro fuſſe perfetto, perche dalle unità, che monades Grecamente ſi chiamano, è fornito il
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                  dieci, che è la prima croce:il quale poi, che è fatto undici, ouero dodici, non puo eſſer per
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                  fetto, fin che non peruiene all'altro incrocciamento; perche le unità ſono particelle di
                    <lb/>
                  quel numero. </s>
                </p>
                <p type="main">
                  <s id="s.002483">
                    <emph type="italics"/>
                  Detto hauemo di ſopra, che parte uer amente è quella, che preſa quante fiate ſi puo, compone
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                  il tutto ſenza piu. </s>
                  <s id="s.002484">dal che naſce la intelligenza di quello, che ſi dirà. </s>
                  <s id="s.002485">Dico adunque, che alcu­
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                  ni numeri riſpetto alle parti loro, delle quali ſono compoſti, ſi poſſono chiamare poueri, & dimi­
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                  nuti, altri ſuperflui, & ricchi, altri ueramente ſofficienti, & perfetti. </s>
                  <s id="s.002486">La onde poueri ſono quel
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                  li, le parti de i quali inſieme raccolte non fanno la ſomma del tutto. </s>
                  <s id="s.002487">per eſſempio ſia otto. </s>
                  <s id="s.002488">le par
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                  ti del quale ſono, uno, due, & quattro, che raccolte inſieme non fanno otto. </s>
                  <s id="s.002489">Ricchi ſono quel
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                  li, le parti de i quali ſommate fanno ſomma maggiore, come dodici le cui parti ſono, uno, due,
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                  tre, quattro, & ſei, lequali partiraccolte in uno paſſano la ſomma del tutto, & fanno ſedici. </s>
                  <s id="s.002490">
                    <lb/>
                  Perfetti ſono quelli, le parti intiere de quali con la ſomma loro rendeno preciſamente il tutto, co­
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                  me ſei, & uentiotto. </s>
                  <s id="s.002491">ecco uno, due, & tre, che ſono parti del ſei raccolte inſieme rendeno a pun
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                  to ſei. </s>
                  <s id="s.002492">coſi uno, due, quattro, ſette, & quattordici ſono parti di uentotto, & ſommate inſieme
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                  fanno uent'otto a punto. </s>
                  <s id="s.002493">La generatione de i numeri perfetti s'intenderà, poſte prima alcune dif
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                  finitioni. </s>
                  <s id="s.002494">Sono adunque alcuni numeri, che ſi chiamano parimenti pari, & ſon quelli, che eſſendo
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                  pare la ſomma loro, ſi diuideno ſempre in numero pare fin'all'unità, come ſarebbe ſeſſanta quat­
                    <lb/>
                  tro, che è numero pare, & ſi diuide in trentadue, ſedici, otto, quattro, due, fin' all'unità, in
                    <lb/>
                  numeri pari. </s>
                  <s id="s.002495">Sono anche altri numeri, che ſi chiamano primi, & incompoſti, i quali ſono quel­
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                  li, che ſolo dalla unità ſono miſurati, & non hanno altro numero, che gli partiſca intieramen­
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                  te, come tre, cinque, ſette, undici, & altri ſimili. </s>
                  <s id="s.002496">La generatione adunque de i numeri perfet­
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                  ti ſi fa ponendo a fila per ordine i parimenti pari, & ſommandogli inſieme: & quando s'incontra
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                  in una ſomma, che multiplicata per quello, che è ultimo di quella ſomma, ſi fa il numero perfetto:
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                  pur che il numero della ſomma ſia primo, & incompoſto, altrimenti non riuſcirebbe il numero
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                  perfetto. </s>
                  <s id="s.002497">Ecco uno, & due fanno tre. </s>
                  <s id="s.002498">Eſſendo adunque tre numero primo, & incompoſto egli ſi
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                  moltiplica per due, che era l'ultimo nella ſomma, & nel raccoglimento, la doue due fiate tre fan
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                  no ſei, adunque nella decina ſei è numero perfetto. </s>
                  <s id="s.002499">Seguita la generatione dell'altro perfetto:
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                  Ecco, uno, due, & quattro, fanno ſette, che è numero primo, & incompoſto, moltiplica ſette
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                  per quattro, ſe ne raccoglie uentotto, che è il ſecondo perfetto nel centinaio. </s>
                  <s id="s.002500">Seguita uno, due,
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                  quattro, otto, che fanno quindici, ma quindici non è numero primo, & incompoſto, perche è miſu
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                  rato oltra la unità, anche da altri numeri, come da tre, & cinque, però ſi paſſa piu inanzi all'altro
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                  parimente pare, che è ſedici, queſti aggiunto al quindici fa trent'uno, il quale eſſendo numero
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                  primo, & incompoſto, ſe ſarà moltiplicato per ſedici, che era l'ultimo della ſomma, farà quat
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                  trocento & nonanta ſei, che ſara il numero perfetto nel millenario. </s>
                  <s id="s.002501">con la iſteſſa ragione ſi fan
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                  no gli altri perfetti, i quali ſono rari, perche rare ſono le coſe perfette. </s>
                  <s id="s.002502">Hanno i numeri perfetti
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                  </s>
                </p>
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