Vitruvius Pollio, I dieci libri dell?architettura, 1567
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                  quatrro ttiangoli. </s>
                  <s id="s.006435">Con quella ragione (come appare per la ſottopoſta figura) per uia
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                  di linee da Platone ſu fatto il raddoppiamento del campo quadrato. </s>
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                  Qui non ci è altro che dichiarire per hora, eſſendo Vitr. da ſe manifesto, & chiaro: impero­
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                  che il quadrato ſi raddoppia tirando la diagonale, & di quella ſacendo un lato del quadrato, che
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                  deue eſſer doppio al primo. </s>
                  <s id="s.006437">Ecco il quadrato a b c d. da eſſere raddoppiato, è di dieci piedi
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                  per lato. </s>
                  <s id="s.006438">La diagonale è, a b. che lo parte m due trianguli a d b. & a c b. di piedi
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                  cinquanta l'uno di piano. </s>
                  <s id="s.006439">Della diagonale a b. ſi fa un lato a b dfe. </s>
                  <s id="s.006440">che è doppio al qua­
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                  drato a b c d. </s>
                  <s id="s.006441">Puo ben eſſere che la diagonale ſi troui per uia di numeri, ma ci potranno an­
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                  che entrare de i rotti, ilche non è al propoſito nostro. </s>
                  <s id="s.006442">Egli ſi ritruoua la diagonale a questo mo­
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                  do. </s>
                  <s id="s.006443">Moltiplica due lati del quadrato in ſe ciaſcuno ſeparatamente, & raccogli inſieme tutta
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                  la ſomma di quella moltiplicatione, & cauane di quella la radice quadrata, tanto ſarà la diago­
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                  nale. </s>
                  <s id="s.006444">Ecco ſia il quadrato a b c d. di piedi cinque per lato, moltiplica a b. in ſe, cioè cin­
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                  que uia cinque fa uenticinque, & coſi farai del lato b c. che farà ſimilmente uenticinque,
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                  che posti inſieme col primo uenticinque produce cinquanta. </s>
                  <s id="s.006445">la cui radice quadrata è
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                  7 1/14
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                  &
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                  di tanti piedi ſarà la diagonale. </s>
                  <s id="s.006446">ſimilmente farai nelle altre figure quadre di anguli dritti, co
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                  me nella figura e f g h.
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                  Della ſquadra inuentione di Pitagor a per formare l'an­
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                  gulo giusto. </s>
                  <s id="s.006448">Cap. II.
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                  <s id="s.006449">Pitagora ſimilmente' dimoſtrò la ſquadra ritrouata ſenza opera di artefice alcu­
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                  no, & fece chiaro con quanto grande fatica i fabri facendola, a pena la poſſo­
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                  no al giuſto ridurre. </s>
                  <s id="s.006450">Queſta coſa con ragioni, & uie emendata, da ſuoi pre­
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                  cetti ſi manifeſta: perche ſe egli ſi prenderà tre regole, una di piedi tre, l'altra
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                  di quattro, la terza di cinque, & queſte regole compoſte ſiano, che con i capi ſi tocchino
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                  inſieme facendo una figura triangulare, condurranno la ſquadra giuſta; & alle lunghezze
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                  di ciaſcuna regola, ſi farà uno quadrato di lati eguali, dico, che del lato di tre piedi ſi fa­
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                  rà un quadrato di noue piedi, & di quello, che ſarà di quattro piedi ſi farà uno quadrato
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                  di ſedici piedi, & di quello, che ſarà di cinque, ſe ne farà uno di uenticinque, & coſi quan­
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                  to di ſpacio ſarà occupato da due quadri, l'uno di tre, l'altro di quattro piedi per lato, tan
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                  to numero di piedi quadri uenirà dal quadrato tirato ſecondo il lato di cinque piedi. </s>
                  <s id="s.006451">Ha­
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                  uendo Pitagora ritrouato queſto, nè dubitando di non eſſere ſtato in quella inuentione
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                  dalle Muſe ammaeſtrato, riferendole grandiſsime gratie, ſi dice, che a quelle ſacrificio
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                  fece delle uittime: & quella ragione come in molte coſe, & in molte miſure è utile, coſi
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                  negli edificij per fare le ſcale, acciochei gradi ſieno di proportionata miſura, è molto eſpe
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                  dita: perche ſe l'altezza del palco da i capi della trauatura al liuello, & piano da baſſo ſarà
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                  in tre parti diuiſa, la aſceſa delle ſcale ſarà in cinque parti di quelle con giuſta lunghezza
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                  de i fuſti: perche quanto grandi ſaranno le tre parti dalla ſomma trauatura al liuello di ſot
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                  to, quattro di quelle ſi hanno a tirare in fuori, & ſcoſtarſi dal dritto: perche a queſto mo­
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                  do ſaranno moderate le collocationi de i gradi, & delle ſcale: & coſi anche di tal coſa ſa­
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                  rà diſegnata la forma. </s>
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                  Pone Vitr. la inuentione della ſquadra, & l'utile, che ſi caua da quella. </s>
                  <s id="s.006453">Pitagora huomo
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                  diuino in molte coſe fu lo inuentore della ragione della ſquadra, nel che egli trapaßò digran lun­
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                  ga la inuentione di molti artefici eccellenti, & però merita grandiſſima commendatione. </s>
                  <s id="s.006454">La ſqua
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                  dra ſi fa di tre righe poſte in triangolo, ſi che la lunghezza di una ſia di tre, dell'altra di quat­
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                  tro, della terza di cinque parti. </s>
                  <s id="s.006455">da queſta inuentione ſi comprende, che facendoſi tre quadri per
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                  fetti, ſecondo la lunghezza di ciaſcuna rigail quadro fatto dalla riga di cinque parti, ſarà tan-
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