Vitruvius Pollio, I dieci libri dell?architettura, 1567

Table of figures

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                  no di lati eguali, ſcnza dubbio haueranno i lati proportionali. </s>
                  <s id="s.006580">Adunque, ſi come nelle prime
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                  parallele hanno proportione tra ſe a e. ad a g. coſi hanno b e. ad e f. & ſi come a c.
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                  ad e g. ſi hanno nelle ſeconde parallele, coſi f e. ad e h. & di nuouo come nelle prime f
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                  e. ad e h. coſi g e. ad c i. ma nelle ſeconde parallele come g e. ad e i. coſi b c. ad
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                  e d. ſono adunque continue proportionali b c. e f. h e. e d. per la iſteſſa ragione ſi di­
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                  moſtra, che ſono continue proportionali, anche a b. f g. h i. d c. perche ſi come ſi ha b
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                  e. b f. coſi ſi ha a b. ad f g. & come f e. ad e h. coſi f g. ad h i. & come h
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                  e ad e d. coſi h i. à c d. </s>
                  <s id="s.006581">Date adunque due dritte linee a b. & c d. ritrouato baue­
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                  mo due di me zo continue proportionali, che ſono, f g. & h i. ilche era nostra intentione di
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                  fare. </s>
                  <s id="s.006582">Queſta è la opinione di Eratoſthene cerca la dimoſtratione: & ſe bene egli uuole, che la li­
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                  nea a b. & la c d. ſiano ad angoli dritti ſopra la linea b d. non è però, che non ſegua la
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                  iſteſſa concluſione in qualunque modo l'una, & l'altra linea cada ſopra la linea b d. pure che
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                  amendue facciano angoli ſimiglianti, & ſiano per ſimili cadimenti egualmente diſtanti: perche
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                  tutto è fondato ſopra queſta ragione, che, di quelli triangoli, che hanno gli angoli eguali, i lati ſo
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                  no proportionali. </s>
                  <s id="s.006583">In ſomma ſe noi uorremo trouare piu di due linee proportionali tra le due da­
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                  te a b. & c d. biſognerà ſecondo il ſopradetto modo formare piu linee parallele, sì delle
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                  prime come delle ſeconde. </s>
                  <s id="s.006584">Ma lo inſtrumento col quale ſi poſſa formare coſi bella proua ſecon­
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                  do Eratoſthene è queſto. </s>
                  <s id="s.006585">Piglia una piana di legno, o di rame piu lunga, che larga di figura qua­
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                  drangulare, & d'angoli dritti. </s>
                  <s id="s.006586">& ſia per eſſempio la tauola a b d c. aeconeia poi tre lamet­
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                  te ſopra di quella di q ualche materia ſoda ſottile, & polita, che ſiano quadrangolari, & di an­
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                  guli dritti, di modo, che una di quelle ſia ferma nel mezo della piana, ſi che non ſi poſſa mouere
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                  nè alla deſtra, nè alla ſiniſtra, & ſia quella. </s>
                  <s id="s.006587">e f g h. habbia poi queſta lamett a ne gli angoli
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                  ſuoi, ne i punti e. & f. fitte due regole con i ſuoi pironi in modo, che ciaſcuna ſi poſſa uolge­
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                  re in ogni uerſo, & ſia una regola e m. & l'altra f n. ma l'altra lametta ſia K d e. che
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                  ſia con le teſte ſue in un canale nella piana ſi che poſſa ſcorrere uerſo la lametta e f g h. &
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                  anche a rimouer da quella, ſi che habbia i lati ſuoi paralleli al lato f h. della lametta ferma;
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                  tenga queſta lametta K d c. ſopra il punto
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                  K.
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                  una regola, che ſi poſſa uolgere & alzare,
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                  & abbaſſare, come le altre & ſia quella K o. & poſſa eſſer parallela con le altre re­
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                  gole. </s>
                  <s id="s.006588">& i loro communi tagli, che fanno con la a g. f h. & l. </s>
                  <s id="s.006589">ſiano nella iſteſſa dritta li­
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                  nea, m n o l. ſimilmente la a m. ſia eguale alla d K. perche la a m. inſenſibilmente
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                  auanza la d K. </s>
                  <s id="s.006590">Eſſendo queſte coſi ordinate tra due linee a b. & c d. ſi danno due di me­
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                  zo in continua proportione, che ſono e n, & f o. per le ſopradette ragioni. </s>
                  <s id="s.006591">Ma ſe per ſorte
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                  le due propoſte linee, come ſarebbe la s. </s>
                  <s id="s.006592">& la t. allequali biſogno ſia ritrouarne due di mezo
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                  in continua proportione, non ſaranno eguali a quelle linee, che ſono nello instrumento, a b &
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                  r d. facciaſi col mouere ſecondo il biſogno la lametta h d c. tirandola uerſo la lametta fer­
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                  ma, o allargandola, & ponendola ſempre egualmente distante: facciaſi dico, che ſi come ſi ha la
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                  s, alla t. coſi ſi habbia la a b alla r d. cioè ſe ſaranno la s, & la t tra ſe in proportio­
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                  ne doppia, o tripla, o ſeſquialtera, coſi ſiano tra ſela a b & la r d. perche alla a b. &
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                  r d. che ſono nello instrumento ritrouate, ritrouate ſi ſono due di mezo proportionate, ſeguita,
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                  che alla s & alla t. proposte trouate ſaranno due di mezo in continua proportione. </s>
                  <s id="s.006593">Quanto
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                  piu adunque artificioſo ſarà lo inſtrumento, & ben fatto, tanto piu facilmente ciſeruirà a ritro­
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                  uare le due proportionali; però le teste delle lamette, che ſi moueno entreranno ne i loro canali
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                  aſſettate, & ſi moueranno dolcemente. </s>
                  <s id="s.006594">Et ſe alcuno uorrà trouare piu di due linee proportio­
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                  nali, egli potrà con la aggiunta di piu regole, & lamette farlo commodamente. </s>
                  <s id="s.006595">& questa è ſta­
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                  ta la inuentione di Eratosthene. </s>
                  <s id="s.006596">Biſogna però auuertire, che le regole ſiano lunghe, perche quan
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                  do biſogna allargare le lamette poſſino aggiugnere a i tagli delle linee, che ſi uorranno proportio­
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                  nare, & tocchino il lato ſuperiore dello instrumento, come e m, f x, K u. anzi per dir me­
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                  glio ſiano tanto grandi quanto ſarebbe la diagonale della lametta e f g h, ouero poco piu.
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