Vitruvius Pollio, I dieci libri dell?architettura, 1567
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                rano due, entrandoui due fiate a punto. </s>
                <s id="s.002204">& tanto ſia detto cerca la diffinitione, & diuiſione della
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                proportione. </s>
                <s id="s.002205">Hora ſi dirà quello, che ne naſce. </s>
                <s id="s.002206">Dalle proportioni adunque naſceno le comparatio­
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                ni, & i riſpetti, che hanno tra ſe, cioè quando una proportione è comparata con l'altra. </s>
                <s id="s.002207">& queſte
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                ſimiglianze di proportioni ſi chiamano proportionalità: & ſi come la proportione è riſpetto, &
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                conuenienza di due quantilà compreſe ſotto un'iſteſſo genere, coſi la proportionalità è riſpetto,
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                & comparatione non d'una quantità all'altra, ma d'una proportione all'altra. </s>
                <s id="s.002208">Come ſa­
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                rebbe a dire la proportione, che è fra quattro & due, eſſer ſimile alla proportione, che è fra
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                otto, & quattro. </s>
                <s id="s.002209">imperoche & l'una, & l'altra è doppia. </s>
                <s id="s.002210">Et però tutte le doppie, tutte le tri­
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                ple, tutte le quadruple, o ſiano d'uno iſteſſo genere, come tra linea, & linea, tra corpo, & cor­
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                po, o ſiano di diuerſi generi, come tra linea, & corpo, tra corpo, & ſpatio, tra ſpatio, et tempo
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                ſono proportionali, & conſeguente ſimili: & doue è proportionalità, iui è neceſſario, che ſia pro
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                portione; perche (come s'è detto) la proportionalità non è altro, che camparatione di propor­
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                tioni. </s>
                <s id="s.002211">ma non per lo contrario, perche fra quattro & dua, è proportione, ma non proportiona­
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                lità. </s>
                <s id="s.002212">Nelle proportionalità conſiſteno tutti i ſecreti dell' Arte. </s>
                <s id="s.002213">Ma perche egli s'intenda bene
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                quanto ſcoprir uolemo; egli è utile a dire, come ſi conoſceno i denominatori delle proportioni, co­
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                me ſi leua, come ſi aggiugne, come ſono moltiplicate, & partite, & poi ſi dir à delle proportiona
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                lità, & termini loro. </s>
                <s id="s.002214">Per ſapere adunque ritrouare i denominatori delle proportioni, il che gio­
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                ua a conoſcere qual proportione ſia maggiore, qual minore: perche nelle fabriche quelle hanno
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                piu del grande, che ſono di maggiore proportione, perche una stanza di due quadri, ha piu gran­
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                dezza, che una di un quadro & mezo eſſendo, che la doppia è maggior proportione che la ſeſqui
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                altera. </s>
                <s id="s.002215">Egli è dunque da conſiderare, che quando la proportione è di agguaglianza, cioè quan­
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                do ſono tante unità, o miſure in un numero, o grandezza, quante ſono in un'altro, non è neceſſa­
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                rio di affaticarſi in ritrouar denominatori, perche di quella ſpecie di proportione non ſi tro­
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                ua diuiſione, non eſſendo tra le coſe pari maggioranza, nè minoranza. </s>
                <s id="s.002216">Resta adunque, che
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                i denominatori ſiano tra le ſpecie della proportione di diſagguaglianza. </s>
                <s id="s.002217">Breue adunque, &
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                iſpedita regola di ritrouare i numeri, dai quali ſono denominate le proportioni, è partire uno eſtre
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                mo della proportione per l'altro. </s>
                <s id="s.002218">Imperoche quello, che ne uiene per tale partimento, è ſempre il
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                denominatore della proportione. </s>
                <s id="s.002219">Partire altro non è, che uedere quante fiate un numeroentra nel­
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                l'altro, & quello, che auanza. </s>
                <s id="s.002220">La doue è ragioneuole, che dal partimento, & da quello, che
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                reſta ſi conoſca il nome di ciaſcuna proportione: ecco lo eſſempio. </s>
                <s id="s.002221">ſe uuoi ſapere come ſi chiama la
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                proportione tra quattro, & otto, partirai otto per quattro, cioè uedi quante fiate il quattro en­
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                tra nell'otto, & trouerai, che quattro entra due fiate a punto: da due adunque chiamerai la pro
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                portione; che è tra otto, & quattro: & dirai, che la proportione è doppia. </s>
                <s id="s.002222">Similmente ſe uuoi
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                ſapere come ſi chiama la proportione, che è tra cinque, & ſedici, partirai ſedici per cinque, &
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                ritrouerai, che'l cinque entra in ſedicitre fiate, & però dirai, che è proportione tripla, eſſendo
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                denominata da tre, & perche gli reſta uno, che è la quinta parte di cinque, però dirai, che quel­
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                la proportione è tripla ſeſquiquinta, & conoſcerai, quella eſſer compoſta, cioè moltiplice ſopra
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                particolare, & coſi farai nelle altre. </s>
                <s id="s.002223">Dalla ſopradetta cognitione (come ho detto) ſi caua que
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                ſta utilità, che ſi puo ſapere; quale proportione è poſta tra le maggiori, & quale tra le minori,
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                & quale tra l'eguali, & ſimili proportioni. </s>
                <s id="s.002224">ſimili ſono quelle, che hanno ſimili, & le iſteſſe
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                denominationi, maggiori ſono quelle, che hanno maggiore denominatione, & minori, mi­
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                nore, perche la denominatione è detta eſſer tanto grande, quanto il numero, che la dinota. </s>
                <s id="s.002225">
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                Et però la quadrupla è maggiore della tripla, perche quella dal quattro, queſta è deno­
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                minata dal tre. </s>
                <s id="s.002226">& coſi la ſeſquialtera è maggiore della ſeſquiterza, perche la ſeſquialtera è deno
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                minata dalla metà, la ſeſquiterza da un terzo. </s>
                <s id="s.002227">& ne i rotti quanto è maggiore il denominatore
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                del rotto, tanto è minore il rotto, & però un quarto è meno d'un terzo. </s>
                <s id="s.002228">perche quattro è mag­
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                giore ditre: & però una tripla ſeſquialtera è maggiore d'una tripla ſeſquiterza: ma una tripla ſeſ­
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                quiterza è maggiore, che una doppia ſeſquialtera, & questo non per la denominatione del rotto,
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                </s>
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