Vitruvius
,
De architectura libri decem
,
1567
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ceptorum late uagantes ſcripturæ, ſi non contrahantur, & </
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<
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<
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</
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<
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<
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xml:space
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<
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<
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<
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xml:space
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">Quod hic dicit {frequentia, multitudineq́; </
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<
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xml:space
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">ſermonis} declarat illud quod initio dixit. </
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<
s
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xml:space
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uoluminibus.</
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<
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xml:space
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<
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<
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explicentur.</
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<
s
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xml:space
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">} Doccndo igitur eße breues oportet. </
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<
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xml:space
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">breuitas enim memoriæ opitulatur, cauendum tamen est
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ne breuitati ſtudentes obſcuri ſimus. </
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<
s
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xml:space
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">offenderetur enim intelligentia. </
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<
s
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xml:space
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">quare ut breuitas, ſic intelligentiæ per-
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ſpicuitas prodeſt. </
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<
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<
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">breuitatem, & </
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<
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<
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xml:space
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">quæ ſi non adſunt in
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ſcriptis {incertas legentium efficient cogitationes.</
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<
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xml:space
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animi partes, memoriam, & </
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<
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<
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<
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<
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occultas nominationes, commenſusq́;</
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tradantur breuiter exponam. </
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<
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xml:space
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<
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ſponderet.</
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<
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<
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<
emph
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>
enim expeditius ea recipere poterunt mentes. </
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<
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xml:space
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">Non minus cum animaduertiſſem diſtentam
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occupationibus ciuitatem publicis, & </
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<
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<
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<
s
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xml:space
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">paucis iudicaui ſcribendum, uti anguſto ſpa-
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tio uacuitatis, ea legentes breuiter percipere poſſent. </
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<
s
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xml:space
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">Alia ratio cur breuis eſſe uoluerit in Archite-
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ctura tradenda, & </
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<
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<
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Pythagorę, hisq́; </
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xml:space
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">qui eius hæreſim fuerunt ſecuti, placuit cubicis rationibus præce-
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ptain uoluminibus ſcribere, conſtitueruntq́; </
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<
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<
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<
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<
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una conſcriptione oportere eſſe putauerunt. </
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<
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xml:space
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">Cubus autem eſt corpus ex ſex lateribus æ quali latitudi-
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ne planitierum quadratum. </
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<
s
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">is cum eſt iactus, quam in partem incubuit, dum eſt intactus, immotam
<
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<
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note-514.01.189-02
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note-514.01.189-02a
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habet ſtabilitatem: </
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<
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<
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">Pythagoreorum præcepta breuia erant, & </
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<
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</
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<
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<
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">maluam transferto, ſed tamen ne co-
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medito: </
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<
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<
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<
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<
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">veſtigiumq́; </
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corporis confundito: </
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<
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">Annulum non geſtato: </
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<
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">ollæ quoque uestigium turbato in cinere: </
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<
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">Hirundines intra
<
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domum ne admittito: </
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<
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xml:space
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">Contra Solem ne meito: </
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<
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xml:space
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">Speculum ne ſpectate ad lucernam: </
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<
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">Dextrum pedem priorem
<
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calciato, ſiniſtrum priorem lauato: </
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<
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">vnguium, criniumq́; </
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<
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">tuorum præ ſegmina ne comingito, ſed in ea conſpuito: </
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<
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<
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a fabis abstineto. </
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<
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">Hæc, & </
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<
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">ſimilia præcepta uerſiculis concludebant, aliudq́; </
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<
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xml:space
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">innuebant, quàm uerba ſona-
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bant. </
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<
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xml:space
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">Cum igitur de aliqua re una tractare uellent, uerſieulis eam certo nemero colligebant. </
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<
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<
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ſiculorum a cubo ſumebant. </
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<
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xml:space
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">Cubus eſt corpus ſex quadratorum laterum, œqualiumq́; </
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<
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">planorum conſtans, a
<
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<
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="
note-514.01.189-03
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note-514.01.189-03a
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">30</
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cuius ſimilitudine cubus quoque numerus est nominatus, qui constat ex ſex planis numeris undequaq; </
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<
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">æqua-
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libus. </
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<
s
xml:id
="
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"
xml:space
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">Oriuntur autem cubi poſt unitatem naturali ſerie, diſpoſitis imparibus numeris, ſi primos duos im-
<
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pares colligas, deinde tres ſequentes impares, atque ita quatuor ſequentes impares. </
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>
<
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xml:space
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<
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">5,
<
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postpoſita unitate ſunt primi impares, horum ſumma est, 8, qui numerus primus eſt cubus. </
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<
s
xml:id
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xml:space
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">Deinde 7, 9,
<
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11, tres ſequentes impares, reddunt, 27, qui numerus eſt ſecundus cubus. </
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<
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xml:id
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xml:space
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">ſic 13, 15, 17, 19, reddunt,
<
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64, tertium cubum. </
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<
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xml:space
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">Cum igitur moto puncto efficiatur linea, & </
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>
<
s
xml:id
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xml:space
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">mota linea fiat planum, & </
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>
<
s
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xml:space
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">plano moto fiat
<
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corpus: </
s
>
<
s
xml:id
="
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"
xml:space
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">non est a ſimilitudine alienum, ſi continuata unitate fiat:</
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>
<
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<
unsure
/>
linearis numerus, quiſuo modo productus
<
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/>
planum efficiat numerum, a quo demum ſolidus constituatur, perinde ac ſi unitati, alia unitas adderetur, qua-
<
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/>
dam ſimilitudine longitudo ſola, quæ lineæ propria est ostenderetur. </
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>
<
s
xml:id
="
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xml:space
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">Si duo tanquam linea moueãtur, perinde
<
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est ac ſi longitudini, etiam latitudo adderetur, & </
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>
<
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xml:id
="
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xml:space
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">planum efficeretur, id eſt, 4, qui numerus planus eſt
<
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<
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position
="
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xlink:label
="
note-514.01.189-04
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xlink:href
="
note-514.01.189-04a
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xml:space
="
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">40</
note
>
ex quo demum eadem ratione cubus, id est ſolidus numerus conſtitueretur. </
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>
<
s
xml:id
="
echoid-s12344
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xml:space
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">nam ſi, 4, per duo multiplicen-
<
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tur, octo reddentur. </
s
>
<
s
xml:id
="
echoid-s12345
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xml:space
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">Vnde uana est eorum ratio, qui dicunt, ſi ſunt ſex ſuperſicies, neceſſe eſt ſex eſſe unitates.
<
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/>
</
s
>
<
s
xml:id
="
echoid-s12346
"
xml:space
="
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">nam ſenarius numerus non eſt ſolidus. </
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>
<
s
xml:id
="
echoid-s12347
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xml:space
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">Inquit igitur Vitru. </
s
>
<
s
xml:id
="
echoid-s12348
"
xml:space
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">Pythagoricos rationibus cubicis numerum uerſi-
<
lb
/>
culorum, quibus aliquid tractabant, concluſiße, nec plus quàm tres cubos in una tractatione collocare uoluiſſe. </
s
>
<
s
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="
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<
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/>
Ideo maiorem cubum ex, 216, verſiculis constituere. </
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>
<
s
xml:id
="
echoid-s12350
"
xml:space
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">multiplicantes igitur ternarium in ſe, nouem efficiebãt,
<
lb
/>
id eſt quadratum numerum, quem per tria ducebant, & </
s
>
<
s
xml:id
="
echoid-s12351
"
xml:space
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">reddebant, 27, primus eorum cubus. </
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>
<
s
xml:id
="
echoid-s12352
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xml:space
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">Simili ratione
<
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/>
alium cubum ex lineari numero faciebant, 4, igitur in ſe ducta, 16, efficiunt. </
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>
<
s
xml:id
="
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xml:space
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">Sed, 16, per, 4, ducta,
<
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/>
64, reddunt, & </
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>
<
s
xml:id
="
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xml:space
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">ita efficitur ſecundus eorum cubus, cui, 27, addita, reddunt 91, inde tertium cubum ex
<
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quinario ducunt. </
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>
<
s
xml:id
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xml:space
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">nam, 5, in ſe ducta efficiunt, 25, quœ ducta per, 5, reddunt, 125, quibus additis 91,
<
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ſumma fit, 216. </
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>
<
s
xml:id
="
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"
xml:space
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">Ad hunc igitur numerum ſumma præceptorum pythagoreorum perueniebat, cubicamq́; </
s
>
<
s
xml:id
="
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"
xml:space
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">ra-
<
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/>
<
note
position
="
left
"
xlink:label
="
note-514.01.189-05
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xlink:href
="
note-514.01.189-05a
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xml:space
="
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">50</
note
>
tionem adamarunt, putantes ea ſirmiter mentibus inbærere, quemadmodum cubus ſi iaciatur, in quacunque
<
lb
/>
parte inſederit, firmã habet stabilitatem. </
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>
<
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">Sed mirum qua ratione primum cubum, ideſt octo nõ admiſerint Py-
<
lb
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thagorei. </
s
>
<
s
xml:id
="
echoid-s12359
"
xml:space
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preserve
">deinde ſecundum id eſt, 27, poſtea tertium, 64, & </
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>
<
s
xml:id
="
echoid-s12360
"
xml:space
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preserve
">non collegerint ſummam 99. </
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>
<
s
xml:id
="
echoid-s12361
"
xml:space
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preserve
">Sed forſan eo-
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rum tractationes in cubos uerſiculorum numeros diuidebant, & </
s
>
<
s
xml:id
="
echoid-s12362
"
xml:space
="
preserve
">ſi eorum præcepta primo cubo non poterant
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contineri, addebant ſecundum, qui ſi ſatis non erat, addebant tertium, qui omnis ſummæ capax erat. </
s
>
<
s
xml:id
="
echoid-s12363
"
xml:space
="
preserve
">Sed quia
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primus, ſcilicet octo, parum est ad propoſitum aliquod unum colligendum, ideo ipſum (ut puto) reliquerunt,
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& </
s
>
<
s
xml:id
="
echoid-s12364
"
xml:space
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preserve
">ideo ad, 27, primo perueniebant a ternario ortum, qui numerus pythagoricis plauſibilis erat; </
s
>
<
s
xml:id
="
echoid-s12365
"
xml:space
="
preserve
">binarius
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autem non item. </
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>
<
s
xml:id
="
echoid-s12366
"
xml:space
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">non igitur ſtatim ad, 216, uerſiculos ueniebant, ſed ſeparatim ad præcedentes cubos, qui ſi
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/>
non erant ſatis, duos colligebant, a duobus demum ad tertium perueniebant, ultra quem progredi nolebant,
<
lb
/>
ne tractationis prolixitati faſtidium afferrent, & </
s
>
<
s
xml:id
="
echoid-s12367
"
xml:space
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preserve
">memoriam, cui ſeruire ſtudebant, longitudine læderent. </
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>
<
s
xml:id
="
echoid-s12368
"
xml:space
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preserve
">nam
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<
note
position
="
left
"
xlink:label
="
note-514.01.189-06
"
xlink:href
="
note-514.01.189-06a
"
xml:space
="
preserve
">60</
note
>
</
s
>
</
p
>
</
div
>
</
div
>
</
text
>
</
echo
>