Vitruvius - De architectura libri decem

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311279NONVS. quo ſolida conduplicari, & multiplicari poſsint, ut uſus organorum ac demonſtrationu nobis facile innoteſcat.
Ac primum ad datum ſolidum ſub data proportione aliud conſtituere demonstrabo. Esto igitur propoſitum
ſolidum a, uolo aliud ſolidum constituere, quod cum præ dicto eam habeat proportionem, quam habet li-
nea b, ad lineam c. ſumatur igitur linea æqualis alicui lateri ex bis, quæ babet ſolidum c, & eſto illa
112[Figure 112]Demonſtratio Eratoſtbenis.a g t c
b f b d113[Figure 113]Instrumentum Eratoſthenis.m a x g n b c n i o l v q
p b e f k d114[Figure 114]Vſ{us} demonſtratio
Eratoſtbenis cum
inſtrumento.a h n ek l i o d b 8 m c 4115[Figure 115]Inſtrumentum Platonis.f i n o m116[Figure 116]cubus.8 8 64 8 8 8 8 512 8
s e117[Figure 117]Demonstratio Archita.p l k b o i m b e d af118[Figure 118]Demonctration
Platonis.d e b c g11102220333044405550 d, & quam rationem habet b, ad c, eandem habeat d, ad e, ſiue dupla, ſiue triplex, ſiue alio modo
ad ipſam comparetur, & iuxta præ cedentium aliquam dem onſtrationum inter rectas d, & e, duæ inuenian-
tur mediæ comparabiles, & ſint illæ ſ, & g, ita ut d, & f, g, & e, ſint continua proportione inuicem
reſpondentes. inde ex aliqua recta æ quali ipſi f, per uigeſimam ſeptimam libri undecimi ſiat ſolidum, quod
ſit b, & ſimiliter poſitum ſolido a, quoniam per trigeſimam tertiam eiuſdem,ſi quatuor lineæ erunt pro-
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