Vitruvius
,
De architectura libri decem
,
1567
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& </
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<
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<
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<
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<
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<
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<
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<
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<
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<
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meridies eſt. </
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<
s
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xml:space
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">Quod ſi ab occaſu uelis horas notare, ad g. </
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<
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<
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<
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<
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<
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<
s
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xml:space
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">ea enim hora est meridies. </
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<
s
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xml:space
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gnabis 17. </
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<
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<
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">12. </
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<
s
xml:id
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xml:space
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">Si autem uelis horas ab ortu ſupra g. </
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>
<
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<
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">inde 1. </
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<
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<
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3. </
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<
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<
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<
s
xml:id
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xml:space
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">& </
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<
s
xml:id
="
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"
xml:space
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">inde regrediens 7. </
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<
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<
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<
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<
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<
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<
s
xml:id
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xml:space
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">his expeditis duces lineam planitiæ uerticalis
<
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quæſit n m. </
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<
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<
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xml:id
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xml:space
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">ſecet lineam a b. </
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>
<
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<
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>
<
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">quanta gnomonis longitudo eſt fu-
<
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tura. </
s
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<
s
xml:id
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xml:space
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">& </
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<
s
xml:id
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xml:space
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">ab horis in meridiano ſignatis duces horarum lineas per centrum e. </
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>
<
s
xml:id
="
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xml:space
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">ubi eſt gnomonis apex duces
<
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ad lineam planitiæ n m. </
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<
s
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xml:space
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">quemadmodum factum est in horologijs deſcriptis in plano finitori parallelo, nam
<
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lineæ illæ longitudinem umbrœ indicabunt. </
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<
s
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xml:space
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">His igitur rationibus horarios arcus inueſtigabis, unde umbrarum
<
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<
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productiones ex Solis altitudine habebis. </
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<
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xml:space
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">Verum ut arcus latitudinis excipias, ducito a punctis l. </
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<
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xml:id
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">lineas
<
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parallelas diametro a e b. </
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<
s
xml:id
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xml:space
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">quæ ad angulos rectos cadant in diametrum uerticalis g e d, in ſignis ubi
<
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eſt litera p h. </
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<
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xml:id
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<
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<
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<
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<
s
xml:id
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xml:space
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">diducto ad ſi-
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gna ubi k, transferas ſingulas illas longitudines ad lineas tranſuerſas a punctis p. </
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<
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<
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taq́; </
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<
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xml:id
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<
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<
s
xml:id
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xml:space
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">ducantur lineæ ad circinationem a g ubi eſt litera r. </
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<
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xml:id
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cate ubi eſt g, & </
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<
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xml:id
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xml:space
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<
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xml:id
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xml:space
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">quilibet horæ illi reſpondebit, a qua linea
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ſumpta erit, hœc autem omnia ſunt aſſeruanda, donec opus erit æquinoctialem diametrum in horologio æqua-
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biliter partire. </
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<
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<
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">uerticales arcus in tropicis, aut alibi inueniantur. </
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<
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culum duces a b g d in centro e. </
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<
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xml:space
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">in quo eædem ſunt diametri, quæ in præcedenti diagrammate, ducan-
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tur diametri tropicorum cum ſuis ſemicirculis, ut in analemmate, quæ ſint t u. </
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<
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<
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</
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<
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<
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diametri illæ iuxta horarum generaq́; </
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<
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">uelis deſcribere. </
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<
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xml:id
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">ducatur item linea planitiæ uerticalis m o n. </
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<
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piamusq́; </
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<
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">a ſemicir culo tropici Capricornis x y. </
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<
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">ubi horarum antiquarum lineæ ductæ ſunt. </
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<
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tis 1 2. </
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<
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<
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<
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">& </
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<
s
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<
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<
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<
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<
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<
s
xml:id
="
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">Sectio autem finitoris & </
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>
<
s
xml:id
="
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"
xml:space
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">tropici iam dicti
<
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/>
est ubi 12. </
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>
<
s
xml:id
="
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xml:space
="
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">per literas t k, indicata. </
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>
<
s
xml:id
="
echoid-s24012
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xml:space
="
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">Ponatur ergo circinus, & </
s
>
<
s
xml:id
="
echoid-s24013
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xml:space
="
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">extendatur ad t. </
s
>
<
s
xml:id
="
echoid-s24014
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xml:space
="
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">& </
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<
s
xml:id
="
echoid-s24015
"
xml:space
="
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">ea dilatatione uer-
<
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/>
tatur circinus ad circinationem meridiani centro in k permanente, & </
s
>
<
s
xml:id
="
echoid-s24016
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xml:space
="
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">notetur r. </
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>
<
s
xml:id
="
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xml:space
="
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">iterum centro k, inter-
<
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/>
uallum k & </
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>
<
s
xml:id
="
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xml:space
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">11. </
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>
<
s
xml:id
="
echoid-s24019
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xml:space
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">1. </
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>
<
s
xml:id
="
echoid-s24020
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xml:space
="
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">transferatur ad meridianum, & </
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>
<
s
xml:id
="
echoid-s24021
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xml:space
="
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">notetur 11. </
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>
<
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xml:id
="
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">& </
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<
s
xml:id
="
echoid-s24023
"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
echoid-s24024
"
xml:space
="
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">nam tantus eſt arcus horarius
<
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/>
primæ, & </
s
>
<
s
xml:id
="
echoid-s24025
"
xml:space
="
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">undecimæ horæ, & </
s
>
<
s
xml:id
="
echoid-s24026
"
xml:space
="
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">tam altus eſt Sol ſupra uerticale planum q d. </
s
>
<
s
xml:id
="
echoid-s24027
"
xml:space
="
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">quantus eſt arcus g. </
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>
<
s
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="
echoid-s24028
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="
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">11. </
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>
<
s
xml:id
="
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">& </
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<
s
xml:id
="
echoid-s24030
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xml:space
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">
<
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/>
1. </
s
>
<
s
xml:id
="
echoid-s24031
"
xml:space
="
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">centro item k, & </
s
>
<
s
xml:id
="
echoid-s24032
"
xml:space
="
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">ſpatio k 10, & </
s
>
<
s
xml:id
="
echoid-s24033
"
xml:space
="
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">2. </
s
>
<
s
xml:id
="
echoid-s24034
"
xml:space
="
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">transferatur illud in meridianum ubi 10 & </
s
>
<
s
xml:id
="
echoid-s24035
"
xml:space
="
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">2. </
s
>
<
s
xml:id
="
echoid-s24036
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s24037
"
xml:space
="
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">habebi-
<
lb
/>
tur arcus horarius decimæ, & </
s
>
<
s
xml:id
="
echoid-s24038
"
xml:space
="
preserve
">ſecundæ horæ. </
s
>
<
s
xml:id
="
echoid-s24039
"
xml:space
="
preserve
">idem in reliquis horarijs arcubus & </
s
>
<
s
xml:id
="
echoid-s24040
"
xml:space
="
preserve
">circunferentijs excipien-
<
lb
/>
dis facies: </
s
>
<
s
xml:id
="
echoid-s24041
"
xml:space
="
preserve
">tanta enim erit circunferentia horaria, quantum eſt ab g, ad ipſas horas in meridiano ſignatas,
<
lb
/>
a quibus ſi lineas duxeris per centrum e. </
s
>
<
s
xml:id
="
echoid-s24042
"
xml:space
="
preserve
">habebis umbrarum longitudines in plano uerticalis m o n. </
s
>
<
s
xml:id
="
echoid-s24043
"
xml:space
="
preserve
">His
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.347-03
"
xlink:href
="
note-514.01.347-03a
"
xml:space
="
preserve
">30</
note
>
expeditis quærendi ſunt arcus uerticales ad excipiendam latitudinem, & </
s
>
<
s
xml:id
="
echoid-s24044
"
xml:space
="
preserve
">partem umbræ per ſigna 1. </
s
>
<
s
xml:id
="
echoid-s24045
"
xml:space
="
preserve
">in
<
lb
/>
præcedenti diagrammate: </
s
>
<
s
xml:id
="
echoid-s24046
"
xml:space
="
preserve
">ducantur lineæ æquidistantes diametro a e b. </
s
>
<
s
xml:id
="
echoid-s24047
"
xml:space
="
preserve
">quæ ad angulos rectos cadant in
<
lb
/>
g e d. </
s
>
<
s
xml:id
="
echoid-s24048
"
xml:space
="
preserve
">in ſigna p. </
s
>
<
s
xml:id
="
echoid-s24049
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s24050
"
xml:space
="
preserve
">perueniant ad circinationem meridiani, & </
s
>
<
s
xml:id
="
echoid-s24051
"
xml:space
="
preserve
">transfer antur longitudines 1. </
s
>
<
s
xml:id
="
echoid-s24052
"
xml:space
="
preserve
">11. </
s
>
<
s
xml:id
="
echoid-s24053
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s24054
"
xml:space
="
preserve
">
<
lb
/>
1. </
s
>
<
s
xml:id
="
echoid-s24055
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s24056
"
xml:space
="
preserve
">1 10. </
s
>
<
s
xml:id
="
echoid-s24057
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s24058
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s24059
"
xml:space
="
preserve
">item 1. </
s
>
<
s
xml:id
="
echoid-s24060
"
xml:space
="
preserve
">9. </
s
>
<
s
xml:id
="
echoid-s24061
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s24062
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s24063
"
xml:space
="
preserve
">atque 1. </
s
>
<
s
xml:id
="
echoid-s24064
"
xml:space
="
preserve
">8. </
s
>
<
s
xml:id
="
echoid-s24065
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s24066
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s24067
"
xml:space
="
preserve
">ac demum 1 7. </
s
>
<
s
xml:id
="
echoid-s24068
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s24069
"
xml:space
="
preserve
">5. </
s
>
<
s
xml:id
="
echoid-s24070
"
xml:space
="
preserve
">ſupra dict as
<
lb
/>
lineas ubi p. </
s
>
<
s
xml:id
="
echoid-s24071
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s24072
"
xml:space
="
preserve
">ſignentur litera s. </
s
>
<
s
xml:id
="
echoid-s24073
"
xml:space
="
preserve
">ab e uero per s. </
s
>
<
s
xml:id
="
echoid-s24074
"
xml:space
="
preserve
">ducantur lineæ ad circinationem meridiani, ubi
<
lb
/>
notetur t. </
s
>
<
s
xml:id
="
echoid-s24075
"
xml:space
="
preserve
">arcus igitur inter g & </
s
>
<
s
xml:id
="
echoid-s24076
"
xml:space
="
preserve
">t, erunt circunferentiæ uerticales, quæ umbræ latitudinem indicabunt.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s24077
"
xml:space
="
preserve
">Eodem modo, & </
s
>
<
s
xml:id
="
echoid-s24078
"
xml:space
="
preserve
">uia a ſemicirculo Cancri r u. </
s
>
<
s
xml:id
="
echoid-s24079
"
xml:space
="
preserve
">deduces circunferentias tam horar as, quàm uerticales, ut
<
lb
/>
longitudinem, & </
s
>
<
s
xml:id
="
echoid-s24080
"
xml:space
="
preserve
">lat itudinem umbræ ſingulis horis habeas, & </
s
>
<
s
xml:id
="
echoid-s24081
"
xml:space
="
preserve
">eas in horologium transferre poſſis. </
s
>
<
s
xml:id
="
echoid-s24082
"
xml:space
="
preserve
">Quod
<
lb
/>
hac ratione efficies. </
s
>
<
s
xml:id
="
echoid-s24083
"
xml:space
="
preserve
">Esto circulus a b c d, pro uerticali plano. </
s
>
<
s
xml:id
="
echoid-s24084
"
xml:space
="
preserve
">cuius centrum ſit e. </
s
>
<
s
xml:id
="
echoid-s24085
"
xml:space
="
preserve
">diametri a c. </
s
>
<
s
xml:id
="
echoid-s24086
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s24087
"
xml:space
="
preserve
">
<
lb
/>
b d. </
s
>
<
s
xml:id
="
echoid-s24088
"
xml:space
="
preserve
">ita quod A, occaſus C. </
s
>
<
s
xml:id
="
echoid-s24089
"
xml:space
="
preserve
">ortus ſit. </
s
>
<
s
xml:id
="
echoid-s24090
"
xml:space
="
preserve
">ſumatur ex diagrammate I. </
s
>
<
s
xml:id
="
echoid-s24091
"
xml:space
="
preserve
">interuallum o 1. </
s
>
<
s
xml:id
="
echoid-s24092
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s24093
"
xml:space
="
preserve
">transferatur in
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.347-04
"
xlink:href
="
note-514.01.347-04a
"
xml:space
="
preserve
">40</
note
>
planum horologij ab e uerſus b. </
s
>
<
s
xml:id
="
echoid-s24094
"
xml:space
="
preserve
">ſupra lineam e b. </
s
>
<
s
xml:id
="
echoid-s24095
"
xml:space
="
preserve
">in f. </
s
>
<
s
xml:id
="
echoid-s24096
"
xml:space
="
preserve
">per f, traijciatur æquidiſtans diameter a e
<
lb
/>
c & </
s
>
<
s
xml:id
="
echoid-s24097
"
xml:space
="
preserve
">ſit illa g f h. </
s
>
<
s
xml:id
="
echoid-s24098
"
xml:space
="
preserve
">quæ pro diametro æquinoctialis habeatur. </
s
>
<
s
xml:id
="
echoid-s24099
"
xml:space
="
preserve
">post hæc a diagrammate I. </
s
>
<
s
xml:id
="
echoid-s24100
"
xml:space
="
preserve
">ſumito lon-
<
lb
/>
gitudinem umbræ, & </
s
>
<
s
xml:id
="
echoid-s24101
"
xml:space
="
preserve
">eam huc transferes a centro e. </
s
>
<
s
xml:id
="
echoid-s24102
"
xml:space
="
preserve
">ſuper æquinoctialem diametrum, aut arcus uerticales
<
lb
/>
utrinque a ſigno d. </
s
>
<
s
xml:id
="
echoid-s24103
"
xml:space
="
preserve
">nam lineæ illæ, quæ ab e, occulte uenient, ſecabunt æquinoctialem diametrum in ſuis lo-
<
lb
/>
cis: </
s
>
<
s
xml:id
="
echoid-s24104
"
xml:space
="
preserve
">erunt autem ſigna maniſeſta. </
s
>
<
s
xml:id
="
echoid-s24105
"
xml:space
="
preserve
">Vt uero in reliquis parallelis horas deſignes, ſumito prius uerticales cir-
<
lb
/>
cunferentias a præcedenti diagrammate I I. </
s
>
<
s
xml:id
="
echoid-s24106
"
xml:space
="
preserve
">a ſigno g. </
s
>
<
s
xml:id
="
echoid-s24107
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s24108
"
xml:space
="
preserve
">transferes eas a ſigno d, hinc inde, in horolo-
<
lb
/>
gijplanum, ducesq́; </
s
>
<
s
xml:id
="
echoid-s24109
"
xml:space
="
preserve
">occultas lineas ab e, centro ad circunferentiam. </
s
>
<
s
xml:id
="
echoid-s24110
"
xml:space
="
preserve
">in quas lineas umbrarum longitudi-
<
lb
/>
nes a præcedenti diagrammate, I I. </
s
>
<
s
xml:id
="
echoid-s24111
"
xml:space
="
preserve
">deſumptas, transferes, & </
s
>
<
s
xml:id
="
echoid-s24112
"
xml:space
="
preserve
">manifeſtas horarum notas appones, a quibus
<
lb
/>
lineæ per ſigna horarum in æquinoctiali notata lineas traijcies ad partem Cancri. </
s
>
<
s
xml:id
="
echoid-s24113
"
xml:space
="
preserve
">ita horarum lineæ erunt
<
lb
/>
deſcriptæ, & </
s
>
<
s
xml:id
="
echoid-s24114
"
xml:space
="
preserve
">in meridiana linea ſignabis 6. </
s
>
<
s
xml:id
="
echoid-s24115
"
xml:space
="
preserve
">ad dexteram 7. </
s
>
<
s
xml:id
="
echoid-s24116
"
xml:space
="
preserve
">8. </
s
>
<
s
xml:id
="
echoid-s24117
"
xml:space
="
preserve
">9. </
s
>
<
s
xml:id
="
echoid-s24118
"
xml:space
="
preserve
">10. </
s
>
<
s
xml:id
="
echoid-s24119
"
xml:space
="
preserve
">11. </
s
>
<
s
xml:id
="
echoid-s24120
"
xml:space
="
preserve
">12. </
s
>
<
s
xml:id
="
echoid-s24121
"
xml:space
="
preserve
">ad ſiniſtram 1. </
s
>
<
s
xml:id
="
echoid-s24122
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s24123
"
xml:space
="
preserve
">3.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s24124
"
xml:space
="
preserve
">
<
note
position
="
left
"
xlink:label
="
note-514.01.347-05
"
xlink:href
="
note-514.01.347-05a
"
xml:space
="
preserve
">50</
note
>
4. </
s
>
<
s
xml:id
="
echoid-s24125
"
xml:space
="
preserve
">5. </
s
>
<
s
xml:id
="
echoid-s24126
"
xml:space
="
preserve
">Erit autem huiuſmodi horologium in plano uertic alis ad meridiem uergenti. </
s
>
<
s
xml:id
="
echoid-s24127
"
xml:space
="
preserve
">Quoniam uero æſtiuo
<
lb
/>
tempore Sol ortus, & </
s
>
<
s
xml:id
="
echoid-s24128
"
xml:space
="
preserve
">occaſus terminos ad ſeptentrionem mutat, opus erit in plano uerticalis ad ſeptentrionem
<
lb
/>
uerſo eas horas deſcribere, quæ erunt prima, & </
s
>
<
s
xml:id
="
echoid-s24129
"
xml:space
="
preserve
">ſecunda matutina, undecima, & </
s
>
<
s
xml:id
="
echoid-s24130
"
xml:space
="
preserve
">decima poſt meridiem. </
s
>
<
s
xml:id
="
echoid-s24131
"
xml:space
="
preserve
">quod
<
lb
/>
meridiani ope facies, producendo lineam hyperboles, quæ terminos horarum Capricorni connectit, & </
s
>
<
s
xml:id
="
echoid-s24132
"
xml:space
="
preserve
">ducen-
<
lb
/>
do lineas horarum undecimæ & </
s
>
<
s
xml:id
="
echoid-s24133
"
xml:space
="
preserve
">primæ, decimæ & </
s
>
<
s
xml:id
="
echoid-s24134
"
xml:space
="
preserve
">ſecundæ pro ut ratio postulat. </
s
>
<
s
xml:id
="
echoid-s24135
"
xml:space
="
preserve
">His rationibus alia quoq;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s24136
"
xml:space
="
preserve
">horarum genera in horologijs uerticalibus deſcribuntur, quæ omnia melius experientia, quàm uerbis compa-
<
lb
/>
rantur: </
s
>
<
s
xml:id
="
echoid-s24137
"
xml:space
="
preserve
">illud autem animaduertendum, ex diagrammate I. </
s
>
<
s
xml:id
="
echoid-s24138
"
xml:space
="
preserve
">pro omnibus horarum generibus in æquinoctiali
<
lb
/>
diametro collocandis arcus deſumi, nam lineæ omnium horarum generum in æquinoctiali diametro cõcurrunt. </
s
>
<
s
xml:id
="
echoid-s24139
"
xml:space
="
preserve
">
<
lb
/>
Explicauimus iam horologia tum quæ in plano finitori æquidistanti deſcribuntur, tũ quæ in plano uerticalis
<
lb
/>
deſignantur: </
s
>
<
s
xml:id
="
echoid-s24140
"
xml:space
="
preserve
">Nunc ad ea pergemus, quæ in plano meridiani fiunt. </
s
>
<
s
xml:id
="
echoid-s24141
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s24142
"
xml:space
="
preserve
">quoniam meridiani est regionem occiduã
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.347-06
"
xlink:href
="
note-514.01.347-06a
"
xml:space
="
preserve
">60</
note
>
</
s
>
</
p
>
</
div
>
</
div
>
</
text
>
</
echo
>