Vitruvius
,
De architectura libri decem
,
1567
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<
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269
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file
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514.01.301
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301
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NONVS.
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tribus pedibuslongitudinis laterum, & </
s
>
<
s
xml:id
="
echoid-s20125
"
xml:space
="
preserve
">quatuor efficiunt; </
s
>
<
s
xml:id
="
echoid-s20126
"
xml:space
="
preserve
">æque tantum numerum reddit unum ex
<
lb
/>
quinque deſcriptum. </
s
>
<
s
xml:id
="
echoid-s20127
"
xml:space
="
preserve
">Id Pythagoras cum inueniffet, non dubitans a mufis ſe in ea inuentione moni-
<
lb
/>
tum, maximas gratias agens,hoſtias dicitur ijs immolauiſſe. </
s
>
<
s
xml:id
="
echoid-s20128
"
xml:space
="
preserve
">Ea autem ratio quemadmodum in multis
<
lb
/>
rebus, & </
s
>
<
s
xml:id
="
echoid-s20129
"
xml:space
="
preserve
">menſuris eſt utilis,etiam in ædificijs ſcalarum ædificationibus uti temperatas habeant graduũ
<
lb
/>
librationes, eſt expedita. </
s
>
<
s
xml:id
="
echoid-s20130
"
xml:space
="
preserve
">Si enim altitudo contignationis ab ſumma coaxatione ad imum libramentũ,
<
lb
/>
diuiſa fuerit in partes tres, erit earum quinque in ſcalis ſcaporum iuſta longitudine inclinatio. </
s
>
<
s
xml:id
="
echoid-s20131
"
xml:space
="
preserve
">Nam
<
lb
/>
quam magnæ fuerint inter contignationem & </
s
>
<
s
xml:id
="
echoid-s20132
"
xml:space
="
preserve
">imum libramentum altitudinis partes tres,quatuor a per
<
lb
/>
pendiculo recedant, & </
s
>
<
s
xml:id
="
echoid-s20133
"
xml:space
="
preserve
">ibi collocentur interiores calces ſcaporum. </
s
>
<
s
xml:id
="
echoid-s20134
"
xml:space
="
preserve
">Ita enim erunt temperatæ graduũ,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s20135
"
xml:space
="
preserve
">ipſarum ſcalarum collocationes: </
s
>
<
s
xml:id
="
echoid-s20136
"
xml:space
="
preserve
">Item eius rei erit ſubſcripta forma.</
s
>
<
s
xml:id
="
echoid-s20137
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s20138
"
xml:space
="
preserve
">Normæ inuentionem, & </
s
>
<
s
xml:id
="
echoid-s20139
"
xml:space
="
preserve
">utilitatem ponit hoc loco vitr. </
s
>
<
s
xml:id
="
echoid-s20140
"
xml:space
="
preserve
">Normam Pyhagoras inuenit, Græc\‘æ γrώμωv
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.301-01
"
xlink:href
="
note-514.01.301-01a
"
xml:space
="
preserve
">10</
note
>
uocatur, eſt autem instrumentum ad exigndos angulos accommodatum, in qua inuentione artificibus excel-
<
lb
/>
lentibus multis Pythagoras præſtantior fuit. </
s
>
<
s
xml:id
="
echoid-s20141
"
xml:space
="
preserve
">efficitur autem ex compactione trium regularum in trigoni for
<
lb
/>
mam, quarum una tribus, altera quatuor, tertia quæ ſubtendit angulum, quinque partibus consttet. </
s
>
<
s
xml:id
="
echoid-s20142
"
xml:space
="
preserve
">Quodſt
<
lb
/>
quælibet regula pro latere quadrati ſumatur, quadratum illud, quod latus babebit ex regula trium partium,
<
lb
/>
nouem partibus conſtabit. </
s
>
<
s
xml:id
="
echoid-s20143
"
xml:space
="
preserve
">Quod uero latus babebit ex regula quatuor partium, ſexdecim partius conſtabit.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s20144
"
xml:space
="
preserve
">Denique quadratum regulæ quinque partium conſtans, 25. </
s
>
<
s
xml:id
="
echoid-s20145
"
xml:space
="
preserve
">partes habebit. </
s
>
<
s
xml:id
="
echoid-s20146
"
xml:space
="
preserve
">partes autem illæ aut pedes ſint,
<
lb
/>
aut alia menſura conſtẽt, modo æquales ſint. </
s
>
<
s
xml:id
="
echoid-s20147
"
xml:space
="
preserve
">Illud uerà mirum eſt, & </
s
>
<
s
xml:id
="
echoid-s20148
"
xml:space
="
preserve
">ad multa utiliſſimum, quod tantum areæ
<
lb
/>
continebit quadratum conſtans ex regula quinque partium, quantum duo illa quadrata ſimul iuncta con-
<
lb
/>
tinebunt. </
s
>
<
s
xml:id
="
echoid-s20149
"
xml:space
="
preserve
">tanta uero eſtanguli recti uis in rebus emetiendis, in ædiſicijs struendis, in machinis instituendis, in
<
lb
/>
horologijs formandis, in omnibus denique astronomicis inſtrumentis componendis, ut nihil aut fieri, aut intel-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.301-02
"
xlink:href
="
note-514.01.301-02a
"
xml:space
="
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">20</
note
>
ligi poſsit ſine recti anguli uſu, & </
s
>
<
s
xml:id
="
echoid-s20150
"
xml:space
="
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">ratione. </
s
>
<
s
xml:id
="
echoid-s20151
"
xml:space
="
preserve
">Excellentiſſimum igitur omnium inſtrumentum normam rectè
<
lb
/>
dixeris, cuius ea quoque commoditas eſt a Vitr. </
s
>
<
s
xml:id
="
echoid-s20152
"
xml:space
="
preserve
">obſeruata, ut ſcalarum diſpoſitio ad normæ formam optime
<
lb
/>
temperetur. </
s
>
<
s
xml:id
="
echoid-s20153
"
xml:space
="
preserve
">Cum uero de ſcalis ponendis bactenus a nobis, & </
s
>
<
s
xml:id
="
echoid-s20154
"
xml:space
="
preserve
">a Vitr. </
s
>
<
s
xml:id
="
echoid-s20155
"
xml:space
="
preserve
">nihil dictum ſit; </
s
>
<
s
xml:id
="
echoid-s20156
"
xml:space
="
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">res poſtulat, ut non-
<
lb
/>
nulla dicamus, quæ ad rem faciant. </
s
>
<
s
xml:id
="
echoid-s20157
"
xml:space
="
preserve
">In ſcalarum collocatione indicium, & </
s
>
<
s
xml:id
="
echoid-s20158
"
xml:space
="
preserve
">experientia requiritur. </
s
>
<
s
xml:id
="
echoid-s20159
"
xml:space
="
preserve
">difficile
<
lb
/>
enim eſt apturn ad ſcalas ponendas locum inuenire, quoniam cæterarum partium, & </
s
>
<
s
xml:id
="
echoid-s20160
"
xml:space
="
preserve
">membrorum diſpoſitiones
<
lb
/>
facile impediripoſſunt. </
s
>
<
s
xml:id
="
echoid-s20161
"
xml:space
="
preserve
">quare qui a ſcalis impedimentum time, impedire ſcalas non debet. </
s
>
<
s
xml:id
="
echoid-s20162
"
xml:space
="
preserve
">Solutas enim & </
s
>
<
s
xml:id
="
echoid-s20163
"
xml:space
="
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">
<
lb
/>
liberas collocationes habere ſcalas oportet, nam ſatis ibi commodæ erunt, ubi nil dabunt incommodi, ut ait
<
lb
/>
Albertus. </
s
>
<
s
xml:id
="
echoid-s20164
"
xml:space
="
preserve
">Cæterum nos hob loco de ædiſiciorum ſcalis mentionem facimus, non de ijs, quæ ad bellorum uſume
<
unsure
/>
<
lb
/>
pertinent, de quibus ſequenti libro ſermo fit. </
s
>
<
s
xml:id
="
echoid-s20165
"
xml:space
="
preserve
">De ſcalis igitur ædificiorum tractantes, genera, ſitum, figuram,
<
lb
/>
apertiones, & </
s
>
<
s
xml:id
="
echoid-s20166
"
xml:space
="
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">partes conſiderabimus. </
s
>
<
s
xml:id
="
echoid-s20167
"
xml:space
="
preserve
">Aſcendimus igitur aut per gradus, aut per accliuia. </
s
>
<
s
xml:id
="
echoid-s20168
"
xml:space
="
preserve
">Accliuia com-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.301-03
"
xlink:href
="
note-514.01.301-03a
"
xml:space
="
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">30</
note
>
modiora ſunt, quoniam ſenſim ſcandimus ſine magna motione. </
s
>
<
s
xml:id
="
echoid-s20169
"
xml:space
="
preserve
">præſertim ſi ſtudium poſuerimus, ut quam le-
<
lb
/>
uiſſimas aſcenſioncs habeant, & </
s
>
<
s
xml:id
="
echoid-s20170
"
xml:space
="
preserve
">hoc modo in montes opera hominum fit aſcenſus. </
s
>
<
s
xml:id
="
echoid-s20171
"
xml:space
="
preserve
">Sedſcaæ illæ, quæ gradus
<
lb
/>
habent, commodæ eſſe debent, & </
s
>
<
s
xml:id
="
echoid-s20172
"
xml:space
="
preserve
">luminoſæ. </
s
>
<
s
xml:id
="
echoid-s20173
"
xml:space
="
preserve
">Commodæ erunt, ſi ( ut dixi ) minus erunt incommodæ. </
s
>
<
s
xml:id
="
echoid-s20174
"
xml:space
="
preserve
">in ædifi-
<
lb
/>
cijs enim loca ſub ſcalis præbent commoditates non paruas. </
s
>
<
s
xml:id
="
echoid-s20175
"
xml:space
="
preserve
">Sed ſi ad eos,qui ſcandunt, & </
s
>
<
s
xml:id
="
echoid-s20176
"
xml:space
="
preserve
">deſcendunt ſcalarũ
<
lb
/>
commoda referamus, illæ erunt commodæ, quœ it a temperabuntur tum in uniuerſum, tum ratione graduum,
<
lb
/>
uit a Vitr. </
s
>
<
s
xml:id
="
echoid-s20177
"
xml:space
="
preserve
">dictum eſt, ſcilicet ut a ſumma contab ulatione ad imum perpendiculum tres ſint partes,ab imo per-
<
lb
/>
pendiculo in receſſu quatuor, ab ultino receſſu ad ſummam contabulationem quinque. </
s
>
<
s
xml:id
="
echoid-s20178
"
xml:space
="
preserve
">Ita enim ad normæ
<
lb
/>
rationem ſcapi ſcalarum tanquam ſubtendentes trigoni lineæ temperabuntur. </
s
>
<
s
xml:id
="
echoid-s20179
"
xml:space
="
preserve
">Graduum uero numerus, & </
s
>
<
s
xml:id
="
echoid-s20180
"
xml:space
="
preserve
">
<
lb
/>
ratio retactionum, quas noſtrirequies uocant, ſic habenda est, ut non multos gradus faciamits fine retra-
<
lb
/>
ctionis, & </
s
>
<
s
xml:id
="
echoid-s20181
"
xml:space
="
preserve
">plani cuiuſpiam interpoſitione, quoniam ſi erit planum commoditati inſeruiemus, & </
s
>
<
s
xml:id
="
echoid-s20182
"
xml:space
="
preserve
">periculo pro-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.301-04
"
xlink:href
="
note-514.01.301-04a
"
xml:space
="
preserve
">40</
note
>
uidebimus, nam aſcendentes feſſi in retractione reſpirant, & </
s
>
<
s
xml:id
="
echoid-s20183
"
xml:space
="
preserve
">qui caſu præcipitant, locum inueniunt planum,
<
lb
/>
in quo firmari poſſunt. </
s
>
<
s
xml:id
="
echoid-s20184
"
xml:space
="
preserve
">altitudo autem graduum, & </
s
>
<
s
xml:id
="
echoid-s20185
"
xml:space
="
preserve
">retractio ita ſunt temperanda, ut quàm minime pes labo-
<
lb
/>
ret, dum eleuatur. </
s
>
<
s
xml:id
="
echoid-s20186
"
xml:space
="
preserve
">Cochlides ſcalæ, quæ ad limacis modum factæ, uocantur, minus areæ tenent. </
s
>
<
s
xml:id
="
echoid-s20187
"
xml:space
="
preserve
">Sed diffici-
<
lb
/>
liorem præbent aſcenſum, præſertim cum neceſſitate fiunt. </
s
>
<
s
xml:id
="
echoid-s20188
"
xml:space
="
preserve
">inepte in angulis ædium in tota ferctà Germania col-
<
lb
/>
locantur, & </
s
>
<
s
xml:id
="
echoid-s20189
"
xml:space
="
preserve
">ea ratione uitioſæ, qua ſunt fenes̃træ, & </
s
>
<
s
xml:id
="
echoid-s20190
"
xml:space
="
preserve
">apertiones aliæ quæ in angulis fiunt. </
s
>
<
s
xml:id
="
echoid-s20191
"
xml:space
="
preserve
">Scalarum mul-
<
lb
/>
titudo improbatur ob impeditiones, qu as faciunt in ædificijs, & </
s
>
<
s
xml:id
="
echoid-s20192
"
xml:space
="
preserve
">graduum multitudo oneroſaest, & </
s
>
<
s
xml:id
="
echoid-s20193
"
xml:space
="
preserve
">granis.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s20194
"
xml:space
="
preserve
">Tres uero apertiones habent ( ut plurimum ) ſcalæ, imam, mediam, & </
s
>
<
s
xml:id
="
echoid-s20195
"
xml:space
="
preserve
">ſummam.</
s
>
<
s
xml:id
="
echoid-s20196
"
xml:space
="
preserve
">ab ima inceptio est aſcenſus. </
s
>
<
s
xml:id
="
echoid-s20197
"
xml:space
="
preserve
">
<
lb
/>
in media aſcendimus, a ſumma in aulas ſupra ingredimur. </
s
>
<
s
xml:id
="
echoid-s20198
"
xml:space
="
preserve
">ima pars ita in proſpectu eß debet, ut quàm primũ
<
lb
/>
ianuam ingredientibus uideatur. </
s
>
<
s
xml:id
="
echoid-s20199
"
xml:space
="
preserve
">media luminoſa ſit, & </
s
>
<
s
xml:id
="
echoid-s20200
"
xml:space
="
preserve
">lumen æquabiliter gradus omnes contingat, hoc ita
<
lb
/>
fiet, ut quæratio fuerit umbræ in planum proiectæ altitudinem totius ſcalæ eadem in gradibus reperiatur. </
s
>
<
s
xml:id
="
echoid-s20201
"
xml:space
="
preserve
">
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.301-05
"
xlink:href
="
note-514.01.301-05a
"
xml:space
="
preserve
">50</
note
>
Summa pars in medio aulæ nos exponat, ita ut uniueræ eius partes æquabiliter cerni poßint, & </
s
>
<
s
xml:id
="
echoid-s20202
"
xml:space
="
preserve
">fenestrarum
<
lb
/>
lumina in medio collocata impari numero ſint, omnes autem partes, & </
s
>
<
s
xml:id
="
echoid-s20203
"
xml:space
="
preserve
">apertiones und in eo conſentiant, ut
<
lb
/>
amplæ ſint, & </
s
>
<
s
xml:id
="
echoid-s20204
"
xml:space
="
preserve
">magnificæ, ut fere uideantur inuitari ad aſcenſum accedentes. </
s
>
<
s
xml:id
="
echoid-s20205
"
xml:space
="
preserve
">conueniunt rectæ eum cochli
<
lb
/>
dibus in proportione graduum, in apertionibus, & </
s
>
<
s
xml:id
="
echoid-s20206
"
xml:space
="
preserve
">alijs rebus,ſed hoc differunt, quodrectarum ſcapus ect
<
lb
/>
tanquam linea tranſmerſa a ſumma coaſſatione ad plani receſſum proiecta, nt linea diagonios,uel bypotenuſa.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s20207
"
xml:space
="
preserve
">Cochlidis uero ſcapus eſt ad perpendiculum collocatus, & </
s
>
<
s
xml:id
="
echoid-s20208
"
xml:space
="
preserve
">circa eum tamq; </
s
>
<
s
xml:id
="
echoid-s20209
"
xml:space
="
preserve
">circa axem gradus ponuntur. </
s
>
<
s
xml:id
="
echoid-s20210
"
xml:space
="
preserve
">
<
lb
/>
cochlides autem ab antiquis facteæ erant, ut in altiſſima conſcenderent, columnas, pyramides, & </
s
>
<
s
xml:id
="
echoid-s20211
"
xml:space
="
preserve
">molesma-
<
lb
/>
ximas æquarent. </
s
>
<
s
xml:id
="
echoid-s20212
"
xml:space
="
preserve
">Ves̃igium cochlidis eſt tanquam uoluta, ſed orthographia a certis uolutæ ſignis erigitur. </
s
>
<
s
xml:id
="
echoid-s20213
"
xml:space
="
preserve
">
<
lb
/>
Albertus Durerus utranque ponit diſpoſitionis ideam, quam nos boc loco ſubiecimus.</
s
>
<
s
xml:id
="
echoid-s20214
"
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
left
"
xml:space
="
preserve
">60</
note
>
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>
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>
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