Vitruvius
,
De architectura libri decem
,
1567
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341
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mur ſane his temporibus tot quadrantum, radiorum, anulorum, regularum, cylindrorum, torquetorum, hemicy-
<
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clioru, planiſpbæriorum, & </
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<
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xml:space
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">cæterorum instrumentorum multitudine, quæ olim a ueteribus accurate inuenta & </
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>
<
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xml:id
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xml:space
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<
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deſcripta ſunt. </
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<
s
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xml:space
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">Habendæ nibilominus gratiæ ſunt ijs, qui faciliorem uſum, & </
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<
s
xml:id
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"
xml:space
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">commodiorem tractationem in-
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uenerunt, uel quæ obſcura erant, & </
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<
s
xml:id
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"
xml:space
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">in tenebris deliteſcebant, ſtudio, & </
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>
<
s
xml:id
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"
xml:space
="
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">diligentia ad communem utilitatem
<
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protulere, & </
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>
<
s
xml:id
="
echoid-s23479
"
xml:space
="
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">præclara ueterum inuenta ab iniurijs ſæculorum uindicarunt. </
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>
<
s
xml:id
="
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xml:space
="
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">Sed ad rem. </
s
>
<
s
xml:id
="
echoid-s23481
"
xml:space
="
preserve
">Inſistam ego quoque
<
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in ijs, quæ a Ptolomæo, & </
s
>
<
s
xml:id
="
echoid-s23482
"
xml:space
="
preserve
">Commandino iacta ſunt fundamenta, & </
s
>
<
s
xml:id
="
echoid-s23483
"
xml:space
="
preserve
">analemmatis uſum, quantum potero fa -
<
lb
/>
sile explicabo, Matbematic as illis demonſtrationes relinquens. </
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>
<
s
xml:id
="
echoid-s23484
"
xml:space
="
preserve
">Nulli dubium eſt, Solem temporibus atque
<
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boris alijs, alias altitudines, & </
s
>
<
s
xml:id
="
echoid-s23485
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xml:space
="
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">ſitus alios occupare. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Cernimus enim æstate orientem, & </
s
>
<
s
xml:id
="
echoid-s23487
"
xml:space
="
preserve
">cadentem Solem,
<
lb
/>
duarum & </
s
>
<
s
xml:id
="
echoid-s23488
"
xml:space
="
preserve
">amplius borarum ſpatio ab oriente, & </
s
>
<
s
xml:id
="
echoid-s23489
"
xml:space
="
preserve
">occidente ſeptentrionem uerſus conſurgere. </
s
>
<
s
xml:id
="
echoid-s23490
"
xml:space
="
preserve
">cernimus quo-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.341-01
"
xlink:href
="
note-514.01.341-01a
"
xml:space
="
preserve
">10</
note
>
que Solem interdum inter orientem', & </
s
>
<
s
xml:id
="
echoid-s23491
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xml:space
="
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">meridiem, & </
s
>
<
s
xml:id
="
echoid-s23492
"
xml:space
="
preserve
">in meridie, ac demum ad occidentem a meridie incli-
<
lb
/>
nari, & </
s
>
<
s
xml:id
="
echoid-s23493
"
xml:space
="
preserve
">ijs temporibus modo altiores, modo depreſſiores cœli partes tenere, quæ omnia noſſe accurate opor-
<
lb
/>
tet, ſieius effectus in mundo ſcire uelimus, unde analemmatum deſcriptiones comparanantur: </
s
>
<
s
xml:id
="
echoid-s23494
"
xml:space
="
preserve
">noſſe autem ex-
<
lb
/>
quiſite illa non poterimus, niſi lineas multas, & </
s
>
<
s
xml:id
="
echoid-s23495
"
xml:space
="
preserve
">circulos angulosq́; </
s
>
<
s
xml:id
="
echoid-s23496
"
xml:space
="
preserve
">fingamus, quibus quaſi cancellis pictorũ
<
lb
/>
certos Solis ſitus inueniamus. </
s
>
<
s
xml:id
="
echoid-s23497
"
xml:space
="
preserve
">Quoniam uero ut libet in diuerſis planis, hoc eſt finitori, uerticali, & </
s
>
<
s
xml:id
="
echoid-s23498
"
xml:space
="
preserve
">meridia-
<
lb
/>
no ( de quibus ſuperius dixi) æquidistantibus conficere boraria poſſumus, ideo ſcire neceſſe est; </
s
>
<
s
xml:id
="
echoid-s23499
"
xml:space
="
preserve
">qui circuli,
<
lb
/>
quæ lineæ, qui anguli, quibus planis inſeruiant, ut illis poſitis tanquam terminis, Solis radios, quorum effectus
<
lb
/>
in mundo conſpicitur per gnomonem, & </
s
>
<
s
xml:id
="
echoid-s23500
"
xml:space
="
preserve
">umbras uenari poſſimus. </
s
>
<
s
xml:id
="
echoid-s23501
"
xml:space
="
preserve
">Formauimus antea tria plana finitorem,
<
lb
/>
uerticale, & </
s
>
<
s
xml:id
="
echoid-s23502
"
xml:space
="
preserve
">meridianum; </
s
>
<
s
xml:id
="
echoid-s23503
"
xml:space
="
preserve
">diametros quoque illvrum poſuimus, & </
s
>
<
s
xml:id
="
echoid-s23504
"
xml:space
="
preserve
">quid unumquodque muneris habeat, ex-
<
lb
/>
poſuimus; </
s
>
<
s
xml:id
="
echoid-s23505
"
xml:space
="
preserve
">nunc dicimus finxiſſe nos ill.</
s
>
<
s
xml:id
="
echoid-s23506
"
xml:space
="
preserve
">i imrnota, & </
s
>
<
s
xml:id
="
echoid-s23507
"
xml:space
="
preserve
">permanentia, & </
s
>
<
s
xml:id
="
echoid-s23508
"
xml:space
="
preserve
">ad ea quoque tria mobilia addenda eſſe,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.341-02
"
xlink:href
="
note-514.01.341-02a
"
xml:space
="
preserve
">20</
note
>
ita ut finitor immotus ſit, & </
s
>
<
s
xml:id
="
echoid-s23509
"
xml:space
="
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">finitor mobilis, itemq; </
s
>
<
s
xml:id
="
echoid-s23510
"
xml:space
="
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">uerticalis firmus, & </
s
>
<
s
xml:id
="
echoid-s23511
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xml:space
="
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">uerticalis motus: </
s
>
<
s
xml:id
="
echoid-s23512
"
xml:space
="
preserve
">eadem ratio de me-
<
lb
/>
ridiano. </
s
>
<
s
xml:id
="
echoid-s23513
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s23514
"
xml:space
="
preserve
">moueatur quodlibet mobile ſupra diametrum ſui immoti. </
s
>
<
s
xml:id
="
echoid-s23515
"
xml:space
="
preserve
">Iam notum eſt, quæ ſint diametri il-
<
lb
/>
lorum planorum, nam finitoris a labro orientis ad occidens terminatur. </
s
>
<
s
xml:id
="
echoid-s23516
"
xml:space
="
preserve
">uerticalis a ſummo uertice ad imas
<
lb
/>
ſub terræ partes. </
s
>
<
s
xml:id
="
echoid-s23517
"
xml:space
="
preserve
">meridiani linea meridiana diameter eſt, atque omnes ſe in centro mundi ad rectos angulos
<
lb
/>
ſecant. </
s
>
<
s
xml:id
="
echoid-s23518
"
xml:space
="
preserve
">Si ergo finit or moueri fingatur, & </
s
>
<
s
xml:id
="
echoid-s23519
"
xml:space
="
preserve
">circum ſuum diametrum, tanquam circa axem conuolui, certe pars
<
lb
/>
una ſupra finitorem immobilem extolletur, & </
s
>
<
s
xml:id
="
echoid-s23520
"
xml:space
="
preserve
">altera deprimetur. </
s
>
<
s
xml:id
="
echoid-s23521
"
xml:space
="
preserve
">Si uero uerticalis moue atur, pars altera
<
lb
/>
progredietur, altera regredietur firma diametro uerticalis permanente. </
s
>
<
s
xml:id
="
echoid-s23522
"
xml:space
="
preserve
">Si demum meridianus mouebitur,
<
lb
/>
pars altera ad finitorem proclinabit, altera ad finitorem conſurget. </
s
>
<
s
xml:id
="
echoid-s23523
"
xml:space
="
preserve
">His poſitis esto Sol ad notum gradibus
<
lb
/>
quadraginta a finitore altus, moueatur finitor, & </
s
>
<
s
xml:id
="
echoid-s23524
"
xml:space
="
preserve
">tantum extollatur ut centrum Solis medium ſecet, mouea-
<
lb
/>
tur item uerticalis, & </
s
>
<
s
xml:id
="
echoid-s23525
"
xml:space
="
preserve
">progrediatur ad notum uſque quo Solem eo loci contingat, quo finitor mobilis So-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.341-03
"
xlink:href
="
note-514.01.341-03a
"
xml:space
="
preserve
">30</
note
>
lem ſecabat. </
s
>
<
s
xml:id
="
echoid-s23526
"
xml:space
="
preserve
">moueatur denique meridianus, & </
s
>
<
s
xml:id
="
echoid-s23527
"
xml:space
="
preserve
">tantum deprimatur, ut Solem quoque medium ſecet, ſanè tria
<
lb
/>
illa mobilia plana relictis immobilibus, ſe ſe mutuo ibi ſecabunt, ubi ſingula Solem ſecant, idest ubi Sol cum
<
lb
/>
fuerit, radios ſuos emittit in mundum. </
s
>
<
s
xml:id
="
echoid-s23528
"
xml:space
="
preserve
">Nunc uideamus eorum planorum effectus, & </
s
>
<
s
xml:id
="
echoid-s23529
"
xml:space
="
preserve
">quo fine eos antiqui fin-
<
lb
/>
xerunt. </
s
>
<
s
xml:id
="
echoid-s23530
"
xml:space
="
preserve
">ac primum in quibus conueniant explicemus. </
s
>
<
s
xml:id
="
echoid-s23531
"
xml:space
="
preserve
">Conueniunt ſanè in eo, quod cum ab immobili quodq;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s23532
"
xml:space
="
preserve
">ſuo diſcedit, & </
s
>
<
s
xml:id
="
echoid-s23533
"
xml:space
="
preserve
">cum Sole mouetur, duos conficiunt angulos, alterum ex rectis lineis, alterum ex planis eo-
<
lb
/>
rum circulorum, idest mobilis, & </
s
>
<
s
xml:id
="
echoid-s23534
"
xml:space
="
preserve
">immobilis. </
s
>
<
s
xml:id
="
echoid-s23535
"
xml:space
="
preserve
">Quoniam uero angulos ex circinatione circuli metimur, ideo
<
lb
/>
alia circinationis pars ſubtendet angulos a lineis rectis, alia ab illis planis confectos. </
s
>
<
s
xml:id
="
echoid-s23536
"
xml:space
="
preserve
">vterque uero angulus
<
lb
/>
neceſſarius est, ut uerus Solis ſitus habeatur. </
s
>
<
s
xml:id
="
echoid-s23537
"
xml:space
="
preserve
">ideſt Solis altitudo, & </
s
>
<
s
xml:id
="
echoid-s23538
"
xml:space
="
preserve
">pars unde Sol ſuos radios demittit in
<
lb
/>
mundum. </
s
>
<
s
xml:id
="
echoid-s23539
"
xml:space
="
preserve
">Nunc ſeparatim unumquodque ſumamus. </
s
>
<
s
xml:id
="
echoid-s23540
"
xml:space
="
preserve
">Eſto Sol, ut prius, ad notum, moueatur uerticale
<
lb
/>
mobile ad Solem progrediens, & </
s
>
<
s
xml:id
="
echoid-s23541
"
xml:space
="
preserve
">Solem ſecet, ut ante: </
s
>
<
s
xml:id
="
echoid-s23542
"
xml:space
="
preserve
">dico duos ex hoc motu angulos effici, alterumq́; </
s
>
<
s
xml:id
="
echoid-s23543
"
xml:space
="
preserve
">rectis
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.341-04
"
xlink:href
="
note-514.01.341-04a
"
xml:space
="
preserve
">40</
note
>
lineis conſtare, alterum planis illis, ideſt uerticalis fixi, & </
s
>
<
s
xml:id
="
echoid-s23544
"
xml:space
="
preserve
">uerticalis mobilis. </
s
>
<
s
xml:id
="
echoid-s23545
"
xml:space
="
preserve
">Angulus rectis lineis constans,
<
lb
/>
fit Solis radio, & </
s
>
<
s
xml:id
="
echoid-s23546
"
xml:space
="
preserve
">diametro uerticalis, ideſt gnomonis, & </
s
>
<
s
xml:id
="
echoid-s23547
"
xml:space
="
preserve
">ambitus ſeu circinatio hunc angulum ſubtendens,
<
lb
/>
eſt pars ſiue arcus ille uerticalis mobilis, quod uertice nostro, & </
s
>
<
s
xml:id
="
echoid-s23548
"
xml:space
="
preserve
">puncto, in quo eſt Sol, continetur. </
s
>
<
s
xml:id
="
echoid-s23549
"
xml:space
="
preserve
">cum igi-
<
lb
/>
tur uertex a finitore tetrantem distet, ſequitur reliquum arcus uerticali, quod eſt a Sole ad finitorem, Solis
<
lb
/>
altitudinem ſupra finitorem oſtendere. </
s
>
<
s
xml:id
="
echoid-s23550
"
xml:space
="
preserve
">ideo ſi uerticalis arcus a uertice ad Solem erit partium quinquagin-
<
lb
/>
ta, Sola finitore tolletur gradus quadraginta, hoc eſt reliquum tetrantis a uertice ad finitorem. </
s
>
<
s
xml:id
="
echoid-s23551
"
xml:space
="
preserve
">huius ergo
<
lb
/>
anguli cognitio ad Solis altitudinem cognoſcendam ſpectat, unde umbrarum longitudo deprehenditur. </
s
>
<
s
xml:id
="
echoid-s23552
"
xml:space
="
preserve
">Sed
<
lb
/>
angulus a uertic ali mobili, & </
s
>
<
s
xml:id
="
echoid-s23553
"
xml:space
="
preserve
">firmo factus comprehenditur eo finitoris ambitu, qui inter cipitur inter punctum
<
lb
/>
orientis, & </
s
>
<
s
xml:id
="
echoid-s23554
"
xml:space
="
preserve
">punctum, quo uerticalis mobilis finitorem ſecat. </
s
>
<
s
xml:id
="
echoid-s23555
"
xml:space
="
preserve
">atque ambitus hic uel arcus, latitudo Solis, uel
<
lb
/>
arcus horizontalis nominatur. </
s
>
<
s
xml:id
="
echoid-s23556
"
xml:space
="
preserve
">huius anguli cognitio id nobis præſtat, ut parum ſciamus in quam radius Solis
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.341-05
"
xlink:href
="
note-514.01.341-05a
"
xml:space
="
preserve
">50</
note
>
uergat, unde partem in quam umbra protenditur agnoſcamus, ſemper enim umbra in oppoſitam radio par-
<
lb
/>
tem proijcitur. </
s
>
<
s
xml:id
="
echoid-s23557
"
xml:space
="
preserve
">nam ſi ab euro radius emittitur, umbra in caurum tendit. </
s
>
<
s
xml:id
="
echoid-s23558
"
xml:space
="
preserve
">ſi ab aquilone Sol, umbra in
<
lb
/>
africum uergit. </
s
>
<
s
xml:id
="
echoid-s23559
"
xml:space
="
preserve
">Ecce uſum horum angulorum, & </
s
>
<
s
xml:id
="
echoid-s23560
"
xml:space
="
preserve
">munus uerticalis mobilis. </
s
>
<
s
xml:id
="
echoid-s23561
"
xml:space
="
preserve
">nam ſi in plano finitori paral-
<
lb
/>
lelo uolueris horologium deſcribere, duos hos angulos neceſſarios cognoſces, quos uerticalis mobilis facit .
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s23562
"
xml:space
="
preserve
">Sed ad reliquos mutatur meridianus mobilis ad Solem in noto poſitum, cum eo peruenerit, ut Solem ſecet,
<
lb
/>
duos & </
s
>
<
s
xml:id
="
echoid-s23563
"
xml:space
="
preserve
">ipſe angulos reddet, alterum ex rectis lineis, alterum faciet ipſe cum meridiano immobili. </
s
>
<
s
xml:id
="
echoid-s23564
"
xml:space
="
preserve
">rectæ lineæ
<
lb
/>
quæ angulum conſtituunt erunt Solis radius, & </
s
>
<
s
xml:id
="
echoid-s23565
"
xml:space
="
preserve
">diametros meridiani; </
s
>
<
s
xml:id
="
echoid-s23566
"
xml:space
="
preserve
">ambitus hunc angulum ſubtendens, in-
<
lb
/>
tercipitur interpunctum extremum diametri meridiani, & </
s
>
<
s
xml:id
="
echoid-s23567
"
xml:space
="
preserve
">punctum in quo est Sol. </
s
>
<
s
xml:id
="
echoid-s23568
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s23569
"
xml:space
="
preserve
">hinc Solis altitudo ter
<
lb
/>
minatur ſupra uerticalem circulum. </
s
>
<
s
xml:id
="
echoid-s23570
"
xml:space
="
preserve
">Angulus autem ex meridiano mobili, & </
s
>
<
s
xml:id
="
echoid-s23571
"
xml:space
="
preserve
">meridiano firmo factus, com-
<
lb
/>
prebenditur ambitu decl inationis meridiani mobilis a meridiano immo bili in circulo uerticali. </
s
>
<
s
xml:id
="
echoid-s23572
"
xml:space
="
preserve
">Huius anguli
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.341-06
"
xlink:href
="
note-514.01.341-06a
"
xml:space
="
preserve
">60</
note
>
cognitio eò ſpectat, ut partem & </
s
>
<
s
xml:id
="
echoid-s23573
"
xml:space
="
preserve
">ſitum Solis agnoſcamus, ut umbræ partem eliciamus in plano </
s
>
</
p
>
</
div
>
</
div
>
</
text
>
</
echo
>