Vitruvius, De architectura libri decem, 1567

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          <div xml:id="echoid-div710" type="section" level="2" n="133">
            <p>
              <s xml:id="echoid-s20124" xml:space="preserve">
                <pb o="269" file="514.01.301" n="301" rhead="NONVS."/>
              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="preserve">20</note>
              ligi poſsit ſine recti anguli uſu, & </s>
              <s xml:id="echoid-s20150" xml:space="preserve">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="preserve">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="preserve">
                <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="preserve">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="preserve">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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