Vitruvius, De architectura libri decem, 1567

Table of figures

< >
[111] Orthographia meſolabij Architæ.
[112] Demonſtratio Eratoſtbenis. a g t cb f b d
[113] Instrumentum Eratoſthenis. m a x g n b c n i o l v q p b e f k d
[114] Vſ{us} demonſtratio Eratoſtbenis cum inſtrumento. a h n ek l i o d b 8 m c 4
[115] Inſtrumentum Platonis. f i n o m
[116] cubus. 8 8 64 8 8 8 8 512 8s e
[117] Demonstratio Archita. p l k b o i m b e d af
[118] Demonctration Platonis. d e b c g
[119] Demostratio ter tiæ proprietatis, & aſſumptionis Nicomedis.instrumentum Nicomedis. f h d g b s n m k a
[120] Duplicatio cubi. e a b c d f g
[121] Dimonctratio prrima proprie tatis. s n m l k
[122] Vſus inſtrume ti Nicomedis & eius demő ſtratio. l e b c g f a k h i
[123] h
[124] b d c e f g
[125] a b c e d
[126] Secunda proprietas lineæ flexæ.f n e b g i d m k c
[127] a. centrum mundi.b. oculus in ſuperficie terræc. ſydus.d. uertex.b c a. angulus diuerſitatis. c d 6 a
[128] a b deferens.c. deferentis centrum.d e. epicyclus.a. centrum epicycli.f. mundi centrum.a. iugum deferentis.b. antiiugum.d. iugum epicycli. d a e c s b
[129] a b g. concentricum.d. eius centrum.e z b. eccentricum.t. eius centrum.k z. epicyclus.b. eius centrum.d t. b z. œquales.t z. d b. œquales.motus { concentrici b d a. \\ epicycli k b z. \\ eccentrici z t e. \\ anguli œquales Sol utroque modo uidetur in z. per li-neam d z. e a t d b z b k
[130] a b g. eccentricum.d. eius centrum.e. centrum mundi.a d g. linea ingi.b. centrm Solis.e z. linea medij motus parallela li-neœ b d.c b. linea ueri motus.b e z. angulus œquatio. z b a d e
[131] a b g. concentricum. d. eius centrũ.t z. eccentricum.h. eius centrum.e z. epicyclus.g. eius centrum.d b. & g z. œquales.d z. parallelogrammum.motus {concentrici a d g. \\ epicycli e g z. \\ eccentrici t b z. uet t dg. \\ iugieccentric. a d t. anguli t b z. & e g z. œqua-les ſunt.angulus a d g. œqualis augulis. {adt. \\ adg. f n b a d o k
[132] b k epicyclus.b. centrum eius.h. uigum.n. Antijugum epicycli.k. punctũ primœ morœ.c. mundi centrum.o. punctũ ſecundæ morœ.h l k. arcus primœ mo rœ.k n o. arcus regreſſus-o b k. arcus directio-nis. L K A H B N O C
[133] Porfioni del cerchio che fannoſe s̃teſſe torno dlaTramòntanaTram ontanaSlmiſifudineTramonſangCarro che uoſge infomoalla Framonlana
[134] a b c d f
[135] A. ſectio parabole.B. vestigium. C. parabole.G. ſectio ellipſis.D. ſectio hyperbole.E. vestigium F. hyperbole. a f a f 1 f f f 1 2 1 1 2 3 2 2 3 4 3 3 4 5 4 4 5 6 C 5 5 6 F 7 A 6 6 8 7 8 7 7 D 8 9 8 8 9 10 11 10 10 11 11 11 11 b 12 g e d b e h d gf g b 6 7 3 1 2 4 6 8 10c g b E a 11 9 7 3 3 1 d 2 4 6 8 10 e ha f 1 2 3 4 5 6 7 8 9 10 11 a b c d 9 8 7 6 3 2 1 f b a H d g 10 9 8 7 6 5 4 3 2 1 ff 1 2 3 4 5 6 7 8 9 10 11 g
[136] m q 0 s k h c b s n L I p q s
[137] Il polo.cqiunot.orizonte c e b a f
[138] l n k mcridl. parte delverno E e h a s i 9 8 7 6 5della jtate 4 3 parte g h f x lacato manaco b r c linca del.piano t
[139] Analemmatis figura.MERIDIAN: S. M. MLSLACITREVM.M.MERIDIAN: .S.OMVERTICAV.M..S.. O. M.ORIZON:W. A.STAB:
[140] 11 ſ x d 11 p k 1 2 1 2 3 4 5f 6 r 11 10 9 8 7 n f m 12 11 10 9 8 7 6 5 1 02 3 4 1g c 1 2 1 2 3 4 5 6 e 11 10 9 8 7 q b o
< >
page |< < (173) of 412 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1" type="section" level="1" n="1">
          <div xml:id="echoid-div457" type="section" level="2" n="79">
            <p style="it">
              <s xml:id="echoid-s13212" xml:space="preserve">
                <pb o="173" file="514.01.204" n="204" rhead="LIBER"/>
              aere fiunt, quoniam undequaque in orbem conuoluuntur, ſphæræ meritò dici poſſunt. </s>
              <s xml:id="echoid-s13213" xml:space="preserve">Conueniunt tamen & </s>
              <s xml:id="echoid-s13214" xml:space="preserve">
                <lb/>
              qui in aqua, & </s>
              <s xml:id="echoid-s13215" xml:space="preserve">qui in aere ſunt, quoniam ſi non impediuntur, ſecundus a priori proxime tertius a ſecundo, & </s>
              <s xml:id="echoid-s13216" xml:space="preserve">
                <lb/>
              quartus a tertio proficiſcuntur latioresq́;</s>
              <s xml:id="echoid-s13217" xml:space="preserve">, & </s>
              <s xml:id="echoid-s13218" xml:space="preserve">ampliores ſemper fiunt, donec ad certum finem perueniant
                <lb/>
              icta enim pars aeris, uel aquœ ulteriorem ſemper impellit, ſed leuiori impulſione, ita ut tandem impulſus ille
                <lb/>
              minus, & </s>
              <s xml:id="echoid-s13219" xml:space="preserve">nihil ualeat. </s>
              <s xml:id="echoid-s13220" xml:space="preserve">hinc eſt, quod Vitr. </s>
              <s xml:id="echoid-s13221" xml:space="preserve">dicit.</s>
              <s xml:id="echoid-s13222" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s13223" xml:space="preserve">
                <emph style="sc">Sed</emph>
              in aqua circuli æqua planitie in latitudine mouentur. </s>
              <s xml:id="echoid-s13224" xml:space="preserve">Vox & </s>
              <s xml:id="echoid-s13225" xml:space="preserve">in latitudinem progreditur, & </s>
              <s xml:id="echoid-s13226" xml:space="preserve">
                <lb/>
              altitudinem gradatim ſcandit. </s>
              <s xml:id="echoid-s13227" xml:space="preserve">Igitur ut in aqua undarum deſignationibus, ita in uoce cum offenſio
                <lb/>
              nulla primam interpellauerit, non diſturbat ſecundam, nec inſequentes, ſed omnes ſua reſonantia per-
                <lb/>
              ueniunt ad imorum, & </s>
              <s xml:id="echoid-s13228" xml:space="preserve">ſummorum aures.</s>
              <s xml:id="echoid-s13229" xml:space="preserve"/>
            </p>
            <p style="it">
              <s xml:id="echoid-s13230" xml:space="preserve">Impidiuntur circulorum deſignationes in aqua, ne fiant perfectæ iniecto alio lapide extra circulos, ualidior
                <lb/>
                <note position="left" xlink:label="note-514.01.204-01" xlink:href="note-514.01.204-01a" xml:space="preserve">10</note>
              enim ictus alias circulorum deſignationes facit, quœ priores diſrumpunt. </s>
              <s xml:id="echoid-s13231" xml:space="preserve">ita impediuntur aeris icti orbes
                <lb/>
              alieno impulſu.</s>
              <s xml:id="echoid-s13232" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s13233" xml:space="preserve">
                <emph style="sc">Ergo</emph>
              ueteres Architecti naturę ueſtigia perſequuti, indagationibus uocis ſcandentes theatrorum
                <lb/>
              perfecerunt gradationes. </s>
              <s xml:id="echoid-s13234" xml:space="preserve">& </s>
              <s xml:id="echoid-s13235" xml:space="preserve">quæſierunt per canonicam mathematicorum, & </s>
              <s xml:id="echoid-s13236" xml:space="preserve">muſicam rationem, ut
                <lb/>
              quæcunque uox eſſet in ſcena, clarior, & </s>
              <s xml:id="echoid-s13237" xml:space="preserve">ſuauior ad ſpectatorum perueniret aures.</s>
              <s xml:id="echoid-s13238" xml:space="preserve"/>
            </p>
            <p style="it">
              <s xml:id="echoid-s13239" xml:space="preserve">Cum uox in aere circumuoluatur, certe orbicularis forma theatro conueniet. </s>
              <s xml:id="echoid-s13240" xml:space="preserve">nam ſi angulari forma thea-
                <lb/>
              tra eſſent conſtituta, non œqualiter uox terminationes ſuas efficeret, alij enim ideſt uiciniores clarius uocem
                <lb/>
              perciperent, alij tanquam remotiores impedirentur, & </s>
              <s xml:id="echoid-s13241" xml:space="preserve">uocis deſignationes interminat æ in aere frangerentur.
                <lb/>
              </s>
              <s xml:id="echoid-s13242" xml:space="preserve">Architecti igitur, qui & </s>
              <s xml:id="echoid-s13243" xml:space="preserve">muſici, & </s>
              <s xml:id="echoid-s13244" xml:space="preserve">phyſici eſſe debent, ſi nomen Architecti conſequi uelint, animaduerten-
                <lb/>
                <note position="left" xlink:label="note-514.01.204-02" xlink:href="note-514.01.204-02a" xml:space="preserve">20</note>
              tes ad uocis motiones, & </s>
              <s xml:id="echoid-s13245" xml:space="preserve">ſpeculatione numerorum, & </s>
              <s xml:id="echoid-s13246" xml:space="preserve">experientia ſonorum (ita enim mathematicorum ca-
                <lb/>
              nonicam, & </s>
              <s xml:id="echoid-s13247" xml:space="preserve">muſicam rationem intelligo ) theatrorum conformationes fecere, & </s>
              <s xml:id="echoid-s13248" xml:space="preserve">ut locus magis reſonaret,
                <lb/>
              prœter orbicularem theatrorum formam, pr œter gradationes uno funiculo, ut linea in cacuminibus, & </s>
              <s xml:id="echoid-s13249" xml:space="preserve">an-
                <lb/>
              gulis ab imo ad ſummam contactas, in ſummo quoq; </s>
              <s xml:id="echoid-s13250" xml:space="preserve">contectas fecere porticus in theatrum apertas, retro pa-
                <lb/>
              rietibus cir cundatas, ut uox in eas amplitudines, tanquam in cauernas ſubintrando undique reſonaret.</s>
              <s xml:id="echoid-s13251" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s13252" xml:space="preserve">
                <emph style="sc">Vti</emph>
              in organa in æneis laminis, aut corneis dieſi ad chordarum ſonituum claritatem perſiciunt,
                <lb/>
              ſic theatrorum per harmonicen ad augendam uocem, ratiocinationes ab antiquis ſunt conſtitutæ.</s>
              <s xml:id="echoid-s13253" xml:space="preserve"/>
            </p>
            <p style="it">
              <s xml:id="echoid-s13254" xml:space="preserve">Quemadmodum ad chordarum rationem, & </s>
              <s xml:id="echoid-s13255" xml:space="preserve">ad earum ſonum organa, quœ cannis, & </s>
              <s xml:id="echoid-s13256" xml:space="preserve">tibijs conficiuntur,
                <lb/>
              & </s>
              <s xml:id="echoid-s13257" xml:space="preserve">alia inſtrumenta perficiuntur, ita harmonica ratione ad uocis claritatem, ut augumentum theatra ab anti-
                <lb/>
              quis conſtituta fuere: </s>
              <s xml:id="echoid-s13258" xml:space="preserve">œque ac ſi diceret, ut dieſis, quœ minima eſt audibilis, & </s>
              <s xml:id="echoid-s13259" xml:space="preserve">in muſicam rationem apta uox
                <lb/>
              principium organorum perficiendorum regulam illis dedit. </s>
              <s xml:id="echoid-s13260" xml:space="preserve">Ita uocis naturam, & </s>
              <s xml:id="echoid-s13261" xml:space="preserve">motionem ab Architectis
                <lb/>
                <note position="left" xlink:label="note-514.01.204-03" xlink:href="note-514.01.204-03a" xml:space="preserve">30</note>
              comprehenſam illis theatrorum occaſionem faciendorum dediſſe, & </s>
              <s xml:id="echoid-s13262" xml:space="preserve">theatra ad uocis rationem accommodaſ-
                <lb/>
              ſe. </s>
              <s xml:id="echoid-s13263" xml:space="preserve">hac occaſione de harmonia loquetur Vitr. </s>
              <s xml:id="echoid-s13264" xml:space="preserve">Oſtendetq́; </s>
              <s xml:id="echoid-s13265" xml:space="preserve">quid ſit, quid de ea ſenſerit Ariſtoxenus, quot ſint
                <lb/>
              eius genera, quomodo partiantur, & </s>
              <s xml:id="echoid-s13266" xml:space="preserve">qua ratione uocum diagraminata constituantur.</s>
              <s xml:id="echoid-s13267" xml:space="preserve"/>
            </p>
          </div>
          <div xml:id="echoid-div469" type="section" level="2" n="80">
            <head xml:id="echoid-head83" style="it" xml:space="preserve">De Harmonia ſecundum Aristoxeni traditio-
              <lb/>
            nem. # Cap. IIII.</head>
            <p>
              <s xml:id="echoid-s13268" xml:space="preserve">
                <emph style="sc">HArmonia</emph>
              autem eſt muſica literatura obſcura, & </s>
              <s xml:id="echoid-s13269" xml:space="preserve">difficilis, maxime quidem, quibus Grę
                <lb/>
              cæ literæ non ſunt notæ, quam ſi uolumus explicare, neceſſe eſt etiam Græcis uerbis uti,
                <lb/>
                <note position="left" xlink:label="note-514.01.204-04" xlink:href="note-514.01.204-04a" xml:space="preserve">40</note>
              quod nonnulla eorum latinas non habent appellationes. </s>
              <s xml:id="echoid-s13270" xml:space="preserve">Itaque ut potero, quàm aper-
                <lb/>
              tiſsime ex Ariſtoxeni ſcripturis interpretabor, & </s>
              <s xml:id="echoid-s13271" xml:space="preserve">eius diagramma ſubſcribã, finitionesq́;
                <lb/>
              </s>
              <s xml:id="echoid-s13272" xml:space="preserve">fonituum deſignabo, uti qui diligentius attenderit, facilius perſpicere poſsit.</s>
              <s xml:id="echoid-s13273" xml:space="preserve"/>
            </p>
            <p style="it">
              <s xml:id="echoid-s13274" xml:space="preserve">Ad muſicæ rationem ſpectat ſpeculari, uerſariq́; </s>
              <s xml:id="echoid-s13275" xml:space="preserve">circa eos numeros, qui ad alios referuntur ſoni adiunctio-
                <lb/>
              ne, quare in duas partes prœcipue muſicen diuidemus, quarum alteram in ratione iudicij totam ponemus, de
                <lb/>
              qua parum loquitur Aristoxenus, tanquam de ea, quæ uim, & </s>
              <s xml:id="echoid-s13276" xml:space="preserve">naturam, differentiam, & </s>
              <s xml:id="echoid-s13277" xml:space="preserve">proprietatem pro-
                <lb/>
              portionum, & </s>
              <s xml:id="echoid-s13278" xml:space="preserve">concentuum conſiderat, & </s>
              <s xml:id="echoid-s13279" xml:space="preserve">diſcrimem inter ea ponit, quæ ob eorum ſubtilitatem ſenſum latere
                <lb/>
              ſolent. </s>
              <s xml:id="echoid-s13280" xml:space="preserve">Alteram in exercitationem ſtatuimus tam uocum, quàm ſonorum dulci modulatione defatigatos mor-
                <lb/>
              talium ſenſus demulcentem, & </s>
              <s xml:id="echoid-s13281" xml:space="preserve">animos ſuauitate uerborum delinitos ad præclara uitæ studia exhortantem,
                <lb/>
              quemadmodum in poetarum carminibus eſt uidere, quorum ratio non habetur in postremis muſicæ partibus.
                <lb/>
              </s>
              <s xml:id="echoid-s13282" xml:space="preserve">
                <note position="left" xlink:label="note-514.01.204-05" xlink:href="note-514.01.204-05a" xml:space="preserve">50</note>
              Muſica igitur ratio eſt, & </s>
              <s xml:id="echoid-s13283" xml:space="preserve">exercitium natur æ harmonicæ. </s>
              <s xml:id="echoid-s13284" xml:space="preserve">Naturam harmonicam uoco, quæ aptari ſimul po-
                <lb/>
              teſt numerorum ſuauium coniunctione. </s>
              <s xml:id="echoid-s13285" xml:space="preserve">Ratio abſque ſenſuum ratione operari, id est ratiocinari non potest.
                <lb/>
              </s>
              <s xml:id="echoid-s13286" xml:space="preserve">non enim iudicat de rebus non ante perceptis. </s>
              <s xml:id="echoid-s13287" xml:space="preserve">Neceſſe est igitur utramque partem coniungere, ita ut ſtatim
                <lb/>
              ſenſus, mox ratio ſuo fungatur munere. </s>
              <s xml:id="echoid-s13288" xml:space="preserve">Vnderecte a Boetio dicitur pulchrum eſſe ratione, & </s>
              <s xml:id="echoid-s13289" xml:space="preserve">uia cognoſcere
                <lb/>
              quid ſit, & </s>
              <s xml:id="echoid-s13290" xml:space="preserve">quid ferat illud, quod omnibus uiuentibus est commune. </s>
              <s xml:id="echoid-s13291" xml:space="preserve">De ijs uulgus non dubitat, torquentur
                <lb/>
              docti, delectantur periti. </s>
              <s xml:id="echoid-s13292" xml:space="preserve">hinc ea muſica, quæ mentem, & </s>
              <s xml:id="echoid-s13293" xml:space="preserve">aures oblectat, morali, & </s>
              <s xml:id="echoid-s13294" xml:space="preserve">ſpeculatrici coniuncta
                <lb/>
              officio uidetur eſſe. </s>
              <s xml:id="echoid-s13295" xml:space="preserve">Vt igitur ſonorum communio ad aures pertineat, & </s>
              <s xml:id="echoid-s13296" xml:space="preserve">orbes illi aeris ab ictu uocis deſignati,
                <lb/>
              non impediti, ſuauiter uniantur, & </s>
              <s xml:id="echoid-s13297" xml:space="preserve">ut mens ad conſiderationem cauſarum tantæ ſuauitatis uertatur, neceſſe
                <lb/>
              est principium illud habere, a quo uox aptitudinem ſumit, ut regi poſſit, ita, ut ſub harmoniæ rationem cadat,
                <lb/>
              & </s>
              <s xml:id="echoid-s13298" xml:space="preserve">quo motionis genere feratur, & </s>
              <s xml:id="echoid-s13299" xml:space="preserve">quaratione in perfectam ueniat compoſitionem, & </s>
              <s xml:id="echoid-s13300" xml:space="preserve">ordinationem, quod
                <lb/>
                <note position="left" xlink:label="note-514.01.204-06" xlink:href="note-514.01.204-06a" xml:space="preserve">60</note>
              </s>
            </p>
          </div>
        </div>
      </text>
    </echo>