Vitruvius, De architectura libri decem, 1567

Table of figures

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[Figure 101]
[102] FRONTE.
[103] A
[104] Græcorum ædes earumq́; partium diſpoſitiones.A. peristylium amplum.E. peristylium primum.C. aditus amplus.D. aditus ab uno ad aliudperiſtylium.E. proſtas ubi eraut duæ antæ.F. G. Antithalamus.H. I. gynæconitides.K. cu-bicuUmdiebria.L. S. oeci,& bibliotecæ,& ubi ſunt pictores.M. R. pinacotbecæ.N. cyzicena triclinia.O. porticus ad ſeptentrionem.P. cellæ hostiariæ.Q. oeci quadrati.T. V. porticus ad triclinia cizcena.X. hypæthra loca.r. oeci magni ubi matres familiarũ cum lanificijs habent ſeſſiones.Z. hoſpitalia.1. thirorium.2. Equilia.3. cubicula.4. meſaulæ & andronæ.5. triclinia quo-tidiana.6. posthalamus.7. thalamus.8. porticus Rhodiaca altior. T QVNMRN8SALKICHXYYFEG76B543O32P21
[105] Pauimentorum genera.Filandri.Anticum.
[106] c d f b c 8
[107] CHOROBATES.2 I 3 2
[108] d 10 10 a d 50 50 50 c 50 ba s d s 7 {1/14} 25 s b ce 8 8 10 84 f hm 5 43 3 4 4 3 3 4 4 5 5 5 53 5 4
[109] Figura ex meſolabio Architæ ad inueniendas medias.c t @ @ q p o n m l k l h g f p e o ξ v M @ k I o h j ε δ r B d s R q P o N M L K I H G F E L x c 6 N ς ε ξ γ B a
[110] Veſtigium meſolabij Architæ.
[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
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            <p style="it">
              <s xml:id="echoid-s13300" xml:space="preserve">
                <pb o="173" file="514.01.205" n="205" rhead="QVINTVS."/>
              uteſſiceretur, oportuit prius uocem diffinire, & </s>
              <s xml:id="echoid-s13301" xml:space="preserve">eius motiones quales eſſent oſtendere, quod hactenus factum
                <lb/>
              est, mox ad earum motionum diſcrimina effectusq́; </s>
              <s xml:id="echoid-s13302" xml:space="preserve">ueniendum.</s>
              <s xml:id="echoid-s13303" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s13304" xml:space="preserve">Vox enim mutationibus cũ flectitur, aliàs fit acuta, aliàs fit grauis, duobusq́; </s>
              <s xml:id="echoid-s13305" xml:space="preserve">modis mouetur, e q
                <unsure/>
              uibus
                <lb/>
              unus habet effectus cõtinuatos, alter diſtantes. </s>
              <s xml:id="echoid-s13306" xml:space="preserve">Continua uox neq; </s>
              <s xml:id="echoid-s13307" xml:space="preserve">in finitionibus conſiſtit, neq; </s>
              <s xml:id="echoid-s13308" xml:space="preserve">in loco
                <lb/>
              ullo, efficitq́; </s>
              <s xml:id="echoid-s13309" xml:space="preserve">terminationes non apparentes; </s>
              <s xml:id="echoid-s13310" xml:space="preserve">interualla autem media patenria uti ſermone cum dici-
                <lb/>
              mus. </s>
              <s xml:id="echoid-s13311" xml:space="preserve">Sol, Lux, flos, Nox. </s>
              <s xml:id="echoid-s13312" xml:space="preserve">Nunc enim nec unde incipit, nec ubi deſinit intelligitur, ſed neque ex acuta
                <lb/>
              facta eſt grauis, nec ex graui acuta apparet auribus. </s>
              <s xml:id="echoid-s13313" xml:space="preserve">Per diſtantiam autem e contrario, namque cum
                <lb/>
              flectitur in mutatione uox, ſtatuit ſe in alicuius ſonitus ſinitionem, deinde in alterius, & </s>
              <s xml:id="echoid-s13314" xml:space="preserve">id ultro citroq́;
                <lb/>
              </s>
              <s xml:id="echoid-s13315" xml:space="preserve">crebro faciendo incoſtans apparet ſenſibus, uti in cantionibus cum flectentes uocem uarietatem faci-
                <lb/>
                <note position="left" xlink:label="note-514.01.205-01" xlink:href="note-514.01.205-01a" xml:space="preserve">10</note>
              mus modulationis. </s>
              <s xml:id="echoid-s13316" xml:space="preserve">Itaque interuallis ea cum uerſatur, & </s>
              <s xml:id="echoid-s13317" xml:space="preserve">unde initium fecit, & </s>
              <s xml:id="echoid-s13318" xml:space="preserve">ubi deſijt apparet in
                <lb/>
              ſonorum patentibus finitionibus. </s>
              <s xml:id="echoid-s13319" xml:space="preserve">Mediana autem patentia interuallis θbſcurantur.</s>
              <s xml:id="echoid-s13320" xml:space="preserve"/>
            </p>
            <p style="it">
              <s xml:id="echoid-s13321" xml:space="preserve">Propoſita uocis distinctio eo tendit, ut diſtinguatur uox illa, quæ apta eſt harmoniæ, ab ea, quæ inepta est,
                <lb/>
              vox igitur duobus modis mouetur. </s>
              <s xml:id="echoid-s13322" xml:space="preserve">primum, ut auribus uideatur, ut uere eſt continuata, & </s>
              <s xml:id="echoid-s13323" xml:space="preserve">in nullam termi-
                <lb/>
              nationem finita, hæc ab effectu continua nominatur, ſed ab uſu rationalis dicitur, eo enim uocis motu loqui, & </s>
              <s xml:id="echoid-s13324" xml:space="preserve">
                <lb/>
              ratiocinari ſolemus, nullo modo uocis tenorem alterando. </s>
              <s xml:id="echoid-s13325" xml:space="preserve">Deinde mouetur uox, ita, ut diſtincta appareat,
                <lb/>
              & </s>
              <s xml:id="echoid-s13326" xml:space="preserve">ab uno altitudinis gradu in alterum uarijs, & </s>
              <s xml:id="echoid-s13327" xml:space="preserve">determinatis finitionibus proficiſcens, quæ ab effectu diſtin-
                <lb/>
              cta, ab uſu melodica nominatur, id eſt qua qui canunt, aut poemata recitant, uti ſolent, nam dum canimus,
                <lb/>
              aut carmina proferimus, modo efferentes, modo deprimentes uocem, & </s>
              <s xml:id="echoid-s13328" xml:space="preserve">diſtincte finientes, reſumentes ſenſui
                <lb/>
              occaſionem damus, ut diſcrimina inter uoces conſtituat. </s>
              <s xml:id="echoid-s13329" xml:space="preserve">Licet Boetio placeat in recitandis poematibus me-
                <lb/>
                <note position="left" xlink:label="note-514.01.205-02" xlink:href="note-514.01.205-02a" xml:space="preserve">20</note>
              dia quadam uoce inter continuam, & </s>
              <s xml:id="echoid-s13330" xml:space="preserve">diſtinctam nos uti ſolere, ſed parum refert, modo continuam a diſtincta
                <lb/>
              ſeparemus. </s>
              <s xml:id="echoid-s13331" xml:space="preserve">Continua igitur uox, & </s>
              <s xml:id="echoid-s13332" xml:space="preserve">unius tenoris a muſicæ cõſideratione aliena eſt, nam ubi graue, & </s>
              <s xml:id="echoid-s13333" xml:space="preserve">acutum
                <lb/>
              non eſt, ibi concentus eſſe non potest. </s>
              <s xml:id="echoid-s13334" xml:space="preserve">Diſtincta uero apta eſt melodiæ, at non ſtatim, ſed tunc primnm cum
                <lb/>
              ad certum locum peruenerit, quemadmodum corporibus aduenit, quæ non prius apta ſunt ſub aliquam pon-
                <lb/>
              deris rationem cadere, quàm ad certam peruenerint magnitudinem, nec ſub opticen uenire poſſunt, niſi id
                <lb/>
              habeant, quod finis eſt inuiſibilis, & </s>
              <s xml:id="echoid-s13335" xml:space="preserve">principium uiſibilis rationis. </s>
              <s xml:id="echoid-s13336" xml:space="preserve">non enim fert natura minim is rerum diffe-
                <lb/>
              rentias ſenſibus humanis ſubijci. </s>
              <s xml:id="echoid-s13337" xml:space="preserve">Sonus igitur distinctus, & </s>
              <s xml:id="echoid-s13338" xml:space="preserve">ad certam, & </s>
              <s xml:id="echoid-s13339" xml:space="preserve">ſenſibilem terminationem relatus
                <lb/>
              harmoniæ principium dicitur, quemadmodum unitas numeri principium eſt, & </s>
              <s xml:id="echoid-s13340" xml:space="preserve">punctum lineæ, & </s>
              <s xml:id="echoid-s13341" xml:space="preserve">inſtans tem-
                <lb/>
              poris. </s>
              <s xml:id="echoid-s13342" xml:space="preserve">Cæterum natura uocem cuiuſque ita circumſcripſit, ut prima eius ſedes, tanquam gradus grauior, & </s>
              <s xml:id="echoid-s13343" xml:space="preserve">
                <lb/>
              depreßior ſit, quam in aliquo reperiatur. </s>
              <s xml:id="echoid-s13344" xml:space="preserve">Sed quoniam ſi uno ſemper tenore firmata uox, multas haberet diſtin-
                <lb/>
              ctas diffinitiones nulla fieret harmonia, ideo uoces mutari, & </s>
              <s xml:id="echoid-s13345" xml:space="preserve">aſcendere oportet, ut grauior & </s>
              <s xml:id="echoid-s13346" xml:space="preserve">depreßior acu-
                <lb/>
                <note position="left" xlink:label="note-514.01.205-03" xlink:href="note-514.01.205-03a" xml:space="preserve">30</note>
              tiori, & </s>
              <s xml:id="echoid-s13347" xml:space="preserve">altiori concinens proportione reſpondeat. </s>
              <s xml:id="echoid-s13348" xml:space="preserve">Iter igitur aſcenſus, immo & </s>
              <s xml:id="echoid-s13349" xml:space="preserve">ipſe idem aſcenſus, ſpatium,
                <lb/>
              diſtinctio, & </s>
              <s xml:id="echoid-s13350" xml:space="preserve">interuallum nominatur. </s>
              <s xml:id="echoid-s13351" xml:space="preserve">Sed comparatio ratione terminorum diuerſa eſt, ideo ſit, ut cum ſpatium
                <lb/>
              metimur, quando uox ab imo ad altum effertur, uocem dicimus intendi, acutiorem elatioremq́; </s>
              <s xml:id="echoid-s13352" xml:space="preserve">fieri, cum
                <lb/>
              uero contra a ſummo ad imum fertur, remitti, grauiorem, depreſſioremq́; </s>
              <s xml:id="echoid-s13353" xml:space="preserve">fieri, & </s>
              <s xml:id="echoid-s13354" xml:space="preserve">quemadmodum ab imo natu-
                <lb/>
              ra uocis principium in ſingulis hominibus collocauit, ita aſcendendo quaſi per gradus, neceſſe eſt ſummum ter-
                <lb/>
              minum inuenire, ad quem natura ſua cum uox apte peruenerit, optima cum prima reddatur concentus conue-
                <lb/>
              nientia, & </s>
              <s xml:id="echoid-s13355" xml:space="preserve">inter ca ſpatia, & </s>
              <s xml:id="echoid-s13356" xml:space="preserve">interualla reliqua omnes conſonantiæ collocentur, ita ut ſi ultra ſummum ter-
                <lb/>
              minũ progrediatur iterum ad caſdem conſonantias repetendas perueniat, perinde ac ſi ad denarium cum per-
                <lb/>
              uenerimus, iterum ad eoſdem numeros, qui denario incluſi erant, ueniremus. </s>
              <s xml:id="echoid-s13357" xml:space="preserve">Sed quoniam ab imo ad ſum-
                <lb/>
              mum uox non effertur ſine medijs, ideo dumiter aſcenſionis facit, plures uocis gradus intermedios tangat opor-
                <lb/>
                <note position="left" xlink:label="note-514.01.205-04" xlink:href="note-514.01.205-04a" xml:space="preserve">40</note>
              tet, qui iustis ſpatijs, & </s>
              <s xml:id="echoid-s13358" xml:space="preserve">interuallis mutuam quandam habeant inter ſe comparationem. </s>
              <s xml:id="echoid-s13359" xml:space="preserve">Ordinatio igitur
                <lb/>
              aſcenſionis uocis a Græcis ſyſ
                <unsure/>
              tema, a nostris ſcala nominatur: </s>
              <s xml:id="echoid-s13360" xml:space="preserve">& </s>
              <s xml:id="echoid-s13361" xml:space="preserve">quoniam ad manus, digitorumq́; </s>
              <s xml:id="echoid-s13362" xml:space="preserve">diuiſiones
                <lb/>
              eos terminos, dum principia docent, reducere ſolent. </s>
              <s xml:id="echoid-s13363" xml:space="preserve">ideo & </s>
              <s xml:id="echoid-s13364" xml:space="preserve">Manum eam uocant, aut quia ad manus tanquam
                <lb/>
              enchiridion haberi debet, Græci ordinatam compoſitionem, nostri commodam, & </s>
              <s xml:id="echoid-s13365" xml:space="preserve">aptam aſcenſionem innuunt,
                <lb/>
              quam lincis, & </s>
              <s xml:id="echoid-s13366" xml:space="preserve">ſpatijs in exercendo declarant, unde adagium de eo, qui nihili penſi eſt dicitur eum neque li-
                <lb/>
              nea, neque ſpatio contineri. </s>
              <s xml:id="echoid-s13367" xml:space="preserve">Scala igitur eſt constitutio linearum, & </s>
              <s xml:id="echoid-s13368" xml:space="preserve">interuallorum directæ deſcriptorum, in
                <lb/>
              quibus cuiuſque melodiæ notulæ deſcribantur. </s>
              <s xml:id="echoid-s13369" xml:space="preserve">Linearum & </s>
              <s xml:id="echoid-s13370" xml:space="preserve">interuallorum uſus est, ut diſtincte uocis ſpatia dũ
                <lb/>
              ſcandit, & </s>
              <s xml:id="echoid-s13371" xml:space="preserve">deſcendit, cognoſcamus. </s>
              <s xml:id="echoid-s13372" xml:space="preserve">Notæ autem dicuntur, quia ſunt tanquam ſigna emittendæ uocis. </s>
              <s xml:id="echoid-s13373" xml:space="preserve">Ha-.
                <lb/>
              </s>
              <s xml:id="echoid-s13374" xml:space="preserve">ctenus igitur habemus qualis, & </s>
              <s xml:id="echoid-s13375" xml:space="preserve">quanta ea uox eſſe debet, quæ habet ad harmoniam aptitudinem. </s>
              <s xml:id="echoid-s13376" xml:space="preserve">Et Vitr. </s>
              <s xml:id="echoid-s13377" xml:space="preserve">
                <lb/>
              multa omittens, quæ ab Ariſtoxeno interim dicuntur, modulationum genera diſtinguit hoc modo.</s>
              <s xml:id="echoid-s13378" xml:space="preserve"/>
            </p>
            <note position="left" xml:space="preserve">50</note>
            <p>
              <s xml:id="echoid-s13379" xml:space="preserve">
                <emph style="sc">Genera</emph>
              uero modulationum ſunt tria. </s>
              <s xml:id="echoid-s13380" xml:space="preserve">Primum, quod Græci nominant harmoniam, ſecundum
                <lb/>
              chroma, tertium diatonum. </s>
              <s xml:id="echoid-s13381" xml:space="preserve">Eſt autem harmoniæ modulatio ab arte concepta, & </s>
              <s xml:id="echoid-s13382" xml:space="preserve">ea re cantio eius
                <lb/>
              maxime grauem, & </s>
              <s xml:id="echoid-s13383" xml:space="preserve">egregiam habet authoritatem. </s>
              <s xml:id="echoid-s13384" xml:space="preserve">Chroma ſubtili ſolertia, ac crebritate modulorum
                <lb/>
              ſuauiorem habet delectationem. </s>
              <s xml:id="echoid-s13385" xml:space="preserve">Diatoni uero, quod naturalis eſt, facilior in interuallorum diſtantia.</s>
              <s xml:id="echoid-s13386" xml:space="preserve"/>
            </p>
            <p style="it">
              <s xml:id="echoid-s13387" xml:space="preserve">Simihi integrum eſſet de muſica pertractare, alia uia, ordinationeq́; </s>
              <s xml:id="echoid-s13388" xml:space="preserve">mihi utendum eſſe proponere
                <unsure/>
              m. </s>
              <s xml:id="echoid-s13389" xml:space="preserve">Sed
                <lb/>
              quia Vitr. </s>
              <s xml:id="echoid-s13390" xml:space="preserve">exponimus, Vitruuium ſequamur. </s>
              <s xml:id="echoid-s13391" xml:space="preserve">Genera modulationum distinguit. </s>
              <s xml:id="echoid-s13392" xml:space="preserve">Genus autem eſt compoſitio,
                <lb/>
              uel diſtributio interuallorum in ſcala, & </s>
              <s xml:id="echoid-s13393" xml:space="preserve">in ordinatione, quæ diuerſas ideas, & </s>
              <s xml:id="echoid-s13394" xml:space="preserve">ſpecies harmoniæ refert. </s>
              <s xml:id="echoid-s13395" xml:space="preserve">De ijs
                <lb/>
              ſigillatim dicemus inferius, ea explicantes. </s>
              <s xml:id="echoid-s13396" xml:space="preserve">quæ multis difficilia, & </s>
              <s xml:id="echoid-s13397" xml:space="preserve">obſcura uidentur. </s>
              <s xml:id="echoid-s13398" xml:space="preserve">Modulationis igitur tria
                <lb/>
              ſunt genera. </s>
              <s xml:id="echoid-s13399" xml:space="preserve">Chromaticum, diatonicum, & </s>
              <s xml:id="echoid-s13400" xml:space="preserve">harmonicum. </s>
              <s xml:id="echoid-s13401" xml:space="preserve">horum nominationes ſumuntur a longinquitate,
                <lb/>
              uel proximitate interuallorum in ſcalis, & </s>
              <s xml:id="echoid-s13402" xml:space="preserve">ordinationibus. </s>
              <s xml:id="echoid-s13403" xml:space="preserve">Harmonicum enim eſt, quod in ſua conſtjtutione,
                <lb/>
                <note position="left" xlink:label="note-514.01.205-06" xlink:href="note-514.01.205-06a" xml:space="preserve">60</note>
              </s>
            </p>
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