Vitruvius, De architectura libri decem, 1567

Table of figures

< >
[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
Page: 321
[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
Page: 323
[133] Porfioni del cerchio che fannoſe s̃teſſe torno dlaTramòntanaTram ontanaSlmiſifudineTramonſangCarro che uoſge infomoalla Framonlana
Page: 332
[134] a b c d f
Page: 335
[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
Page: 336
[136] m q 0 s k h c b s n L I p q s
Page: 337
[137] Il polo.cqiunot.orizonte c e b a f
Page: 338
[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
Page: 339
[139] Analemmatis figura.MERIDIAN: S. M. MLSLACITREVM.M.MERIDIAN: .S.OMVERTICAV.M..S.. O. M.ORIZON:W. A.STAB:
Page: 342
[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: 342
[141] 1 3 b x z g 2 5 f p 0 1 4 t I c e o n m r u 6 q i h 8 y d 5
Page: 343
[142] 5 4 b 3 2 7 8 9 10 f 6 5 7 1 11 6 5 7 9 4 4 8 8 N 9 x 12 1 11 2 10 3 9 4 8 5 7 3 39 9 F 6 g 2 2 10 10 o a @ d 1 11 7 6 z 1 11 8 6 7 c 1 12 10 1@ 1 2 1 1 11 11 5 11 2 2 10 21 11 b f @ 8 3 3 9 9 12 1 4 5 g 6 10 8 11 1 9 10 2 2 2 10 5 7 2 z 9 c 8 4 7 5 9 3 10 4 8 8 4 3 7 2 10 7 5 9 3 1 11 12 8 4 11 1 10 2 0 @ d 7 5 9 3 I 8 4 7 5 6 c &
Page: 344
[143] 5 6 7 4 8 3 9 2 10 1 11 4 8 3 9 d d 2 3 4 5 6 7 8 9 10 10 1 1 v n c
Page: 345
[144] 12 1 1 1111 2 2 10 10 3 3 9 9 4 4 8 8 5 5 7 7 6 6 6 T 7 7 5 5 8 8 4 4 9 9 3 3 10 10 2 2 11 11 1 1 12
Page: 345
[145] 11 10 9 8 7 6 5 4 3 2 1 11 10 9 8 7 6 5 4 3 2 1 11 1 2 3 10 4 5 E 6 6 7
Page: 345
[146] 9 3 4 2 8 10 11 12 1 5 7 6 6 G
Page: 345
[147] 8 9 10 7 6 5 11 1 8 1 11 F
Page: 345
[148] 16 15 17 14 14 18 19 19 13 13 20 20 12 12 21 21 11 11 H 22 22 10 10 23 23 9 9 24 16 16 23 23 17 17 22 22 18 18 21 21 29 20
Page: 346
[149] 19 20 21 18 17 22 23 17 16 18 17 9 15 14 13 11 13 20 16 12 21 17 20 22 21 11 22 10 23 9 18 L 17 18 19
Page: 346
[150] 23 17 22 16 18 9 21 23 19 10 19 20 22 11 21 20 13 19 14 18 15 17 16 K
Page: 346
[151] 17 18 19 20 21 22 16 23 15 14 13 12 11 10 11 12 21 22 10 9 23 M
Page: 346
[152] Q K r n r 12 11 K 2 2 @ 4 p 8 7 e t 8 9 c P 7 4 3 10 7 @ P 5 q P 6 2 8 7 q P t t 11 1 I 1 11 7 q p 2 10 q p 3 9 @ a e b 4 8 2 7 6 5 P 10 6 f P 9 3 8 4 f P 1 f P 11 10 2 a f b e 4 9 3 11 10 2 11 1 11 1 u m 12 15 @ d 12 4 5 m 3 4 5 7 8 9 d @ 2 @ 0 10 2 11 1 a 0 s 7 1 n P p 5 6 7 10 6 6 6 3 4 8 9 7 e 5 5 7 4 5 3 10 11 12 1 2 3 8 9 3 1 e H 23 10 22 24 23 22 15 16 17 18 19 21 13 14 20
Page: 348
[153] Horologia in plano meridiani.6 5 4 3 2 1 7 8 9 10 11 12 u l d 7 4 8 3 9 2 10 b n n n n n 5 4 3 2 1 a c e c y n n n n n p 1 2 3 4 5 n ſ ſ 4 3 2 1 r 4 3 2 1 e 4 3 2 1 B 9 10 11 12 13 14 e H 5 6 7 8 9 10 11 e E g r 7 6 5 4 3 2 1 F g d 23 22 21 20 19 18 18 c g G d f a b e g c 1 2 3 4 5 4 3 2 1 8 7 6 5 4 3 2 1 f D e 11 10 19 18
Page: 349
[154] Horologia in plano æquinoctialis.d b 5 6 7 4 8 9 3 g f k L @ m 2 10 l 8 1 11 a e b B L 1 f k m h @ z r s 1 n 11 A 2 1 10 12 3 9 11 1 4 8 10 1 2 5 6 7 b d 9 3 8 4 7 5 6 c 6 7 5 8 4 9 3 18 17 16 10 2 16 17 18 19 11 12 1 19 20 14 14 20 21 13 13 21 22 12 12 22 23 11 23 24 24 14 14 23 15 23 22 15 22 16 16 21 17 21 20 19 18 17 18 19 20
Page: 350
[155] 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1
Page: 356
[156] Instrumenta è regione poſita ſeruiunt fronti horologij ſequentis, illud uero inſerius eſt immobil-le ad aliud, & aliud ab artiſicio aquæ mouetur.B 270 A 360 stella.p.@ f 180 C 10 hircuſ@ 20 30 40 x cani ſminor* 50 60 70 80 90 C@nis Maior* D
Page: 357
[157] 6 5 7 4 8 3 9 2 10 1 11 12 T R 12 L 11 1 A f C 10 2 9 3 8 4 7 5 6
Page: 357
[Figure 158]
Page: 358
[Figure 159]
Page: 359
[Figure 160]
Page: 360
< >
page |< < (176) 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-div469" type="section" level="2" n="80">
            <p style="it">
              <s xml:id="echoid-s13567" xml:space="preserve">
                <pb o="176" file="514.01.208" n="208" rhead="LIBER"/>
              in nouem. </s>
              <s xml:id="echoid-s13568" xml:space="preserve">numeri uero trium tonorum ſunt 729, 648, 512. </s>
              <s xml:id="echoid-s13569" xml:space="preserve">ducendo 81, 72, 64, per nouem, & </s>
              <s xml:id="echoid-s13570" xml:space="preserve">643
                <unsure/>
                <lb/>
              per octo, & </s>
              <s xml:id="echoid-s13571" xml:space="preserve">ita toni cum numeris continenter efficiuntur, in quibus maioris ad minus comparatio ſemper est
                <lb/>
              ſeſquioctaua. </s>
              <s xml:id="echoid-s13572" xml:space="preserve">Ditonus autem eſt ſpatium a linea ad lineam ſpatio unico interiecto, modo hemitonium non inter
                <lb/>
              iaceat. </s>
              <s xml:id="echoid-s13573" xml:space="preserve">oblect. </s>
              <s xml:id="echoid-s13574" xml:space="preserve">it quidem ſed non eſt c
                <unsure/>
              bſoluta conſonantia, & </s>
              <s xml:id="echoid-s13575" xml:space="preserve">a noſtris tertia maior nominatur, quemadmodum
                <lb/>
              eſt ab ut, ad mi, ſcandendo, uel a mi, ad ut, deſcendendo. </s>
              <s xml:id="echoid-s13576" xml:space="preserve">Trihemitonium, quod est ſeſquitonum, uocant, est
                <lb/>
              ſpatium toni, & </s>
              <s xml:id="echoid-s13577" xml:space="preserve">hemitonij minoris, quemadmodum ab re, ad fa, aſcendendo; </s>
              <s xml:id="echoid-s13578" xml:space="preserve">& </s>
              <s xml:id="echoid-s13579" xml:space="preserve">a fa, ad re, ſi deſcendas. </s>
              <s xml:id="echoid-s13580" xml:space="preserve">ad au-
                <lb/>
              res etiam cum ſuauitate peruenit, ſed nondum concentum facit: </s>
              <s xml:id="echoid-s13581" xml:space="preserve">a noſtris tertia minor appellatur, eſtq́; </s>
              <s xml:id="echoid-s13582" xml:space="preserve">ſpatiũ
                <lb/>
              a linea ad lineam hemitonio intercepto. </s>
              <s xml:id="echoid-s13583" xml:space="preserve">Conueniunt omnia ſupra dicta interualla, quia muſicæ deſeruiunt.
                <lb/>
              </s>
              <s xml:id="echoid-s13584" xml:space="preserve">Tonus, & </s>
              <s xml:id="echoid-s13585" xml:space="preserve">hemitonium tetrachordorum coniunctionibus tanquam fundamenta ſubſternuntur. </s>
              <s xml:id="echoid-s13586" xml:space="preserve">Trithemito-
                <lb/>
              nium, & </s>
              <s xml:id="echoid-s13587" xml:space="preserve">ditonus, quia delectant, & </s>
              <s xml:id="echoid-s13588" xml:space="preserve">quoniam in generum diuiſiones incidunt. </s>
              <s xml:id="echoid-s13589" xml:space="preserve">Delectant etiam alij ſoni, qui
                <lb/>
                <note position="left" xlink:label="note-514.01.208-01" xlink:href="note-514.01.208-01a" xml:space="preserve">10</note>
              tamen conſonantias abſolutas minime reddunt. </s>
              <s xml:id="echoid-s13590" xml:space="preserve">constat enim proportione ſuprapartiente, cuiuſmodi ſunt & </s>
              <s xml:id="echoid-s13591" xml:space="preserve">
                <lb/>
              iam dicti trihemitonium, & </s>
              <s xml:id="echoid-s13592" xml:space="preserve">ditonus. </s>
              <s xml:id="echoid-s13593" xml:space="preserve">item & </s>
              <s xml:id="echoid-s13594" xml:space="preserve">quæ ſexta maior a noſtris dicitur, hemitonio, & </s>
              <s xml:id="echoid-s13595" xml:space="preserve">diapente con-
                <lb/>
              stans, id eſt additione hemitonij ad ſeſquialteram, quæ ſit cum a quaque linea ad tertium ſpatium aſcendimus,
                <lb/>
              continens duo hemitonia uel dieſes, & </s>
              <s xml:id="echoid-s13596" xml:space="preserve">tres tonos, quemadmodum ab mi, ad fa, ſi per ſextam modulentur.
                <lb/>
              </s>
              <s xml:id="echoid-s13597" xml:space="preserve">Eſt etiam iucundus tonus cum diapente, a quaque linea ad tertium ſpatium progrediens, unico hemitonio in-
                <lb/>
              tercepto, tonis quatuor incidentibus, quemadmodum ab ut, ad la, per ſextam modulari, quam ſextam maio-
                <lb/>
              rem uocant. </s>
              <s xml:id="echoid-s13598" xml:space="preserve">Oblectat etiam ſeptima minor duabus dieſibus, & </s>
              <s xml:id="echoid-s13599" xml:space="preserve">quatuor tonis comprehenſa, quemadmodum
                <lb/>
              ab ut, ad mi, ab uno ſpatio ad quartum, uel ab una linea ad quartam progrediens. </s>
              <s xml:id="echoid-s13600" xml:space="preserve">Sunt & </s>
              <s xml:id="echoid-s13601" xml:space="preserve">alia interualla. </s>
              <s xml:id="echoid-s13602" xml:space="preserve">
                <lb/>
              exercentibus nota, qualia ſunt nona, decima, undecima, & </s>
              <s xml:id="echoid-s13603" xml:space="preserve">duodecima a nostris dicta, quorum incunditas
                <lb/>
              exercitio potius, quàm regulis cognoſcitur. </s>
              <s xml:id="echoid-s13604" xml:space="preserve">Sed hæc ſatis ad intellectnm eorum, quæ a Vitruuio dicuntur. </s>
              <s xml:id="echoid-s13605" xml:space="preserve">in-
                <lb/>
                <note position="left" xlink:label="note-514.01.208-02" xlink:href="note-514.01.208-02a" xml:space="preserve">20</note>
              quit enim Vitru.</s>
              <s xml:id="echoid-s13606" xml:space="preserve"/>
            </p>
            <figure number="71">
              <caption xml:id="echoid-caption28" xml:space="preserve">EXEMPLVM MONOCHORDI.</caption>
              <description xml:id="echoid-description40" xml:space="preserve">Vniſonum
                <lb/>
              Tonus
                <lb/>
              Semitonium
                <lb/>
              Ditonus
                <lb/>
              Semiditonus
                <lb/>
              Tuo no</description>
            </figure>
            <note position="left" xml:space="preserve">30</note>
            <note position="left" xml:space="preserve">40</note>
            <p style="it">
              <s xml:id="echoid-s13607" xml:space="preserve">{In tribus generibus diſſimiles eſſe tetrachordorum diſpoſitones} ratio eſt quoniam diuerſis rerum qualitati-
                <lb/>
              tibus corum temperamenta applicantur, & </s>
              <s xml:id="echoid-s13608" xml:space="preserve">ideas referunt diuerſas uel magnarum, uel mediocrium, uel infir-
                <lb/>
              marum rerum. </s>
              <s xml:id="echoid-s13609" xml:space="preserve">In ſingulis tetrachordis quatuor ſonitus, aut gradus uocis continentur, tribus autem inter-
                <lb/>
              uallis ſingula conſtant, & </s>
              <s xml:id="echoid-s13610" xml:space="preserve">inter imum, & </s>
              <s xml:id="echoid-s13611" xml:space="preserve">ſummum gradum ſeſquitertia proportio, & </s>
              <s xml:id="echoid-s13612" xml:space="preserve">comparatio habetur,
                <lb/>
              & </s>
              <s xml:id="echoid-s13613" xml:space="preserve">in omnibus eſt eadem ratio extremorum, ſed interualla media dißimilibus diſpoſitionibus conſtituuntur in
                <lb/>
              ſingulis. </s>
              <s xml:id="echoid-s13614" xml:space="preserve">Nam harmonicum tetracbordum a dimidia dieſi, ad dimidiam ſcandit, inde ad ditonum, quæ ſimul
                <lb/>
              poſita duos tonos, & </s>
              <s xml:id="echoid-s13615" xml:space="preserve">hemitonium minus, uel dieſim unam continent. </s>
              <s xml:id="echoid-s13616" xml:space="preserve">in quibus ſeſquitertia proportio habetur.
                <lb/>
              </s>
              <s xml:id="echoid-s13617" xml:space="preserve">Sed chromaticum primum interuallum hemitonij vel dieſeos, ſecundum bemitonij uel apotomes, tertium trihe-
                <lb/>
                <note position="left" xlink:label="note-514.01.208-05" xlink:href="note-514.01.208-05a" xml:space="preserve">50</note>
              mitonij, quæ omniatonos duos, & </s>
              <s xml:id="echoid-s13618" xml:space="preserve">dieſim unam referunt, quemadmodum, ſpatia harmonici generis referebat.
                <lb/>
              </s>
              <s xml:id="echoid-s13619" xml:space="preserve">Similiter diatonicum primo interuallo tonum, ſecundo item tonum, tertio dieſim continet, & </s>
              <s xml:id="echoid-s13620" xml:space="preserve">ipſum quoque duo-
                <lb/>
              bus tonis, & </s>
              <s xml:id="echoid-s13621" xml:space="preserve">dieſi ordinatur. </s>
              <s xml:id="echoid-s13622" xml:space="preserve">Atque hoc illud eſt, quod Vitr. </s>
              <s xml:id="echoid-s13623" xml:space="preserve">dicit. </s>
              <s xml:id="echoid-s13624" xml:space="preserve">{Ita in tribus generibus tetrachorda
                <lb/>
              cx duobus tonis, & </s>
              <s xml:id="echoid-s13625" xml:space="preserve">hemitonio ſunt peræquata} extremis enim conueniunt, ſed medijs differunt. </s>
              <s xml:id="echoid-s13626" xml:space="preserve">Armonicum
                <lb/>
              genus, quod Vitr. </s>
              <s xml:id="echoid-s13627" xml:space="preserve">harmoniam uocat, ex parte graui, & </s>
              <s xml:id="echoid-s13628" xml:space="preserve">ima, ad acuta, & </s>
              <s xml:id="echoid-s13629" xml:space="preserve">elatum ſcandit in ſui tetrachordi
                <lb/>
              diſpoſitione a dimidia dieſi. </s>
              <s xml:id="echoid-s13630" xml:space="preserve">in qua ponitur primum interuallum, ad aliam dimidiam, in qua ſecundum eſt inter-
                <lb/>
              uallum, inde ad ditonum, in qua tertium eſt interuallum. </s>
              <s xml:id="echoid-s13631" xml:space="preserve">Intelligebat Ariſto xenum dimidium uerum, ſed ita
                <lb/>
              non eſt (ut dixi) claudit ergo tetrachordum huiuſmodi concentum illum, quem diateſſaron Græci, noſtri quar-
                <lb/>
              tam uocænt. </s>
              <s xml:id="echoid-s13632" xml:space="preserve">Ordinatio igitur, & </s>
              <s xml:id="echoid-s13633" xml:space="preserve">ſcala harmonici tetrachordi conſtituta, uoce ima, & </s>
              <s xml:id="echoid-s13634" xml:space="preserve">graui ſcandit a pro-
                <lb/>
              portione ſeſquiquadrageſima quinta, ad ſeſquiuigeſimam tertiam, & </s>
              <s xml:id="echoid-s13635" xml:space="preserve">inde ad ſeſquiquartam terminatur, deſcen
                <lb/>
                <note position="left" xlink:label="note-514.01.208-06" xlink:href="note-514.01.208-06a" xml:space="preserve">60</note>
              </s>
            </p>
          </div>
        </div>
      </text>
    </echo>
Impressum