Vitruvius, De architectura libri decem, 1567

Table of figures

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[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
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              <s xml:id="echoid-s13794" xml:space="preserve">
                <pb o="179" file="514.01.211" n="211" rhead="QVINTVS."/>
              natura rerum appellationes ſumpſere. </s>
              <s xml:id="echoid-s13795" xml:space="preserve">Quatuor igitur tetrachordi uoces, & </s>
              <s xml:id="echoid-s13796" xml:space="preserve">ſonitus, uel chordæipſæ his uoca
                <lb/>
              bulis exprim antur. </s>
              <s xml:id="echoid-s13797" xml:space="preserve">Prima, ad primam, penultima, ultima. </s>
              <s xml:id="echoid-s13798" xml:space="preserve">Verum quia antiqui unico tetrachordo, & </s>
              <s xml:id="echoid-s13799" xml:space="preserve">ſin-
                <lb/>
              gulari eius concentu non fuere contenti, ſed plures ſonitus addidere, ideo ob diuerſam eorum, & </s>
              <s xml:id="echoid-s13800" xml:space="preserve">mutuam
                <lb/>
              comparationem plura ſonituum, & </s>
              <s xml:id="echoid-s13801" xml:space="preserve">uocum nomina fabricarunt, donec tandem poſt duo, & </s>
              <s xml:id="echoid-s13802" xml:space="preserve">tria tetrachorda
                <lb/>
              fimul coniuncta, ad quartum peruenerint, cuius extremum omnes concentus mirabili proportione contineret,
                <lb/>
              & </s>
              <s xml:id="echoid-s13803" xml:space="preserve">ita perfectam & </s>
              <s xml:id="echoid-s13804" xml:space="preserve">abſolutam ſonituum ordinationem perfecere. </s>
              <s xml:id="echoid-s13805" xml:space="preserve">Grauiorem igitur, & </s>
              <s xml:id="echoid-s13806" xml:space="preserve">imum ſonitum proſlam-
                <lb/>
              banomenon dixere, quaſi aſſumptum, additumq́; </s>
              <s xml:id="echoid-s13807" xml:space="preserve">poſtea, quoniam nullam cum alijs tetrachordis communionem
                <lb/>
              habet, ſed extra aſcitus medio reſpondeat. </s>
              <s xml:id="echoid-s13808" xml:space="preserve">hæc uox a noſtris ponitur, ubi in manu collocatur, a re, ſed quo-
                <lb/>
              niam, & </s>
              <s xml:id="echoid-s13809" xml:space="preserve">ipſi aliam quoque ad partem grauem infra ipſam poſuere, ideo, gamma ut, ipſam uocauere, græca lit-
                <lb/>
                <note position="left" xlink:label="note-514.01.211-01" xlink:href="note-514.01.211-01a" xml:space="preserve">10</note>
              tera notantes, ut ſignificarent, eam uocem ab ipſis quoque aſſumptam, & </s>
              <s xml:id="echoid-s13810" xml:space="preserve">in manu collocatam, ideoq́; </s>
              <s xml:id="echoid-s13811" xml:space="preserve">ea lit-
                <lb/>
              tera in cæteris uocibus non amplius uſi ſunt. </s>
              <s xml:id="echoid-s13812" xml:space="preserve">uocari autem poſſet uox illa epiproſlambanomenos, uel hypo-
                <lb/>
              proſlanuanomenos. </s>
              <s xml:id="echoid-s13813" xml:space="preserve">Secundus ſonus hypate dicitur, ideo conſiderandum est, quod ſi ſeparatim ſingula tetra-
                <lb/>
              chorda ordinamus, & </s>
              <s xml:id="echoid-s13814" xml:space="preserve">nullam rationem ad perfectam ordinationem habemus, prima, ad primam, penultima,
                <lb/>
              & </s>
              <s xml:id="echoid-s13815" xml:space="preserve">ultima chorda ſuas retinent nominationes. </s>
              <s xml:id="echoid-s13816" xml:space="preserve">hoc est hypate, parhypate, paranete, & </s>
              <s xml:id="echoid-s13817" xml:space="preserve">nete. </s>
              <s xml:id="echoid-s13818" xml:space="preserve">Sed cum plu-
                <lb/>
              ra tetrachorda componuntur, prima quidem eorum chorda hypate dicitur, ſed & </s>
              <s xml:id="echoid-s13819" xml:space="preserve">additamento, ut hypate,
                <lb/>
              hypaton, hoc est prima primarum dicatur. </s>
              <s xml:id="echoid-s13820" xml:space="preserve">est enim prima ratione tetrachordi, ſed eſt prima primarum, ra-
                <lb/>
              tione earum, quæ primæ ſunt in alijs tetrachordis, & </s>
              <s xml:id="echoid-s13821" xml:space="preserve">ita alia uocatur parhypate hypaton, id eſt ad primam
                <lb/>
              primarum, ut a ſecundis aliorum tetrachordorum diſtinguatur. </s>
              <s xml:id="echoid-s13822" xml:space="preserve">Tertia chorda, quia non amplius ultimæ pro-
                <lb/>
              xima eſt, aliæ enim ſunt additæ ad alia tetrachorda cõſtituenda, ideo hyperparhypate a loco nominatur, hoc eſt
                <lb/>
                <note position="left" xlink:label="note-514.01.211-02" xlink:href="note-514.01.211-02a" xml:space="preserve">20</note>
              ſupra eam, quæ eſt ad primam, altior enim, & </s>
              <s xml:id="echoid-s13823" xml:space="preserve">acutior eſt parhypate. </s>
              <s xml:id="echoid-s13824" xml:space="preserve">Vocatur & </s>
              <s xml:id="echoid-s13825" xml:space="preserve">lycanos, id eſt index, quo-
                <lb/>
              niam quemadmodum index inter digitos magis diſtat a craßiori digito qui pollex eſt, & </s>
              <s xml:id="echoid-s13826" xml:space="preserve">interdum minus quam
                <lb/>
              a cæteris: </s>
              <s xml:id="echoid-s13827" xml:space="preserve">ita quarta chorda, quæ tertia eſt in tetrachordorum ordinatione poſita proſlambanomenos pro pri-
                <lb/>
              ma, cum interdum maioribus, interdum minoribus distet interuallis ſecundum modulationum, diſcrimina (ut
                <lb/>
              uidebimus) a ſimilitudine indicis digiti, lycanos nominatur, bæc in ſeparatis tetrachordis parhypate nomina-
                <lb/>
              retur, ſed in ordinatione, a loco, quem tenet, ſic nominatur. </s>
              <s xml:id="echoid-s13828" xml:space="preserve">Quinta hypate meſon dicitur. </s>
              <s xml:id="echoid-s13829" xml:space="preserve">hypate quidem,
                <lb/>
              quoniam prima eſt ſecundi tetrachordi, dicitur meſon, id est mediorum, quoniam ſecundum tetrachordum,
                <lb/>
              medium uocatur, quoniam inter duo tetrachorda ponitur, quorum unum dicitur hypaton, id eſt primorum,
                <lb/>
              quod a grauiori parte ponitur, & </s>
              <s xml:id="echoid-s13830" xml:space="preserve">illud est, quod hactenus abſoluimus. </s>
              <s xml:id="echoid-s13831" xml:space="preserve">alterum eſt coniunctarum, quemad-
                <lb/>
              modum dicam, quod ad acutiorem partem ſpectat, ideo hæc chorda non dicitur nete, id est ultima, licet ſit
                <lb/>
                <note position="left" xlink:label="note-514.01.211-03" xlink:href="note-514.01.211-03a" xml:space="preserve">30</note>
              ultima primi tetrachordi, nec dicitur hypate, i. </s>
              <s xml:id="echoid-s13832" xml:space="preserve">prima, licet ſit prima ſecundi tetrachordi, ſed dicitur hypate me-
                <lb/>
              ſon, id est prima mediarum: </s>
              <s xml:id="echoid-s13833" xml:space="preserve">neceſſe igitur erat additione aliarum chordarum, & </s>
              <s xml:id="echoid-s13834" xml:space="preserve">nouarum eomparatione
                <lb/>
              ſubiunctione, uocabula immutari primarum, ita ut ipſa penè loquente natura, & </s>
              <s xml:id="echoid-s13835" xml:space="preserve">ab imperitis eadem nomina
                <lb/>
              imponi facile fuißet, nam quid facilius, quàm ab ordine, & </s>
              <s xml:id="echoid-s13836" xml:space="preserve">ſitu res nominare ? </s>
              <s xml:id="echoid-s13837" xml:space="preserve">ut quæ primum locum, primæ;
                <lb/>
              </s>
              <s xml:id="echoid-s13838" xml:space="preserve">quæ proſtremum, ultimæ; </s>
              <s xml:id="echoid-s13839" xml:space="preserve">quæ medium tenent, mediæ nominentur ? </s>
              <s xml:id="echoid-s13840" xml:space="preserve">Quoniam igitur colligantur tetrachorda,
                <lb/>
              & </s>
              <s xml:id="echoid-s13841" xml:space="preserve">diuerſæ ſunt ſonituum, & </s>
              <s xml:id="echoid-s13842" xml:space="preserve">chordarum, ſeu uocum comparationes, ideo alia nomina ſingularibus, & </s>
              <s xml:id="echoid-s13843" xml:space="preserve">per ſe
                <lb/>
              poſitis; </s>
              <s xml:id="echoid-s13844" xml:space="preserve">alia colligatis, coniunctisq́; </s>
              <s xml:id="echoid-s13845" xml:space="preserve">tribuuntur. </s>
              <s xml:id="echoid-s13846" xml:space="preserve">Cum uero ſint duo octochorda, quæ abſolutam ſimphoniam
                <lb/>
              continent, unum a grauiori, alterum ab acutori parte, & </s>
              <s xml:id="echoid-s13847" xml:space="preserve">cum octochordũ duobus conſtet tetrachordis, quoniam
                <lb/>
              hypatis nomen grauioribus, netis uero acutioribus caſibus datur, ideo utriſque prioribus tetrachordis ex
                <lb/>
              parte grauiori d antur uocabula, ſumpta ab hypate, unde primum tetrachordum parte ima, dicitur tetrachor-
                <lb/>
                <note position="left" xlink:label="note-514.01.211-04" xlink:href="note-514.01.211-04a" xml:space="preserve">40</note>
              dum hypaton, id eſt primarum, & </s>
              <s xml:id="echoid-s13848" xml:space="preserve">ſecundum dicitur tetrachordum, mediarum, & </s>
              <s xml:id="echoid-s13849" xml:space="preserve">eius prima chorda dicitur
                <lb/>
              hypate meſon, idest prima mediarum: </s>
              <s xml:id="echoid-s13850" xml:space="preserve">hisq́; </s>
              <s xml:id="echoid-s13851" xml:space="preserve">conſiderationibus faeile fit quod ſupereſt. </s>
              <s xml:id="echoid-s13852" xml:space="preserve">Ideo ſexta chorda
                <lb/>
              parhypatemeſon dicitur, ideſt ad primam mediarum, quæ ſecunda eſt ſecundi tetrachordi. </s>
              <s xml:id="echoid-s13853" xml:space="preserve">Septima dicitur
                <lb/>
              hyperparhypate, idest ſupra ad primam. </s>
              <s xml:id="echoid-s13854" xml:space="preserve">Octaua meſon, id eſt media nominatur, quoniam uere media est
                <lb/>
              tetrachordorum. </s>
              <s xml:id="echoid-s13855" xml:space="preserve">Sed ſi ulterius non progrederemur, & </s>
              <s xml:id="echoid-s13856" xml:space="preserve">ſonitus octochordo complecterentur, ipſa non media,
                <lb/>
              ſed nete, id eſt ultima diceretur. </s>
              <s xml:id="echoid-s13857" xml:space="preserve">Sed quoniam eſt finis octochordi grauioris, & </s>
              <s xml:id="echoid-s13858" xml:space="preserve">initium acutioris, cuius ipſa eſt
                <lb/>
              grauior cæteris utraque connectens, ideo media dicitur, tanquam commune duobus octochordis medium, & </s>
              <s xml:id="echoid-s13859" xml:space="preserve">
                <lb/>
              uinculum, & </s>
              <s xml:id="echoid-s13860" xml:space="preserve">tanquam ea, quæ æque ab extremis diſtet. </s>
              <s xml:id="echoid-s13861" xml:space="preserve">Nona a ſitu dicitur parameſe, idest ad mediam; </s>
              <s xml:id="echoid-s13862" xml:space="preserve">hoc
                <lb/>
              est proximam mediæ, hæc est ſecunda tertij tetrachordi. </s>
              <s xml:id="echoid-s13863" xml:space="preserve">Decima dicitur tritediezeugmenon, idest tertia diſ-
                <lb/>
              iunctarum, quoniam in ueterum eptachordis tertia erat in ordine ad ultimam, & </s>
              <s xml:id="echoid-s13864" xml:space="preserve">uocabatur parameſe, idest
                <lb/>
                <note position="left" xlink:label="note-514.01.211-05" xlink:href="note-514.01.211-05a" xml:space="preserve">50</note>
              ad mediam in tertio tetrachordo, & </s>
              <s xml:id="echoid-s13865" xml:space="preserve">in ſecundo octochordo. </s>
              <s xml:id="echoid-s13866" xml:space="preserve">Sed quoniam hæc chorda ratione octochordi ab
                <lb/>
              acutiori parte coniungitur, & </s>
              <s xml:id="echoid-s13867" xml:space="preserve">ratione octochordi grauioris diſiungitur, ideſt colligatur proportione aliqua
                <lb/>
              cum illo, & </s>
              <s xml:id="echoid-s13868" xml:space="preserve">non cum iſto, ideo diezeugmenon uocatur, ideſt diſiunctarum, & </s>
              <s xml:id="echoid-s13869" xml:space="preserve">ſeparatarum quemadmodum
                <lb/>
              clarius infra patebit. </s>
              <s xml:id="echoid-s13870" xml:space="preserve">Vndecima dicitur paranete diezeugmenon, idest penultima diſiunctarum. </s>
              <s xml:id="echoid-s13871" xml:space="preserve">Duodecima
                <lb/>
              dicitur nete diezeugmenon, ideſt ultima diſiunctarum, quoniam quarta eſt, & </s>
              <s xml:id="echoid-s13872" xml:space="preserve">ultima tertij tetrachordi, & </s>
              <s xml:id="echoid-s13873" xml:space="preserve">
                <lb/>
              prima quarti tetrachordi hyperboleon, ideſt excellentium, & </s>
              <s xml:id="echoid-s13874" xml:space="preserve">acutißimarum, quoniam ad acutas uoces per-
                <lb/>
              tinet. </s>
              <s xml:id="echoid-s13875" xml:space="preserve">Tertiadecima dicitur trite hyperboleon, ideſt tertia excellentium, quoniam tertia eſt ab extremis in
                <lb/>
              acutiori parte. </s>
              <s xml:id="echoid-s13876" xml:space="preserve">Quartadecima dicitur paranete hyperboleon, ideſt penultima excellentium a ſitu, & </s>
              <s xml:id="echoid-s13877" xml:space="preserve">poſi-
                <lb/>
              tione ſic nominata. </s>
              <s xml:id="echoid-s13878" xml:space="preserve">Quintadecima nete hyperboleon dicitur, idest excellentium postrema, ultra quam uoces,
                <lb/>
              ſon itusq́; </s>
              <s xml:id="echoid-s13879" xml:space="preserve">perfectæ conſonantiæ non progrediuntur. </s>
              <s xml:id="echoid-s13880" xml:space="preserve">hanc ordinationem, nostri, ut dixi, ſcalam nominant, in
                <lb/>
                <note position="left" xlink:label="note-514.01.211-06" xlink:href="note-514.01.211-06a" xml:space="preserve">60</note>
              qua uoces per gradus componunt, ſyllabis, literisq́; </s>
              <s xml:id="echoid-s13881" xml:space="preserve">utentes, dicentes gamma ut. </s>
              <s xml:id="echoid-s13882" xml:space="preserve">A re, b mi, & </s>
              <s xml:id="echoid-s13883" xml:space="preserve">reliqua. </s>
              <s xml:id="echoid-s13884" xml:space="preserve"/>
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