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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            <p>
              <s xml:id="echoid-s22945" xml:space="preserve">
                <pb o="302" file="514.01.334" n="334" rhead="LIBER"/>
              magni fuerint, qui ab ipſa natione Chaldęorum profluxerunt, oſtendunt. </s>
              <s xml:id="echoid-s22946" xml:space="preserve">Primusq́; </s>
              <s xml:id="echoid-s22947" xml:space="preserve">Beroſus in in-
                <lb/>
              ſula, & </s>
              <s xml:id="echoid-s22948" xml:space="preserve">ciuitate Coo conſedit, ibiq́; </s>
              <s xml:id="echoid-s22949" xml:space="preserve">aperuit diſciplinam. </s>
              <s xml:id="echoid-s22950" xml:space="preserve">poſtea ſtudens Antipater, itemq́; </s>
              <s xml:id="echoid-s22951" xml:space="preserve">Achina-
                <lb/>
              polus, qui etiam none naſcentia, ſed ex conceptione genethliologiæ rationes explicatas reliquit.
                <lb/>
              </s>
              <s xml:id="echoid-s22952" xml:space="preserve">De natu ralibus autem rebus Thales Mileſius, Anaxagoras Clazomenius, Pythagoras Samius, Xeno-
                <lb/>
              phantes Colophonius, Democritus Abderites, rationes, quibus e rebus natura rerum gubernaretur,
                <lb/>
              quemadmodum quoſque affectus habent,excogitatas reliquerunt. </s>
              <s xml:id="echoid-s22953" xml:space="preserve">Quorum inu enta ſequuti, ſyde-
                <lb/>
              rum ortus, & </s>
              <s xml:id="echoid-s22954" xml:space="preserve">occaſus, tempeſtatumq́; </s>
              <s xml:id="echoid-s22955" xml:space="preserve">ſignificatus Eudoxus, Eudamon, Calliſtus, Melo, Philippus,
                <lb/>
              Hipparchus, Aratus, cæteriq́; </s>
              <s xml:id="echoid-s22956" xml:space="preserve">ex Aſtrologia parapegmatorum diſciplinis inuenerunt, & </s>
              <s xml:id="echoid-s22957" xml:space="preserve">eas poſteris
                <lb/>
              explicatas reliquerunt. </s>
              <s xml:id="echoid-s22958" xml:space="preserve">Quorum ſcientiæ ſunt hominibus ſuſpiciendę, quod tanta cura fuerunt, ut
                <lb/>
                <note position="left" xlink:label="note-514.01.334-01" xlink:href="note-514.01.334-01a" xml:space="preserve">10</note>
              etiam uideantur diuina mente tempeſtatum ſignificatus poſt ſuturos, ante pronunciare, quas ob res
                <lb/>
              hæc eorum curis, ſtudijsq; </s>
              <s xml:id="echoid-s22959" xml:space="preserve">ſunt concedenda.</s>
              <s xml:id="echoid-s22960" xml:space="preserve"/>
            </p>
            <p style="it">
              <s xml:id="echoid-s22961" xml:space="preserve">Aedificiorum, ciuitatum, & </s>
              <s xml:id="echoid-s22962" xml:space="preserve">urbium, ne dum hominum genituras mathematici ſolent explorare, ſyderaq́;
                <lb/>
              </s>
              <s xml:id="echoid-s22963" xml:space="preserve">orientia, & </s>
              <s xml:id="echoid-s22964" xml:space="preserve">cadentia perpendere, ut cognoſcant quid cuique euenturum ſit, & </s>
              <s xml:id="echoid-s22965" xml:space="preserve">prænuntient fata rerum. </s>
              <s xml:id="echoid-s22966" xml:space="preserve">Vitr. </s>
              <s xml:id="echoid-s22967" xml:space="preserve">
                <lb/>
              reijcit ab Architecto eam curam, quam multo magis renuere Chriſtiani debent, quare & </s>
              <s xml:id="echoid-s22968" xml:space="preserve">nos eam a noſtris
                <lb/>
              studijs ( ut diximus ) meritò abdicauimus. </s>
              <s xml:id="echoid-s22969" xml:space="preserve">Sunt autem parapegmata ( ut Philander notat ) Astronomica
                <lb/>
              inſtrumenta, quibus ortus, occaſusq; </s>
              <s xml:id="echoid-s22970" xml:space="preserve">ſyderum, tempeſtatumq́; </s>
              <s xml:id="echoid-s22971" xml:space="preserve">ſignificationes cogno ſcuntur, atque inueniun-
                <lb/>
              tur; </s>
              <s xml:id="echoid-s22972" xml:space="preserve">dicta, quod ex multis uarijsq́; </s>
              <s xml:id="echoid-s22973" xml:space="preserve">concinnata eſſent, ſiue tabellis, ſiue armillis, ſiue dioptris, & </s>
              <s xml:id="echoid-s22974" xml:space="preserve">ligulis,
                <lb/>
              ſiue aliqua alia parte. </s>
              <s xml:id="echoid-s22975" xml:space="preserve">Cæterum Vitru. </s>
              <s xml:id="echoid-s22976" xml:space="preserve">ea ſelegit ex Astronomia, ex quibus Gnomonum æquinoctialibus
                <lb/>
              umbris analemmatorum inueniuntur deſcriptiones. </s>
              <s xml:id="echoid-s22977" xml:space="preserve">Sunt autem illa, quæ ad cœli motum pertinent, ſyderumq́; </s>
              <s xml:id="echoid-s22978" xml:space="preserve">
                <lb/>
                <note position="left" xlink:label="note-514.01.334-02" xlink:href="note-514.01.334-02a" xml:space="preserve">20</note>
              contrarias motiones ſpectant, & </s>
              <s xml:id="echoid-s22979" xml:space="preserve">diſpoſitio imaginum, utrinque ad Zonam ſignorum diſtributa. </s>
              <s xml:id="echoid-s22980" xml:space="preserve">Quare ad
                <lb/>
              rem ueniamus, in fine libri poſitas inſpicientes Tabulas a nostro præceptore Federico Delpbino conditas, è
                <lb/>
              quibus ſtellarum ſitus, & </s>
              <s xml:id="echoid-s22981" xml:space="preserve">ſiguratio, partes, latitudines, & </s>
              <s xml:id="echoid-s22982" xml:space="preserve">longitudines, itemq́; </s>
              <s xml:id="echoid-s22983" xml:space="preserve">magnitudines elicere poteri-
                <lb/>
              mus, & </s>
              <s xml:id="echoid-s22984" xml:space="preserve">ſolidum ſphæræ,ſtellarumq́; </s>
              <s xml:id="echoid-s22985" xml:space="preserve">globum conformare.</s>
              <s xml:id="echoid-s22986" xml:space="preserve"/>
            </p>
          </div>
          <div xml:id="echoid-div769" type="section" level="2" n="142">
            <head xml:id="echoid-head150" style="it" xml:space="preserve">De horologiorum rationibus, & umbris gnomonum æquinoctia-
              <lb/>
            li tempore Romæ, & nonnullis alijs locis.
              <lb/>
            Cap. VIII.</head>
            <note position="left" xml:space="preserve">30</note>
            <p>
              <s xml:id="echoid-s22987" xml:space="preserve">
                <emph style="sc">NObis</emph>
              autem ab his ſeparandæ ſunt horologiorum rationes, & </s>
              <s xml:id="echoid-s22988" xml:space="preserve">explicandæ menſtruæ die-
                <lb/>
              rum breuitates, atque depalationes.</s>
              <s xml:id="echoid-s22989" xml:space="preserve"/>
            </p>
            <p style="it">
              <s xml:id="echoid-s22990" xml:space="preserve">Poſt longam, neceſſariam tamen digreſſionem, Vitr. </s>
              <s xml:id="echoid-s22991" xml:space="preserve">aggreditur analemmatis tractationem,
                <lb/>
              quod eſt gnomonices fundamentum, non enim conficere genus aliquod horologij docet, uiam
                <lb/>
              tamen aperit ad horologia cuiuſuis generis deſignanda. </s>
              <s xml:id="echoid-s22992" xml:space="preserve">Agit de Analemmate Ptolomæus: </s>
              <s xml:id="echoid-s22993" xml:space="preserve">in eius tractatum
                <lb/>
              Federicus Commandinus ſcite commentarios ſcripſit, cui multæ habendæ gratiæ ſunt, cum pro communi uti-
                <lb/>
              litate ſemper inuigilet: </s>
              <s xml:id="echoid-s22994" xml:space="preserve">ego certe ab eius ſententia nunquam diſcedam, atque ut illi demonſtr ationes rerum
                <lb/>
              relinquam, ita cum eo uſum analemmatis declarabo. </s>
              <s xml:id="echoid-s22995" xml:space="preserve">Eſt autem quod Ptolomæi ingenium admireris, & </s>
              <s xml:id="echoid-s22996" xml:space="preserve">Com-
                <lb/>
                <note position="left" xlink:label="note-514.01.334-04" xlink:href="note-514.01.334-04a" xml:space="preserve">40</note>
              mandini honestos labores commendes, utriuſque tamen induſtriam multum conferre ad Vitruuiani analemma
                <lb/>
              tis uſum exiſtimabis, quod s̃tatim manifes̃tum fiet. </s>
              <s xml:id="echoid-s22997" xml:space="preserve">Age igitur ad Vitruuium accedamus, & </s>
              <s xml:id="echoid-s22998" xml:space="preserve">mentem eius uni-
                <lb/>
              uerſam aperiamus altius repetentes. </s>
              <s xml:id="echoid-s22999" xml:space="preserve">Propoſitum igitur eſt de ſecunda Architecturæ parte, quæ gnomonice
                <lb/>
              a Græcis dicitur, pertractare. </s>
              <s xml:id="echoid-s23000" xml:space="preserve">Vocabuli eius ratio a gnomone deducta eſt. </s>
              <s xml:id="echoid-s23001" xml:space="preserve">gnomon enim norma uocatur, & </s>
              <s xml:id="echoid-s23002" xml:space="preserve">
                <lb/>
              quodcunque ad normam erectum eſt. </s>
              <s xml:id="echoid-s23003" xml:space="preserve">Conſueuere autem veteres ab umbris in planum a Gnomonibus proiectis
                <lb/>
              partes diei, hoc est horas cognoſcere. </s>
              <s xml:id="echoid-s23004" xml:space="preserve">Eam cognitionem gnomonicen a gnomone nominauerunt. </s>
              <s xml:id="echoid-s23005" xml:space="preserve">Quoniam
                <lb/>
              uero circa gnomonem aliæ aliàs pro temporum & </s>
              <s xml:id="echoid-s23006" xml:space="preserve">horarum diμerſitate umbræ in oppoſitis planis proijcie-
                <lb/>
              bantur, id obſeruantes, analemmata cœperunt deſignare. </s>
              <s xml:id="echoid-s23007" xml:space="preserve">Analemma enim eſtreſumptio quædam:</s>
              <s xml:id="echoid-s23008" xml:space="preserve">nam priuſ-
                <lb/>
              quam horologia deſcriberent, deſignationes quaſdam ſumebant conquiſitas ex Solis curſu, & </s>
              <s xml:id="echoid-s23009" xml:space="preserve">umbra gno-
                <lb/>
              monis ad deſcribendorum horologiorum rationes accommodatas. </s>
              <s xml:id="echoid-s23010" xml:space="preserve">Gnomonem uero ſchiathira, quaſi umbræ
                <lb/>
                <note position="left" xlink:label="note-514.01.334-05" xlink:href="note-514.01.334-05a" xml:space="preserve">50</note>
              indagatorem primo libro Vitruuium uocaſse uidimus: </s>
              <s xml:id="echoid-s23011" xml:space="preserve">quemadmodum uero in ædibus fabricandis modulus ac-
                <lb/>
              cipiebatur, hoc eſt certa illa, & </s>
              <s xml:id="echoid-s23012" xml:space="preserve">minima menſura, qua ædificiorum partes metiri ſolemus, ita & </s>
              <s xml:id="echoid-s23013" xml:space="preserve">in horologijs
                <lb/>
              deſcribendis analemma pro modulo habetur. </s>
              <s xml:id="echoid-s23014" xml:space="preserve">His poſitis & </s>
              <s xml:id="echoid-s23015" xml:space="preserve">stabilitis animaduertendum eſt ad ea. </s>
              <s xml:id="echoid-s23016" xml:space="preserve">quæ di-
                <lb/>
              cturus ſum, nam utilia erunt tum alijs multis ſpeculationibus, tum gnomonices intelligentiæ,quã optices quan-
                <lb/>
              dam partẽ eſſe manifeſtum est, de qua libellum ſtatim ædituri ſumus. </s>
              <s xml:id="echoid-s23017" xml:space="preserve">Ad eas mathematicas figuras, quæ nobis
                <lb/>
              in hoc opere mir a iucunditate inſeruiunt, præcipua conus accedit, & </s>
              <s xml:id="echoid-s23018" xml:space="preserve">ſuperficies illa, quæ conica nominatur.
                <lb/>
              </s>
              <s xml:id="echoid-s23019" xml:space="preserve">Quid uero ſit conus, & </s>
              <s xml:id="echoid-s23020" xml:space="preserve">conica ſuperficies hinc patebit. </s>
              <s xml:id="echoid-s23021" xml:space="preserve">Imagin emur immotum ſignum, infra quod circulus de-
                <lb/>
              ſcriptus ſit, ex ſigno immoto ducatur linea ad ambitum circuli, quæ ambiat integram circinationis lineam,
                <lb/>
              deſcribet illa figuram, quam conum mathematici,pyramidem vulgus appellant. </s>
              <s xml:id="echoid-s23022" xml:space="preserve">Eſto ſignum immotum ubi a. </s>
              <s xml:id="echoid-s23023" xml:space="preserve">
                <lb/>
              circulus infra poſitus b c d. </s>
              <s xml:id="echoid-s23024" xml:space="preserve">a ſigno a deſcendat linea a b. </s>
              <s xml:id="echoid-s23025" xml:space="preserve">quæ circunferatur per ambitum circuli,
                <lb/>
              donec eo redeat, unde diſceßit, aio ita deformari conum, & </s>
              <s xml:id="echoid-s23026" xml:space="preserve">inde ſuperficiem fieri, quæ conica nominatur: </s>
              <s xml:id="echoid-s23027" xml:space="preserve">quæ
                <lb/>
                <note position="left" xlink:label="note-514.01.334-06" xlink:href="note-514.01.334-06a" xml:space="preserve">60</note>
              </s>
            </p>
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