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 style="it">
              <s xml:id="echoid-s22442" xml:space="preserve">
                <pb o="296" file="514.01.328" n="328" rhead="LIBER"/>
              modo a Vitr. </s>
              <s xml:id="echoid-s22443" xml:space="preserve">exponunttur. </s>
              <s xml:id="echoid-s22444" xml:space="preserve">Aliud quoque docet, quod eſt: </s>
              <s xml:id="echoid-s22445" xml:space="preserve">ſigna ab Ariete iuxta præ ſcriptum ordinem, ſep-
                <lb/>
              tentrionalia nominari, quæ uero a Libra ad Arietem collocantur, dici meridiana, quoniam illa ſunt citra æqui-
                <lb/>
              noctialem in noſtris regionibus, illa uero ultra æquinoctialem uerſus partes meridianas, idq́; </s>
              <s xml:id="echoid-s22446" xml:space="preserve">aio ratione noſtri,
                <lb/>
              nam ſigna, quæ nobis meridiana ſunt, illis, qui ultra æquinoctia ſunt, ſigna eorum cardinis dicuntur, quæue-
                <lb/>
              ro nobis ſeptentrionalia habentur, ullis meridiana uocantur. </s>
              <s xml:id="echoid-s22447" xml:space="preserve">Amplius & </s>
              <s xml:id="echoid-s22448" xml:space="preserve">illud dicit, verunque æquinoctium,
                <lb/>
              ſolſtitium item, & </s>
              <s xml:id="echoid-s22449" xml:space="preserve">brumam ſieri in octauis partibus ſignorum, quod quomodo intelligendum ſit, ut mihi uidetur
                <lb/>
              exponam. </s>
              <s xml:id="echoid-s22450" xml:space="preserve">Veteres ut obliquum circulum dignoſcerent, conſider auere duo diuerſa temporis interualla, quibus
                <lb/>
              dies par nocti cerneretur, maximasq́; </s>
              <s xml:id="echoid-s22451" xml:space="preserve">dierum diſſimilitudines geminas perpenderunt, hyemis ſcilicet, & </s>
              <s xml:id="echoid-s22452" xml:space="preserve">æſta
                <lb/>
              tis, quando Sol circulos regreſſionis iniret, atque id non ſine iudicij, & </s>
              <s xml:id="echoid-s22453" xml:space="preserve">ingenij, & </s>
              <s xml:id="echoid-s22454" xml:space="preserve">ingeij acumine fecerunt, existiman-
                <lb/>
                <note position="left" xlink:label="note-514.01.328-01" xlink:href="note-514.01.328-01a" xml:space="preserve">10</note>
              tes inter hos terminos Solem eundem itineris tenorem, modumq́; </s>
              <s xml:id="echoid-s22455" xml:space="preserve">ſeruare, & </s>
              <s xml:id="echoid-s22456" xml:space="preserve">ita illis uiſum est ea ſpatia ſub
                <lb/>
              uno orbis ambitu contineri debere, vnde quatuor circuli puncta tanquam initia obliqui orbis habuere, ita e-
                <lb/>
              nim ſigniferum prius uocatum fuiſſe credimus. </s>
              <s xml:id="echoid-s22457" xml:space="preserve">Ex hoc alia argumenta ſumentes, eum circulum in partes æ-
                <lb/>
              quas duodenas diuiſerunt, quæ perpetuo eſſent immutabiles. </s>
              <s xml:id="echoid-s22458" xml:space="preserve">Inde ut ſibi & </s>
              <s xml:id="echoid-s22459" xml:space="preserve">poſteris eam inuentionem memora
                <lb/>
              bilem facerent, circulum illum quibuſdam ſyderibus, quæ in ea parte cernuntur, deformarunt, non tamen ut
                <lb/>
              imago quæque duodecimam partem æqualem occuparet omnino, ſed quatenus prœdicto orbi uicinæ eſſent, atq;
                <lb/>
              </s>
              <s xml:id="echoid-s22460" xml:space="preserve">ita Arietem, Taurum, & </s>
              <s xml:id="echoid-s22461" xml:space="preserve">reliqua nominarunt, unde obliquus ille circulus, ſigniferi nomen obtinuit. </s>
              <s xml:id="echoid-s22462" xml:space="preserve">Quod uero
                <lb/>
              imagines ill æ non penitus duodecimam partem ſigniferi occu parent, docet V itr. </s>
              <s xml:id="echoid-s22463" xml:space="preserve">cum dicit. </s>
              <s xml:id="echoid-s22464" xml:space="preserve">Caput & </s>
              <s xml:id="echoid-s22465" xml:space="preserve">pectus
                <lb/>
              Leonis Cancro tribui, & </s>
              <s xml:id="echoid-s22466" xml:space="preserve">ſinum ueſtis V irgine æ partes Libræ priores occupare. </s>
              <s xml:id="echoid-s22467" xml:space="preserve">& </s>
              <s xml:id="echoid-s22468" xml:space="preserve">femina Sagittarij pertinere
                <lb/>
              ad Capricornum, & </s>
              <s xml:id="echoid-s22469" xml:space="preserve">ſimilia. </s>
              <s xml:id="echoid-s22470" xml:space="preserve">Qnare Vitr. </s>
              <s xml:id="echoid-s22471" xml:space="preserve">exponendo, dicam primas Arietis partes, quæ uſque ad cornua pro-
                <lb/>
                <note position="left" xlink:label="note-514.01.328-02" xlink:href="note-514.01.328-02a" xml:space="preserve">20</note>
              tenduntur, gradus occupare ſenos, & </s>
              <s xml:id="echoid-s22472" xml:space="preserve">dimidium, & </s>
              <s xml:id="echoid-s22473" xml:space="preserve">poſtrem as uſque ad Arietis caudam gradus habere octo
                <lb/>
              & </s>
              <s xml:id="echoid-s22474" xml:space="preserve">uiginti, ita quod a primis partibus ad postremas uiginti cum dimidio ſumuntur, quarum pars octaua est
                <lb/>
              ſpatium duarum partium cum dimidio, quibus Aries æqualitatem dierum ſuperat, idem de alijs ſignis in-
                <lb/>
              telligitur. </s>
              <s xml:id="echoid-s22475" xml:space="preserve">ſed hoc quanquam ad amuſſim non exigatur, ob proximitatem tamen ſatis eſſe poteſt, & </s>
              <s xml:id="echoid-s22476" xml:space="preserve">quæſtioni
                <lb/>
              reſpondere. </s>
              <s xml:id="echoid-s22477" xml:space="preserve">Veruntamen Columella libro nono, licet Hypparcbi ſententiam uideatur approbare, qui dixit,
                <lb/>
              æquinoctia, & </s>
              <s xml:id="echoid-s22478" xml:space="preserve">ſolſtitia in primis ſignorum partibus fieri, ſequitur tamen Eudoxum, & </s>
              <s xml:id="echoid-s22479" xml:space="preserve">Myronem ueteres aſtro
                <lb/>
              nomos, qui in octauis partibus ea fieri dixere. </s>
              <s xml:id="echoid-s22480" xml:space="preserve">Admiſerunt hæc ueteres illi, conſuetudinem ſequuti: </s>
              <s xml:id="echoid-s22481" xml:space="preserve">dies enim
                <lb/>
              illi ſacrificijs certis dedicati cum eſſent, a vulgaribus nominati, & </s>
              <s xml:id="echoid-s22482" xml:space="preserve">obſeruati fuerunt, ita ut in octauis ſigno-
                <lb/>
              rum partibus ea temporum diſcrimina fieri putarentur, quare uereor ne nimis ſubtiliter Vitruuium aliquid
                <lb/>
              uulgo concedentem, interpretati ex Zieglero fuerimus. </s>
              <s xml:id="echoid-s22483" xml:space="preserve">Verba enim Columellæ ſunt bæc lib. </s>
              <s xml:id="echoid-s22484" xml:space="preserve">9. </s>
              <s xml:id="echoid-s22485" xml:space="preserve">cap. </s>
              <s xml:id="echoid-s22486" xml:space="preserve">14.
                <lb/>
              </s>
              <s xml:id="echoid-s22487" xml:space="preserve">
                <note position="left" xlink:label="note-514.01.328-03" xlink:href="note-514.01.328-03a" xml:space="preserve">30</note>
              Nec me fallit Hypparchi ratio, quæ docet ſolſtitia, & </s>
              <s xml:id="echoid-s22488" xml:space="preserve">æquinoctia non octauis, ſed primis partibus ſignorum
                <lb/>
              confici. </s>
              <s xml:id="echoid-s22489" xml:space="preserve">Verum in hac ruris diſciplina ſequor nunc Eudoxi, & </s>
              <s xml:id="echoid-s22490" xml:space="preserve">Metonis antiquorum faſtos aſtrologorum, qui
                <lb/>
              ſunt aptati publicis ſacrificijs, quia & </s>
              <s xml:id="echoid-s22491" xml:space="preserve">notior est ista uetus agricolis concepta opinio. </s>
              <s xml:id="echoid-s22492" xml:space="preserve">Nec tamen Hyppar-
                <lb/>
              chi ſubtilitas pinguioribus, ut aiunt ruſticorum literis neceſſaria eſt. </s>
              <s xml:id="echoid-s22493" xml:space="preserve">Quaſi dicat Colummella eos qui æqui-
                <lb/>
              noctia, & </s>
              <s xml:id="echoid-s22494" xml:space="preserve">ſolſtitia in primis ſignorum partibus confici dicunt, ut Hypparchus, rem ſubtiliter conſiderare, ſe
                <lb/>
              autem ſequi rusticam craſſitudinem, cum rusticis præceptaruſtica tradat. </s>
              <s xml:id="echoid-s22495" xml:space="preserve">Obſeruandum quoque in Vitru.
                <lb/>
              </s>
              <s xml:id="echoid-s22496" xml:space="preserve">quali conueniant reſponſu dies anni, cum ſol ſignum aliud, atque aliud init, nam Leo Geminis, Virgo Tauro,
                <lb/>
              Aries Libræ conuenit, atque alia buiuſmodi, quæ a Vitr. </s>
              <s xml:id="echoid-s22497" xml:space="preserve">notantur. </s>
              <s xml:id="echoid-s22498" xml:space="preserve">quoniam eadem ratio eſt acceſſus, & </s>
              <s xml:id="echoid-s22499" xml:space="preserve">re-
                <lb/>
              ceſſus. </s>
              <s xml:id="echoid-s22500" xml:space="preserve">Concludit autem inquiens, quemadmodum augentur, & </s>
              <s xml:id="echoid-s22501" xml:space="preserve">minuuntur dierum ſpatia, ita creſcere, & </s>
              <s xml:id="echoid-s22502" xml:space="preserve">
                <lb/>
              decreſcere horarum interualla, cum eadem ratio ſit partis ad partem, quæ totius ad totum. </s>
              <s xml:id="echoid-s22503" xml:space="preserve">Sed ut aperta re-
                <lb/>
              rum demonſtratio tradatur, dicam: </s>
              <s xml:id="echoid-s22504" xml:space="preserve">quocunque loco fueris, ſiue longi, ſeu breues ſint diei, & </s>
              <s xml:id="echoid-s22505" xml:space="preserve">noctis termini,
                <lb/>
                <note position="left" xlink:label="note-514.01.328-04" xlink:href="note-514.01.328-04a" xml:space="preserve">40</note>
              non ſolum ſemper dimidium ſigniferi ſupra borizontem eſſe, ſed etiam interdiu dimidium oriri, & </s>
              <s xml:id="echoid-s22506" xml:space="preserve">noctu etiam
                <lb/>
              aliud dimidium conſurgere. </s>
              <s xml:id="echoid-s22507" xml:space="preserve">Die conſurgit dimidium illud, quo apuncto a puncto, ſignoq́; </s>
              <s xml:id="echoid-s22508" xml:space="preserve">in quo tunc tempo-
                <lb/>
              ris eſt Sol, incipiens iuxta ſignorum or dinem progreditur, & </s>
              <s xml:id="echoid-s22509" xml:space="preserve">emergit. </s>
              <s xml:id="echoid-s22510" xml:space="preserve">& </s>
              <s xml:id="echoid-s22511" xml:space="preserve">oppoſita ſub terris puncta occul-
                <lb/>
              tantur, & </s>
              <s xml:id="echoid-s22512" xml:space="preserve">ex aduerſo nocte illa pars dimidia conſurgit, & </s>
              <s xml:id="echoid-s22513" xml:space="preserve">iſta deprimitur: </s>
              <s xml:id="echoid-s22514" xml:space="preserve">& </s>
              <s xml:id="echoid-s22515" xml:space="preserve">hoc rationi conſentit, quoniam
                <lb/>
              cum ſignifer, & </s>
              <s xml:id="echoid-s22516" xml:space="preserve">horizon in maioribus ſphær æ circulis habeantur, neceſſe est utrosq; </s>
              <s xml:id="echoid-s22517" xml:space="preserve">medios æquabiliter ſe ſe
                <lb/>
              utrinque ſecare. </s>
              <s xml:id="echoid-s22518" xml:space="preserve">ideo tam die, quàm nocte in omni borizonte ſex ſigna oriuntur, & </s>
              <s xml:id="echoid-s22519" xml:space="preserve">ſex cadunt. </s>
              <s xml:id="echoid-s22520" xml:space="preserve">ideo in obliquo
                <lb/>
              horizonte bis, qui citra æquinoctialem orbem babitant, in die ipſo æquinoctij uerni conſurgit dimidium illud
                <lb/>
              ſigniferi, quod ad cardinẽ manifeſtum declinat, quod ſena continet ſigna ab Ariete ad Libram, & </s>
              <s xml:id="echoid-s22521" xml:space="preserve">ex aduerſo
                <lb/>
              æquinoctij autumnalis die conſurgit dimidium aliud, & </s>
              <s xml:id="echoid-s22522" xml:space="preserve">aliud iam dictum deprimitur ſub terris. </s>
              <s xml:id="echoid-s22523" xml:space="preserve">Verum dimi-
                <lb/>
              dium ſigniferi, quod cum Solis ſigno æstiuo ſolſtitio in cipit, longiſſimo ſpatio aſcendit, & </s>
              <s xml:id="echoid-s22524" xml:space="preserve">breuißimo deſcen-
                <lb/>
                <note position="left" xlink:label="note-514.01.328-05" xlink:href="note-514.01.328-05a" xml:space="preserve">50</note>
              dit, & </s>
              <s xml:id="echoid-s22525" xml:space="preserve">in puncto brumæ dimidium, quo minori ſpatio conſurgit, longiori demergitur, nam tantum æstiua nocte
                <lb/>
              quantum brumali die breuiſſimo interuallo ſupra fertur. </s>
              <s xml:id="echoid-s22526" xml:space="preserve">& </s>
              <s xml:id="echoid-s22527" xml:space="preserve">tam die æstiua, quàm nocte brumali longiſſimum
                <lb/>
              eſt, unde bis qui ſub cardinum orbibus babitant, dimidium ſigniferi, quod cum ſolſtitij puncto exoritur, ut 24.
                <lb/>
              </s>
              <s xml:id="echoid-s22528" xml:space="preserve">horarum ſpatio conſurgit, ita momento demergitur, & </s>
              <s xml:id="echoid-s22529" xml:space="preserve">aduerſa parte dimidium aliud, quemadmodum conſur-
                <lb/>
              git, ita 24. </s>
              <s xml:id="echoid-s22530" xml:space="preserve">horarum ſpatio deprimitur. </s>
              <s xml:id="echoid-s22531" xml:space="preserve">Vnde quantum ſigniferi dimidium initium proxime magis ad altum
                <lb/>
              ſolſtitium ſumit, tanto prolixiori ſpatio ſcandit, & </s>
              <s xml:id="echoid-s22532" xml:space="preserve">tanto minori deſcendit, atque ita duo dimidia, quæ cum ſi-
                <lb/>
              gnis a ſolstitij pariter diſtantibus oriuntur, æquis interuallis oriuntur, & </s>
              <s xml:id="echoid-s22533" xml:space="preserve">occidunt. </s>
              <s xml:id="echoid-s22534" xml:space="preserve">nam ſurgunt, decumbuntq́; </s>
              <s xml:id="echoid-s22535" xml:space="preserve">
                <lb/>
              noctibus, & </s>
              <s xml:id="echoid-s22536" xml:space="preserve">diebus æqualibus. </s>
              <s xml:id="echoid-s22537" xml:space="preserve">Sed quæ cum ſignis ab æquinoctijs æquè diſtantibus incipiunt, quanto tempo-
                <lb/>
              re alterum conſurgit, tanto alter um cadit. </s>
              <s xml:id="echoid-s22538" xml:space="preserve">At que hoc eſt, quod Vitr. </s>
              <s xml:id="echoid-s22539" xml:space="preserve">dicit. </s>
              <s xml:id="echoid-s22540" xml:space="preserve">redire Solem in Geminorum æ-
                <lb/>
                <note position="left" xlink:label="note-514.01.328-06" xlink:href="note-514.01.328-06a" xml:space="preserve">60</note>
              qualem curſum, & </s>
              <s xml:id="echoid-s22541" xml:space="preserve">æquare eam, quam habet Taurus curſum rationem, & </s>
              <s xml:id="echoid-s22542" xml:space="preserve">eum curſum æquare eam </s>
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