Vitruvius, De architectura libri decem, 1567

Table of figures

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[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
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[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
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[133] Porfioni del cerchio che fannoſe s̃teſſe torno dlaTramòntanaTram ontanaSlmiſifudineTramonſangCarro che uoſge infomoalla Framonlana
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[134] a b c d f
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[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
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[136] m q 0 s k h c b s n L I p q s
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[137] Il polo.cqiunot.orizonte c e b a f
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[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
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[139] Analemmatis figura.MERIDIAN: S. M. MLSLACITREVM.M.MERIDIAN: .S.OMVERTICAV.M..S.. O. M.ORIZON:W. A.STAB:
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[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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[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
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[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 &
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[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
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[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
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[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
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[146] 9 3 4 2 8 10 11 12 1 5 7 6 6 G
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[147] 8 9 10 7 6 5 11 1 8 1 11 F
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[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
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[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
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[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
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[151] 17 18 19 20 21 22 16 23 15 14 13 12 11 10 11 12 21 22 10 9 23 M
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[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
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[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
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[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
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[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
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[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
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[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
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[Figure 158]
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[Figure 159]
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[Figure 160]
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            <p style="it">
              <s xml:id="echoid-s23137" xml:space="preserve">
                <pb o="305" file="514.01.337" n="337" rhead="NONVS."/>
              gnomonis radios iaciente, umbra rectam deſeribet parallelam, communi ſectioni æquinoctialis, & </s>
              <s xml:id="echoid-s23138" xml:space="preserve">horarij pla-
                <lb/>
              ni. </s>
              <s xml:id="echoid-s23139" xml:space="preserve">Sed quoniam diurno motu Sol quotidie circulum peragit æquinoctiali æquabilem,ac parallelum, & </s>
              <s xml:id="echoid-s23140" xml:space="preserve">obli-
                <lb/>
              que means continenter ab æquinoctiali abſcedit, ideo cum non eſt in æquinoctiali accidere potes̃t, ut planum in
                <lb/>
              quoda Gnomone umbra proijcitur, ſecetur ab eo circulo, quem Solfacit mundum ambiendo, atque etiam fie-
                <lb/>
              ripoteſt, ut non ſecet, pro ut finitorum ratio postulat. </s>
              <s xml:id="echoid-s23141" xml:space="preserve">Fingamus Solem quotidie ſcandendo circumagi, & </s>
              <s xml:id="echoid-s23142" xml:space="preserve">ue-
                <lb/>
              stigia ſui motus euidentia in cœlo relinquere,ut puta orbem igneum, aut alterius apparentis imaginis: </s>
              <s xml:id="echoid-s23143" xml:space="preserve">certe or-
                <lb/>
              bis ille, aut circinatio illa apparcns,uel integra ſupra planum erit, uei ab ſcindet planum illud. </s>
              <s xml:id="echoid-s23144" xml:space="preserve">Fingamus pla-
                <lb/>
              num ſecari ab ea circinatione, ita ut pars eius ſit ſupraterram, & </s>
              <s xml:id="echoid-s23145" xml:space="preserve">pars infra, tunc extremi gnomonis apicis
                <lb/>
              umbra, quo tempore Soleam circinationem ambiet, hyperbolem in plano deſcribet. </s>
              <s xml:id="echoid-s23146" xml:space="preserve">At ſiinteger ille circu-
                <lb/>
                <note position="left" xlink:label="note-514.01.337-01" xlink:href="note-514.01.337-01a" xml:space="preserve">10</note>
              lus ſupra finitorem extabit, aut continget planum horologij, aut non continget, ſi primum erit, deſcribetur
                <lb/>
              parabole in plano, ſi ſecundum, aut circinatio illa a plano æquabiliter diſtabit, aut altera parte ad planum
                <lb/>
              magis accedet, ſi æquabiliter ſe ad planum habuerit circulum, ſi non, ellipſim deſcribet umbra, bæc omnia
                <lb/>
              experiri poteris, ſi ſupra tabellam aliquam plano horologij paratam circulos poſueris ſecundum partes ex-
                <lb/>
              tantes ſinitori, & </s>
              <s xml:id="echoid-s23147" xml:space="preserve">a circinationis linea, in qua Sol statuetur, ferreus,aut ligneus axiculus ad apicem gnomo-
                <lb/>
              nis perforatum, mittas, ita ut altero extremo planum tangat. </s>
              <s xml:id="echoid-s23148" xml:space="preserve">Sanè axiculusille, qui radium Solis refert, in
                <lb/>
              plano lineas illas deſcribet, quas diximus: </s>
              <s xml:id="echoid-s23149" xml:space="preserve">hyperbolem ſi circulus planum ſecabit, parabolem ſi continget,
                <lb/>
              circulum ſi æque ellipſim, ſi non æque distabit a plano. </s>
              <s xml:id="echoid-s23150" xml:space="preserve">hæc unico exemplo in ſequenti diagrammate intelliges.
                <lb/>
              </s>
              <s xml:id="echoid-s23151" xml:space="preserve">Eſto. </s>
              <s xml:id="echoid-s23152" xml:space="preserve">a. </s>
              <s xml:id="echoid-s23153" xml:space="preserve">gnomonis apex perforatns b c d. </s>
              <s xml:id="echoid-s23154" xml:space="preserve">portio alicuius paralleli ſupra terram, ( circulus enim planum
                <lb/>
              ſecat.) </s>
              <s xml:id="echoid-s23155" xml:space="preserve">Eſto Sol in e. </s>
              <s xml:id="echoid-s23156" xml:space="preserve">ferreus axiculus ab e, per foramen gnomonis ad planum uſque ad f, mittatur aſcen-
                <lb/>
                <note position="left" xlink:label="note-514.01.337-02" xlink:href="note-514.01.337-02a" xml:space="preserve">20</note>
              dat, deinde Sol ad h. </s>
              <s xml:id="echoid-s23157" xml:space="preserve">& </s>
              <s xml:id="echoid-s23158" xml:space="preserve">axiculus in h, ponatur, tranſeatque per for amen gnomonis uſque ad i. </s>
              <s xml:id="echoid-s23159" xml:space="preserve">deinde in
                <lb/>
              k, poſito Sole, & </s>
              <s xml:id="echoid-s23160" xml:space="preserve">axiculo idem faciamus, quod ſupra per foramen axiculo ad 1. </s>
              <s xml:id="echoid-s23161" xml:space="preserve">tranſeunte, atque ita ab
                <lb/>
              m. </s>
              <s xml:id="echoid-s23162" xml:space="preserve">o. </s>
              <s xml:id="echoid-s23163" xml:space="preserve">q. </s>
              <s xml:id="echoid-s23164" xml:space="preserve">p. </s>
              <s xml:id="echoid-s23165" xml:space="preserve">d. </s>
              <s xml:id="echoid-s23166" xml:space="preserve">adreliqua puncta, quæ una linea connectantur in plano. </s>
              <s xml:id="echoid-s23167" xml:space="preserve">tunc fiet hyperbole, reliqua tuo
                <lb/>
              ingenio experiri poteris.</s>
              <s xml:id="echoid-s23168" xml:space="preserve">#Cæterum his tanquam fundamentis optime iactis, ſi bene perpendantur com-
                <lb/>
                <figure xlink:label="fig-514.01.337-01" xlink:href="fig-514.01.337-01a" number="136">
                  <variables xml:id="echoid-variables93" xml:space="preserve">m q 0 s k h c b s n L I p q s</variables>
                </figure>
                <note position="left" xlink:label="note-514.01.337-03" xlink:href="note-514.01.337-03a" xml:space="preserve">30</note>
              mode ad analemmatis deſcriptionem accedere poterimus.
                <lb/>
              </s>
              <s xml:id="echoid-s23169" xml:space="preserve">Quon: </s>
              <s xml:id="echoid-s23170" xml:space="preserve">am uero in analemmate quidam ſunt circuli, qui com-
                <lb/>
              munes in omnibus aſſumuntur, quidam ſeorſum pro cuiuſque
                <lb/>
              horologij deſcriptione ſeparatim deſcribuntur, ideo, ut eam fa-
                <lb/>
              cilitatem, quam polliciti ſumus, præſtare quoque ualeamus,
                <lb/>
              etiam rudibus, ita animo nostro fingemus, ut quiſque ſe pu-
                <lb/>
              tet ſtare in media, & </s>
              <s xml:id="echoid-s23171" xml:space="preserve">ampliſſima planitie oculis ad meridiem
                <lb/>
              directis, e xpanſis in crucem manibus, certe ſiniſtra orientem,
                <lb/>
              dextra occidentem, tergo ſepientrionem, ore meridiem indica-
                <lb/>
              bit. </s>
              <s xml:id="echoid-s23172" xml:space="preserve">Fingamus etiam planitiem illam, in qua ſtat, uſque ad
                <lb/>
              extremos orbis fines pertin gere, ita ut in duas æquas partes
                <lb/>
              orbem ſecet, pars altera infra planitiem, altera ſupra erit,
                <lb/>
              planum igitur ill ud horizontis, ac finitoris nomine donabimus,
                <lb/>
              eſt enim hem iſphæriorum diſcriminator, cuius munus eſt infe-
                <lb/>
              ram partem a ſupera ſeparare. </s>
              <s xml:id="echoid-s23173" xml:space="preserve">Fingamus etiam planum aliud
                <lb/>
              a ſiniſtra in orientis puncto per uerticem ad labrum occiden-
                <lb/>
                <note position="left" xlink:label="note-514.01.337-04" xlink:href="note-514.01.337-04a" xml:space="preserve">40</note>
              tis peruenire, atque inde ſub terra per medium ad orientem pertinere: </s>
              <s xml:id="echoid-s23174" xml:space="preserve">planum hoc uerticis planum uocemus:
                <lb/>
              </s>
              <s xml:id="echoid-s23175" xml:space="preserve">cuius proprietas erit ſeparare partem, quæ ante nos erit, a parte posteriori, ideſt hemiſphærium meridia-
                <lb/>
              num a reliquo ſeptentrionali. </s>
              <s xml:id="echoid-s23176" xml:space="preserve">Fingamus demum planum aliud a labro finitoris medio inter orientem & </s>
              <s xml:id="echoid-s23177" xml:space="preserve">oc-
                <lb/>
              cidentem ad uerticem post tergus noſtrum infra terram ad eundem locum unde ortum fuit peruenire. </s>
              <s xml:id="echoid-s23178" xml:space="preserve">Pla-
                <lb/>
              num huiuſmodi meridianum uocamus, cuius officium eſt orientalem plagam ab occidua ſeparare. </s>
              <s xml:id="echoid-s23179" xml:space="preserve">Plana
                <lb/>
              hæc orbicularia finitor, uerticale, ac meridianum ſe ſe adrectos angulos ſecabunt. </s>
              <s xml:id="echoid-s23180" xml:space="preserve">Finitor cum meridiano ſe-
                <lb/>
              catur m punctis medijs inter orientem, & </s>
              <s xml:id="echoid-s23181" xml:space="preserve">occidentem in meridianæ lineæ extremis, quorum alterum ante,
                <lb/>
              alterum ponè nos eſt. </s>
              <s xml:id="echoid-s23182" xml:space="preserve">Finitor, & </s>
              <s xml:id="echoid-s23183" xml:space="preserve">uerticale in orientis, & </s>
              <s xml:id="echoid-s23184" xml:space="preserve">occidentis partibus ſe ſecant. </s>
              <s xml:id="echoid-s23185" xml:space="preserve">quarum altera a
                <lb/>
              ſinistris eſt, altera a dextris: </s>
              <s xml:id="echoid-s23186" xml:space="preserve">verticale & </s>
              <s xml:id="echoid-s23187" xml:space="preserve">meridianus ſe in uertice ſupra nos, & </s>
              <s xml:id="echoid-s23188" xml:space="preserve">infra in altero hemiſphærio
                <lb/>
              medio ſecant. </s>
              <s xml:id="echoid-s23189" xml:space="preserve">plana huiuſmodi propterea poſita ſunt, ut certi fines ſtatuantur,a quibus Solis effectus in mun-
                <lb/>
                <note position="left" xlink:label="note-514.01.337-05" xlink:href="note-514.01.337-05a" xml:space="preserve">50</note>
              do determinari poſſint. </s>
              <s xml:id="echoid-s23190" xml:space="preserve">Similia his fingunt ſibi nautæ, ut regiones uentorum, & </s>
              <s xml:id="echoid-s23191" xml:space="preserve">itinerum directiones, & </s>
              <s xml:id="echoid-s23192" xml:space="preserve">ho-
                <lb/>
              rarum diſtinctione s intelligant. </s>
              <s xml:id="echoid-s23193" xml:space="preserve">Cum ergo huiuſmodi planorum proprietates, & </s>
              <s xml:id="echoid-s23194" xml:space="preserve">fines perceperimus iam illa
                <lb/>
              neceſſaria, & </s>
              <s xml:id="echoid-s23195" xml:space="preserve">communia in analemmatis deſcriptione cognoſcemus. </s>
              <s xml:id="echoid-s23196" xml:space="preserve">Illud præterea anvmaduertendum est,
                <lb/>
              quod quemadmodum tria illa plana finitor,uertex, meridianus ſe ſe ad angulos rectos diſpeſcunt, ita eorum
                <lb/>
              diametros in mundi centro ſe mutuo ſecant. </s>
              <s xml:id="echoid-s23197" xml:space="preserve">hic duo admiratione digna ſunt conſideranda, alterum eſt, plu-
                <lb/>
              res tribus lineis rectis non poſſe ad angulos rectos in unum concurrere, ſeq́; </s>
              <s xml:id="echoid-s23198" xml:space="preserve">mutuo ſecare, inde eſt quod non
                <lb/>
              plures tribus dimenſionibus, eſſè Ptolomæus ostenderit, & </s>
              <s xml:id="echoid-s23199" xml:space="preserve">propterea tria illa plana ad analemmatis conſtru-
                <lb/>
              ctionem ſumpſerit. </s>
              <s xml:id="echoid-s23200" xml:space="preserve">Alterum est, quod diuina prouidentia eò loci poſitus est Sol, ut commodißime inſtrumen-
                <lb/>
              tis omnibus utamur, tanquam ſi in orbis centro eſſemus, hinc apices gnomonum in horologijs mundi cen-
                <lb/>
              trum referre ſolent. </s>
              <s xml:id="echoid-s23201" xml:space="preserve">ſed ad rem noſtram redeamus. </s>
              <s xml:id="echoid-s23202" xml:space="preserve">Ex his diametris ergo, quæ ſe mutuo ſecant, ſectio illa,
                <lb/>
              quam finitor cum meridiano facit, ſectio meridiana uocatur: </s>
              <s xml:id="echoid-s23203" xml:space="preserve">quam uero meridianus cum uerticali facit gno-
                <lb/>
                <note position="left" xlink:label="note-514.01.337-06" xlink:href="note-514.01.337-06a" xml:space="preserve">60</note>
              </s>
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