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
[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
[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
[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 &
[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
[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
[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
[146] 9 3 4 2 8 10 11 12 1 5 7 6 6 G
[147] 8 9 10 7 6 5 11 1 8 1 11 F
[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
[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
[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
[151] 17 18 19 20 21 22 16 23 15 14 13 12 11 10 11 12 21 22 10 9 23 M
[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
[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
[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
[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
[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
[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
[Figure 158]
[Figure 159]
[Figure 160]
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            <p style="it">
              <s xml:id="echoid-s23472" xml:space="preserve">
                <pb o="309" file="514.01.341" n="341" rhead="ONVS."/>
              mur ſane his temporibus tot quadrantum, radiorum, anulorum, regularum, cylindrorum, torquetorum, hemicy-
                <lb/>
              clioru, planiſpbæriorum, & </s>
              <s xml:id="echoid-s23473" xml:space="preserve">cæterorum instrumentorum multitudine, quæ olim a ueteribus accurate inuenta & </s>
              <s xml:id="echoid-s23474" xml:space="preserve">
                <lb/>
              deſcripta ſunt. </s>
              <s xml:id="echoid-s23475" xml:space="preserve">Habendæ nibilominus gratiæ ſunt ijs, qui faciliorem uſum, & </s>
              <s xml:id="echoid-s23476" xml:space="preserve">commodiorem tractationem in-
                <lb/>
              uenerunt, uel quæ obſcura erant, & </s>
              <s xml:id="echoid-s23477" xml:space="preserve">in tenebris deliteſcebant, ſtudio, & </s>
              <s xml:id="echoid-s23478" xml:space="preserve">diligentia ad communem utilitatem
                <lb/>
              protulere, & </s>
              <s xml:id="echoid-s23479" xml:space="preserve">præclara ueterum inuenta ab iniurijs ſæculorum uindicarunt. </s>
              <s xml:id="echoid-s23480" xml:space="preserve">Sed ad rem. </s>
              <s xml:id="echoid-s23481" xml:space="preserve">Inſistam ego quoque
                <lb/>
              in ijs, quæ a Ptolomæo, & </s>
              <s xml:id="echoid-s23482" xml:space="preserve">Commandino iacta ſunt fundamenta, & </s>
              <s xml:id="echoid-s23483" xml:space="preserve">analemmatis uſum, quantum potero fa -
                <lb/>
              sile explicabo, Matbematic as illis demonſtrationes relinquens. </s>
              <s xml:id="echoid-s23484" xml:space="preserve">Nulli dubium eſt, Solem temporibus atque
                <lb/>
              boris alijs, alias altitudines, & </s>
              <s xml:id="echoid-s23485" xml:space="preserve">ſitus alios occupare. </s>
              <s xml:id="echoid-s23486" xml:space="preserve">Cernimus enim æstate orientem, & </s>
              <s xml:id="echoid-s23487" xml:space="preserve">cadentem Solem,
                <lb/>
              duarum & </s>
              <s xml:id="echoid-s23488" xml:space="preserve">amplius borarum ſpatio ab oriente, & </s>
              <s xml:id="echoid-s23489" xml:space="preserve">occidente ſeptentrionem uerſus conſurgere. </s>
              <s xml:id="echoid-s23490" xml:space="preserve">cernimus quo-
                <lb/>
                <note position="left" xlink:label="note-514.01.341-01" xlink:href="note-514.01.341-01a" xml:space="preserve">10</note>
              que Solem interdum inter orientem', & </s>
              <s xml:id="echoid-s23491" xml:space="preserve">meridiem, & </s>
              <s xml:id="echoid-s23492" xml:space="preserve">in meridie, ac demum ad occidentem a meridie incli-
                <lb/>
              nari, & </s>
              <s xml:id="echoid-s23493" xml:space="preserve">ijs temporibus modo altiores, modo depreſſiores cœli partes tenere, quæ omnia noſſe accurate opor-
                <lb/>
              tet, ſieius effectus in mundo ſcire uelimus, unde analemmatum deſcriptiones comparanantur: </s>
              <s xml:id="echoid-s23494" xml:space="preserve">noſſe autem ex-
                <lb/>
              quiſite illa non poterimus, niſi lineas multas, & </s>
              <s xml:id="echoid-s23495" xml:space="preserve">circulos angulosq́; </s>
              <s xml:id="echoid-s23496" xml:space="preserve">fingamus, quibus quaſi cancellis pictorũ
                <lb/>
              certos Solis ſitus inueniamus. </s>
              <s xml:id="echoid-s23497" xml:space="preserve">Quoniam uero ut libet in diuerſis planis, hoc eſt finitori, uerticali, & </s>
              <s xml:id="echoid-s23498" xml:space="preserve">meridia-
                <lb/>
              no ( de quibus ſuperius dixi) æquidistantibus conficere boraria poſſumus, ideo ſcire neceſſe est; </s>
              <s xml:id="echoid-s23499" xml:space="preserve">qui circuli,
                <lb/>
              quæ lineæ, qui anguli, quibus planis inſeruiant, ut illis poſitis tanquam terminis, Solis radios, quorum effectus
                <lb/>
              in mundo conſpicitur per gnomonem, & </s>
              <s xml:id="echoid-s23500" xml:space="preserve">umbras uenari poſſimus. </s>
              <s xml:id="echoid-s23501" xml:space="preserve">Formauimus antea tria plana finitorem,
                <lb/>
              uerticale, & </s>
              <s xml:id="echoid-s23502" xml:space="preserve">meridianum; </s>
              <s xml:id="echoid-s23503" xml:space="preserve">diametros quoque illvrum poſuimus, & </s>
              <s xml:id="echoid-s23504" xml:space="preserve">quid unumquodque muneris habeat, ex-
                <lb/>
              poſuimus; </s>
              <s xml:id="echoid-s23505" xml:space="preserve">nunc dicimus finxiſſe nos ill.</s>
              <s xml:id="echoid-s23506" xml:space="preserve">i imrnota, & </s>
              <s xml:id="echoid-s23507" xml:space="preserve">permanentia, & </s>
              <s xml:id="echoid-s23508" xml:space="preserve">ad ea quoque tria mobilia addenda eſſe,
                <lb/>
                <note position="left" xlink:label="note-514.01.341-02" xlink:href="note-514.01.341-02a" xml:space="preserve">20</note>
              ita ut finitor immotus ſit, & </s>
              <s xml:id="echoid-s23509" xml:space="preserve">finitor mobilis, itemq; </s>
              <s xml:id="echoid-s23510" xml:space="preserve">uerticalis firmus, & </s>
              <s xml:id="echoid-s23511" xml:space="preserve">uerticalis motus: </s>
              <s xml:id="echoid-s23512" xml:space="preserve">eadem ratio de me-
                <lb/>
              ridiano. </s>
              <s xml:id="echoid-s23513" xml:space="preserve">& </s>
              <s xml:id="echoid-s23514" xml:space="preserve">moueatur quodlibet mobile ſupra diametrum ſui immoti. </s>
              <s xml:id="echoid-s23515" xml:space="preserve">Iam notum eſt, quæ ſint diametri il-
                <lb/>
              lorum planorum, nam finitoris a labro orientis ad occidens terminatur. </s>
              <s xml:id="echoid-s23516" xml:space="preserve">uerticalis a ſummo uertice ad imas
                <lb/>
              ſub terræ partes. </s>
              <s xml:id="echoid-s23517" xml:space="preserve">meridiani linea meridiana diameter eſt, atque omnes ſe in centro mundi ad rectos angulos
                <lb/>
              ſecant. </s>
              <s xml:id="echoid-s23518" xml:space="preserve">Si ergo finit or moueri fingatur, & </s>
              <s xml:id="echoid-s23519" xml:space="preserve">circum ſuum diametrum, tanquam circa axem conuolui, certe pars
                <lb/>
              una ſupra finitorem immobilem extolletur, & </s>
              <s xml:id="echoid-s23520" xml:space="preserve">altera deprimetur. </s>
              <s xml:id="echoid-s23521" xml:space="preserve">Si uero uerticalis moue atur, pars altera
                <lb/>
              progredietur, altera regredietur firma diametro uerticalis permanente. </s>
              <s xml:id="echoid-s23522" xml:space="preserve">Si demum meridianus mouebitur,
                <lb/>
              pars altera ad finitorem proclinabit, altera ad finitorem conſurget. </s>
              <s xml:id="echoid-s23523" xml:space="preserve">His poſitis esto Sol ad notum gradibus
                <lb/>
              quadraginta a finitore altus, moueatur finitor, & </s>
              <s xml:id="echoid-s23524" xml:space="preserve">tantum extollatur ut centrum Solis medium ſecet, mouea-
                <lb/>
              tur item uerticalis, & </s>
              <s xml:id="echoid-s23525" xml:space="preserve">progrediatur ad notum uſque quo Solem eo loci contingat, quo finitor mobilis So-
                <lb/>
                <note position="left" xlink:label="note-514.01.341-03" xlink:href="note-514.01.341-03a" xml:space="preserve">30</note>
              lem ſecabat. </s>
              <s xml:id="echoid-s23526" xml:space="preserve">moueatur denique meridianus, & </s>
              <s xml:id="echoid-s23527" xml:space="preserve">tantum deprimatur, ut Solem quoque medium ſecet, ſanè tria
                <lb/>
              illa mobilia plana relictis immobilibus, ſe ſe mutuo ibi ſecabunt, ubi ſingula Solem ſecant, idest ubi Sol cum
                <lb/>
              fuerit, radios ſuos emittit in mundum. </s>
              <s xml:id="echoid-s23528" xml:space="preserve">Nunc uideamus eorum planorum effectus, & </s>
              <s xml:id="echoid-s23529" xml:space="preserve">quo fine eos antiqui fin-
                <lb/>
              xerunt. </s>
              <s xml:id="echoid-s23530" xml:space="preserve">ac primum in quibus conueniant explicemus. </s>
              <s xml:id="echoid-s23531" xml:space="preserve">Conueniunt ſanè in eo, quod cum ab immobili quodq;
                <lb/>
              </s>
              <s xml:id="echoid-s23532" xml:space="preserve">ſuo diſcedit, & </s>
              <s xml:id="echoid-s23533" xml:space="preserve">cum Sole mouetur, duos conficiunt angulos, alterum ex rectis lineis, alterum ex planis eo-
                <lb/>
              rum circulorum, idest mobilis, & </s>
              <s xml:id="echoid-s23534" xml:space="preserve">immobilis. </s>
              <s xml:id="echoid-s23535" xml:space="preserve">Quoniam uero angulos ex circinatione circuli metimur, ideo
                <lb/>
              alia circinationis pars ſubtendet angulos a lineis rectis, alia ab illis planis confectos. </s>
              <s xml:id="echoid-s23536" xml:space="preserve">vterque uero angulus
                <lb/>
              neceſſarius est, ut uerus Solis ſitus habeatur. </s>
              <s xml:id="echoid-s23537" xml:space="preserve">ideſt Solis altitudo, & </s>
              <s xml:id="echoid-s23538" xml:space="preserve">pars unde Sol ſuos radios demittit in
                <lb/>
              mundum. </s>
              <s xml:id="echoid-s23539" xml:space="preserve">Nunc ſeparatim unumquodque ſumamus. </s>
              <s xml:id="echoid-s23540" xml:space="preserve">Eſto Sol, ut prius, ad notum, moueatur uerticale
                <lb/>
              mobile ad Solem progrediens, & </s>
              <s xml:id="echoid-s23541" xml:space="preserve">Solem ſecet, ut ante: </s>
              <s xml:id="echoid-s23542" xml:space="preserve">dico duos ex hoc motu angulos effici, alterumq́; </s>
              <s xml:id="echoid-s23543" xml:space="preserve">rectis
                <lb/>
                <note position="left" xlink:label="note-514.01.341-04" xlink:href="note-514.01.341-04a" xml:space="preserve">40</note>
              lineis conſtare, alterum planis illis, ideſt uerticalis fixi, & </s>
              <s xml:id="echoid-s23544" xml:space="preserve">uerticalis mobilis. </s>
              <s xml:id="echoid-s23545" xml:space="preserve">Angulus rectis lineis constans,
                <lb/>
              fit Solis radio, & </s>
              <s xml:id="echoid-s23546" xml:space="preserve">diametro uerticalis, ideſt gnomonis, & </s>
              <s xml:id="echoid-s23547" xml:space="preserve">ambitus ſeu circinatio hunc angulum ſubtendens,
                <lb/>
              eſt pars ſiue arcus ille uerticalis mobilis, quod uertice nostro, & </s>
              <s xml:id="echoid-s23548" xml:space="preserve">puncto, in quo eſt Sol, continetur. </s>
              <s xml:id="echoid-s23549" xml:space="preserve">cum igi-
                <lb/>
              tur uertex a finitore tetrantem distet, ſequitur reliquum arcus uerticali, quod eſt a Sole ad finitorem, Solis
                <lb/>
              altitudinem ſupra finitorem oſtendere. </s>
              <s xml:id="echoid-s23550" xml:space="preserve">ideo ſi uerticalis arcus a uertice ad Solem erit partium quinquagin-
                <lb/>
              ta, Sola finitore tolletur gradus quadraginta, hoc eſt reliquum tetrantis a uertice ad finitorem. </s>
              <s xml:id="echoid-s23551" xml:space="preserve">huius ergo
                <lb/>
              anguli cognitio ad Solis altitudinem cognoſcendam ſpectat, unde umbrarum longitudo deprehenditur. </s>
              <s xml:id="echoid-s23552" xml:space="preserve">Sed
                <lb/>
              angulus a uertic ali mobili, & </s>
              <s xml:id="echoid-s23553" xml:space="preserve">firmo factus comprehenditur eo finitoris ambitu, qui inter cipitur inter punctum
                <lb/>
              orientis, & </s>
              <s xml:id="echoid-s23554" xml:space="preserve">punctum, quo uerticalis mobilis finitorem ſecat. </s>
              <s xml:id="echoid-s23555" xml:space="preserve">atque ambitus hic uel arcus, latitudo Solis, uel
                <lb/>
              arcus horizontalis nominatur. </s>
              <s xml:id="echoid-s23556" xml:space="preserve">huius anguli cognitio id nobis præſtat, ut parum ſciamus in quam radius Solis
                <lb/>
                <note position="left" xlink:label="note-514.01.341-05" xlink:href="note-514.01.341-05a" xml:space="preserve">50</note>
              uergat, unde partem in quam umbra protenditur agnoſcamus, ſemper enim umbra in oppoſitam radio par-
                <lb/>
              tem proijcitur. </s>
              <s xml:id="echoid-s23557" xml:space="preserve">nam ſi ab euro radius emittitur, umbra in caurum tendit. </s>
              <s xml:id="echoid-s23558" xml:space="preserve">ſi ab aquilone Sol, umbra in
                <lb/>
              africum uergit. </s>
              <s xml:id="echoid-s23559" xml:space="preserve">Ecce uſum horum angulorum, & </s>
              <s xml:id="echoid-s23560" xml:space="preserve">munus uerticalis mobilis. </s>
              <s xml:id="echoid-s23561" xml:space="preserve">nam ſi in plano finitori paral-
                <lb/>
              lelo uolueris horologium deſcribere, duos hos angulos neceſſarios cognoſces, quos uerticalis mobilis facit .
                <lb/>
              </s>
              <s xml:id="echoid-s23562" xml:space="preserve">Sed ad reliquos mutatur meridianus mobilis ad Solem in noto poſitum, cum eo peruenerit, ut Solem ſecet,
                <lb/>
              duos & </s>
              <s xml:id="echoid-s23563" xml:space="preserve">ipſe angulos reddet, alterum ex rectis lineis, alterum faciet ipſe cum meridiano immobili. </s>
              <s xml:id="echoid-s23564" xml:space="preserve">rectæ lineæ
                <lb/>
              quæ angulum conſtituunt erunt Solis radius, & </s>
              <s xml:id="echoid-s23565" xml:space="preserve">diametros meridiani; </s>
              <s xml:id="echoid-s23566" xml:space="preserve">ambitus hunc angulum ſubtendens, in-
                <lb/>
              tercipitur interpunctum extremum diametri meridiani, & </s>
              <s xml:id="echoid-s23567" xml:space="preserve">punctum in quo est Sol. </s>
              <s xml:id="echoid-s23568" xml:space="preserve">& </s>
              <s xml:id="echoid-s23569" xml:space="preserve">hinc Solis altitudo ter
                <lb/>
              minatur ſupra uerticalem circulum. </s>
              <s xml:id="echoid-s23570" xml:space="preserve">Angulus autem ex meridiano mobili, & </s>
              <s xml:id="echoid-s23571" xml:space="preserve">meridiano firmo factus, com-
                <lb/>
              prebenditur ambitu decl inationis meridiani mobilis a meridiano immo bili in circulo uerticali. </s>
              <s xml:id="echoid-s23572" xml:space="preserve">Huius anguli
                <lb/>
                <note position="left" xlink:label="note-514.01.341-06" xlink:href="note-514.01.341-06a" xml:space="preserve">60</note>
              cognitio eò ſpectat, ut partem & </s>
              <s xml:id="echoid-s23573" xml:space="preserve">ſitum Solis agnoſcamus, ut umbræ partem eliciamus in plano </s>
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