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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              <s xml:id="echoid-s23757" xml:space="preserve">
                <pb o="312" file="514.01.344" n="344" rhead="LIBER"/>
              lineas æque diſtantes diametro uerticalis, quarum extremum alterum circinationis lineam, alterum finitoris
                <lb/>
              diametrum tangat. </s>
              <s xml:id="echoid-s23758" xml:space="preserve">has numeris horarum ſignabis. </s>
              <s xml:id="echoid-s23759" xml:space="preserve">poſt hæc ex diagrammate O. </s>
              <s xml:id="echoid-s23760" xml:space="preserve">longitudines linearum ho-
                <lb/>
              rariarum a cir cumferentia ad diametrum f g. </s>
              <s xml:id="echoid-s23761" xml:space="preserve">transferes in ſequentem deſcriptionem. </s>
              <s xml:id="echoid-s23762" xml:space="preserve">Poſito circino in dia-
                <lb/>
              metro finitoris ſupra lineam horæ reſpondentis borariæ lineæ, quam ex f. </s>
              <s xml:id="echoid-s23763" xml:space="preserve">diagrammate O ſumpſiſti. </s>
              <s xml:id="echoid-s23764" xml:space="preserve">uerbi
                <lb/>
              gratia ſi ex diagrammate O. </s>
              <s xml:id="echoid-s23765" xml:space="preserve">ſumpſiſti longitudinem lineæ horæ undecimæ, eam in lineam horæ undecimæ trãſ.
                <lb/>
              </s>
              <s xml:id="echoid-s23766" xml:space="preserve">feras aſigno II. </s>
              <s xml:id="echoid-s23767" xml:space="preserve">in finitoris diametro collocato, & </s>
              <s xml:id="echoid-s23768" xml:space="preserve">eo termino in ea linea ſignato per centrum e. </s>
              <s xml:id="echoid-s23769" xml:space="preserve">& </s>
              <s xml:id="echoid-s23770" xml:space="preserve">
                <lb/>
              terminum illum lineam occultam duces ad circinationis lineam, ubi notabis II. </s>
              <s xml:id="echoid-s23771" xml:space="preserve">& </s>
              <s xml:id="echoid-s23772" xml:space="preserve">idem de reliquis hora-
                <lb/>
              rijs lineis faciendum eſt. </s>
              <s xml:id="echoid-s23773" xml:space="preserve">itaque habebis arcus horizontales, ſeu latitudines Solid, qui arcus intercipientur in-
                <lb/>
              ter finitorem immobilem, & </s>
              <s xml:id="echoid-s23774" xml:space="preserve">uerticalem mobilem, ut dixi, & </s>
              <s xml:id="echoid-s23775" xml:space="preserve">ſunt arcus ſubtendentes angulos ex duobus pla
                <lb/>
                <note position="left" xlink:label="note-514.01.344-01" xlink:href="note-514.01.344-01a" xml:space="preserve">10</note>
              nis factos. </s>
              <s xml:id="echoid-s23776" xml:space="preserve">quæ omnia ex diagrammate facile colliguntur. </s>
              <s xml:id="echoid-s23777" xml:space="preserve">Nunc ad horologium deſcribendum ueniamus .
                <lb/>
              </s>
              <s xml:id="echoid-s23778" xml:space="preserve">Circulum facies æqualem meridiano analemmatis, & </s>
              <s xml:id="echoid-s23779" xml:space="preserve">ſit ille a b c d. </s>
              <s xml:id="echoid-s23780" xml:space="preserve">ſit b c. </s>
              <s xml:id="echoid-s23781" xml:space="preserve">diameter pro meridiana
                <lb/>
              linea, ſit a d. </s>
              <s xml:id="echoid-s23782" xml:space="preserve">pro linea planitiæ, quæ occulte ducenda est ſit centrum e. </s>
              <s xml:id="echoid-s23783" xml:space="preserve">in quo linea planitiæ meridianam
                <lb/>
              ſecat, ubi gnomon eſſe fingitur. </s>
              <s xml:id="echoid-s23784" xml:space="preserve">Sume a diagrammate præcedenti I. </s>
              <s xml:id="echoid-s23785" xml:space="preserve">inter uallum ſeu arcum, a ſigno Z, uer-
                <lb/>
                <figure xlink:label="fig-514.01.344-01" xlink:href="fig-514.01.344-01a" number="142">
                  <variables xml:id="echoid-variables98" xml:space="preserve">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
                    <lb/>
                  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 &</variables>
                </figure>
                <note position="left" xlink:label="note-514.01.344-02" xlink:href="note-514.01.344-02a" xml:space="preserve">20</note>
                <note position="left" xlink:label="note-514.01.344-03" xlink:href="note-514.01.344-03a" xml:space="preserve">30</note>
                <note position="left" xlink:label="note-514.01.344-04" xlink:href="note-514.01.344-04a" xml:space="preserve">40</note>
              ticalis ad undecimam in meridiano, & </s>
              <s xml:id="echoid-s23786" xml:space="preserve">id transferas in planum horologij a ſigno d. </s>
              <s xml:id="echoid-s23787" xml:space="preserve">uerſus b. </s>
              <s xml:id="echoid-s23788" xml:space="preserve">ubi eſt litera
                <lb/>
              b. </s>
              <s xml:id="echoid-s23789" xml:space="preserve">inde a centro e. </s>
              <s xml:id="echoid-s23790" xml:space="preserve">ad b. </s>
              <s xml:id="echoid-s23791" xml:space="preserve">duces lineam occultam, & </s>
              <s xml:id="echoid-s23792" xml:space="preserve">habebis latitudinem horæ undecimæ, atque etiam
                <lb/>
              primæ horæ. </s>
              <s xml:id="echoid-s23793" xml:space="preserve">nam eam a puncto a. </s>
              <s xml:id="echoid-s23794" xml:space="preserve">uerſus c. </s>
              <s xml:id="echoid-s23795" xml:space="preserve">ad m. </s>
              <s xml:id="echoid-s23796" xml:space="preserve">duces. </s>
              <s xml:id="echoid-s23797" xml:space="preserve">Sume deinceps a diagrammate longitudinem
                <lb/>
              umbræ horæ undecimæ a puncto Z. </s>
              <s xml:id="echoid-s23798" xml:space="preserve">gnomonis pede, & </s>
              <s xml:id="echoid-s23799" xml:space="preserve">eam transferas a puncto e. </s>
              <s xml:id="echoid-s23800" xml:space="preserve">in lineam e b. </s>
              <s xml:id="echoid-s23801" xml:space="preserve">& </s>
              <s xml:id="echoid-s23802" xml:space="preserve">e
                <lb/>
                <note position="left" xlink:label="note-514.01.344-05" xlink:href="note-514.01.344-05a" xml:space="preserve">50</note>
              m. </s>
              <s xml:id="echoid-s23803" xml:space="preserve">ibi erit principium boræ primæ, & </s>
              <s xml:id="echoid-s23804" xml:space="preserve">undecimæ, quando Sol est in Cancro. </s>
              <s xml:id="echoid-s23805" xml:space="preserve">Sume postea arcum horizonta-
                <lb/>
              lem, ſeu latitudinem horæ decimæ, & </s>
              <s xml:id="echoid-s23806" xml:space="preserve">horæ ſecundæ quæcadem eſt, & </s>
              <s xml:id="echoid-s23807" xml:space="preserve">duc occultas lineas ab e. </s>
              <s xml:id="echoid-s23808" xml:space="preserve">in n, & </s>
              <s xml:id="echoid-s23809" xml:space="preserve">
                <lb/>
              o. </s>
              <s xml:id="echoid-s23810" xml:space="preserve">& </s>
              <s xml:id="echoid-s23811" xml:space="preserve">habebis latitudinem horæ decimæ, & </s>
              <s xml:id="echoid-s23812" xml:space="preserve">horæ ſecundæ, nam interualla ab n. </s>
              <s xml:id="echoid-s23813" xml:space="preserve">ad d. </s>
              <s xml:id="echoid-s23814" xml:space="preserve">& </s>
              <s xml:id="echoid-s23815" xml:space="preserve">ab a. </s>
              <s xml:id="echoid-s23816" xml:space="preserve">ad o.
                <lb/>
              </s>
              <s xml:id="echoid-s23817" xml:space="preserve">ſunt æqualia: </s>
              <s xml:id="echoid-s23818" xml:space="preserve">& </s>
              <s xml:id="echoid-s23819" xml:space="preserve">ſume earum horarum longitudinem umbræ a diagrammate O. </s>
              <s xml:id="echoid-s23820" xml:space="preserve">& </s>
              <s xml:id="echoid-s23821" xml:space="preserve">eam transferes in occul-
                <lb/>
              tas decimæ, & </s>
              <s xml:id="echoid-s23822" xml:space="preserve">ſecundæ horæ lineas latitudinis a puncto e. </s>
              <s xml:id="echoid-s23823" xml:space="preserve">& </s>
              <s xml:id="echoid-s23824" xml:space="preserve">habebis principia horæ decimæ, & </s>
              <s xml:id="echoid-s23825" xml:space="preserve">ſecundæ in
                <lb/>
              tropico Cancri. </s>
              <s xml:id="echoid-s23826" xml:space="preserve">Similis ratio erit præfiniendis reliquis horis tam in tropico Cancri, quam in tropico Capri-
                <lb/>
              corni, unde hyperboles duas oppoſitas uidebis. </s>
              <s xml:id="echoid-s23827" xml:space="preserve">quod ſi lineas ab hyperbole Cancri ad hyperbolem Capri-
                <lb/>
              corni duxeris, ut quæque ad ſuas horas reſpondeat, deſignatum habebis horologium in plano æquedistanti
                <lb/>
              plano finitoris. </s>
              <s xml:id="echoid-s23828" xml:space="preserve">Quod ſi hyperboles ab alijs circulis factas in horologio ponere libuerit, eadem uia uti po-
                <lb/>
              teris, qua Cancri, & </s>
              <s xml:id="echoid-s23829" xml:space="preserve">Capricorni byperboles poſuiſti. </s>
              <s xml:id="echoid-s23830" xml:space="preserve">ſemper autem æquinoctialis rectam ſibi dabit, tantum
                <lb/>
                <note position="left" xlink:label="note-514.01.344-06" xlink:href="note-514.01.344-06a" xml:space="preserve">60</note>
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