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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            <pb o="86" file="514.01.118" n="118" rhead="LIBER"/>
            <p style="it">
              <s xml:id="echoid-s8187" xml:space="preserve">Secundus compoſitionis modus eſt in quo ratio
                <lb/>
              primi ad ſecundum, constat ex ratione tertij ad ſex-
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              tum, atque ratione quinti ad quartum.</s>
              <s xml:id="echoid-s8188" xml:space="preserve"/>
            </p>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            subtripla. # 3--9
              <lb/>
            Seſquialiera. # 6--4
              <lb/>
            Subdupla # 18--36
              <lb/>
            </note>
            <p style="it">
              <s xml:id="echoid-s8189" xml:space="preserve">Tertius modus est in quo ratio primi termini ad
                <lb/>
              tertium conſtat ex ratione ſecundi ad quartum, & </s>
              <s xml:id="echoid-s8190" xml:space="preserve">
                <lb/>
              quinti ad ſextum.</s>
              <s xml:id="echoid-s8191" xml:space="preserve"/>
            </p>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            Subdupla # 2--4
              <lb/>
            Subſeſquialtera # 6--9
              <lb/>
            Subtripla. 1. ad 3. # 12--36
              <lb/>
            </note>
            <p style="it">
              <s xml:id="echoid-s8192" xml:space="preserve">Quartus modus eſt in quo ratio primi ad tertium
                <lb/>
              constat ex ratione ſecundi ad ſextum, & </s>
              <s xml:id="echoid-s8193" xml:space="preserve">ex ratione
                <lb/>
              quinti ad quartum.</s>
              <s xml:id="echoid-s8194" xml:space="preserve"/>
            </p>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            Subquadrupla ſeſquialtera. # 2--9
              <lb/>
            Seſquialtera # 12--36
              <lb/>
            Subtripla ut 1. ad 3. # 12--36
              <lb/>
            </note>
            <p style="it">
              <s xml:id="echoid-s8195" xml:space="preserve">Quintus modus eſt in quo ratio primi ad quin-
                <lb/>
              tum componitur ex ratione ſecundi ad ſextum, & </s>
              <s xml:id="echoid-s8196" xml:space="preserve">
                <lb/>
              tertij ad quartum.</s>
              <s xml:id="echoid-s8197" xml:space="preserve"/>
            </p>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            Subquadrupla ſeſquialtera # 2--9
              <lb/>
            Subſeſquitertia ut 1. ad 6. # 3--4
              <lb/>
            Subſextupla ut 1. ad 6 # 6--36
              <lb/>
            </note>
            <p style="it">
              <s xml:id="echoid-s8198" xml:space="preserve">Sextus modus est in quo eiuſdem primi numeri ad
                <lb/>
              ipſum quintũ conſtat ex rationibus ſecundi ad quar-
                <lb/>
              tum, & </s>
              <s xml:id="echoid-s8199" xml:space="preserve">tertij ad ſextum.</s>
              <s xml:id="echoid-s8200" xml:space="preserve"/>
            </p>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            Subdupla # 2--4
              <lb/>
            Subtripla # 3--9
              <lb/>
            Subſextupla # 6--36
              <lb/>
            </note>
            <p style="it">
              <s xml:id="echoid-s8201" xml:space="preserve">Septimus modus eſt in quo ratio ſecundi ad quar-
                <lb/>
              tum fit ex ratione primi ad tertium, & </s>
              <s xml:id="echoid-s8202" xml:space="preserve">ſexti ad
                <lb/>
              quintum.</s>
              <s xml:id="echoid-s8203" xml:space="preserve"/>
            </p>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            Subtripla # 1--3
              <lb/>
            Seſquialtera # 9--6
              <lb/>
            Subdupla ut 2. ad 4. # 9--18
              <lb/>
            </note>
            <p style="it">
              <s xml:id="echoid-s8204" xml:space="preserve">Octauus modus est in quo ratio eiuſdem ſecundi
                <lb/>
              termini ad quartum fit ex ratione primi ad quintũ,
                <lb/>
              & </s>
              <s xml:id="echoid-s8205" xml:space="preserve">ſexti ad tertium.</s>
              <s xml:id="echoid-s8206" xml:space="preserve"/>
            </p>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            Subſextupla # 1--6
              <lb/>
            Tripla # 9--3
              <lb/>
            Subdupla # 9--18
              <lb/>
            </note>
            <p style="it">
              <s xml:id="echoid-s8207" xml:space="preserve">Nonus modus eſt in quo ratio ſecundi ad ſextum
                <lb/>
              conſtat ex rationibus primi ad tertium, & </s>
              <s xml:id="echoid-s8208" xml:space="preserve">quarti ad
                <lb/>
              quintum.</s>
              <s xml:id="echoid-s8209" xml:space="preserve"/>
            </p>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            Subtripla # 1--3
              <lb/>
            Subſeſquialtera # 4--6
              <lb/>
            Subquadrupla ſeſquialtra # 4--18
              <lb/>
            </note>
            <p style="it">
              <s xml:id="echoid-s8210" xml:space="preserve">Decimus modus eſt in quo ratio ſecundi ad ſex-
                <lb/>
              tum redditur ex ratione primi ad quintum, & </s>
              <s xml:id="echoid-s8211" xml:space="preserve">quar-
                <lb/>
              ti ad terntium.</s>
              <s xml:id="echoid-s8212" xml:space="preserve"/>
            </p>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            Subſextupla # 1--6
              <lb/>
            Seſquitertia # 4--3
              <lb/>
            Subquadrupla ſeſquialtera # 4--18
              <lb/>
            </note>
            <p style="it">
              <s xml:id="echoid-s8213" xml:space="preserve">Vndecimus modus eſt, in quo tertij
                <unsure/>
              ad quartum
                <lb/>
              comparatio fit ex rationibus primi ad ſecundnm, & </s>
              <s xml:id="echoid-s8214" xml:space="preserve">
                <lb/>
              ſexti ad quintum.</s>
              <s xml:id="echoid-s8215" xml:space="preserve"/>
            </p>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            Subdupla # 1--2
              <lb/>
            Seſquialtera # 9--6
              <lb/>
            Subſeſquitertia ut 3. ad 4. # 9--12
              <lb/>
            </note>
            <p style="it">
              <s xml:id="echoid-s8216" xml:space="preserve">Duodecimus modus eſt in quo tertij ratio ad quar-
                <lb/>
              tum fit ex rationibus primi ad quintum, & </s>
              <s xml:id="echoid-s8217" xml:space="preserve">ſexti ad
                <lb/>
              ſecundum.</s>
              <s xml:id="echoid-s8218" xml:space="preserve"/>
            </p>
            <note position="left" xml:space="preserve">10</note>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            Subſextupla # 1--6
              <lb/>
            Quadrupla ſeſquialtera # 9--2
              <lb/>
            Subſeſquitertia # 9--12
              <lb/>
            </note>
            <p style="it">
              <s xml:id="echoid-s8219" xml:space="preserve">Decimus tertius modus es
                <unsure/>
              t, in quo tertij ad ſextü
                <lb/>
              reſponſus fit ex ratione primi ad ſecundum, et quar-
                <lb/>
              ti ad quintum.</s>
              <s xml:id="echoid-s8220" xml:space="preserve"/>
            </p>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            Subdupla # 1--2
              <lb/>
            Subſeſquialtera # 4--6
              <lb/>
            Subtripla # 4--12
              <lb/>
            </note>
            <note position="left" xml:space="preserve">20</note>
            <p style="it">
              <s xml:id="echoid-s8221" xml:space="preserve">Decimus quartus modus eſt in quo ratio eiuſdem
                <lb/>
              tertij ad ſextum conficitur ex ratione primi ad quin
                <lb/>
              tum, & </s>
              <s xml:id="echoid-s8222" xml:space="preserve">quarti ad ſecundum.</s>
              <s xml:id="echoid-s8223" xml:space="preserve"/>
            </p>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            Subſextupla # 1--6
              <lb/>
            Dupla # 4--2
              <lb/>
            Subtripla # 4--12
              <lb/>
            </note>
            <p style="it">
              <s xml:id="echoid-s8224" xml:space="preserve">Decimus quintus modus est, in quo quarti ratio
                <lb/>
              ad quintum fit ex rationibus ſecundi ad primum, & </s>
              <s xml:id="echoid-s8225" xml:space="preserve">
                <lb/>
              tertij ad ſextum.</s>
              <s xml:id="echoid-s8226" xml:space="preserve"/>
            </p>
            <note position="left" xml:space="preserve">30</note>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            Dupla # 2--1
              <lb/>
            Subtripla # 3--9
              <lb/>
            Subſeſquialtera # 6--9
              <lb/>
            </note>
            <p style="it">
              <s xml:id="echoid-s8227" xml:space="preserve">Decimus ſextus modus eſt in quo quarti ad quin-
                <lb/>
              tum relatio ex relatione ſecundi ad ſextum, & </s>
              <s xml:id="echoid-s8228" xml:space="preserve">tertij
                <lb/>
              ad primum efficitur.</s>
              <s xml:id="echoid-s8229" xml:space="preserve"/>
            </p>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            Subquadrupla ſeſquialtera # 2--9
              <lb/>
            Tripla # 3--1
              <lb/>
            Subſeſquialtera # 6--9
              <lb/>
            </note>
            <p style="it">
              <s xml:id="echoid-s8230" xml:space="preserve">Decimus ſeptimus modus est in quo ratio quinti
                <lb/>
                <note position="left" xlink:label="note-514.01.118-19" xlink:href="note-514.01.118-19a" xml:space="preserve">40</note>
              ad ſextum componitur ex ratione primi ad ſecundũ,
                <lb/>
              & </s>
              <s xml:id="echoid-s8231" xml:space="preserve">quarti ad tertium.</s>
              <s xml:id="echoid-s8232" xml:space="preserve"/>
            </p>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            Subdupla # 1--2
              <lb/>
            Seſquitertia # 4--3
              <lb/>
            Subſeſquialtera # 4--6
              <lb/>
            </note>
            <p style="it">
              <s xml:id="echoid-s8233" xml:space="preserve">Decimus octauus modus eſt in quo quinti ratio
                <lb/>
              ad ſextum conſtat ex rationibus primi ad tertium,
                <lb/>
              & </s>
              <s xml:id="echoid-s8234" xml:space="preserve">quarti ad ſecundum.</s>
              <s xml:id="echoid-s8235" xml:space="preserve"/>
            </p>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            Subtripla # 1--3
              <lb/>
            Dupla # 4--2
              <lb/>
            Subſeſquialtera # 4--6
              <lb/>
            </note>
            <note position="left" xml:space="preserve">50</note>
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