Vitruvius, De architectura libri decem, 1567

Table of figures

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[Figure 101]
[102] FRONTE.
[103] A
[104] Græcorum ædes earumq́; partium diſpoſitiones.A. peristylium amplum.E. peristylium primum.C. aditus amplus.D. aditus ab uno ad aliudperiſtylium.E. proſtas ubi eraut duæ antæ.F. G. Antithalamus.H. I. gynæconitides.K. cu-bicuUmdiebria.L. S. oeci,& bibliotecæ,& ubi ſunt pictores.M. R. pinacotbecæ.N. cyzicena triclinia.O. porticus ad ſeptentrionem.P. cellæ hostiariæ.Q. oeci quadrati.T. V. porticus ad triclinia cizcena.X. hypæthra loca.r. oeci magni ubi matres familiarũ cum lanificijs habent ſeſſiones.Z. hoſpitalia.1. thirorium.2. Equilia.3. cubicula.4. meſaulæ & andronæ.5. triclinia quo-tidiana.6. posthalamus.7. thalamus.8. porticus Rhodiaca altior. T QVNMRN8SALKICHXYYFEG76B543O32P21
[105] Pauimentorum genera.Filandri.Anticum.
[106] c d f b c 8
[107] CHOROBATES.2 I 3 2
[108] d 10 10 a d 50 50 50 c 50 ba s d s 7 {1/14} 25 s b ce 8 8 10 84 f hm 5 43 3 4 4 3 3 4 4 5 5 5 53 5 4
[109] Figura ex meſolabio Architæ ad inueniendas medias.c t @ @ q p o n m l k l h g f p e o ξ v M @ k I o h j ε δ r B d s R q P o N M L K I H G F E L x c 6 N ς ε ξ γ B a
[110] Veſtigium meſolabij Architæ.
[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
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          <div xml:id="echoid-div276" type="section" level="2" n="61">
            <p style="it">
              <s xml:id="echoid-s7981" xml:space="preserve">
                <pb o="84" file="514.01.116" n="116" rhead="LIBER"/>
              reliquæ rationis antecedens, & </s>
              <s xml:id="echoid-s7982" xml:space="preserve">ita quaſi decuſſatim ducendo rationis diuidendæ numerum conſequentem, per
                <lb/>
              diuidentis antecedentem, naſcetur reliquæ ſeu ortæ rationis conſequens numerus. </s>
              <s xml:id="echoid-s7983" xml:space="preserve">Exempla id aperte oſten-
                <lb/>
              dunt. </s>
              <s xml:id="echoid-s7984" xml:space="preserve">In multiplicibus primum id experiemur. </s>
              <s xml:id="echoid-s7985" xml:space="preserve">Subtrahenda ſit dupla a tripla, partire denominatorem triplæ,
                <lb/>
              per duo ipſius duplæ rationis deominatorem , fiet 1. </s>
              <s xml:id="echoid-s7986" xml:space="preserve">cum dimidio; </s>
              <s xml:id="echoid-s7987" xml:space="preserve">orietur igitur ex hac partitione ſeſquial-
                <lb/>
              tera proportio. </s>
              <s xml:id="echoid-s7988" xml:space="preserve">Similiter ſubducenda quadrupla ab octupla , reliqua erit dupla . </s>
              <s xml:id="echoid-s7989" xml:space="preserve">ſint huius numeri in quadru-
                <lb/>
              pla proportione 16. </s>
              <s xml:id="echoid-s7990" xml:space="preserve">& </s>
              <s xml:id="echoid-s7991" xml:space="preserve">4. </s>
              <s xml:id="echoid-s7992" xml:space="preserve">& </s>
              <s xml:id="echoid-s7993" xml:space="preserve">64. </s>
              <s xml:id="echoid-s7994" xml:space="preserve">& </s>
              <s xml:id="echoid-s7995" xml:space="preserve">8. </s>
              <s xml:id="echoid-s7996" xml:space="preserve">in octupla. </s>
              <s xml:id="echoid-s7997" xml:space="preserve">duc octo in ſexdecim fient centum uiginti octo, & </s>
              <s xml:id="echoid-s7998" xml:space="preserve">
                <lb/>
              4. </s>
              <s xml:id="echoid-s7999" xml:space="preserve">in 64. </s>
              <s xml:id="echoid-s8000" xml:space="preserve">fient. </s>
              <s xml:id="echoid-s8001" xml:space="preserve">256. </s>
              <s xml:id="echoid-s8002" xml:space="preserve">interigitur 128. </s>
              <s xml:id="echoid-s8003" xml:space="preserve">& </s>
              <s xml:id="echoid-s8004" xml:space="preserve">256. </s>
              <s xml:id="echoid-s8005" xml:space="preserve">erit proportio dupla, nam bis 128. </s>
              <s xml:id="echoid-s8006" xml:space="preserve">producunt. </s>
              <s xml:id="echoid-s8007" xml:space="preserve">256.
                <lb/>
              </s>
              <s xml:id="echoid-s8008" xml:space="preserve">
                <note style="it" position="right" xlink:label="note-514.01.116-01" xlink:href="note-514.01.116-01a" xml:space="preserve">
                  <lb/>
                64--8 # Octupla.
                  <lb/>
                16--4 # quadrupla.
                  <lb/>
                128--256 # dupla.
                  <lb/>
                </note>
              In ſuperparticularibus quoque rationibus ablatio huiuſmodi hoc modo fiet.
                <lb/>
              </s>
              <s xml:id="echoid-s8009" xml:space="preserve">Auferenda ſit a ſeſquialtera ſeſquitertia. </s>
              <s xml:id="echoid-s8010" xml:space="preserve">partiri 1. </s>
              <s xml:id="echoid-s8011" xml:space="preserve">cum dimidio denomina-
                <lb/>
                <note position="left" xlink:label="note-514.01.116-02" xlink:href="note-514.01.116-02a" xml:space="preserve">10</note>
              torem ſeſquialteræ per 1. </s>
              <s xml:id="echoid-s8012" xml:space="preserve">& </s>
              <s xml:id="echoid-s8013" xml:space="preserve">tertiam denominatorem ſeſquitertiæ, reliqua
                <lb/>
              ratio erit 1 octaua hoc eſtſeſquioctaua.</s>
              <s xml:id="echoid-s8014" xml:space="preserve"/>
            </p>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            6--4 # ſeſquialtera.
              <lb/>
            8--6 # ſeſquitertia.
              <lb/>
            36--32 # ſeſquioctaua.
              <lb/>
            </note>
            <p style="it">
              <s xml:id="echoid-s8015" xml:space="preserve">In ſuperpartientibus demum auferatur bipartiens tertias , a tripartiente
                <lb/>
              quartas , diuide 1. </s>
              <s xml:id="echoid-s8016" xml:space="preserve">& </s>
              <s xml:id="echoid-s8017" xml:space="preserve">tres quartæ per 1. </s>
              <s xml:id="echoid-s8018" xml:space="preserve">& </s>
              <s xml:id="echoid-s8019" xml:space="preserve">duas tertias fiet vnum & </s>
              <s xml:id="echoid-s8020" xml:space="preserve">
                <lb/>
              vigeſima pars, a quibus ſeſquigeſima ratio denominatur.</s>
              <s xml:id="echoid-s8021" xml:space="preserve"/>
            </p>
            <note position="right" xml:space="preserve">
              <lb/>
            7--4 # tripartiens quartas.
              <lb/>
            5--3 # bipartiens tertias.
              <lb/>
            21--20 # ſeſquigeſima.
              <lb/>
            </note>
            <p style="it">
              <s xml:id="echoid-s8022" xml:space="preserve">Partita igitur ratione maioris inæqualitatis per rationem maioris, cum diſ-
                <lb/>
              ſimiles fuerint, ratio fiet maioris inæqualitatis, & </s>
              <s xml:id="echoid-s8023" xml:space="preserve">utraque minor.
                <lb/>
              </s>
              <s xml:id="echoid-s8024" xml:space="preserve">Eodem reſponſu intelliges de diſſimilibus minoris inæqualitatis com-
                <lb/>
              parationibus, fiet enim comparatio minoris inæqualitatis , & </s>
              <s xml:id="echoid-s8025" xml:space="preserve">utra-
                <lb/>
              que ſimili modo minor. </s>
              <s xml:id="echoid-s8026" xml:space="preserve">At ſi utræque rationes, aut maioris aut
                <lb/>
                <note position="left" xlink:label="note-514.01.116-05" xlink:href="note-514.01.116-05a" xml:space="preserve">20</note>
              minoris inæqualitatis fuerint, & </s>
              <s xml:id="echoid-s8027" xml:space="preserve">ſimiles, quod æque eſt, ac ſi data
                <lb/>
              ratio per ſe ipſam diuidatur, quæ ueniet ratio erit æqualitatis. </s>
              <s xml:id="echoid-s8028" xml:space="preserve">Sed ſi altera maioris, alter a minoris inæquali-
                <lb/>
              tatis extiterit, ea quę prodibit ratio, in ipſa ratione diuidenda firmabitur, quæ ſcilicet per maiorem numerum fie
                <lb/>
              ri ſolet. </s>
              <s xml:id="echoid-s8029" xml:space="preserve">Cæterum ſi ordinem mutaueris, ita ut rationẽ ſubtrahendam, alteri ſupraponas, eademq́; </s>
              <s xml:id="echoid-s8030" xml:space="preserve">multiplicandi
                <lb/>
              forma ſeruata permutatam rationem ſenties, ita ut quemadmodum in priori exemplo ſublata tripla, una ex
                <lb/>
              dupla, fit ſeſquialtera, ita hic inuerſo ordine fiet ſubſeſquialtera, ſimilis ratio in reliquis.</s>
              <s xml:id="echoid-s8031" xml:space="preserve"/>
            </p>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            Dupla. # 8--4
              <lb/>
            Tripla. # 18--6
              <lb/>
            Subſeſquialtera. # 48--72
              <lb/>
            </note>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            ſeſquitertia # 8--6
              <lb/>
            ſeſquialtera # 6--4
              <lb/>
            ſubſeſquioctaua # 32--36
              <lb/>
            </note>
            <note style="it" position="right" xml:space="preserve">
              <lb/>
            bipartiens tertias. # 5--3
              <lb/>
            tripartiens quartas. # 7--4
              <lb/>
            ſubſeſquigeſima. # 20--21
              <lb/>
            </note>
            <p style="it">
              <s xml:id="echoid-s8032" xml:space="preserve">Poſſem hoc loco proportionum proprietates afferre, ac attendere quod ab æqualitate, inæqualitas omnis
                <lb/>
                <note position="left" xlink:label="note-514.01.116-09" xlink:href="note-514.01.116-09a" xml:space="preserve">30</note>
              prouenit, æqualitatemq; </s>
              <s xml:id="echoid-s8033" xml:space="preserve">eſſe inæqualitatis principium, ac demum ad æqualitatem omnem inæqualitatem redu-
                <lb/>
              ci. </s>
              <s xml:id="echoid-s8034" xml:space="preserve">quibus in rebus multa ſecretioris philoſophiæ arcana continentur, ſed hæc ſuo loco reſeruanda ſunt, altio-
                <lb/>
              ris enim ſunt indagationis, & </s>
              <s xml:id="echoid-s8035" xml:space="preserve">uſque ad diuinitatem pertingunt. </s>
              <s xml:id="echoid-s8036" xml:space="preserve">nunc de perquirendis ignotis numeris per eos,
                <lb/>
              qui noti ſunt, regulas aureas apponemus, ac primum id in minimis terminis exequemur. </s>
              <s xml:id="echoid-s8037" xml:space="preserve">Duo igitur ad minus
                <lb/>
              ſunt numerorum termini, quibus cognitis, tertium inueſtigamus, ſiue ille terminus extremus ſit , ſiue medius,
                <lb/>
              loquor autem nunc de ijs, qui ſe mutua ac continenti comparatione reſpiciunt. </s>
              <s xml:id="echoid-s8038" xml:space="preserve">Esto duo numeri præcedentes
                <lb/>
              inter ſe , aliqua ratione comparati. </s>
              <s xml:id="echoid-s8039" xml:space="preserve">Verbi gratia. </s>
              <s xml:id="echoid-s8040" xml:space="preserve">36. </s>
              <s xml:id="echoid-s8041" xml:space="preserve">12. </s>
              <s xml:id="echoid-s8042" xml:space="preserve">uolo tertium inuenire, ad quem posterior
                <lb/>
              ſcilicet 12. </s>
              <s xml:id="echoid-s8043" xml:space="preserve">ſe habeat, quemadmodũ. </s>
              <s xml:id="echoid-s8044" xml:space="preserve">36. </s>
              <s xml:id="echoid-s8045" xml:space="preserve">ad ipſum. </s>
              <s xml:id="echoid-s8046" xml:space="preserve">Multiplicetur ſeu diuidatur in ſe poſterior ille nume-
                <lb/>
              rus , qui ſecundum locum tenere debet idest. </s>
              <s xml:id="echoid-s8047" xml:space="preserve">12. </s>
              <s xml:id="echoid-s8048" xml:space="preserve">inſe, qui ab ea ductione prouenit numerus, id erit 144.
                <lb/>
              </s>
              <s xml:id="echoid-s8049" xml:space="preserve">
                <note position="left" xlink:label="note-514.01.116-10" xlink:href="note-514.01.116-10a" xml:space="preserve">40</note>
              per 144. </s>
              <s xml:id="echoid-s8050" xml:space="preserve">priorem hoc eſt 36. </s>
              <s xml:id="echoid-s8051" xml:space="preserve">partiare, certe prodibit numerus ille, quem uolebam, id eſt 4. </s>
              <s xml:id="echoid-s8052" xml:space="preserve">qui ſe ad
                <lb/>
              duodecim, uel ad quem 12. </s>
              <s xml:id="echoid-s8053" xml:space="preserve">ſe habebunt, quemadmodum 36. </s>
              <s xml:id="echoid-s8054" xml:space="preserve">ad 12. </s>
              <s xml:id="echoid-s8055" xml:space="preserve">in tripla enim proportione erit.
                <lb/>
              </s>
              <s xml:id="echoid-s8056" xml:space="preserve">Quod ſi duxeris 36. </s>
              <s xml:id="echoid-s8057" xml:space="preserve">inſe, emergent 1296. </s>
              <s xml:id="echoid-s8058" xml:space="preserve">quæ per 12. </s>
              <s xml:id="echoid-s8059" xml:space="preserve">partita reddent 108. </s>
              <s xml:id="echoid-s8060" xml:space="preserve">quare 108. </s>
              <s xml:id="echoid-s8061" xml:space="preserve">primus
                <lb/>
              erit trium proportione ſe conſequentium numerorum, propoſitis numeris præponendus; </s>
              <s xml:id="echoid-s8062" xml:space="preserve">nam numerus 108. </s>
              <s xml:id="echoid-s8063" xml:space="preserve">
                <lb/>
              comparatus ad 36. </s>
              <s xml:id="echoid-s8064" xml:space="preserve">eandem ſeruabit rationem ad 36. </s>
              <s xml:id="echoid-s8065" xml:space="preserve">quam idem 36. </s>
              <s xml:id="echoid-s8066" xml:space="preserve">ad 12. </s>
              <s xml:id="echoid-s8067" xml:space="preserve">triplam ſcilicet , quæ
                <lb/>
              est ex genere multip licium. </s>
              <s xml:id="echoid-s8068" xml:space="preserve">Datis igitur duobus numeris tertium ſeu poſtremum inuenimus. </s>
              <s xml:id="echoid-s8069" xml:space="preserve">quod ſi medium
                <lb/>
              uoluerimus inuenire inter duos propoſitos numeros proportione reſpondentiem, ducendi ſunt propoſiti illi nume-
                <lb/>
              ri inter ſe, & </s>
              <s xml:id="echoid-s8070" xml:space="preserve">quadrata ipſorum radix inuenienda, nempe ea erit medius ille numerus, ad quem prior ita ſe ha-
                <lb/>
              bebit, quemadmodum ille ad poſteriorem. </s>
              <s xml:id="echoid-s8071" xml:space="preserve">Hic ad Arithmeticos accedendum, qui de extrahendis numerorum
                <lb/>
              radicibus regulas ponunt. </s>
              <s xml:id="echoid-s8072" xml:space="preserve">Radices autem numerorum intelligo eos numeros, qui in ſe ducti efficiunt eam ſum
                <lb/>
              mam, de qua radicem trahimus, nam quatuor radix est ſexdecim, ducta enim in ſe quatuor efficiunt ſexde-
                <lb/>
                <note position="left" xlink:label="note-514.01.116-11" xlink:href="note-514.01.116-11a" xml:space="preserve">50</note>
              cim. </s>
              <s xml:id="echoid-s8073" xml:space="preserve">Exemplo ſint 25. </s>
              <s xml:id="echoid-s8074" xml:space="preserve">& </s>
              <s xml:id="echoid-s8075" xml:space="preserve">4. </s>
              <s xml:id="echoid-s8076" xml:space="preserve">uolo numerum medium inuenire, ad quem 25. </s>
              <s xml:id="echoid-s8077" xml:space="preserve">ſe habeat ea ratione, qua
                <lb/>
              ille ſe ad 4. </s>
              <s xml:id="echoid-s8078" xml:space="preserve">habebit. </s>
              <s xml:id="echoid-s8079" xml:space="preserve">dueigitur 4. </s>
              <s xml:id="echoid-s8080" xml:space="preserve">in 25. </s>
              <s xml:id="echoid-s8081" xml:space="preserve">fient 100. </s>
              <s xml:id="echoid-s8082" xml:space="preserve">cuius radix eſt decem, ergo 25. </s>
              <s xml:id="echoid-s8083" xml:space="preserve">ad decem ſe ha-
                <lb/>
              bebit, ut decem ad 4. </s>
              <s xml:id="echoid-s8084" xml:space="preserve">nempe in proportione dupla ſexquialtera. </s>
              <s xml:id="echoid-s8085" xml:space="preserve">Atque hæc ſatis dicta ſint in minimo nu-
                <lb/>
              merorum ordine. </s>
              <s xml:id="echoid-s8086" xml:space="preserve">Nunc ad plures ordines tranſeundum, & </s>
              <s xml:id="echoid-s8087" xml:space="preserve">quærendum, qua ratione tribus terminis nume-
                <lb/>
              rorum propoſitis, & </s>
              <s xml:id="echoid-s8088" xml:space="preserve">notis alius inueniatur . </s>
              <s xml:id="echoid-s8089" xml:space="preserve">Fieri autem potest, ut uel primus, uel ſecundus, uel tertius, uel
                <lb/>
              quartus ignotus ſit, reliquis tribus perſpectis. </s>
              <s xml:id="echoid-s8090" xml:space="preserve">debemus tamen in experiendo quartum locum ignoto numero
                <lb/>
              reſeruare. </s>
              <s xml:id="echoid-s8091" xml:space="preserve">ita ut primus tertio re, & </s>
              <s xml:id="echoid-s8092" xml:space="preserve">ratione conueniat, nam ita fiet, ut ſecundus quarto ignoto reſpondeat.
                <lb/>
              </s>
              <s xml:id="echoid-s8093" xml:space="preserve">Eſto exempli gratia 30. </s>
              <s xml:id="echoid-s8094" xml:space="preserve">20. </s>
              <s xml:id="echoid-s8095" xml:space="preserve">24. </s>
              <s xml:id="echoid-s8096" xml:space="preserve">16. </s>
              <s xml:id="echoid-s8097" xml:space="preserve">quiſeſquialte ratione reſpiciant, eſto etiam ignotus numerus 16. </s>
              <s xml:id="echoid-s8098" xml:space="preserve">
                <lb/>
              duc 24. </s>
              <s xml:id="echoid-s8099" xml:space="preserve">per 20. </s>
              <s xml:id="echoid-s8100" xml:space="preserve">efficies 480. </s>
              <s xml:id="echoid-s8101" xml:space="preserve">partire 480. </s>
              <s xml:id="echoid-s8102" xml:space="preserve">per 30. </s>
              <s xml:id="echoid-s8103" xml:space="preserve">reſultabit ignotus ille, & </s>
              <s xml:id="echoid-s8104" xml:space="preserve">quæſitus numerus ſex
                <lb/>
              decim. </s>
              <s xml:id="echoid-s8105" xml:space="preserve">At ſi primus numerus quæratur uidelicet 30. </s>
              <s xml:id="echoid-s8106" xml:space="preserve">eum quarto loco ponito, nam cum ſit 30. </s>
              <s xml:id="echoid-s8107" xml:space="preserve">ad 20. </s>
              <s xml:id="echoid-s8108" xml:space="preserve">
                <lb/>
                <note position="left" xlink:label="note-514.01.116-12" xlink:href="note-514.01.116-12a" xml:space="preserve">60</note>
              </s>
            </p>
          </div>
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