Vitruvius, De architectura libri decem, 1567

Table of figures

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[91] A. Templum diui Marci.B. Turris diui Marci.C. Duæ columne.D. Forum diui ’Marci.E. D. Geminianus.F. D. Moyſes.G. D. Baſſus.H. D. Theodorus.I. D. Zacharias.K. D. Ioan. embracora.L. D. Martinus.M. D. Dominicus.N. D. Antonius.O. D. Petrus.P. D. Daniel.Q. D. Donatus.R. Dogana.S. Nauale.T. D. Cœleſtis.V. D. Franciſcus.X. D. Io. & Paulus.Y. D. Laurentius.Z. D. Seuerus.a. D. Marina.b. D. Cantianus.c. D. Apoſtoli.d. Crucigeri.e. D. Sophia.f. D. Maria ab hortis.g. D. Iob.h. S. Crux.i. D. Margarita.k. Magna domus Franciſcanorum.l. D. Paulus.m. D. Auguſtinus.n. D. Agatha.o. D. Maria mater domini.p. D. Caßiani.q. D. Matthia.r. D. Iacobus in riuo alto.ΔΔΔ. Magnus canalis.ſ. Forum riui alti.t. Pons riui alti.@. D. Maria Iubanica.x. D. Stephanus.y. Templum charitatis.Z. D. Gregorius. TRAMONTANAPONENTELEVANTE
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[92] B G F M A H I N E C D
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[93] A. tetrastylon cauum ædium.F. cellæ F A FF A F
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[94] B. Tuſcanicum cauum ædium.E. cellæ.D. interpenſiua. E B E
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[95] D D E B E
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[96] C. diſpluuiatum.G. cellæ. G C G
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[97] G C G
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[98] D. cauædium teſtudinatum.M. cellæ.P. lumen. M D MM D P M
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[99] O. cauum ædium.P. alæ.Q. uiridaria.T. ueſtibulum.Z. baſilica.r. tablinum. Z Y Q Q O Q Q T
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[Figure 100]
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[Figure 101]
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[102] FRONTE.
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[103] A
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[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
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[105] Pauimentorum genera.Filandri.Anticum.
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[106] c d f b c 8
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[107] CHOROBATES.2 I 3 2
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[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
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[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
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[110] Veſtigium meſolabij Architæ.
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[111] Orthographia meſolabij Architæ.
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[112] Demonſtratio Eratoſtbenis. a g t cb f b d
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[113] Instrumentum Eratoſthenis. m a x g n b c n i o l v q p b e f k d
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[114] Vſ{us} demonſtratio Eratoſtbenis cum inſtrumento. a h n ek l i o d b 8 m c 4
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[115] Inſtrumentum Platonis. f i n o m
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[116] cubus. 8 8 64 8 8 8 8 512 8s e
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[117] Demonstratio Archita. p l k b o i m b e d af
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[118] Demonctration Platonis. d e b c g
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[119] Demostratio ter tiæ proprietatis, & aſſumptionis Nicomedis.instrumentum Nicomedis. f h d g b s n m k a
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[120] Duplicatio cubi. e a b c d f g
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          <div xml:id="echoid-div713" type="section" level="2" n="134">
            <pb o="272" file="514.01.304" n="304" rhead="LIBER"/>
            <p style="it">
              <s xml:id="echoid-s20297" xml:space="preserve">Iucundas, & </s>
              <s xml:id="echoid-s20298" xml:space="preserve">gratas bominibus Architæ, & </s>
              <s xml:id="echoid-s20299" xml:space="preserve">Eratosthenis inuentiones fuiſſe, dicit Vitr. </s>
              <s xml:id="echoid-s20300" xml:space="preserve">Sed Cum ambo
                <lb/>
              eandem quæs̃tionem tractarent, nitereturq́; </s>
              <s xml:id="echoid-s20301" xml:space="preserve">alter, atque alter ratione diuerſa eam ſoluere, ambo ſuſpecti fue-
                <lb/>
              runt, non quia res eadem diuerſis modis inueniri non poßit, ſed quia, quineſcirent, cum uiderent Architam
                <lb/>
              ratione una, & </s>
              <s xml:id="echoid-s20302" xml:space="preserve">Eratoſthenem. </s>
              <s xml:id="echoid-s20303" xml:space="preserve">alia uti, ob eorum contentionem ſuſpicabantur, cogitantes ſtudioſe inter-ſe
                <lb/>
              contendere. </s>
              <s xml:id="echoid-s20304" xml:space="preserve">Quod perinde eſt, ac ſi quis turris altitudinem quadrante,alius radio, alius astrolabio, alius ſpe-
                <lb/>
              culo, alius alio instrumento metiretur, cum vulgus neſciat eandem eſſe omnium horum inſtrumentorum ra-
                <lb/>
              tionem, & </s>
              <s xml:id="echoid-s20305" xml:space="preserve">viam, quæ ab angulorum menſura diſceernitur, ſuſpicatur menſorum contertionem, atque æmu-
                <lb/>
              lationem uerum inuoluere, ac confundere inſtrumentorum diuerſitate. </s>
              <s xml:id="echoid-s20306" xml:space="preserve">Simile euenit ob Erathoſthenis, & </s>
              <s xml:id="echoid-s20307" xml:space="preserve">
                <lb/>
              Architæ contentiones. </s>
              <s xml:id="echoid-s20308" xml:space="preserve">Propoſita quæſtio erat, qua ratione cubus duplicari oporteret. </s>
              <s xml:id="echoid-s20309" xml:space="preserve">Cubus eſt, (ut dixi li-
                <lb/>
                <note position="left" xlink:label="note-514.01.304-01" xlink:href="note-514.01.304-01a" xml:space="preserve">10</note>
              bro quinto ) ſolidum corpus,planis ſex, & </s>
              <s xml:id="echoid-s20310" xml:space="preserve">lateribus conſtans æquaiibus Metiemur cubum, ſi duxerimus
                <lb/>
              aliquod unum ex ſuis lateribus in ſeipſum, & </s>
              <s xml:id="echoid-s20311" xml:space="preserve">eam ſummam quoque duxerimus per idem latus. </s>
              <s xml:id="echoid-s20312" xml:space="preserve">Detur cubus
                <lb/>
              cuius latera ſingula octo conſtet pedibus, duc octo in ſe,reddentur 64. </s>
              <s xml:id="echoid-s20313" xml:space="preserve">ducito rurſtus 64. </s>
              <s xml:id="echoid-s20314" xml:space="preserve">per octo,redden-
                <lb/>
              tur 5 12. </s>
              <s xml:id="echoid-s20315" xml:space="preserve">tot igitur quadratis perdibus conſtabit cubus. </s>
              <s xml:id="echoid-s20316" xml:space="preserve">Cum igitur cubusiam 512. </s>
              <s xml:id="echoid-s20317" xml:space="preserve">pedibus comſtare cogni-
                <lb/>
              tum ſit. </s>
              <s xml:id="echoid-s20318" xml:space="preserve">iuxta propoſitam quæstionem duplicationdus eſt. </s>
              <s xml:id="echoid-s20319" xml:space="preserve">Quod ut commode ſaciamus, neceſſario eſt ſcire, qua
                <lb/>
              ratione duabus propoſitis rectis. </s>
              <s xml:id="echoid-s20320" xml:space="preserve">& </s>
              <s xml:id="echoid-s20321" xml:space="preserve">inæqualibus lmeis. </s>
              <s xml:id="echoid-s20322" xml:space="preserve">duas medias inueniamus, quæ inter ſe & </s>
              <s xml:id="echoid-s20323" xml:space="preserve">cum primis
                <lb/>
              continua proportione reſpondeant. </s>
              <s xml:id="echoid-s20324" xml:space="preserve">Vt igitur inutniretur ea mediarum linearum comparatio, modi undecim
                <lb/>
              ab antiquis reperti ſunt. </s>
              <s xml:id="echoid-s20325" xml:space="preserve">Alij euidentibud matbematicorum rationibus uſi ſunt, alij. </s>
              <s xml:id="echoid-s20326" xml:space="preserve">& </s>
              <s xml:id="echoid-s20327" xml:space="preserve">præter demonſtra-
                <lb/>
              tiones inſtrument a ad id aptainuenere. </s>
              <s xml:id="echoid-s20328" xml:space="preserve">Archimedes organo uſus. </s>
              <s xml:id="echoid-s20329" xml:space="preserve">quod meſolabium, ideſt medicapium, ſi licet
                <lb/>
              ita dicere, numcupauit. </s>
              <s xml:id="echoid-s20330" xml:space="preserve">nam eo mediæ inter duas datas comparabiles inuenimus. </s>
              <s xml:id="echoid-s20331" xml:space="preserve">Plato quoque alio inſtrumẽto
                <lb/>
                <note position="left" xlink:label="note-514.01.304-02" xlink:href="note-514.01.304-02a" xml:space="preserve">20</note>
              uſus eſt, quod pari ratione dmeſolabium nocare poſſumus. </s>
              <s xml:id="echoid-s20332" xml:space="preserve">Architas demoſtrationes attulit lineis a dimidio
                <lb/>
              Cylindro ſumptis, quas in opus redigere numquam potuit. </s>
              <s xml:id="echoid-s20333" xml:space="preserve">Ego rationes, & </s>
              <s xml:id="echoid-s20334" xml:space="preserve">inſtrumenta explicabo, oſten-
                <lb/>
              damq́ quomodo ad duplicationem cubi, mediarum linearum inuentio nos ducat. </s>
              <s xml:id="echoid-s20335" xml:space="preserve">Quætionis primum afferam
                <lb/>
              occaſionem, e qua ſumma utilitas erit maniſeſta, quam habituri ſunt Architecti in egregijs eorum operibus
                <lb/>
              deformandis. </s>
              <s xml:id="echoid-s20336" xml:space="preserve">Legitur ergo Epiſtola Eratosthenis ad Potlemæum Regem in hunc modumperſcripta.</s>
              <s xml:id="echoid-s20337" xml:space="preserve"/>
            </p>
          </div>
          <div xml:id="echoid-div718" type="section" level="2" n="135">
            <head xml:id="echoid-head143" xml:space="preserve">PTOLEM AEO REGI ERATOSTHENES. S.</head>
            <p style="it">
              <s xml:id="echoid-s20338" xml:space="preserve">Dicitur ex antiquis tragædiarum compoſitoribus unum introducere Minoa Glauco ſepulchrum excitare
                <lb/>
              uolentem, cumq; </s>
              <s xml:id="echoid-s20339" xml:space="preserve">dictum fuiſſet illud quaqua uerſus eſſe pedes centum: </s>
              <s xml:id="echoid-s20340" xml:space="preserve">Dixit paruam fore arcam pro Regio
                <lb/>
              ſepulchro, duplicetur igitur, & </s>
              <s xml:id="echoid-s20341" xml:space="preserve">cubus non mutetur. </s>
              <s xml:id="echoid-s20342" xml:space="preserve">certe qui unum quodque latus duplicare uoluerit, non
                <lb/>
                <note position="left" xlink:label="note-514.01.304-03" xlink:href="note-514.01.304-03a" xml:space="preserve">30</note>
              erit erroris expers. </s>
              <s xml:id="echoid-s20343" xml:space="preserve">nam lateribus duplicatis planum quodlibet quadruplum efficietur, ipſum uero ſolidum
                <lb/>
              octuplum. </s>
              <s xml:id="echoid-s20344" xml:space="preserve">Quæſitum igitur est a geometris, qua ratione ſolido in eadem figura permanens duplum efficeretur.
                <lb/>
              </s>
              <s xml:id="echoid-s20345" xml:space="preserve">Quæſtio hæc cubi duplicatio nominata eſt. </s>
              <s xml:id="echoid-s20346" xml:space="preserve">nam propoſito cubo quærebant, qua uia alterum illi duplum effice-
                <lb/>
              rent. </s>
              <s xml:id="echoid-s20347" xml:space="preserve">Ambigentibus, & </s>
              <s xml:id="echoid-s20348" xml:space="preserve">labor antibus cæteris, prius extitit Hippocrates, qui indicauit id fieri poſſe,ſi con-
                <lb/>
              ſtitutis duabus lineis, quarum maior minoris eſſet dupla, duæ. </s>
              <s xml:id="echoid-s20349" xml:space="preserve">in continua proportione inuenirentur. </s>
              <s xml:id="echoid-s20350" xml:space="preserve">
                <lb/>
              Quare ea res dubia in maiorem difficultatem uerſa es̃t. </s>
              <s xml:id="echoid-s20351" xml:space="preserve">Aliquanto poſt Delij morbo laborantes, cum oraculo
                <lb/>
              Apollinis iuberentur aram ipſius duplicare, neque qua id fieri poſſet ratione ſatis uiderent,in eandem dubietatẽ
                <lb/>
              incidere, & </s>
              <s xml:id="echoid-s20352" xml:space="preserve">obiurgante Platone eos geometras, qui erant in Academia, ab ijs quæſitũ est, ut inuenirent quod
                <lb/>
              propoſitũfuerat. </s>
              <s xml:id="echoid-s20353" xml:space="preserve">ij cum lahori ſeſe dediſſent,& </s>
              <s xml:id="echoid-s20354" xml:space="preserve">conantes inuenter duas medias proportione reſpondentes dua-
                <lb/>
              bus propoſitis lineis: </s>
              <s xml:id="echoid-s20355" xml:space="preserve">dicitur Architam Tarentinum eas inueniſſe bemicylindrorum ratione. </s>
              <s xml:id="echoid-s20356" xml:space="preserve">Eudo xus uero fle-
                <lb/>
                <note position="left" xlink:label="note-514.01.304-04" xlink:href="note-514.01.304-04a" xml:space="preserve">40</note>
              xis quibuſdam lineis, cæterum uterque ſane approbatam harum rerum rationem inuenire, ſed neuter eas ad
                <lb/>
              uſum potuit accommodare, & </s>
              <s xml:id="echoid-s20357" xml:space="preserve">manibus experiri, excepto uno Menechmo, qui tamen parum fecit, & </s>
              <s xml:id="echoid-s20358" xml:space="preserve">id parũ
                <lb/>
              maxima cum difficultate.</s>
              <s xml:id="echoid-s20359" xml:space="preserve">Sed nos excogitauimus per organd facilem inuentionem,qua nõ tantum duas medias
                <lb/>
              proportionabiles duabus datis, ſed quotquot propoſitum fuerit, utinueniamus, & </s>
              <s xml:id="echoid-s20360" xml:space="preserve">eo inuento, poterimus de-
                <lb/>
              mum ad cubum reducere propoſitum ſolidum lineis æquè diſtantibus contentum, aut etiam ex una aliam
                <lb/>
              figuram formare, quæ aut æqualis, aut maior ſit ſeruata ſimilitudine. </s>
              <s xml:id="echoid-s20361" xml:space="preserve">Quoniam nullidubium eſt, quin huiuſ-
                <lb/>
              modi inſtrumento duplicari poßint aræ, ædificiaq́, & </s>
              <s xml:id="echoid-s20362" xml:space="preserve">ad cubum referri liquidonum, &</s>
              <s xml:id="echoid-s20363" xml:space="preserve">ſiccorum menſuræ, ut
                <lb/>
              modiorum, & </s>
              <s xml:id="echoid-s20364" xml:space="preserve">ſimilium, quarum menſurarum larteribus uaſorum capacitas dignoſcitur.</s>
              <s xml:id="echoid-s20365" xml:space="preserve">& </s>
              <s xml:id="echoid-s20366" xml:space="preserve">ut ſummatim dicã,
                <lb/>
              quæſtionis buius cognitio utilies est uolentibus duplicare,aut maiorareddere organa, e quibus tela, ſaxa, aut
                <lb/>
              ferreæ pilæ mittuntur. </s>
              <s xml:id="echoid-s20367" xml:space="preserve">nam neceſſe eſt omnia in latum, & </s>
              <s xml:id="echoid-s20368" xml:space="preserve">in longum creſcere proportione quadam, ſiue fo-
                <lb/>
              ramina ſint, ſiue nerui, & </s>
              <s xml:id="echoid-s20369" xml:space="preserve">immiſſa alia, aut quicquid opus fuerit, ſi totum proportione quadam, ſiue fo-
                <lb/>
                <note position="left" xlink:label="note-514.01.304-05" xlink:href="note-514.01.304-05a" xml:space="preserve">50</note>
              fieri non poteſt ſine medij inuentione. </s>
              <s xml:id="echoid-s20370" xml:space="preserve">Demonſtrationem igitur, & </s>
              <s xml:id="echoid-s20371" xml:space="preserve">apparaiumprædicti organi tibi ſubſcripſi,
                <lb/>
              ac primum demonſtrationem.</s>
              <s xml:id="echoid-s20372" xml:space="preserve">#Proponantur duæ rectæ, & </s>
              <s xml:id="echoid-s20373" xml:space="preserve">inæquales lineæ, quarum altera ſit a b, al-
                <lb/>
              tera c, d, quæramus inter duas medias comparabiles ratione continua, ita quidem ut quemadmodum ſe ha
                <lb/>
              bet prima ad ſecundam, ita ſe habeat ſecunda ad tertiam, & </s>
              <s xml:id="echoid-s20374" xml:space="preserve">tertia ad quartam. </s>
              <s xml:id="echoid-s20375" xml:space="preserve">Detur utranque ex pro-
                <lb/>
              poſitis lineis ad perpendiculum cadere in rectam, quæ ſit b d, & </s>
              <s xml:id="echoid-s20376" xml:space="preserve">maior ſit a b, monor uero c d, ab. </s>
              <s xml:id="echoid-s20377" xml:space="preserve">a,
                <lb/>
              autem ad c, ducatur linea, quæ ulterius producta cadat in lineam b d, ibierit e. </s>
              <s xml:id="echoid-s20378" xml:space="preserve">Ducatur etiam ab a,
                <lb/>
              ſigno in lineam b d, linea, quæſit a f, & </s>
              <s xml:id="echoid-s20379" xml:space="preserve">ab f, rurſum ducatur linea a b, æquè distans, quæ ſitf g.
                <lb/>
              </s>
              <s xml:id="echoid-s20380" xml:space="preserve">quæ lineam a c, in puncto, g, tangat. </s>
              <s xml:id="echoid-s20381" xml:space="preserve">Similiter ducatur linea a ſigno g, æquidiſtans lineæ a f, & </s>
              <s xml:id="echoid-s20382" xml:space="preserve">
                <lb/>
              fit illa g h, quæ lineam b d, tangat, in ſigno b, a quo ſigno erigatur linea æquidistans ipſi a b, & </s>
              <s xml:id="echoid-s20383" xml:space="preserve">ſit
                <lb/>
                <note position="left" xlink:label="note-514.01.304-06" xlink:href="note-514.01.304-06a" xml:space="preserve">60</note>
              </s>
            </p>
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