Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N1013B" level="3" n="1" type="preface">
              <pb chead="Prohemium" file="0006" n="6"/>
              <p xml:id="N10143">
                <s xml:id="N10144" xml:space="preserve">PReclara philonis in libro ſa­
                  <lb/>
                pientie exſtat ſantentia deum
                  <reg norm="maximum" type="context">maximū</reg>
                  <lb/>
                  <reg norm="optimumque" faithful="optimum" type="simple">optimumqꝫ</reg>
                rerum omnium natura ↄ̨-
                  <lb/>
                ſtantium opificem, cunctorum
                  <reg norm="ſubſtantiam" type="context">ſubſtãtiam</reg>
                  <reg norm="atque" faithful="at" type="simple">atqꝫ</reg>
                  <reg norm="com- paginem" type="context">cõ-
                    <lb/>
                  paginem</reg>
                numero, menſura, ac pondere procre-
                  <lb/>
                aſſe
                  <reg norm="atque" faithful="at" type="simple">atqꝫ</reg>
                diſpoſuiſſe: cui applaudit illud prophe-
                  <lb/>
                te qui profert numero ſeculum.
                  <note position="left" xlink:href="note-0006-01a" xlink:label="note-0006-01" xml:id="N10229" xml:space="preserve">plato in
                    <lb/>
                  thimeo.</note>
                </s>
                <s xml:id="N10158" xml:space="preserve">Cui etiam aſtipu-
                  <lb/>
                latur diuus ille plato in thimeo. magna auctori-
                  <lb/>
                tate commendans deum numeris mundum fabri­
                  <lb/>
                caſſe.
                  <note position="left" xlink:href="note-0006-02a" xlink:label="note-0006-02" xml:id="N10231" xml:space="preserve">Auguſti-
                    <lb/>
                  nꝰ .12. de
                    <lb/>
                  ciuitate.
                    <lb/>
                  c. 18.</note>
                </s>
                <s xml:id="N10166" xml:space="preserve">Quam
                  <reg norm="ſcententiam" type="context">ſcentētiam</reg>
                . Aurelius. Auguſtinus
                  <lb/>
                libro de ciuitate dei
                  <reg norm="commendat" type="context">cõmendat</reg>
                . </s>
                <s xml:id="N1016B" xml:space="preserve">Quapropter inti­
                  <lb/>
                ma,
                  <reg norm="ſecretioraque" faithful="ſecretiora" type="simple">ſecretioraqꝫ</reg>
                nature
                  <reg norm="atque" faithful="at" type="simple">atqꝫ</reg>
                minerue penetralia,
                  <lb/>
                  <reg norm="rerumque" faithful="rerum" type="simple">rerumqꝫ</reg>
                  <reg norm="omnium" type="wordlist">oīm</reg>
                naturalium reconditas paſſiones,
                  <lb/>
                ac motus qui numeris
                  <reg norm="conſiſtunt" type="context">cõſiſtunt</reg>
                  <reg norm="perſcrutari" type="simple">ꝑſcrutari</reg>
                  <reg norm="atque" faithful="at" type="simple">atqꝫ</reg>
                ri-
                  <lb/>
                mari volentes. </s>
                <s xml:id="N10176" xml:space="preserve">arithmeticam at geometricã aut
                  <lb/>
                ſaltem harū ſcententiaꝝ quedam requiſita docu-
                  <lb/>
                mēta neceſſum eſt anteponãt.
                  <note position="left" xlink:href="note-0006-03a" xlink:label="note-0006-03" xml:id="N1023D" xml:space="preserve">pliniꝰ ī .2
                    <lb/>
                  nahiſ. c.
                    <lb/>
                  22.</note>
                </s>
                <s xml:id="N10182" xml:space="preserve">Et non abs re quidē
                  <lb/>
                quoniam non ſolū elementaris hec regio: et natu­
                  <lb/>
                ralia illa entia: que in ea natura ꝓcreãda cenſuit
                  <lb/>
                his nuēris et geometricis ponderibus conſtant:
                  <lb/>
                verumetiam ethereus ille celorum globus (vt inq̇t
                  <lb/>
                plinius et ariſtoteles) pythagore ſcententia arith­
                  <lb/>
                meticis ꝓportionibus, muſiciſ tonis circūuolui­
                  <lb/>
                tur. </s>
                <s xml:id="N10193" xml:space="preserve">Inquit enim ſaturnum dorio moueri, mercu­
                  <lb/>
                rium pthogo iouem phrygio. </s>
                <s xml:id="N10198" xml:space="preserve">Quantã vim arith­
                  <lb/>
                metica ſcententia habeant ad philoſophiam vni-
                  <lb/>
                uerſaſ diſciplinas. </s>
                <s xml:id="N1019F" xml:space="preserve">luculenter in libro de legibꝰ
                  <lb/>
                diuus plato hoſtendit inquiens Legiſlator ciuibꝰ
                  <lb/>
                omnibus p̄cipiat ne a numerorum ordine quo ad
                  <lb/>
                poſſunt diſcedant </s>
                <s xml:id="N101A8" xml:space="preserve">Nã nulla alia diſciplina ad rei
                  <lb/>
                familiaris gubernationē, ad rē publicã, ad artes
                  <lb/>
                deni vniuerſas, tãtã hꝫ vim: quantã hmõi nume­
                  <lb/>
                rorū cognitio. </s>
                <s xml:id="N101B1" xml:space="preserve">Sõnolentos, etiã a natura rudes,
                  <lb/>
                excitat. </s>
                <s xml:id="N101B6" xml:space="preserve">et dociles, memores, ſolerteſ, facit p̄ter
                  <lb/>
                naturã ſuã diuīa arte ꝓficientes </s>
                <s xml:id="N101BB" xml:space="preserve">Incõcuſſa em̄ et in­
                  <lb/>
                uiolata eſt arithmetice at geometrice ſcīa. </s>
                <s xml:id="N101C0" xml:space="preserve">cuiꝰ
                  <lb/>
                veritati ſacratiſſime ſanctiones auctoritatem pre­
                  <lb/>
                bēt īquiētes arithmeticã et geometricã in ſe ita­
                  <lb/>
                tē cõtinere et quãuis pietatis ſcīe non ſint:
                  <note position="left" xlink:href="note-0006-04a" xlink:label="note-0006-04" xml:id="N10247" xml:space="preserve">auguſti-
                    <lb/>
                  nus .3. de
                    <lb/>
                  doc chriſ</note>
                ſunt tñ
                  <lb/>
                maxīo admīculo at adiumento ipſi ſcīe pietatis
                  <lb/>
                vt p̄clare. Aureliꝰ ille Auguſtinꝰ ī libro de doctri­
                  <lb/>
                na chriſtiana ſacrꝪ ↄ̨probat rõibus. </s>
                <s xml:id="N101D4" xml:space="preserve">Has eī ſapiēs
                  <lb/>
                ille ſalomõ dicit pediſſeq̈s, at ancillas theolo-
                  <lb/>
                gie: q̈s iubet vocari ad turrim, et ad menica cinita­
                  <lb/>
                tis.
                  <note position="left" xlink:href="note-0006-05a" xlink:label="note-0006-05" xml:id="N10251" xml:space="preserve">boetiꝰ ṗ-
                    <lb/>
                  mo de cõ.
                    <lb/>
                  phi. ꝓpri­
                    <lb/>
                  ma.</note>
                </s>
                <s xml:id="N101E2" xml:space="preserve">His eī ꝓſtergatis: qui ad theologiſãdū et phi-
                  <lb/>
                loſophãdū ꝓgredit̄̄ (ſi diuo Seuerino boetio cre­
                  <lb/>
                dimꝰ) ſuꝑflue conat̄̄. </s>
                <s xml:id="N101E9" xml:space="preserve">Ad philoſophiã vti temere
                  <lb/>
                his mathemathicis omiſſis documētis accedētes
                  <lb/>
                phīa ipſa ſacrilogos, ſui minimis īuaſores ve­
                  <lb/>
                ſtem ſuã in fruſtra lacerantes (teſte boetio) appel-
                  <lb/>
                lat. </s>
                <s xml:id="N101F4" xml:space="preserve">Et vt verū fatear hinc eſt /  nr̄is tꝑibus ob ha­
                  <lb/>
                rū diſciplinarū defectū: balbutiens at cõcutiēs
                  <lb/>
                viſa ē phīa. </s>
                <s xml:id="N101FB" xml:space="preserve">Plurimū em̄ apḋ grecos phīa valuit
                  <lb/>
                ṗmatū obtinuit: q2 (vt inq̇t cicero) ī ſūmo hono-
                  <lb/>
                re apud illos geometrica fuit nihil apḋ eos ma­
                  <lb/>
                thematicis illuſtriꝰ </s>
                <s xml:id="N10204" xml:space="preserve">Nõ ī merito igit̄̄: ſpeculationi­
                  <lb/>
                bus phyſicis triplicis motus: tractaculū ꝓportio­
                  <lb/>
                nū ex mathematicis codicibus deprõptū duximꝰ
                  <lb/>
                p̄ponēdū et quãtū ingenioli nr̄i vires ſupetūt ab-
                  <lb/>
                ſoluēdū. </s>
                <s xml:id="N1020F" xml:space="preserve">¶ Ad rē ipſaꝫ veniēdo: tractatulus hic ṗn­
                  <lb/>
                cipaliter tripatient̄̄. </s>
                <s xml:id="N10214" xml:space="preserve">In prīa / em̄ ꝑte prīcipali q̄dã
                  <lb/>
                cõmunia mathemathicalia cū terminoꝝ declara­
                  <lb/>
                tionibus ponã. </s>
                <s xml:id="N1021B" xml:space="preserve">In ſecūda / ꝓportionalitatē ꝓpor­
                  <lb/>
                tionū declarabo. </s>
                <s xml:id="N10220" xml:space="preserve">In tertia / vero parte principali
                  <lb/>
                ea applicabo ad motus et motuum ꝓportiones.</s>
              </p>
            </div>
            <div xml:id="N1025D" level="3" n="1" type="chapter" type-free="capitulum">
              <cb chead="Incipiunt proportiones"/>
              <head xml:id="N10264" xml:space="preserve">Capitulum primum de
                <lb/>
              proportione et eius diuiſione.</head>
              <note position="right" xml:id="N10269" xml:space="preserve">propoſi-
                <lb/>
              tio nicho­
                <lb/>
              machi.</note>
              <p xml:id="N10271">
                <s xml:id="N10272" xml:space="preserve">OMnis numerus: et ſimiliter
                  <lb/>
                oīs qunatitas ad alium numerum relatus
                  <lb/>
                (vt ait nichomachus et boetius in primo
                  <lb/>
                arithmetice) aut eſt ei equalis: aut inequalis. </s>
                <s xml:id="N1027B" xml:space="preserve">ſi eſt
                  <lb/>
                equalis: conſtituit ꝓportionem equalitatis: ſi ve-
                  <lb/>
                ro inequalis: ex eo cū altero inequalitatis propor­
                  <lb/>
                tio conſurgit. </s>
                <s xml:id="N10284" xml:space="preserve">¶ Unde proportio eſt duorū nume-
                  <lb/>
                roꝝ: vel duarū quãtitatū: vnius ad alterã certa ha­
                  <lb/>
                bitudo. </s>
                <s xml:id="N1028B" xml:space="preserve">vt habitudo que eſt inter quatuor et .4. et
                  <lb/>
                que eſt inter duo et quatuor: et que eſt īter bipeda­
                  <lb/>
                le et pedale. </s>
                <s xml:id="N10292" xml:space="preserve">Proportio em̄ eſt terminus collecti-
                  <lb/>
                uus: pro duabus rebus et ſignanter quantis vel ꝓ
                  <lb/>
                pluribus ſupponens: cõnotando ipſas eſſe equa-
                  <lb/>
                les: vel vnam alteram aliquo exceſſu excedere. </s>
                <s xml:id="N1029B" xml:space="preserve">Un­
                  <lb/>
                de iſta conſequentia nichil valet. </s>
                <s xml:id="N102A0" xml:space="preserve">hec proportio eſt
                  <lb/>
                vna proportio / ergo eſt vnuꝫ ens: quia demonſtra­
                  <lb/>
                to pedali et bipedali non conſtituentibus vnū de
                  <lb/>
                illis eſt verum dicere:  ſunt aliqua ꝓportio puta
                  <lb/>
                dupla: et tamen illa duo non ſunt vnū ens. </s>
                <s xml:id="N102AB" xml:space="preserve">¶ Du-
                  <lb/>
                plex autē eſt proportio. </s>
                <s xml:id="N102B0" xml:space="preserve">q2 quedã eſt ꝓportio equa­
                  <lb/>
                litatis: alia vero inequalitatis.
                  <note position="right" xlink:href="note-0006-06a" xlink:label="note-0006-06" xml:id="N102EB" xml:space="preserve">diuiſio ꝓ­
                    <lb/>
                  portionū</note>
                </s>
                <s xml:id="N102BA" xml:space="preserve">¶ Proportio eq̈-
                  <lb/>
                litatis: eſt habitudo duarum quantitatum vel nu­
                  <lb/>
                merorū equalium. </s>
                <s xml:id="N102C1" xml:space="preserve">vt habitudo q̄ eſt inter .8. et .8.
                  <lb/>
                pedale et pedale. </s>
                <s xml:id="N102C6" xml:space="preserve">Et ſumat̄̄ hic quãtitas: tã ꝓ quã-
                  <lb/>
                titate molis: quam pro quantitate virtutis.
                  <note position="right" xlink:href="note-0006-07a" xlink:label="note-0006-07" xml:id="N102F3" xml:space="preserve">auguſti-
                    <lb/>
                  nus .5. de
                    <lb/>
                  trinitate</note>
                </s>
                <s xml:id="N102D0" xml:space="preserve">vt ca-
                  <lb/>
                pit beatus. Auguſtinus quinto de trinitate </s>
                <s xml:id="N102D5" xml:space="preserve">¶ Sed
                  <lb/>
                proportio inequalitatis eſt duarum quantitatuꝫ
                  <lb/>
                vel numerorum: vnius ad alterum certa habitudo
                  <lb/>
                vt ꝓportio que eſt inter .2. et .4. pedale et bipedale
                  <lb/>
                </s>
                <s xml:id="N102DF" xml:space="preserve">¶ Item proportionum inequalitatis: quedam eſt
                  <lb/>
                maioris inequalitatis: quedam. </s>
                <s xml:id="N102E4" xml:space="preserve">vero minoris.</s>
              </p>
              <note position="right" xml:id="N102FD" xml:space="preserve">diuiſio ꝓ­
                <lb/>
              portionū
                <lb/>
              īeq̈litatꝪ</note>
              <p xml:id="N10305">
                <s xml:id="N10306" xml:space="preserve">¶ Proportio maioris inequalitatis eſt habitu-
                  <lb/>
                do maioris quantitatis ad minorem. </s>
                <s xml:id="N1030B" xml:space="preserve">vt habitudo
                  <lb/>
                que eſt inter .quattuor. et .2. </s>
                <s xml:id="N10310" xml:space="preserve">¶ Sed proportio mi-
                  <lb/>
                noris inequalitatis: eſt habitudo minoris quan-
                  <lb/>
                titatis ad maiorē. </s>
                <s xml:id="N10317" xml:space="preserve">vt habitudo duorū ad .4. </s>
                <s xml:id="N1031A" xml:space="preserve">¶ Ex
                  <lb/>
                quo ſequitur /  pro eiſdem ſupponunt iſti duo ter­
                  <lb/>
                mini proportio maioris inequalitatis et propor-
                  <lb/>
                tio minoris inequalitatis. </s>
                <s xml:id="N10323" xml:space="preserve">Connotat tamen
                  <lb/>
                iſte terminus proportio maioris inequalitatis 
                  <lb/>
                numerus maior excedat minorem. </s>
                <s xml:id="N1032A" xml:space="preserve">iſte vero termi-
                  <lb/>
                nus ꝓportio minoris inequalitatis: connotat: 
                  <lb/>
                numero minor ſiue quantitatis minor exceditur a
                  <lb/>
                a maiore. </s>
                <s xml:id="N10333" xml:space="preserve">Quando tamen ꝓportio maioris ine­
                  <lb/>
                qualitatis: non capitur pro aggregato ex nume-
                  <lb/>
                ris proportionem habentibus inequalitatis: ſed
                  <lb/>
                pro maiore numero. </s>
                <s xml:id="N1033C" xml:space="preserve">proportio vero minoris ine-
                  <lb/>
                qualitatis pro minore. </s>
                <s xml:id="N10341" xml:space="preserve">Et iſto modo non ſunt ter­
                  <lb/>
                mini conuertibiles </s>
                <s xml:id="N10346" xml:space="preserve">Nam iſto modo capiendo ſi .8
                  <lb/>
                comparentur ad .4.8. ſunt ꝓportio maioris ine-
                  <lb/>
                qualitatis .2.4. minoris inequalitatis.
                  <note position="right" xlink:href="note-0006-08a" xlink:label="note-0006-08" xml:id="N10444" xml:space="preserve">alia diui­
                    <lb/>
                  ſio ꝓpor­
                    <lb/>
                  tionu ieq̈­
                    <lb/>
                  litatis.</note>
                </s>
                <s xml:id="N10352" xml:space="preserve">¶ Item ꝓ-
                  <lb/>
                portio inequalitatis. </s>
                <s xml:id="N10357" xml:space="preserve">eſt duplex. </s>
                <s xml:id="N1035A" xml:space="preserve">quia quedem eſt
                  <lb/>
                rationalis: et quedam irrationalis. </s>
                <s xml:id="N1035F" xml:space="preserve">¶ Propor-
                  <lb/>
                tio ratiõalis: eſt illa ꝓportio q̄ īmediate denomi-
                  <lb/>
                nat̄̄ ab aliq̊ certo nūero vĺ nūeroꝝ fractõe. </s>
                <s xml:id="N10366" xml:space="preserve">vt du-
                  <lb/>
                pla: ſexq̇altera .etc̈. </s>
                <s xml:id="N1036B" xml:space="preserve">Alio mõ ꝓportio rõalis: ē dua­
                  <lb/>
                rum quantitatum ſic ſe habentiū:  idem eſt pars
                  <lb/>
                aliquota vtriuſ idē inquam ad bonum ſenſum.
                  <lb/>
                </s>
                <s xml:id="N10373" xml:space="preserve">¶ Ex quo ſequitur /  cuiuſlibet numeri ad quemli­
                  <lb/>
                bet alium numerum eſt proportio rationalis. </s>
                <s xml:id="N10378" xml:space="preserve">quo­
                  <lb/>
                niam cuiuſlibet numeri vnitas eſt pars aliquota.
                  <lb/>
                  <note position="right" xlink:href="note-0006-09a" xlink:label="note-0006-09" xml:id="N10450" xml:space="preserve">pars ali­
                    <lb/>
                  quota.</note>
                </s>
                <s xml:id="N10384" xml:space="preserve">¶ Unde pars aliquota: ē illa que aliquoties ſum-
                  <lb/>
                pta reddit ſuum totum adequate. </s>
                <s xml:id="N10389" xml:space="preserve">vt vnitas eſt
                  <lb/>
                pars aliquota numeri quarternarii. </s>
                <s xml:id="N1038E" xml:space="preserve">quoniã vni- </s>
              </p>
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