Vitruvius
,
De architectura libri decem
,
1567
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ſic 24. </
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<
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xml:space
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<
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<
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xml:space
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<
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xml:space
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</
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<
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xml:space
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<
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<
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xml:space
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">Pari ratione ignoretur ſecundus numerus ſcilicet 20. </
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Collocato ante primum duos poſteriores terminos hoc modo 24. </
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<
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xml:space
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16. </
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<
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<
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per 16. </
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<
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<
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xml:space
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">quæ partita per 24. </
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<
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<
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xml:space
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">Cæterum ſi tertius ignoratur numerus, ſcili-
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cet 24. </
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<
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ad 30. </
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<
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<
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<
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<
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Sed poſtquàm partitione abſoluta ipſius producti per primum, & </
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">partiens eſt numerus, reliquus erit numerus
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aliquis diuidens minor, obſeruabis eum in ſubtiliores partes distribuendum ea ratione, quam tertius numerus
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ſeu terminus obtinet, atque productus inde numerus iterum per primum eſt partiendus, idq́; </
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<
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dum, quatenus ex continenti partitione nil amplius relinquatur, quare & </
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<
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numerum, cum ipſo tertio, re ac nomine ſeu qualitate ſemper conuenire. </
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<
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xml:space
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">Vnde ſi primus trium numerorum
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ſolis integris numeris cons
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titerit, tertius uero fractis, uel contra, illud prius conaberis , quàm prædictam re-
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gulam experiaris, ut alterum propoſitorum numerorum , ad alterius denominationem reuoces. </
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<
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">De ijs rebus
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exempla plurima ex Arithmeticorum abacis deſumere potes. </
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<
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">Probabis autem an recte ipſam regulam ex
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pertus fueris, ſi primum in quartum duxeris, nam idem reddetur terminus, qui ex ductu ſecundi in tertium
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redditur. </
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<
s
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xml:space
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">nam ſi inæquales prædictos numeros inueneris , ſcito te erraſſe , ad calculum igitur redeundum eſt .
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<
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">Ac ut abſolutam reddamus hanc pulcherrimam quæſtionem, ex Alchindo addemus admir abilem illam regu-
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lam , quæ quinque terminis propoſitis, ſextum ignotum dignoſcere, quemcunque locum teneat, facile poſſimus. </
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nam dari poſſunt ſex numerorum termini, ſic ſe mutua ratione reſpondentes , ut ratio primi ad ſecundum com-
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ponatur, ex rationibus tertij ad quartum, & </
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<
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"># Dentur igitur ſex termini ſibi ratio-
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ne aliqua comparati. </
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3. </
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<
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xml:space
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<
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<
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pra diximus ordine, fiet enim ratio 18. </
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<
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<
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huiuſmodi primorum terminorum caput, & </
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">radix eſt omnium aliarum, quæ numero ſunt decem & </
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</
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mum, constare dignoſcitur . </
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<
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<
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cet uſus ſum in materna lingua literis a, b, c, d, e, f, ita enim Alchindus poſuerat. </
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gentiam numerorum notas appingam. </
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<
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quintum, & </
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rum ratione cum ſecundis in omnibus ordinibus, intelliguntur eſſe compoſitæ, ex rationibus tertij ad quartum,
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& </
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# ###### Ordo numerorum.
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Modi compa- \\ rabiles. # Trimus. # Secundus. # Tertius. # Quartus. # Quintus. # Sextus.
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Trimus modus. # 1 # 2 # 3 # 4 # 6 # 9
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Secundus modus. # 1 # 2 # 3 # 9 # 6 # 4
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Tertius modus. # 1 # 3 # 2 # 4 # 6 # 9
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Quartus. # 1 # 3 # 2 # 9 # 6 # 4
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Quintus. # 1 # 6 # 2 # 9 # 3 # 4
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Sextus. # 1 # 6 # 2 # 4 # 3 # 9
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Septimus. # 2 # 4 # 1 # 3 # 9 # 6
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Octauus. # 2 # 4 # 1 # 6 # 9 # 3
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Nonus. # 2 # 9 # 1 # 3 # 4 # 6
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<
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eſt in quo ratio primi numeri ad ſecundum con-
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ſtat ex ratione tertij ad quartum, & </
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<
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ti ad ſextum.</
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# #### Ordo numerorum.
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Modi compa- \\ rabiles. # Trimus. # Secundus. # Tertius. # Quartus. # Quintus. # Sextus.
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Decimus. # 2 # 9 # 1 # 6 # 4 # 3
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Vndecimus. # 3 # 4 # 1 # 2 # 9 # 6
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Duodecimus. # 3 # 4 # 1 # 6 # 9 # 2
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Decimus tertius. # 3 # 9 # 1 # 2 # 4 # 6
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Decimus quartus. # 3 # 9 # 1 # 6 # 4 # 2
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Decimus quinturs. # 4 # 6 # 2 # 1 # 3 # 9
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Decimus ſextus. # 4 # 6 # 2 # 9 # 3 # 1
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Decimus ſeptimus. # 6 # 9 # 1 # 2 # 4 # 3
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Decimus octauus. # 6 # 9 # 1 # 3# 4 # 2
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Subſeſquitertia. # 3--4
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Subſeſquialtera. # 6--9
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Subdupla, ut 1. ad 2 # 18--36
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