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[76] Anonymus

COMPENDIUM BREVE DE PROPORTIONIBUS

Br1 9v-11r

De proportionibus breviter

Capitulum 1

Br1 9v

De proportionibus aliquid clarius tractare intendimus pro rudium acceleratione; ne prolixitas in subscriptis regulis, quibus magis utimur, reperiatur, breve compendium compilabo. Et primo cum proportio sit quaedam habitudo duorum terminorum inter se, scilicet ad invicem, est sciendum quod proportio non minus quam de tribus summi potest qua in re augentur numeri, ut inferius denotabo. Unde sciendum est quod genera inaequalitatis sunt quinque, scilicet multiplex, superparticulare, superpartiens, multiplex superparticulare, et multiplex superpartiens.

De gradibus seu generibus inaequalitatis

Capitulum 2

Br1 10r

Primum genus inaequalitatis tres habet gradus, scilicet duplum ut duo ad unum, triplum ut tres ad unum, quadruplum ut quattuor ad unum. Exemplum in multiplici:

[77] [CSM38:77,1; text: Tenor, Primus gradus, Secundus gradus, Tertius gradus] [ANOCBP 01GF]

Secundum genus inaequalitatis tres habet gradus, scilicet sexquialtera ut tres ad duo, sexquitertia ut quattuor ad tres, sexquiquarta ut quinque ad quattuor. Exemplum superparticulare: (Vide ubi est "A"):

[CSM38:77,2; text: Tenor, Primus gradus, Secundus gradus, Tertius gradus in superparticulare, Subdupla, per thesim, Subsexquialtera superbipartiens. Ista proferuntur] [ANOCBP 01GF]

Tertium genus inaequalitatis tres habet gradus, scilicet superbipartiens ut quinque ad tres, supertripartiens ut septem ad quattuor, superquadripartiens ut novem ad quinque. Exemplum superbipartiente: (Vide ubi est "B"):

[78] [CSM38:78,1; text: Tenor, Primus gradus, Secundus gradus, Tertius gradus per arsim] [ANOCBP 02GF]

Quartum genus inaequalitatis habet tres gradus, scilicet dupla sexquialtera ut quinque ad duo, dupla sexquitertia ut septem ad tres, tripla sexquialtera ut septem ad duo. Exemplum in multiplici superparticulare:

[CSM38:78,2; text: Tenor, Primus gradus, Secundus gradus, Tertius gradus] [ANOCBP 02GF]

Quintum genus inaequalitatis habet tres gradus, scilicet dupla superbipartiens ut octo ad tres, dupla supertripartiens ut undecim ad quattuor, dupla superquadripartiens ut 14 ad quinque.

[79] [CSM38:79; text: Tenor, Primus gradus, Secundus gradus, Tertius gradus] [ANOCBP 02GF]

Arbor eius est sequens.

[80-81] [CSM38:80-81; text: ARBOR, PRIMUM GENUS, Dupla Diapason, MULTIPLEX, Tripla Diapason, Diapente, Quadrupla, Bis Diapason, Subcomes, SUPERBIPARTIENS, Sexquialtera, Emiola, Sexquidupla, SUPERTRIPARTIENS, TERTIUM GENUS, SUPERPARTIENS, Comes, Diatessaron, Sexquitertia, Epitrita Sistema, SUPERPARTICULARE, Diapason tonus, Sexquiquarta, SECUNDUM GENUS, Superquadripartiens, Diapason Diatessaron, Dupla Superbipartiens, MULTIPLEX SUPERPARTIENS, Dupla Supertripartiens, Dupla Superquadripartiens, Dupla Sexquialtera, Dupla Sexquitertia, Dupla Sexquiquarta, MULTIPLEX SUPERPARTICULARE, QUARTUM GENUS, Tonus Epogdous, Sexquioctava Diastema, Ad secundum genus, In radicibus autem dat diastema ut hic:] [ANOCBP 03GF]



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