6939LIBER PRIMVS.
10.
Qvando intra Quadrantem non deſcripti ſunt plures quadrantes,
11Quo pact@
per circinum
deprehendan-
tur Minuta,
ac ſecunda in
quauis propo-
ſita grad{us}
particula.
ſed vnicus tantum adeſt in 90. gradus exquiſitè diſtributus, cognoſcemus ſo-
lo circinibeneſicio, quot Minuta, ac ſecunda in quauis gradus particula conti-
neantur: id quod etiam in libello de vſu, & fabrica inſtrumenti horologiorũ,
& in Aſtrolabio fecimus, hoc ſcilicet modo. Sit data verbigratia particulatu,
in gradu 20. ſuperioris Quadrantis BC. Sumatur ea diligentiſsimè beneſicio
circini, & à principio Quadrantis, id eſt, à puncto C, incipiendo, eadem aper-
tura circini accipiantur 60. æquales particulæ vſque ad punctum X, ita vt arcus
CX, ſexagecuplus ſit arcus t u: Quot. n. gradus integri in hoc arcu ſexagecu-
plo comprehenduntur, tot minuta complectetur particula data tu. Et ſi vl-
tra gradus integros in arcu CX, ſuperſit aliqua particula, accipiatur ea ſexagies
quoque, initio facto à puncto C. Nam quot gradus integri in hoc arcu ſexa-
gecuplo continentur, tot ſecunda vltra Minuta inuenta continebuntur in da-
2424[Handwritten note 24]2525[Handwritten note 25]2626[Handwritten note 26]2727[Handwritten note 27]2828[Handwritten note 28]2929[Handwritten note 29] ta particula t u. Quod ſi adhuc aliquid ſuperſit, reperientur eodem modo Ter-
tia, & c. Ita que cumin arcu CX, quiſexagecuplus eſt particulæ t u, continean-
tur 40. gradus integri, comprehendet particula t u, quadraginta Minuta, & in-
ſuper tot ſecunda, quot gradus continenturin arcu, qui ſexagecuplus ſit par-
ticulæ vltra 40. gradus in arcu CX, contentæ, & c.
11Quo pact@
per circinum
deprehendan-
tur Minuta,
ac ſecunda in
quauis propo-
ſita grad{us}
particula.
ſed vnicus tantum adeſt in 90. gradus exquiſitè diſtributus, cognoſcemus ſo-
lo circinibeneſicio, quot Minuta, ac ſecunda in quauis gradus particula conti-
neantur: id quod etiam in libello de vſu, & fabrica inſtrumenti horologiorũ,
& in Aſtrolabio fecimus, hoc ſcilicet modo. Sit data verbigratia particulatu,
in gradu 20. ſuperioris Quadrantis BC. Sumatur ea diligentiſsimè beneſicio
circini, & à principio Quadrantis, id eſt, à puncto C, incipiendo, eadem aper-
tura circini accipiantur 60. æquales particulæ vſque ad punctum X, ita vt arcus
CX, ſexagecuplus ſit arcus t u: Quot. n. gradus integri in hoc arcu ſexagecu-
plo comprehenduntur, tot minuta complectetur particula data tu. Et ſi vl-
tra gradus integros in arcu CX, ſuperſit aliqua particula, accipiatur ea ſexagies
quoque, initio facto à puncto C. Nam quot gradus integri in hoc arcu ſexa-
gecuplo continentur, tot ſecunda vltra Minuta inuenta continebuntur in da-
2424[Handwritten note 24]2525[Handwritten note 25]2626[Handwritten note 26]2727[Handwritten note 27]2828[Handwritten note 28]2929[Handwritten note 29] ta particula t u. Quod ſi adhuc aliquid ſuperſit, reperientur eodem modo Ter-
tia, & c. Ita que cumin arcu CX, quiſexagecuplus eſt particulæ t u, continean-
tur 40. gradus integri, comprehendet particula t u, quadraginta Minuta, & in-
ſuper tot ſecunda, quot gradus continenturin arcu, qui ſexagecuplus ſit par-
ticulæ vltra 40. gradus in arcu CX, contentæ, & c.
Hoc autem ita demonſtro.
Quã proportionem habet arcus 60.
graduum
2424[Handwritten note 24]2525[Handwritten note 25]2626[Handwritten note 26]2727[Handwritten note 27]2828[Handwritten note 28]2929[Handwritten note 29] ad 1. gradum, eam habetarcus CX. ad particulam tu, cum vtrobique propor-
tio ſit ſexagecupla. Igitur permutando erit, vt arcus 60. graduum ad arcum
CX, ita 1. gradus ad particulam t u: Ac proinde quot partes ſexageſimæ arcus
60. graduum, hoc eſt, quot gradus in arcu C X, continentur, tot ſexageſimæ
partes vnius gradus, id eſt, tot minuta in particula tu, exiſtent. Item quam
proportionem haber arcus 60. Minutorum adi. Minutum eam habet arcus ſe-
xagecuplus particulæ, quæ vltra gradus integros vſque ad X, ſupereſt ad hanc
ipſam particulam. Permutando igitur erit, vt arcus 60. Minutorum ad arcum
ſexagecuplum dictæ particulæ reliquæ, ita 1. Minutum ad dictam particulam re-
liquam. Quare quot partes ſexageſimæ arcus 60. Minutorum, hoc eſt, quot
minuta in arcu dictæ particulæ ſexagecuplo (ſumendo nunc gradus Quadran-
tis BC, pro Minutis) continentur, tot partes ſexageſimæ vnius Minuti, id eſt, tot
Secunda, in reliqua illa particula includentur, & ſic deinceps, ſi opus ſit, de
Tertijs, Quartis, & c. intelligatur. Sed ſatis eſt, meo iudicio, ſi minuta diligen-
ter inquirantur. Etſi quidem particula remanens maior fuerit ſemiſſe gradus,
2424[Handwritten note 24]2525[Handwritten note 25]2626[Handwritten note 26]2727[Handwritten note 27]2828[Handwritten note 28]2929[Handwritten note 29] pro illa Minutum aſſumatur, Minutiſque inuentis adij ciatur, quod tunc in illa
particula contineantur plura Secunda quam 30. Si verò eadem particula ſe-
miſſe gradus fuerit minor, nihil Minutis inuẽtis adijciatur, quod tuncin illa par-
ticula pauciora Secũ da includantur, ꝗ̃ 30. Si deniq; dicta particula ſemiſsi grad.
fuerit æqualis, liberũ ſit addere Minutis inuẽtis vnum Minutũ, vel non addere.
2424[Handwritten note 24]2525[Handwritten note 25]2626[Handwritten note 26]2727[Handwritten note 27]2828[Handwritten note 28]2929[Handwritten note 29] ad 1. gradum, eam habetarcus CX. ad particulam tu, cum vtrobique propor-
tio ſit ſexagecupla. Igitur permutando erit, vt arcus 60. graduum ad arcum
CX, ita 1. gradus ad particulam t u: Ac proinde quot partes ſexageſimæ arcus
60. graduum, hoc eſt, quot gradus in arcu C X, continentur, tot ſexageſimæ
partes vnius gradus, id eſt, tot minuta in particula tu, exiſtent. Item quam
proportionem haber arcus 60. Minutorum adi. Minutum eam habet arcus ſe-
xagecuplus particulæ, quæ vltra gradus integros vſque ad X, ſupereſt ad hanc
ipſam particulam. Permutando igitur erit, vt arcus 60. Minutorum ad arcum
ſexagecuplum dictæ particulæ reliquæ, ita 1. Minutum ad dictam particulam re-
liquam. Quare quot partes ſexageſimæ arcus 60. Minutorum, hoc eſt, quot
minuta in arcu dictæ particulæ ſexagecuplo (ſumendo nunc gradus Quadran-
tis BC, pro Minutis) continentur, tot partes ſexageſimæ vnius Minuti, id eſt, tot
Secunda, in reliqua illa particula includentur, & ſic deinceps, ſi opus ſit, de
Tertijs, Quartis, & c. intelligatur. Sed ſatis eſt, meo iudicio, ſi minuta diligen-
ter inquirantur. Etſi quidem particula remanens maior fuerit ſemiſſe gradus,
2424[Handwritten note 24]2525[Handwritten note 25]2626[Handwritten note 26]2727[Handwritten note 27]2828[Handwritten note 28]2929[Handwritten note 29] pro illa Minutum aſſumatur, Minutiſque inuentis adij ciatur, quod tunc in illa
particula contineantur plura Secunda quam 30. Si verò eadem particula ſe-
miſſe gradus fuerit minor, nihil Minutis inuẽtis adijciatur, quod tuncin illa par-
ticula pauciora Secũ da includantur, ꝗ̃ 30. Si deniq; dicta particula ſemiſsi grad.
fuerit æqualis, liberũ ſit addere Minutis inuẽtis vnum Minutũ, vel non addere.
11.
Qvia verò fa cilè error committi poteſt, ſi circino particulam dictam
2424[Handwritten note 24]2525[Handwritten note 25]2626[Handwritten note 26]2727[Handwritten note 27]2828[Handwritten note 28]2929[Handwritten note 29] gradus, vel minuti ſexagies ordine ſumere velimus, rectius feceris, quando
particula data ſemiſſe gradus minor eſt, ſi eam vna cum præcedente graduacce-
ptam primo loco quintuples, deinde hunc arcum quintuplũ duples, tertio hũc
2424[Handwritten note 24]2525[Handwritten note 25]2626[Handwritten note 26]2727[Handwritten note 27]2828[Handwritten note 28]2929[Handwritten note 29] arcum duplum triples, ac tandem quarto hunc arcum triplum iterum duples.
Vltimus enim hic arcus erit datæ particulæ vna cum gradu accepto ſexagecu-
plus. Quareſi ex eo demãtur 60. gradus, in dicabuntreliqui gradus numerũ mi-
nutorumin data particula contentorum. Qnod ſi per æſtimationẽ cognoueris,
2424[Handwritten note 24]2525[Handwritten note 25]2626[Handwritten note 26]2727[Handwritten note 27]2828[Handwritten note 28]2929[Handwritten note 29]
2424[Handwritten note 24]2525[Handwritten note 25]2626[Handwritten note 26]2727[Handwritten note 27]2828[Handwritten note 28]2929[Handwritten note 29] gradus, vel minuti ſexagies ordine ſumere velimus, rectius feceris, quando
particula data ſemiſſe gradus minor eſt, ſi eam vna cum præcedente graduacce-
ptam primo loco quintuples, deinde hunc arcum quintuplũ duples, tertio hũc
2424[Handwritten note 24]2525[Handwritten note 25]2626[Handwritten note 26]2727[Handwritten note 27]2828[Handwritten note 28]2929[Handwritten note 29] arcum duplum triples, ac tandem quarto hunc arcum triplum iterum duples.
Vltimus enim hic arcus erit datæ particulæ vna cum gradu accepto ſexagecu-
plus. Quareſi ex eo demãtur 60. gradus, in dicabuntreliqui gradus numerũ mi-
nutorumin data particula contentorum. Qnod ſi per æſtimationẽ cognoueris,
2424[Handwritten note 24]2525[Handwritten note 25]2626[Handwritten note 26]2727[Handwritten note 27]2828[Handwritten note 28]2929[Handwritten note 29]