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# Title: [Quo Continentur Claudii Ptolemaei, Porphyrii, Manuelis Bryennii Harmonica: Archimedis Arenarius, & Dimensio Circuli; Cum Eutocii Commentario: Aristarchi Samii, de Magnitudinibus & Distantiis Solis & Lunae, Liber: Pappi Alexandrini, Libri Secundi Collectaneorum, hactenus desiderati, Fragmentum ; Graece & Latine Edita, cum Notis ; Accedunt Epistolae nonnullae, rem Mathematicam spectantes; Et Opuscula quaedam Miscellanea] Quo Continentur Claudii Ptolemæi, Porphyrii, Manuelis Bryennii Harmonica: Archimedis Arenarius, & Dimensio Circuli; Cum Eutocii Commentario: Aristarchi Samii, de Magnitudinibus & Distantiis Solis & Lunæ, Liber: Pappi Alexandrini, Libri Secundi Collectaneorum, hactenus desiderati, Fragmentum ; Græce & Latine Edita, cum Notis ; Accedunt Epistolæ nonnullæ, rem Mathematicam spectantes; Et Opuscula quædam Miscellanea (shelfmark Leibn. Marg. 100:3)
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liliadDEEEEOCLMI
Ciap. 25.
Appendix ad NNotas C. A P. ZV. L.
Abellas Prolemaei ad Capur hoc spectantes (in omnibus quos habuimus Codicibus deprava
ta5) qua Mechodo nos relticuimus, dicendum reltat.
Ceneris Diaroni Toniei (Cap. 15. Lib. L.) Ponuntur rationes, 3X3 X33 =3: Quae (ad inte
orum Dia palon) bis reperenda lune, incerpolita Zoni ratione 8. Adeoque, potuto primo (ono
(hoc est acuristimo) E, reliqui habencur hac concinua mulciplicatione,
2: 182 5139: 23: 2 34 3 4 2, = 2
Onde prodenne hi numeri,
3 3 3 28 2 2
pro Tonis octo unius Dia paton (in illo genere) cujus Mese est in Mese naturali; pro PonO
(Teu Modo) Dorio. (Numerus minor pro acuriori lono ponitur; major, pro craviori; in ca
ratione quam exisir chordarum aequitonarum lonsicudo.)
Cumque (per Cap. 20. lib. 2.) Modus Phrygius ponitur (quam Dorins) uno Tono acutior,
(seu acurior in racione 3;) et Lydius, uno achuc Pono acurior; et Mixolydius, achuc Lim-
mate acutior (seu in rarione 333:) Hypolrdius vero (quam Dorius) Limmate grarior; et FIypo.
phrysius, grarior adhue Tono; et Flypodorius (quam hic) Tono iridem grarior: Si numeri
jam expolici (pro Dorio) ducantur linguli in 3; habentur numeri (uno tono acutiores) Dro
Phrysio: acque his iterum ductis iridem in 3, habentur numeri pro Lydio: qui demum ducti in
215, exhibent numeros pro Mixolydio: Tidemque numeri (pro Dorio) ducti in 36, exhibene nu-
merOS (Limmate graviores) pro Flypolydio: atque hi in 3, numeros pro Hypophrygio: acque
hi demum in 8, numeros pro Hypodorio. Nempe, pro Modo
Mixolydio
Lydio
Phrysio
Dorio
Hopolcio
Hypophrysio
Fypodorio.
87 15 2 C9 3i
Suntque hi numeri porro concinuandi, in utramvis partem, Facili opera: Nempe, Scut (rerbi
gracia) in Modo Phiysio, numerus octarus s, est primi s duplus, (quoniam eodem cst, 1010
Dia palon, grarior; adeoque in ratione dupla:) sic, qui hunc securueus cAt 2 in loco nono,
erit duplus numeri r in loco secundo; et lic deinceps: Fr similiter, in Modo Fypolydio, ut pri
mus scu acurissimus 335, elt octari seu graristimi 3,3 semistis: Sic (si modus idem sic in acutum
continuandus) qui eodem numero pruno proxime sucurus est acucior, erit 5t, semistis septimi
23: Ex sic ubique. Franseundo nimirum in aliud Dia palon, quod sic expolito grarius aeu-
ciutre.
Jam rero, eum (per Cap. 1Y. lib. 2.) quo Modi expolici melius inter le comparentur, et
chorda qua est cujusque (poreltate) Media, (nimirum, qui acurioris DiazeuXeos, sive Toni
disjunctiri, prariorem lonum retere,) Cuam ibi ledem altignaram habeat, (reliquaeque, cum re-
spectu ad hane, suas sibi singulae Cortiancur;) Nimirum Dorii Media, in Mese nacurali; Ppr-
eii, in Paramete; Lydii, in Prite diereusmenon; Mixolydii, in Paranete diczeusmenon: item-
que Hypolydii in Lichano melon; Fypophrysii, in Parypate meton; ee Hypodorii denique,
in Hypace meton: Numeri jam expoliti, pro cujusque Modi Dia paton, sic crumt luis ledibus
consticuri. Nimirum
et 183 1929 32 15 83 l243
nian
H