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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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CaP. 25.
EL AVDII PTOLF M X
Hoc ett, in numeris Pcolemxi: pro Modo
Mlixols. ) Lydio. ) Phrysio.) Dorio. J Hypoly. ( HypO. Jypodo
dio.
60 050 5760
67 30(63 13(63
80 382 1680
90
084 X7(OF
FOT 25(94 4994
T25 43)106 40, 106
120 0121 54 +20
60L 10180
0(84
5 04.
17 o2
49(94
40(100 40(108 22]206
OT20
8+12 221121 54(120
04
Acque hi quidem tunc numeri (medio loco potici) in Canoniis septem posterioribus, pro mo.
dis Cingulis (Generis Diaconi Foniei puri) in Dia paton do utons.
Suntque horum Rationes; pro modo
Mixolydio 3X 3 x33: X 3: X 8 X 3 X3
Lydio
Phryeio
Dorio
Hyvolydio
37: X 8 X 3 X3  : X 3: X 8 X 
3 233: X 8 X 3 X3G: X 8: X 2
BX 3 X23: X 8 X 3 X23: X Z
8: X 8 X 9 239: X 8 X 4 XZ
Fypophrysio 33: X 8: X 8 X 3 X33: X 8 X 3
Hypodorio 4 x33 : X 3: X 8 X 3 x3 : X Z
Ad eandem tormam, pro reliquis Generibus (quae eum Ponico Diatono conitmiscet Pcolemaeus)
habencur numeri: (Unde videre eric, quinam ex uno zenere, quinam ex alio, in miltura com-
Derianeur.)
Nimirum, Chroma Incensum Pcolemai, pro Dia paton d̀ Nere diereuxmenon ad FTypaten Me.
Ton, in Modo Borio, componitur (ur liquet C ap. 25. lib. T.) ex his racionibus,
F: X3X FZ X 3F: X8: X Z X YZ X 37 = 20
Unde hi habentur numeri, (pro modo Dorio,)
8 1t 3 2 4 21 2.
Acque hi concinue ducti Cuc prius) in 3x3 x 328 (pro Phrygio, Lydio, et Mixolydio,) atque
in 35 3XB (pro Hypolydio, Hypophrysio, et Hypodorio;) exhibeni hos numeros: nempes
o
Mixolydio
Lydio
Phrysio
Dorio
Fypolydio
Hypophrysio
Hypodorio
8
i6
a10. (PAI3SIO. XIP.
57 60
T36E
C
8
491O2
2
1160
1363
060
3467
8Sc
0156
3063
2090
49j202
qu(106
L
 235 8 215 37 si 297 18
38
40 B
7
295 3us 383 10
3
e
3 (73 2
37 16 402 13
dio duobus; unoque in PhrySIO.  e PocOIbuS, in Hypodor libus; in Hypophrygio
duohus; unoque in Fypolydio: ut qui ledes Tuas habicuri sunt extra Bia palon espolcum: )
coridemque ex contraria parre suppletis, (pro locis racuis replendis:) habentur guasici pr.
meri (ad Dia paton d Nete) in lingulis Modis (pro Incenso Chromare puro) hi qui sequun-
EUT. Nempe
tItu;) indeque rescistis qui reduncan heipe, ex pnoribus, i Meoigeto tribus; in Lv.
NetE