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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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CiL AVDLCCLLOBLM LL.1
2A
Denigue; quoniam hujulmodi numeri fracti haud ita commode poterane ab illis exprimI quL
Fjeuras Indicas (quibus nunc utimur) non habebant; numerique abloluri, qui omnes has in le
rationes continerent, fururi ellene majores quam quos illi commode tractare possene: Prolemxeus
(pro more tuo in aliis iltiusmodi calibus) nuissero 60 exprimir id quod eso per L; adeoque per
220, quod eso per 2; numerolque intermedios (quam proxime) per hilce proportionales, ad
junetis icidem scrupulis sexagesimis (sire, ur loquuncur, iminuris primis) ad majorem (quantum
OpuS erat) accurarionem. Nempen pro numeris nottris, hos haber, in lingulis respectire ModiS.
17
Minoly. ) Fydio.  Phryeio. ) Dorio. ) Eypols. ) Elypo. sEypodo.
cio.
160
67
1
186
d
0,60. 57, 60
3063
56(7Y
47,80
7368
IL
0180
0lor 26 50
C0
Ol9c
1OT 15]94 48)1O2 5E TOF
125 43 106, 40 106 50) FI5
120 0)12F 54 220 0720
dio. phrysio. 210.
4. 3 100
5760
1368
7IDE
060
40 106 40 106
5T2F 54(120
2L.
Atque hi quidem sunt numeri (de sic excogitari) quos habet (in medio loco Dotites ) in Ca-
noniis seprem primoribus (pro Fonorum mutationibus) in modis lingulis; nimirum Generis Dia-
coni Fonici puri (nempe, prout per se cancatur, absque mixtura cum modis aliis,) pro illo Dia-
palon quod o rims vocar: nempe, a Vere dicreugmenon (in grare) ad Fyparen melon; in
quo, Tonus diazeuctieus, medius incercedis, inter duo disjuncta Dia. tellaron.
Sunt aucem horum Raciones, in Modo
Mixolydio 8: X 8 X 3 x3 : X 8 X
Lydio
Phrgeio
Dorio
23 : X 8: X 8 X 4 X39: X 8 X 3
3 453: X 8: X B X B x33: X 8
X 8 X33: X 8: X 8 + 3 x2
Hypolydio c 3: n 3 43 137:
Fyxopheysio 1E X 33 : X 8 X 3 X5G: X 8: X 8
riypodorio
3 4.3: 4 8
8 X ix
Seguitur aliud Dia. paTOn, qyod srô utons YOCaE; nempe d Mele (in grave) ad Prollambanome
non; aut etiam (quod cantundem cHt) a Nere Hyperbolxon ad Melen.
Hoc aliud Dia palon (in eodem Genere, Diatono Fonico,) sro uions dictum, numeros (uOS eo-
dem arciticio obrincbir; nili quod hic (propter Fonum duobus conjunetis Dia cellaron, ad grare,
subjectum,) sumendi sinc illi ex hac conrinua musciplicatione,
+: X34 = X 33 : X 8X = X 3 4: X 3 = 2
Onde habentur numeri (pro Modi Dorii Dia paton ind̀ vions,)
5
15 2
Aeque hi quidem ducti (ue prius) in 5X5 x 273 (pro Modis Phrygio, Lydio, MiXolydio;) de l
3x8X8 (pro Hypolydio, Fypopheysio, et Eypodorio;) exhibebunt numeros sequentes; sedi
bus suis (more quo prius) sie recommodandos,
CiaD. 75.
08
57
26
49 102
5XC
40IF
600
30(03
18
25]94
16 BC
43,94
060
34,67
Patdnete
Ae
Mele
peteor