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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)
# Folio 623, page id 867984570:0659
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3
N
GOLL F CFIO.
ua
q
7X2
Exemplum F. FA Vcc F  (seu cet and =) = c + 26 80 160 128C 2568
c
Nam, in hoc catu, elt P = 5C, O = = , M = F, n = 2, A (= P == cd2) = 6. B(= AC)
NX
2c
m-n
8∞ Et AC deinceps.
2n B∞) =-
C(=
Fnemplum 2. EA p: 8 = et X = v3: (id elle, ∞ + et x = 1) 5) = c + = 
= 26 w 4 + 4 ct _ = 2. 4. 
2563
S PO n E pEO P, e = pro . Pocest eriam = n Subsliui pro P, et -
Et cunc eradet 13: 53 = c _ - ~3 : = - _ +  _ + 8 , 20 ~ x + 40 x +c
5 q
25 X
modus eligendus est, si x valde parrum sIC; posterior, si valde magnum.
aa
3y
Nam P = y. 0 = =  a. m = - 1. n = 3. A (= p = = p  = 2) -
B(=  AO = = = n = 2 = a a) = aa ecc.
50
3) SEgit c.
 hoc est -.
Exempl. 4. Radix Cubiea ex Ouadrato quadrato iptius d = e, (hoc cAt, dF 9 3) est
23 + 4ed3, 2ec 40
= a3. ec.
da 8caz t dc. Nam P = d. O = . m = 4. n = 3. A (= p = )
Eodem modo simplices etiam Poteltates eliciuntur. Vr, Si quadrato cubus (Supersolidum in-
cellieit ) iptius a = e, (hoc est, a + d seu a te) desideretmr: Frit, juxta Regulam, P = d.
Q = 7. m = 5. _ n = r. Adeoque A (= P ) = a3. B(= = A9) = 5 d e. _ fiC
m - 5n
C = 10a3 ec. D = 10a a C. F. = 5 d et. F = 0. _ C (= -  F 9) = O. Hoc cs.
a + d = a = 5a2 C = 20 a3 ec = 20 a de + 5 d et f 8.
Ouineciam Dirisio, lire simplex sic sire reverica, per eandem Regulam perticitur. VE, CI
Y F (hoc est, a F e sire a + d) in seriem timplieium cerminorum resolvendum sic; Frit,
juxta Regulam, P = d.  = . m = - =. n = 1. _ A (= P  = dE) = d seu-
ee 83
ad +3  + ec.
2d EthCC =  D = ec. H0C et,  
Sic e d Fd, (hoc est, Unicas cer divita per a = C, vel semet per cnbum ejus, ) eradit
ZC, 6eC 10C3
45 91  95
40 L ec
Et NX a Fa 3, (hOC est, N diritum per Radicem cubicam ipsius d F e) eradit N X:
2ec 14 e X l
23 343  943 82d 5
ELN X a. Fet 3, (hoc ett, N diritum per radicem quadrato cubicam (seu supersolidam) ex C ubo
52C3
ipsius a te, tive p. 40. +3date t Sac f csd eradit N : = - 30  12e0
43 543 25 d3, 125 418 + ec.
Pet