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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 637, page id 867984570:0673
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COF L F C FTO.
637
Hloc tundamento conatus sum etiam reddere speculationes de Ouacratura Currarum simpli-
ciores; perrenique ad Theoremata quadam generaliora. Et, ut candide agam, cece primum
Theorema.
Ad curram aliquam sic d 2 X C. f f 2 Ordinarim. applicata, cermino abscilsae seu batis Z nor-
malicer intistens: Obi licerx des denorane quastiber quancicates Dacas; d On n indices PO.
restatum sire Dignitatum quantitatum quibus aNixx sunE. Fac - = = r, a f r = 5
5 20 +5 2s
eB
5 = 2 52
=2, e ru -  = r: _ Area Curvoe erius D in 2 - 
E
eC
-3 F21
et
= +
4
521
minos proxime ancecedemes; Nempe A cerminum =, B cerminum -  =    c. Hac
+
Series, ubi r fractio est vel numerus negarirus, concinuacur in intinicum; ubi reror inceger est
EE altirmacirus, continuatur ad toc terminos cantum quor sunt Unitares in codemr; et sic extibet
Geometricam Ouacracuram Curvae. Rem L. xemplis illustro.
Exemplum t. Proponatur Parabola, cujus Ordinarim. applicata sit Ya Z. Haec in Forman Re.
Sulae reducta Fic 2 x 0 +, 4 2. Ouare d = 1, D =0, 0 = 0, 5 = a, n = 1, 1 = :. Adeoque
p = 1, 5 = 23,  = = 2 a 5, r = 0. EC Area quaelica = n a D in ; HoC est, 3 ~ Va ~. Ft
sic in genere, Si C 2n Bonacur Ordinarim applicata, prodibit Area, en + F
Fxempl. 2. Sie Ordinacim applicala
Vel eriam at 2 3 x = 1 = C023,. In priori catu elt d = a, D = 1, e = 60, f = = 2, n = 2,
 = = 2. Adeoque r = 1, 5. = - 1, 0 =  2 cc - 22), hoc eAt 
= = 1, 5 = 6c, n-
a 22
2C+ = 2662∞
266 - 22 2
=-2, 2 = - 2, 1 - 1 5 = - 1,  =-
d
 = O. FL Area = Q in =, hoc est -
a2
2 = 0. Et
=x = 1 + 608 5), id est
266
at 22
26 = 2CCZ2
Area his calibus di-
vertimode exhibetur, quatenus computatur 3 diversis sinibus, quorum altienatio, per hos inventos
ralores arearum, Facilis ell.
Exempl. 3. Sic Ordinarim. applicata  V: b Z. f 2. S: hoc est, per Rcductionem ad debicam
cormam; vel ad 2 3 nb = 2; vel a 2 2 X F. + B ~ 12. Eerie, in priori cale, d = a, 0 = - 3
C = b, f = 2, n = 2, n = 3. Adeoque r = - 3, _c. OuarC, CUm r nOn sit numeruS aHtir-
macirus, procedo ad alterum casum. Hic est d = a3, D = - 4, 0 = 1, f = b, n = - 1, a = 5.
Adeogue r = 3, 5 = 33, D = =, X F = bZ ), seu -
FE Area, C in =
a2. + a b
b22
2
2, 2
c
22 35b  25 et 356
13∞ + b2.
a32 +
B22
Y33 + B∞,  = = 2.
30bb. + 24b2 - 1622
105bb22
Exempl. 4. Sic denique Ordinacim applieaca p: P = 3 acc 3 3 + 3 a a6 23 = a 2. 2 Hlaec
ad formam Regulae reducta, tic B 3. J nc - a 2) 3. Indeque est d = b, D = 3, e = C, f = -
r = 2, 5 = 3, 0-
nC = a23, n = 3. EL Aea, O v: 3 3-
NRnn 3
c
50