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# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
# Folio 23, page id 824573315:0043
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 semicirenli.
2d 28 c x illud demonstrac; iis camen Ridem altumpiis qua
E nihilo minus dubia LanE, Bc qu_ eodem ipIO HOmIHE TETNE re
prehendenda. Ouam jocta aurem ista sc Euclicis reprehentio.
non hic racac inguirere: at lalcem eadem racione, ne dicam )on
demajoris reprehendendus essec cam ille quam Archimedes, si
modohoc poltularum, quod indilcriminacim asumitur, non
eset unirerlalicer rerum: acq; Clarius, Pnclidis reprehenlor, II-
lud (h DOSTec) demonstraset de aliis omnibus quancicacibus ve-
rumeste, quamris de aneulis contactuum verum non (IE. Ouod.
Eneq; Clarius, neg: quilpiam alius pocerie demonstrare, aliis
quancicacibus magis illud conrenire quam hujulmodi anculis
(li Talcem lint ansuli _ rere quanEI;) concedendum erie illuic
unirersalier verum esse, prout Fuclices de Archimedes viden-
cur Centisse.
20 Sic ulcerius arguo, Dux quancicates, quarum alcera major
alcera minor est, lunc incer CcHomogeneae, de quidem (li illud inrer.
DonerenecesC TIC) quo id Rarionem hoo enex: Sed an puS
concactus, E quide (ic angnlus, ec anoulus quiris rectilineur, eE-
modi lune quancicares. Prgo. Propolicione minorem demonstrat
seuclides 10 c 3. Major provolicio paricer videtur indubicnea.
NNam quae racionem habent id invicem Cunc homogenea, per
3d5. Ac quae le habene ad invicem ue majus e minis, ca (a1-
cem ad inricem Racionem habene. Oui enim heri poccA uc
quenticas quancicaceminor lic, in nulla camen Racione minore
Imorero, Ouancicacem quancicace minorem esse, nec tamen
ad illam Racionem habere, est concradictio in adjecto; nam ip.
Cumminus esse e rationem habere. Rcq; hoc quidem ne iplcCla-
viusncoare debet; nam se ille Proxorcionem sive Rarionem
(quae apud illum concundem signiticone, ideoq; _ hic pasim pro-
milcue ulurpancur) dirilic in proportionem Aqualicacie e
proporcionem lnrgualicaris, e tanc icerum subdiridie in pro-
porcionem Majoris lnaequasiacis, _ Minoris luaqualicacis, live
Majoricacis e Minoritaris: Adeo ve guicouid liE alceri vel A-
ouase vel Inaegnalc, quicquid alcero Majus cA vel Minus, illud
Talcem Racionem habet. Si ixitur aneulus concactiis sErevera
angulus, sicq: aneulo rectilinco Minor, habebic ad illum ra-
tionem Minoricacis, sivc Minoris Inaegualicatis; Ouae autem
cacionem habene, ca poliune mulciplicata LC muIO (uPCrBIC
ac angulus concactus, quancumris mulciplicacus, rectilineum
NOF
 P