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# Title: [Bernhardi Nieuwentiit Analysis Infinitorum, Seu Curvilineorum Proprietates Ex Polygonorum Natura Deductae] Bernhardi Nieuwentiit Analysis Infinitorum, Seu Curvilineorum Proprietates Ex Polygonorum Natura Deductæ (shelfmark Leibn. Marg. 149)
# Folio 284, page id 1032977698:0306
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284.
nalysis Infinitorum.
C AP. VIII.
sine quancirares quorlibet astignabiles, sed numero siniex
3+c+ a + 8 80; quxe (posiro k pro numero quolibet
sinico quancum libet maEnO) sIIE = K9. exit _ q quan
cicas altignabilis; jam si Cumantur sinsularum parces infi
nicetimae, erit earum summa m L m + in L 1
_C. m, Ceu aequalis parri inEniresimae ipsuS kg.
Temm. II. Sine infinicesimae, numero infirirx ac
sibimucum equales, eric earum summa x qualis qugnritaci
Mr
assignabili; sic intinicesima in insinicies sumca est= m
r. Ccu quancicaciastignabili.
Cemm. IIT. SInE ErCSGUTanEIEaTeS, A, B, C, quarum A
est minima, C maxima, B incer ucramque magnirudine
media. Dico A A _ C sint astignabileS, eriam P FOrC
assisnabilem, hoc estnec infinicamnec infiniresimam.
Demonstr. Sineges, sicprimo B intinica, ergo C finira
a astignabilis, erit major ipsa B intinira, quod absur-
dum. Secundo, sc infiniresima, ergo dabitur quanricas asi-
nabilis A minor guanticare infinicesms B, contra lemma 7.
Cemm. IV. Sincinfinicesimx quae libet numero infiniex,
eric earum summa B equalis quancicari astignabili. De-
monstr. E enim omnes supponancur xqualesmaximxe, erit ea-
rum summa C quancitas assignabilis juxta lemm. hujusII.
sin vero supponantur aqualesminimee, erie quoque summa
earum A quanciras assignabilisjaxta lemma II. hujus; unde
cum summa B media sic magnicudine inter A e C, et
harum urraque sic altignabilis, erir e juxta lem. preced.
summa B allionabilis. Sed adrem.
Resumtisiisdem Ermbolis, aC Fig. L. ZZZLIII. SIE VP: B,
DZ: Z. WV A: B, erIC ZWV = y + b, WVV
AIE C, _E Z Y: X,
erir proprer criangulorum FOD e D H F. Similicudinem
equatio prima re:=ra; insuper d ob criangulorum. VZW
_ WV X similicudinem, CA VZ: ZWV:: WVZ: YX seu
B + 1+Z: y + b:: e: x unde Bx L FX F Z∞  1 y e = BC, PEO
aequatione secunda. Ex quibus sequeneia dedueuneur.
Corol. I.