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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 152, page id 1032977698:0174
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153
analysis Infinitorum.
CAP. II.
pectirae ZQ seu + perpetim adXquatIE) erie
E  = BP = + + C F I, adcoque n  = e + I; _
Facta subtangenti PIA: B, CM h: t: : a: e F i; un-
de Fa = hC +hi, Scd ta:=: Ye, er8Oy e= he
+hi, quare Factis 3 = Z 8 = Ha, donec
enata sint currilinea A Z P _C AFB, exithoc
 omnia h2, illud = omnia hc, ec utriu (que
summa aequalis currilineo expolito AP P Ceu
omnibus re, undehoc theorema:
Si in qualibet currE A D E ad applicatam F p
ordinetur currilineum subrangentiale P 2 HI
hujusque inquiratur (ubtansens HA: exit exDO-
situm currilincum AF P Temper aquale duo-
rum currilineorum summae AZ PdC A F B; Quo-
rum haec est proprietas, ut applicatarum 9 3 e
8 lingulae, utrique subtangentis respectira r9
extremitati insistentes, inventae currae subtan
Bentialis subtansenti FTa jusirer adaequentur.
EY. B. QuoM OdO IAMBCUIErA ADE proprietate
coonita, caeterarum relationes inter applicatas
interceptasque constiturae inveniri possinc, cui-
libet medioeriter in analyh verlato plusquam
cornirum eAt.
26. SIC, FIC. XLII, idem curvilineum APF,
item duo alia AG P et A8 FB, quorum alte-
rum ad intexceptam, A 9: x, alterum ad subtan-
gentis abscistam AT, =it -- X= p
est; sineque in utroque respectirae axplicata O+