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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)
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ProD. 165.
Arithmetica Insinitorum.
dracura C irculi vel Fllip(eos, (aliarum q; aliguoc curvarum: s
nempe uc inquiracur jam racio quam habet intinica series Ra-
dicum univertalium Binomiorum, Sicur illiC APOLOMATUMI.
Ec quidem aliquando procliris eram ut crederem rem pla-
ne impostibilem esse uc Radices Curdx numero intiniex ec invi-
cem incommensurabiles ita in unum asoreeatum coire postine
ut illud, ad expolicam aliquam quancicacem racionalem, cario-
nem habene explicabilem.
Acq; hoc quidem eo masis adhue contirmatum esse videba-
cur, quoniam ejulmodi series finica ad seriem cocidem maximz
aequalium rix aliam passa est racionis explicacione quam om-
nec Exillatim repecendo, raro enim duXe vel pIUreS OCCUTKUnE
commenlurabiles qua in unam addicione colliei postinE.
Verbioracia, si ponatur circuli radiuc parcium 6 sinus recti
in Ouadrance lineulis parcium iltarum cerminis insistentes, e-
rUNE, V: 36  O: F V: 36 = 2. FV: 36  4: tV: 36 = 9: + V: 36
16: + Y: 36  25: +V: 36 =36: (per ea quae dicta Lunc ad pr. 121.)
vel quod eodem recidic, 36t135+132+ 1277V20+177+10;
vel, uc irrationalicos ad minimos cer minos rcducatur, 6 + V33
+ 4V2+313+215 4V2210: Racio ixicur quam habet illud
radicum axxresarum ad radicem maximum cocies politam,
Puca 7V: 36 = O: vel 7V36 vel 7xo hoc est 42; non explica-
eius efferri porest quam
6+35+412+313+215+ ~21+0
42
ACq: ca eA ratio quam habene illi sinus recti in Ouadrance ad
cocidem rectas radio aequales e Parallelas in Ouadraco circum-
Icripco.
Paricer, Eponacur radius parcium 10; crunc Enus recti
N: 200 = O: +V: 100 - 1: 4 V: 100  4: f V: 100 , 9: 4V:
100n 16: fV: 100 25: + : 100- 36: + V: 100 40: +
100 in 64: F.V: 100 = 81: t v: 100  100: HOc ck
~100+ 199 + 196 + ~ 92 + V 89+ 1757 V6a + ~51+ 136
+ Vi9 +V0. Vel ciom 10+3~FI + 4V6 + vor + 2V 21+
3V3+8+ N 5T + 6F ~19+0. GuOd APETCERLN nen alitee
abbreriari porest quam pro 10+8 + 6 +0 1WRir. et do 24; uC
Facio iltins aeeresaci ad radicem n eX: M Am ICLIES PCLEZM, PU.
ca 2d 22V 100 vel 11X1O vel 11O, nen explicarius cAcrrI FO-
test quam
4t3.114416+ 191 +21214513+ 451+ Y19