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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 41, page id 824573315:0061
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tT. 12
 semicirenli.
Velixicur concedendum eRt, demonstrationem illam Arctii-
medis, aliasq; eju smodi innumeras, opud omnes Gcommerras re-
cepeas, Coptristicas esse e plane Fallaces; quod neminem Cobri
um dicturum exiltimo: vel, quod porius olterendum erit. Dit.
ferentiam illam, quae cA omni altignabili spacio minor. nullum
essc: hoc ck, Quod omni alsisnabili quancicace minus ett, id ni-
hil cA, GrCnon-quamtum.
Hoc aurem quod postulatur concetto, hc licebit arxumen.
TarI.
10 Subsimamus aliquaneisper, pro circulo, Polygonum re-
culare rectilineum circulo inscripium quocriscunq; lareru.
FROq; numerus lacerum quanrum libet magnus, N; cricq:
idem numerus angulorum Perimeeri, (coc enim lune ansuli
quoc lacera,) quorum angulorum omnium aggrezacum exic 
quale angulis rectis 2N= 4, (per ca quae habet C larius ad
32C +) nempebis coc angulis rectis, dempeis quacuor, quoe
sunc Rieura lacera; BrBo angulus quilibet. 
4
unius recti:
hunc nucem bilecat recta a cenero; quae isicur angulum cum pe-
rimeero Facic ps untus recti, ret r= p; hoc ett, angulum
rectum dempro recti: Differencia isicur ictius ab an =ulo re.
ccocanco minor est, quanto numerus lacerum major; cum 1gi-
turnumerus lacerum auxeri possie in infinicum, ica e differen-
cia istius angulia recto in infinicum minui, in eadem Temper ra-
eione qua numerus lacerum auxecur. Ideoq; in Polygono infi-
nicorum lacerum, iltius anpuli differencia ab angulo recto cA
intinice parra, (nam EsicNinhinicum, eric p intinice par-
rem;) AC, quod eA infnice parrum, illud est omni polcira
quancicare minus, ideoq; d non quancum. Jam rero Polvgo.
num infinicorum lacerum, rel circulus eAt, vel Talcem circulo
inlcripcibile: Si prius; erie igicur ditferencia anguli Cemicir-
culi ab angulo recto intinice parra: Si polterius; erit ca diste-
rencia adhuc minor, (nam lacus polysoni circulo inseripis
cum excremitace diamerri, ansulum Facie minorem quam la-
cic peripheria cum eadem diamerri excremitare, ideog; magio
a rectc