408 SVPPLEMENTFM CIRCJ PROBLEMA 



etc. emnt Hi,H i,H3,H3,H5,H5,etc. et flidores in 

 quibiib infunt collnus arcuum huius feriei -^ , ^ ^ IT > ¥ » 

 ^^,^,etc. erunt Ho , H2 , H4, H4, H(5, etc. ^ 



Fig r. Vnusquisque vero fiicflor H eft linea ex pun(flo dato P 



in diametro AD femicirculi ABD ccntro O dcfcripti, 

 ad aliquod circumferentiae pundiim B dudta , nempe 

 PB, vbi radius AOzri, etOPzzs;. Nam demiffa 

 ex B perpendiculari BC in diametrum, et \ocando 

 cofunim arcus AB, qui eft OC,/;, erit BP^~i — 

 ^ksi-hz^y adeoque BPzz-V {i — 2kz-{-z-). 



Corollarium 5. 



His pofitis , fi exponcns X eft numerus par , feries 

 arcuum x" , |:, x , ¥, x% "x^ etc. praebet fadores Hi, 

 Hi,H3,H3,H5,H5, etc. adeoque HixHixHs 

 :«H3xH5xH5— ]f H-a^ 



Series vero arcuum x->T'->^i^^->Tr-) ctc. fub-» 

 miniftrat fiidores H o, H 2, H2, H4, H 4, H 6 , etc. Cum 

 vero prlmus arcus fit o, et eius cofuuis n: -f- i , \1- 

 timus vero femper fit S, cum X eft numerus par, et 

 cofinus S — — I , primus fador erit Ho zr V ( i — 2^ 

 -|-5;2 )— I — s;, et vltimus feu H-y— y( i -{-zz-^-z^) 

 nz I -\-z; quare cum produdiim Ho>.Hv fit —i—z^ , 

 erit HoxH2xH2xH4xH4xH(S:=::i— ^^. Nam fa- 

 dlores medii H2, H2, H4, H4, etc. quippe qui omnes 



bis occurrunt produccnt i 1-~^~^ \bi pun- 



^a termmos medios intcr i et x: denotant. 



Sia 



