(78;) 
V. AdJitio ad Schedulam De Quadraturis. Autore 
'johanne Craig. 
IN Adis Philofophicis Menfis Septembris, Pag. 708. duo 
exhibui Theoremata ad Figurarum Geometrice irrationa- 
Hum Qaadraturas fpsdantia : utq; Ledtori facilior fit aditus 
ad haec 5c fitnilia invenieoda^ tertium jam fubjungo Theore- 
ma^ piura (fi opus fueric) poftea exhibiturus. 
Sit ergo in Fig^ loci oiemorad ACF SemicirculuSj ADE 
Curva Geometrice irradonalis^ cojas ordioatlm applicara 
BD feeat femiclrcoluni in G Quantitates vero defigneruur 
tit pnus/fcil Diameter AF=2a, abfcilTa ABnzy, Arcus 
AC^v, Ofdinata BD:rrz ; lirq^ z=:rv^)f" ^quacio exprimens 
NaturasGuFvarum ADE, in qua r denotat quantiratem qiiam- 
libet dataiii &: determinatam, 6c o exponentem indefinichm 
quantitacis indeterminate y. Dico Aream 
i «•fi 2 ra 2ra^x2n'^T ^ 
ABD=:^1I-^ — qv*4" vViay-y^ X ^ n x~l~y 
r* aExin-9 """'^ 2ra« n+i ira^xin+i . 
De hoc Theoremate hsec font notanda {'i.) Qaod com- 
ponatur ex duabus feriebus inlinids, quarum prior (Ogtio + 
connexa) multiplicatur in vViay-y^ ; termini autem pofteri- 
oris (figho— affedi) font abfoluti. (2) Quod in priori fe^ 
rie liters majufcule A^ B, Gj D, E^ &c. deiignent coeffici- 
entes terminorum ipfis relpecSbivepr^ecedentium ; nec non in 
pofteriori eofdem obtineant Valores, quos in priori, (5 J 
Quod Quadratura exbibeatur per quantiratem finitam, quan- 
do n eft numerus integer pofitivus^aut nihilo aequalis^veletiam 
fi 2n fit numerus impar : nam in his cafibus utraque Series 
abrumpitur. 4. Quod zq fifi^equalis ultimo termino abrum^ 
penti prioris feriei. 
