IN TVBIS CAPILLJRIBFS. 305 



rROPOsn 10 XXIX. 



In tuhis cj/ijir/ricis (jnantitas aquac a Jupe^jicic eadem 

 «ttracia viinor cjl iu tuhis diawetri minoris\ maior aiUem 

 in tiU}is iUamctri maioris. 



Dcmonftratio. 



Hiiec propofitio ex natura figunie circulnris vera efl*e '^^^"8*^* 

 intelligitar. Sepnretur in circulo A limbus CEDFi'^^//. 

 Sit diamcter CD~^, latitudo limbi Qczz.b. Diameter 

 circuli Bn ^ , et hititudo limbi G^^ eadem —b. Erit igitiir 

 in circulo A pcriphcri.i C E D F — y <3^} ei peripheria minor 

 ^edf— V ( d— "ib). In circulo B , peripheria maior zil '~o 

 et minor n:y(^~ -^)« Ell autem in quonis circulo area 

 limbi totius zzzyDc.Cc. Erit ergo area limbi dimidii 

 CEDf^-^rry^f^/— ^). Abfcindatur in circulo B portio pe- 

 riphcriae GH, qnac fit acqualis peripheriae dimidiae cir- 

 ciili A , vnde erit G H = y d. Qiiia BH:GH—Bb:gb; 

 critj-Z>— V^^^— . Eft autem arca portionis limbi GHZ'^ 

 i^G^U^^^.lGg -i'j^{o - b). Ergo area limbi di- 

 midii in circiilo A, eft ad aream portionis limbiGH^^ 

 in circulo Bzz\' b(d-b):\'^-fi§ -b)=:zS d-$ b:$ d-bd. 

 Hoc eft: erunt inter fe in ratione compofita, ex reci- 

 proca diametrorum , et direda diffcrcntiae inter diame- 

 tros circulorum et radium adiuitatis. Si igitnr S^d] 

 erit etiam S b^db. €tSb-Sb<^Sd—bd. Covjsqucnter 

 eadem peripberia CED et GH in minori circuh A mi- 

 nus attrabit aquae ., qnam in maiore B. 



Corollariiim r* 



Qiiia in quouis circulo area limbi CEDFf^///:rr 

 ^Di-.Cf: erunt arcae limborum in duobiis circulis A 

 Tom. VIIL Qq ct 



