Dr. Barrow to Mr. Willughby. 363 



Your Obfervation concerning the Equality, of the 

 Annuli with Spherical Portions is alfo true, and inge- 

 nioufly proved, but may be more briefly by plain In- 



divifibles, thus. Cif* 



M 



A, 







y ! 



cuius radio H E aqua- 

 tur. circulo ^ cujus ra- 

 dius A H minus cir- 

 culo cujus radius AE, 

 vel E F Item annu- 

 Jus ex circumdu^a CF 

 aquatur circulo cujus 

 radius E C {vel A H) 

 minus circulo cujus radius E F. ac fie ubique \ ergo^ Sec. 



As to your lart thing, driving as I underftand to 

 the finding of a Spherical Portion by Indivifibles, the 

 fhorteft and cleared way of fatisfying that Attempt is 

 I think this. 



Call ZA — i.ZB~ia ZC— -a. 



&c. ZD = ». ZXq 

 h^—U — da. 



CXqz=z}da — cjaa. 

 DXqzzzdn — nn. 



da, 



Summ. .dnn — n\ eft: fumma quadratorum ex radii's 



dnn — nnp 



n3l>. ergo nnp — nip. 

 3d 2 3d 



3 2. 



hoc eft: Cylindrus 

 bafe np y alt. n — nn 



ir id 



Eft portio XZtf. 



•Aaa 2 



1 



As 



