31(19)
Taking any three of them N, O, M, ad libitum, they will form a triangle,
about which a circle ANOM may be circumſcribed, which will be given in
magnitude and poſition. That this circle is in the ſurface of the ſphere
ſought appears from hence; becauſe if a ſphere be cut by any plane, the
ſection will be a circle; but only one circle can be drawn to paſs through the
three given points N, O, M; therefore this circle muſt be in the ſurface of
the ſphere. Let the center of this circle be C, from whence let CB be
erected perpendicular to it’s plane; it is evident that the center of the ſphere
ſought will be in this line CB. From the fourth given point F let FB be
drawn perpendicular to CB, which FB will be alſo given in magnitude and
poſition. Through C draw ACD parallel to FB, and this line will be
about which a circle ANOM may be circumſcribed, which will be given in
magnitude and poſition. That this circle is in the ſurface of the ſphere
ſought appears from hence; becauſe if a ſphere be cut by any plane, the
ſection will be a circle; but only one circle can be drawn to paſs through the
three given points N, O, M; therefore this circle muſt be in the ſurface of
the ſphere. Let the center of this circle be C, from whence let CB be
erected perpendicular to it’s plane; it is evident that the center of the ſphere
ſought will be in this line CB. From the fourth given point F let FB be
drawn perpendicular to CB, which FB will be alſo given in magnitude and
poſition. Through C draw ACD parallel to FB, and this line will be