(a2+c2)(b2+d2)=a2b2+b2c2+a2d2+d2c2(ab+cd)2=a2b2+c2d2+2abcd因为a/b=c/d ad=bc(ab+cd)2=a2b2+c2d2+2abcd=a2b2+c2d2+2b2c2=a2b2+c2d2+b2c2+a2d2=(a2+c2)(b2+d2)所以是他的比例中项