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Derivation of Torricelli's Theorem from Bernoulli's Equation with the Assumptions Listed

(1)  Both the top and the hole are open to atmospheric pressure.

(2)  The fluid is incompressible

(3)  Radius of exit much smaller than radius of tank

v1 = (2 g (y2 - y1))1/2

Note that this is a special case of Bernoulli's equation where P1 = P2  

(both ends open to atmosphere)
V2 is approximately 0 due to the ratio of the openings

P1 + (1/2) r V12 + r g y1 = P2 + (1/2) r V22 + r g y2
(1/2) V12 + g y1 = (1/2) (0)+ g y2
(1/2) V12 + g y1 = g y2   ð  v1 = (2 g (y2 - y1))1/2

Torriceolli discovered it, however, about a century earlier.

Did Bernouolli perhaps borrow from or stand on the ideas of Torricelli?