One may pass from one body to another, however different, simply by changing the relation between its ultimate parts. For its is only relations that change in the universe as a whole, whose parts remain the same.

Gilles Deleuze – Expressionism in Philosophy: Spinoza

We may suppose, then, that the discovery of the common notions occurs precisely at the end of the edited part of the Treatise, and at the beginning of the writing of the Ethics: in about 1661 – 1662. But why would this discovery have forced Spinoza to abandon the already-existing version of the Treatise? The explanation is that the common notions emerge at a time when they cannot fulfil their functions or develop their consequences. They are discovered too late relative to the text of the Treatise. They would have to establish a new point of departure for philosophy; but the point of departure has already ben set in geometric ideas.
They would have to determine an adequate mode of knowledge of what exists, and show how one passes from this mode of knowledge to the ultimate mode, knowledge of essences. But because the modes of knowledge have already been defined in the Treatise, there is no place left for the common notions or for the series of fixed and eternal things, which are thus shifted over to the ultimate mode of knowledge, with the knowledge of essences. In short, in order to give the common notions their place and function, it would have been necessary for Spinoza to rewrite the entire Treatise. It is not only that they invalidate the finished part, but they would have modified it. Spinoza prefers to write the Ethics form the perspective of the common notions, although it means postponing a new treatise that would have focussed on the practical problems that are merely outlined at the end of the Ethics, concerning the origin, the formation, and the series of these common notions, along with the corresponding experiment.
Deleuze – Spinoza: Practical Philosophy, p. 120 – 121

the art of the Ethics itself: organizing good encounters, composing actual relations, forming powers, experimenting.
Deleuze – Spinoza Practical Philosophy, p. 119

Let us consider, then, the way in which one passes from the second kind [of knowledge] to the third. In the Ethics, everything becomes clear in this regard: the second and third kind of knowledge are systems of adequate ideas, but very different from one another. Ideas of the third kind are ideas of essences, inner essences of substance constituted by the attributes, and singular essences of modes involved in the attributes; and the third kind goes from essence to essence.
Deleuze – Spinoza: Practical Philosophy, p. 117

The common notions are more biological than mathematical.
De common notions (algemene begrippen) zijn  het gezichtspunt waaruit de Ethica geschreven is. De common notions vormen de overgang van de tweede naar de derde soort van kennis, we gaan voorbij het verstand en komen in het intuïtieve intellekt als systeem van essentiële waarheden of bewustzijn.

We ervaren de essentie.