the case of geometrical objects, Bolzano says:

> Every spatial extension that is not only similar to another but also geometrically equal (i.e. coincides with it in all characteristics that are conceptually representable through comparison with a given distance) must also have an equal multitude of points. (§49. 2.)

At this point, Bolzano fundamentally breaks with Cantor. For Bolzano it is still true that *the whole is greater than its part* and the existence of the *one-to-one correspondence* does not attest to the equality of multitudes. We will see how Bolzano deals with this further on.

Calculation of the infinite
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The sums of series represent infinite quantities. Is it possible to determine their relationship? Is it possible to compare them or to count them? Bolzano answers that

> a calculation of the infinite done correctly doesn’t aim at calculation of that which is determinable through no number, namely not a calculation of infinite pluralities in itself, but only a determination of the relationship of one infinity to another which is feasible, in certain cases, as we shall show in several examples. (§28).

In fact, our knowledge about Bolzano’s calculation of the infinite comes from examples. Nevertheless, they are clear 