Methods of Study in Natural History

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Yet I insist that all living beings are but the diflFerent modes of expressing these formulae, and that all animals have, within the limits of their own branch of the Animal Kingdom, the same structural elements, though each branch is entirely distinct. If this be true, 204 HOMOLOGIES.
and if these organic formulae have the precision of mathematical formulae, with which I have compared them, they should be susceptible of the same tests.
The mathematician proves the identity of prop- ositions th
...at have the same mathematical value and significance by their convertibility. If they have the same mathematical quantities, it must be possible to transform them, one into another, without changing anything that is essential in either. The problem before us is of the same character. If, for instance, all Radiates, be they Sea- Anemones, Jelly-Fishes, Star-Fishes, or Sea- Urchins, are only various modes of expressing the same organic formula, each having the sum of all its structural elements, it should be possi- ble to demonstrate that they are reciprocally con- vertible.

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