E3P27D
Demonstration — Part III
Latin
Rerum imagines sunt corporis humani affectiones quarum ideæ corpora externa veluti nobis præsentia repræsentant (per scholium propositionis 17 partis II) hoc est (per propositionem 16 partis II) quarum ideæ naturam nostri corporis et simul præsentem externi corporis naturam involvunt. Si igitur corporis externi natura similis sit naturæ nostri corporis, tum idea corporis externi quod imaginamur affectionem nostri corporis involvet similem affectioni corporis externi et consequenter si aliquem nobis similem aliquo affectu affectum imaginamur, hæc imaginatio affectionem nostri corporis huic affectui similem exprimet adeoque ex hoc quod rem aliquam nobis similem aliquo affectu affici imaginamur, simili cum ipsa affectu afficimur. Quod si rem nobis similem odio habeamus, eatenus (per propositionem 23 hujus) contrario affectu cum ipsa afficiemur, non autem simili. Q.E.D.
English (Elwes 1883)
The images of things are modifications of the human body, whereof the ideas represent external bodies as present to us (II. xvii.); in other words (II. x.), whereof the ideas involve the nature of our body, and, at the same time, the nature of the external bodies as present. If, therefore, the nature of the external body be similar to the nature of our body, then the idea which we form of the external body will involve a modification of our own body similar to the modification of the external body. Consequently, if we conceive anyone similar to ourselves as affected by any emotion, this conception will express a modification of our body similar to that emotion. Thus, from the fact of conceiving a thing like ourselves to be affected with any emotion, we are ourselves affected with a like emotion. If, however, we hate the said thing like ourselves, we shall, to that extent, be affected by a contrary, and not similar, emotion. Q.E.D.
Modern English
Images of things are affections of the human body whose ideas represent external bodies as present to us (E2P17S), that is, (E2P16), whose ideas involve the nature of our body and at the same time the present nature of the external body. If, therefore, the nature of an external body is similar to the nature of our body, then the idea of the external body we imagine will involve an affection of our body similar to the affection of the external body. Consequently, if we conceive someone similar to ourselves to be affected with any affect, this imagination will express an affection of our body similar to that affect, and so from the fact that we conceive a thing similar to ourselves to be affected with any affect, we are affected with a like affect.
If, however, we hate the thing that is similar to us, we will be affected with a contrary, not a like, affect (E3P23). Q.E.D.