Prop. X. Towards something future, which we conceive as close at hand, we are affected more intensely, than if we conceive that its time for existence is separated from the present by a longer interval; so too by the remembrance of what we conceive to have not long passed away we are affected more intensely, than if we conceive that it has long passed away. Proof.- In so far as we conceive a thing as close at hand, or not long passed away, we conceive that which excludes the presence of the object less, than if its period of future existence were more distant from the present, or if it had long passed away (this is obvious) therefore (by the foregoing Prop.) we are, so far, more intensely affected towards it. Q.E.D. Corollary.- From the remarks made in IV:Def.vi. of this part it follows that, if objects are separated from the present by a longer period than we can define in conception, though their dates of occurrence be widely separated one from the other, they all affect us equally faintly. Prop. XI. An emotion towards that which we conceive as necessary is, when other conditions are equal, more intense than an emotion towards that which impossible, or contingent, or non-necessary. Proof.- In so far as we conceive a thing to be necessary, we, to that extent, affirm its existence; on the other hand we deny a thing's existence, in so far as we conceive it not to be necessary :xxxiii.note.i.); wherefore (IV.ix.) an emotion towards that which is necessary is, other conditions being equal, more intense than an emotion that which is non-necessary. Q.E.D. Prop. XII. An emotion towards a thing, which we know not to exist at the present time, and which we conceive as possible, is more intense, other conditions being equal, than an emotion towards a thing contingent. Proof.- In so far as we conceive a thing as contingent, we are affected by the conception of some further thing, which would assert the existence of the former (IV:Def.iii.); but, on the other hand, we (by hypothesis) conceive certain things, which exclude its present existence. But, in so far as we conceive a thing to be possible in the future, we there by conceive things which assert its existence (IV:iv.), that is (III:xviii.), things which promote hope or fear: wherefore an emotion towards something possible is more vehement. Q.E.D. Corollary.- An emotion towards a thing, which we know not to exist in the present, and which we conceive as contingent, is far fainter, than if we conceive the thing to be present with us.