Fundamental Principles of Mathematics. 333 



Of Infinites of Various Descriptions. 



(19.) (a.) We shall designate a quantity as being absolutely 

 infinite; if it be so great as to be utterly boundless or destitute of 

 any limit. 



This is the case with " absolute space; 77 which whether we 

 regard it in a direction forward, or backward, or upward, or down- 

 ward, or sidewise, or obliquely, is, in any and every direction, 

 positively boundless or absolutely infinite. 



So too, far back as the imagination can extend — antecedent to 

 all ages past, antecedent to the existence of all created beings or 

 things — we still behold, self-sustained on the throne of his adora- 

 ble perfections, the great first cause ; who being the very ori- 

 gin of the first beginning, himself has none ; but ever was, as 

 now, "from everlasting." It is in this undenved antecedent, 

 this perpetual precedent, of the Divine P re-existence, that we 

 find the realization of Eternity Past. 



For also beyond the ages to come — immeasurable though they 

 may be "by the flight of years" — must still endure the ceaseless 

 and unalterable being of Him "who alone hath immortality" un- 

 derived: and, in that, is Eternity Future. Yet what mental 

 vision shall penetrate the "clouds and darkness' 7 which surround 

 the Divine Pre-existence ; and inform m how it was, that, in 

 Eternity Past, time e'er began. Or — fixing its unfaltering gaze 

 upon "the light inaccesible" which covers, as with a veil of 

 "glory," the designs and capabilities of the future — say what 

 means the duration of an immortality once begun in his pres- 

 ence? Yet is it the combination of both these, of that eternity 

 which always was, and that which " ever shall be" — nothing Jess 

 than this, nothing short of it — that constitutes the absolute infi- 

 nite of duration ? It is the inexhaustible fullness of the being of 

 Him " who inhabiteth eternity," in its twofold sense ; having 

 ever been, as now, "from everlasting to everlasting." 



(b.) We shall designate a quantity as being specifically infinite, 

 if it be as boundless as those already described, in certain res- 

 pects only. 



Thus if a straight line be without termination, in either direc- 

 tion, from a point which might be assumed in that line, such a 

 line will be specifically infinite ; viz., in length — in which res- 

 pect alone a line can be great or small. In this same respect 

 might a surface be said to be infinite, on which such a line could 

 exist, or the solid within or on which such a line would be possi- 

 ble : whatever might be the other dimensions of either the sur- 

 face or the solid. 



[If a line, alike interminable, were any where curved, such a 



line must be regarded as longer than the other; since it would 

 intrude upon what may (by indulgence) be termed the breadth 





