But one might enumerate ad infinitum the causes of the failure of the Crusades.

00From the 14th century to the middle of the 16th, Ubertin of Casale (in his Arbor Vitae crucifixae), Bartholomew of Pisa (author of the Liber Conformitatum), the Calabrian hermit Telesphorus, John of La Rochetaillade, Seraphin of Fermo, Johannes Annius of Viterbo, Coelius Pannonius, and a host of other writers, repeated or complicated ad infinitum the exegesis of Abbot Joachim.

00will be equal to 4AB CD; by the same process find a point C2 such that the rectangle B 1 C 2 will be equal to 1B C I; and so on ad infinitum.

00Examples of this, the leading principle which was followed by the framers of the Sumerian system, might be cited almost ad infinitum.

00so on ad infinitum.

00But apart from this amalgamation of the term with his regular name, and the private right to its use which that bestowed, every emperor had an additional and double right to the title on public grounds, possessed as he was of an imperium infinitum majus, and commanding as he did all the troops of the Empire.

00The second trope deals with the validity of proof; the proof of one so-called fact depends on another fact which itself needs demonstration, and so on ad infinitum.

00(I) If the Existent is Many, it must be at once infinitely small and infinitely great - infinitely small, because the parts of which it consists must be indivisible and therefore without magnitude; infinitely great,, because, that any part having magnitude may be separate from any other part, the intervention of a third part having magnitude is necessary, and that this third part may be separate from the other two the intervention of other parts having magnitude is necessary, and so on ad infinitum.

00(2) In like manner the Many must be numerically both finite and infinite - numerically finite, because there are as many things as there are, neither more nor less; numerically infinite, because, that any two things may be separate, the intervention of a third thing is necessary, and so on ad infinitum.

00(3) If all that is is in space, space itself must be in space, and so on ad infinitum.

00(5) Before a body in motion can reach a given point, it must first traverse the half of the distance; before it can traverse the half of the distance, it must first traverse the quarter; and so on ad infinitum.

00(6) If the tortoise has the start of Achilles, Achilles can never come up with the tortoise; for, while Achilles traverses the distance from his starting-point to the starting-point of the tortoise, the tortoise advances a certain distance, and while Achilles traverses this distance, the tortoise makes a further advance, and so on ad infinitum.

00Consequently, Achilles may run ad infinitum without overtaking the tortoise.

00ad infinitum.

00That might seem a little odd here as we appear to repeat the same commands ad infinitum because the number of colors is fixed.

00Given such sums, key figures within the football industry could be forgiven for thinking that the years of plenty would continue ad infinitum.

00They'd love people to do this ad infinitum.

00Ceramics 1988 upped the stakes and stopped any sense of forming a pattern to be followed ad infinitum.

00Fourthly, be appropriately apologetic and repeat the above process ad infinitum.

00DVDs - While they aren't the most effective way to learn, DVDs have the advantage of being able to rewind, freeze, and repeat ad infinitum any moves you aren't sure of.

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The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.