“I immediately presumed to object that such a number would be too prolix, as it rises through a series of entirely distinct and different numbers, up to 64, and then again to its duplicate 4,096, and on to its triplicate 262,144, before the fourth step commences; so that the difficulty of such a calculus would be incredible, not only in addition and subtraction, but to a still higher degree in multiplication and division; for the memory must necessarily retain in the multiplication table, 3,969 distinct products of the 63 numbers of the first step multiplied into one another; whereas only 49 are necessary in the octonary, and but 81 are required in the denary arithmetic; which last is difficult to be remembered and applied in practice, by some capacities. But the stronger my objections were, the more resolute was his royal mind upon attempting such a calculus. Obstructions made him eagerly aspire All to surmount, and nobly soar the higher. He insisted that the alleged difficulties might be overbalanced by very many advantages. “A few days after this I was called before his Majesty, who, resuming the subject, demanded if I had made a trial. I still urging my former objections, he reached me a paper written with his own hand, in new characters and terms of denomination, the perusal of which, he was pleased, at my entreaty, to grant me; wherein, to my great surprise, I found not only new characters and numbers, (the one almost naturally expressive of the other) in a continued series to 64, so ranged as easily to be remembered, but also new denominations, so contrived by pairs, as to be easily extended to myriads by a continued variation of the character and denomination. And further casting my eye on several new methods of his for addition and multiplication by this calculus, either artificially contrived, or else inherent in the characters of the numbers themselves, I was struck with the profoundest admiration of the force of his Majesty’s genius, and with such strange amazement, as obliged me to esteem this eminent personage, not my rival, but by far my superior in my own art. And having the original still in my custody, at a proper time I may publish it, as it highly deserves; whereby it will appear with what discerning skill he was endowed, or how deeply he penetrated into the obscurest recesses of the arithmetical science. “Besides, his eminent talents in calculation further appear by his frequently working and solving the most difficult numerical problems, barely by thought and memory; in which operations others are obliged to take great pains and tedious labor. “Having duly weighed the vast advantages arising from mathematical and arithmetical knowledge in most occasions of human life, he frequently used it as an adage, that _he who is ignorant of numbers is scarce half a man_. “While he was at Bender, he composed a complete volume of military exercises, highly esteemed by those who are best skilled in the art of war.”