The Complete Works in Philosophy, Politics and Morals of the late Dr. Benjamin Franklin, Vol. 2 [of 3]

By Benjamin Franklin

Page 253

request I now send you the arithmetical curiosity,
of which this is the history.

Being one day in the country, at the house of our common friend, the
late learned Mr. Logan, he showed me a folio French book filled with
magic squares, wrote, if I forget not, by one M. Frenicle, in which
he said the author had discovered great ingenuity and dexterity in
the management of numbers; and though several other foreigners had
distinguished themselves in the same way, he did not recollect that
any one Englishman had done any thing of the kind remarkable.

I said, it was, perhaps, a mark of the good sense of our English
mathematicians, that they would not spend their time in things that
were merely _difficiles nugæ_, incapable of any useful application.
He answered, that many of the arithmetical or mathematical questions,
publicly proposed and answered in England, were equally trifling and
useless. Perhaps the considering and answering such questions, I
replied, may not be altogether useless, if it produces by practice an
habitual readiness and exactness in mathematical disquisitions, which
readiness may, on many occasions, be of real use. In the same way,
says he, may the making of these squares be of use. I then confessed
to him, that in my younger days, having once some leisure (which I
still think I might have employed more usefully) I had amused myself
in making these kind of magic squares, and, at length, had acquired
such a knack at it, that I could fill the cells of any magic square
of reasonable size, with a series of numbers as fast as I could
write them, disposed in such a manner as that the sums of every row,
horizontal, perpendicular, or diagonal, should be equal; but not
being satisfied with these, which I looked on as common and easy
things, I had imposed on myself more difficult tasks, and succeeded
in making other magic squares, with a variety of properties, and
much more curious. He then shewed me several in the same book, of an
uncommon and more curious kind; but as I thought none of them equal
to some I remembered to have made, he desired me to let him see
them; and accordingly, the next time I visited him, I carried him a
square of 8, which I found among my old papers, and which I will now
give you, with an account of its properties. (_See Plate_ V. Fig. 3.)

The properties are,

1. That every strait row (horizontal or vertical) of 8 numbers added
together makes 260, and half each row half 260.

2. That the

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Text Comparison with Memoirs of Benjamin Franklin; Written by Himself. [Vol. 1 of 2] With His Most Interesting Essays, Letters, and Miscellaneous Writings; Familiar, Moral, Political, Economical, and Philosophical, Selected with Care from All His Published Productions, and Comprising Whatever Is Most Entertaining and Valuable to the General Reader

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WITH HIS MOST INTERESTING ESSAYS, LETTERS, AND MISCELLANEOUS WRITINGS; FAMILIAR, MORAL, POLITICAL, ECONOMICAL, AND PHILOSOPHICAL.
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Often.
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I endeavoured to put his press (which he had not yet used, and of which he understood nothing) into order to be worked with; and, promising to come and print off his elegy as soon as he should have got it ready, I returned to Bradford's, who gave me a little job to do for the present, and there I lodged and dieted.
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" As I seemed at first not to think so ill of them as she did, she mentioned some things she had observed and heard that had escaped my notice, but now convinced me she was right.
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They all continued their regard for me as long as they lived.
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Revelation had indeed no weight with me as such; but I entertained an opinion that, though certain actions might not be bad _because_ they were forbidden by it, or good _because_ it commanded them, yet probably those actions might be forbidden _because_ they were bad for us, or commanded _because_ they were beneficial to us, in their own natures, all the circumstances of things considered.
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This was accordingly done, and for some time contented us: finding the advantage of this little collection, I proposed to render the benefit from the books more common, by commencing a public subscription library.
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The request was fortunately made to perhaps the only man in the company who had the firmness not to be affected by the preacher.
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The house approved the nomination, and provided the goods for the presents, though they did not much like treating out of the province; and we met the other commissioners at Albany about the middle of June.
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And for each able horse, with a packsaddle or other saddle and furniture, two shillings per diem.
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The enemy, however, did not take the advantage of his army which I apprehend its long line of march exposed it to, but let it advance without interruption till within nine miles of the place; and then, when more in a body (for it had just passed a river, where the front had halted till all were come over), and in a more open part of the woods than any it had passed, attacked its advanced guard by a heavy fire from behind trees and bushes; which was the first intelligence the general had of an enemy's being near him.
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My answers were to this purpose; that my circumstances, thanks to God, were such as to make proprietary favours unnecessary to me; and that, being a member of the Assembly, I could not possibly accept of any; that, however, I had no personal enmity to the proprietary, and that, whenever the public measures he proposed should appear to be for the good of the people, no one would espouse and forward them more zealously than myself; my past opposition had been founded on this, that the measures which had been urged were evidently intended to serve the proprietary interest with great prejudice to that of the people.
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We were, passengers included, about forty persons; while we stood there, the ship mended her pace, and soon left her neighbour far behind, which proved clearly what our captain suspected, that she was loaded too much by the head.
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This deliverance impressed me strong with the utility of light-houses, and made me resolve to encourage the building some of them in America, if I should live to return thither.
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Had this pretended right been suffered to remain dormant, the colonists would cheerfully have furnished their quota of supplies, in the mode to which they had been accustomed; that is, by acts of their own assemblies, in consequence of requisitions from the secretary of state.
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* * * * * "During the number of years I was in business as a stationer, printer, and postmaster, a great many small sums became due to me, for books, advertisements, postage of letters, and other matters, which were not collected, when, in 1757, I was sent by the Assembly to England as their agent, and by subsequent appointments continued there till 1775; when, on my return, I was immediately engaged in the affairs of Congress, and sent to France in 1776, where I remained nine years, not returning till 1785; and the said debts not being demanded in such a length of time, have become in a manner obsolete, yet are nevertheless justly due.
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* * * * _Q.
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In 1739 they were called upon to assist in the expedition against Carthagena, and they sent three thousand men to join your army.
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Unhappy people! to have lived in such times and by such neighbours.
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p.