The coasts of Angola, Congo, the Gold and the Grain coasts, on the west side of Africa, from whence, since that time, such immense wealth has been drawn, not discovered, nor the least inquiry made after them. All the East India and China trade, not only undiscovered, but out of the reach of expectation! Coffee and tea, (those modern blessings of mankind) had never been heard of: all the unbounded ocean, we now call the South Sea, was hid, and unknown: all the Atlantic Ocean, beyond the mouth of the Straights, was frightful, and terrible in the distant prospect, nor durst any one peep into it, otherwise than as they might creep along the coast of Africa, towards Sallee, or Santa Cruz. The North Seas was hid in a veil of impenetrable darkness; the White Sea, or Arch Angel, was a very modern discovery; not found out, till Sir Hugh Willoughby doubled the North Cape, and paid dear for the adventure, being frozen to death with all his crew, on the coast of Lapland; while his companions ship, with the famous Mr. Chancellor, went on to the Gulph of Russia, called the White Sea where no Christian strangers had ever been before him.

In these narrow circumstances stood the world's knowlege at the beginning of the 15th century, when men of genius began to look abroad, and about them. Now, as it was wonderful to see a world so full of people, and people so capable of improving, yet so stupid, and so blind, so ignorant, and so perfectly unimproved; it was wonderful to see, with what a general alacrity they took the alarm, almost all together; preparing themselves as it were on a sudden, by a general inspiration, to spread knowlege through the earth, and to search into every thing, that it was impossible

to uncover.

us,

How surprising is it to look back, so little a way behind and see, that even in less than two hundred years, all this (now so self-wise) part of the world did not so much as know, whether there was any such place, as a Russia, a China, a Guinea, a Greenland, or a North Cape? That as to America, it was never supposed, there was any such

place, neither had the world, though they stood upon the shoulders of four thousand years experience, the least thought, so much as that there was' any land that way!

As they were ignorant of places, so of things also; so vast are the improvements of science, that all our knowlege of mathematics, of nature, of the brightest part of human wisdom, had their admission among us within these two last centuries.

What was the world then, before? And to what were the heads and hands of mankind applied? The rich had no commerce, the poor no employment; war and the sword was the great field of honor, the stage of preferment, and you have scarce a man eminent in the world, for any thing before that time, but for a furious outrageous falling uponhis fellow-creatures, like Nimrod, and his successors of modern memory.

The world is now daily encreasing in experimental knowlege; and let no man flatter the age, with pretending we have arrived to a perfection of discoveries.

What's now discovered, only serves to show,
That nothing's known, to what is yet to know.

ON THE USEFULNESS OF THE MATHEMATICS.

From the Pennsylvania Gazette, No. 360, Oct. 30, 1735.

MATHEMATICS originally signifies any kind of discipline or learning, but now it is taken for that science, which teaches or contemplates whatever is capable of being numbered or measured. That part of the mathematics which relates to numbers only, is called arithmetic; and that which is concerned about measure in general, whether length, breadth, motion, force, &c. is called geometry.

As to the usefulness of arithmetic, it is well known that no business, commerce, trade, or employment whatsoever, even from the merchant to the shopkeeper, &c. can be managed and carried on, without the assistance of numbers; for by these the trader computes the value of all sorts of goods that he dealeth in, does his business with ease and certainty, and informs himself how matters stand at any VOL. IV.

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time with respect to men, money, or merchandise, to profit and loss, whether he goes forward or backward, grows richer or poorer. Neither is this science only useful to the merchant, but is reckoned the primum mobile (or first mover) of all mundane affairs in general, and is useful for all sorts and degrees of men, from the highest to the lowest.

As to the usefulness of geometry, it is as certain, that no curious art, or mechanic work, can either be invented, improved, or performed, without its assisting principles.

It is owing to this, that astronomers are put into a way of making their observations, coming at the knowlege of the extent of the heavens, the duration of time, the motions, magnitudes, and distances of the heavenly bodies, their situations, positions, risings, settings, aspects, and eclipses; also the measure of seasons, of years, and of

ages.

It is by the assistance of this science, that geographers present to our view at once, the magnitude and form of the whole earth, the vast extent of the seas, the divisions of empires, kingdoms, and provinces.

It is by the help of geometry, the ingenious mariner is instructed how to guide a ship through the vast ocean, from one part of the earth to another, the nearest and safest way, and in the shortest time.

By help of this science the architects take their just measures for the structure. of buildings, as private houses, churches, palaces, ships, fortifications, &c.

By its help engineers conduct all their works, take the situation and plan of towns, forts and castles, measure their distances from one another, and carry their measure into places that are only accessible to the eye.

From hence also is deduced that admirable art of drawing sun-dials on any plane howsoever situate, and for any part of world, to point out the exact time of the day, sun's declination, altitude, amplitude, azimuth, and other astronomical matters.

By geometry, the surveyor is directed how to draw a map of any country, to divide his lands, and to lay down and plot any piece of ground, and thereby discover the

area in acres, rods and perches. The gauger is instructed how to find the capacities or solid contents of all kinds of vessels, in barrels, gallons, bushels, &c. And the measurer is furnished with rules for finding the areas and contents of superfices and solids, and casting up all manner of workmanship. All these and many more useful arts, too many to be enumerated here, wholly depend upon the aforesaid sciences, viz. arithmetic and geometry.

This science is descended from the infancy of the world, the inventors of which were the first propagators of human kind, as Adam, Noah, Abraham, Moses, and divers others.

There has not been any science so much esteemed_and honored as this of the mathematics, nor with so much industry and vigilance become the care of great men, and labored in by the potentates of the world, viz. emperors, kings, princes, &c.

Mathematical demonstrations, are a logic of as much or more use, than that commonly learned at schools, serving to a just formation of the mind, enlarging its capacity, and strengthening it so, as to render the same capable of exact reasoning, and discerning truth from falshood in all occurrences, even subjects not mathematical. For which reason it is said, the Egyptians, Persians, and Lacedemonians, seldom elected any new kings, but such as had some knowlege in the mathematics, imagining those who had not, men of imperfect judgments, and unfit to rule and govern.

Though Plato's censure, that those who did not understand the 117th proposition of the 13th book of Euclid's Elements, ought not to be ranked amongst rational creatures, was unreasonable and unjust; yet to give a man the character of universal learning, who is destitute of a competent knowlege in the mathematics, is no less so.

The usefulness of some particular parts of the mathematics in the common affairs of human life, has rendered some knowlege of them very necessary to a great part of mankind, and very convenient to all the rest that are any way conversant beyond the limits of their own particular callings.

Those whom necessity has obliged to get their bread by manual industry, where some degree of art is required to go along with it, and who have had some insight into these studies, have very often found advantages from them sufficient to reward the pains they were at in acquiring them. And whatever may have been imputed to some other studics, under the notion of insignificancy and loss of time, yet these, I believe, never caused repentance in any, except it was for their remissness in the prosecution of them.

Philosophers do generally affirm, that human knowlege to be most excellent, which is conversant amongst the most excellent things. What science then can there be, more noble, more excellent, more useful for men, more admirably high and demonstrative, than this of the mathematics.

I shall conclude with what Plato says, lib. 7. of his Republic, with regard to the excellence and usefulness of geometry, being to this purpose:

"Dear Friend....You see then that mathematics are necessary, because by the exactness of the method, we get a habit of using our minds to the best advantage: and it is remarkable, that all men being capable by nature to reason and understand the sciences; the less acute, by studying this, though useless to them in every other respect, will gain this advantage, that their minds will be improved in reasoning aright; for no study employs it more, nor makes it susceptible of attention so much; and these who we find have a mind worth cultivating, ought to apply themselves to this study."

CAUSES OF EARTHQUAKES.

From the Pennsylvania Gazette, No. 470, Dec. 15, 1737.

THE late earthquake felt here, and probably in all the neighboring provinces, have made many people desirous to know what may be the natural cause of such violent concussions, we shall endeavor to gratify their curiosity by giving them the various opinions of the learned on that

head.