« ZurückWeiter »
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 the 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 rides for finding the areas and contents of superficies 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 falsehood 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 knowledge 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 knowledge 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 knowledge 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 studies, 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 knowledge 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 tbe 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 those who we find have a mind worth cultivating, ought to apply themselves to this study."
ON TRUE HAPPINESS. From the Pennsylvania Gazette, No. 363, Nov. 20, 1735.
The desire of happiness in general is so natural to us, that all the world are in pursuit of it; all have this one end in view, though they take such different methods to attain it, and are so much divided in their notions of it.
Evil, as evil, can never be chosen; and though evil is often the effect of our own choice, yet we never desire it, but under the appearance of an imaginary good.
Many things we indulge ourselves in may be considered by us as evils, and yet be desirable; but then they are only considered as evils in their effects and consequences, not as evils at present, and attended with immediate misery.
Reason represents things to us, not only as they are at present, but as they are in their whole nature and tendency; passion only regards them in their former light: when this governs us, we are regardless of the future, and are only affected with the present.
It is impossible ever to enjoy ourselves rightly, if our conduct be not such as to preserve the harmony and order of our faculties, and the original frame and constitution of our minds; all true happiness, as all that is truly beautiful, can only result from order. . ■ ,.
Whilst there is a conflict betwixt the two principles of passion and reason, we must be miserable in proportion to the struggle; and when the victory is gained, and reason so far subdued as seldom to trouble us with its remonstrances, the happiness we have then, is not the happiness of our rational nature, but the happiness only of the inferior and sensual part of us, and consequently a very low and imperfect happiness, to what the other would have afforded us.
If we reflect upon any one passion and disposition of mind, abstract from virtue, we shall soon see the disconnexion between that and true solid happiness. It is of the very essence, for instance, of envy to be uneasy and disquieted. Pride meets with provocations and disturbances upon almost every occasion. Covetousness is ever attended with solicitude and anxiety. Ambition has its disappointments to sour us, but never the,