English Polemical Author, Scholar, Mathematician and Christian Theologian
English Polemical Author, Scholar, Mathematician and Christian Theologian
Facetiousness is allowable when it is the most proper instrument of exposing things apparently base and vile to due contempt.
Mathematics - the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human affairs.
The common nature of men disposeth them to be credulous when they are commended?. Every ear is tickled with this sweet music of applause.
When we contemplate the wonderful works of Nature, and, walking about at leisure, gaze upon this ample theatre of the world, considering the stately beauty, constant order, and sumptuous furniture thereof; the glorious splendour and uniform motion of the heavens; the pleasant fertility of the earth; the curious figure and fragrant sweetness of plants; the exquisite frame of animals; and all other amazing miracles of nature, wherein the glorious attributes of God, especially His transcendent goodness, are more conspicuously displayed: so that by them, not only large acknowledgments, but even gratulatory hymns, as it were, of praise have been extorted from the mouths of Aristotle, Pliny, Galen, and such like men, never suspected guilty of an excessive devotion: then should our hearts be affected with thankful sense, and our lips break forth in praise.
For to pass by those Ancients, the wonderful Pythagoras, the sagacious Democritus, the divine Plato, the most subtle and very learned Aristotle, Men whom every Age has hitherto acknowledged as deservedly honored, as the greatest Philosophers, the Ring-leaders of Arts; in whose Judgments how much these Studies [mathematics] were esteemed, is abundantly proclaimed in History and confirmed by their famous Monuments, which are everywhere interspersed and bespangled with Mathematical Reasonings and Examples, as with so many Stars; and consequently anyone not in some Degree conversant in these Studies will in vain expect to understand, or unlock their hidden Meanings, without the Help of a Mathematical Key: For who can play well on Aristotle?s Instrument but with a Mathematical Quill; or not be altogether deaf to the Lessons of natural Philosophy, while ignorant of Geometry? Who void of (Geometry shall I say, or)Arithmetic can comprehend Plato?s 218 Socrates lisping with Children concerning Square Numbers; or can conceive Plato himself treating not only of the Universe, but the Polity of Commonwealths regulated by the Laws of Geometry, and formed according to a Mathematical Plan?
Mathematics is the fruitful Parent of, I had almost said all, Arts, the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to Human Affairs. In which last Respect, we may be said to receive from the Mathematics, the principal Delights of Life, Securities of Health, Increase of Fortune, and Conveniences of Labor: That we dwell elegantly and commodiously, build decent Houses for ourselves, erect stately Temples to God, and leave wonderful Monuments to Posterity: That we are protected by those Rampires from the Incursions of the Enemy; rightly use Arms, skillfully range an Army, and manage War by Art, and not by the Madness of wild Beasts: That we have safe Traffick through the deceitful Billows, pass in a direct Road through the tractless Ways of the Sea, and come to the designed Ports by the uncertain Impulse of the Winds: That we rightly cast up our Accounts, do Business expeditiously, dispose, tabulate, and calculate scattered 248 Ranks of Numbers, and easily compute them, though expressive of huge Heaps of Sand, nay immense Hills of Atoms: That we make pacifick Separations of the Bounds of Lands, examine the Moments of Weights in an equal Balance, and distribute everyone his own by a just Measure: That with a light Touch we thrust forward vast Bodies which way we will, and stop a huge Resistance with a very small Force: That we accurately delineate the Face of this Earthly Orb, and subject the Oeconomy of the Universe to our Sight: That we aptly digest the flowing Series of Time, distinguish what is acted by due Intervals, rightly account and discern the various Returns of the Seasons, the stated Periods of Years and Months, the alternate Increments of Days and Nights, the doubtful Limits of Light and Shadow, and the exact Differences of Hours and Minutes: That we derive the subtle Virtue of the Solar Rays to our Uses, infinitely extend the Sphere of Sight, enlarge the near Appearances of Things, bring to Hand Things remote, discover Things hidden, search Nature out of her Concealments, and unfold her dark Mysteries: That we delight our Eyes with beautiful Images, cunningly imitate the Devices and portray the Works of Nature; imitate did I say? nay excel, while we form to ourselves Things not in being, exhibit Things absent, and represent Things past: That we recreate our Minds and delight our Ears with melodious Sounds, attemperate the inconstant Undulations of the Air to musical Tunes, add a pleasant Voice to a sapless Log and draw a sweet Eloquence from a rigid Metal; celebrate our Maker with an harmonious Praise, and not unaptly imitate the blessed Choirs of Heaven: That we approach and examine the inaccessible Seats of the Clouds, the distant Tracts of Land, unfrequented Paths of the Sea; lofty Tops of the Mountains, low Bottoms of the Valleys, and deep Gulphs of the Ocean: That in Heart we advance to the Saints themselves above, yea draw them to us, scale the etherial Towers, freely range through the celestial Fields, measure the Magnitudes, and determine the Interstices of the Stars, prescribe inviolable Laws to the Heavens themselves, and confine the wandering Circuits of the Stars within fixed Bounds: Lastly, that we comprehend the vast Fabrick of the Universe, admire and contemplate the wonderful Beauty of the Divine 249 Workmanship, and to learn the incredible Force and Sagacity of our own Minds, by certain Experiments, and to acknowledge the Blessings of Heaven with pious Affection.
The Definition in the Elements, according to Clavius, is this: Magnitudes are said to be in the same Reason [ratio], a first to a second, and a third to a fourth, when the Equimultiples of the first and third according to any Multiplication whatsoever are both together either short of, equal to, or exceed the Equimultiples of the second and fourth, if those be taken, which answer one another.... Such is Euclid?s Definition of Proportions; that scare-Crow at which the over modest or slothful Dispositions of Men are generally affrighted: they are modest, who distrust their own Ability, as soon as a Difficulty appears, but they are slothful that will not give some Attention for the learning of Sciences; as if while we are involved in Obscurity we could clear ourselves without Labor. Both of 300 which Sorts of Persons are to be admonished, that the former be not discouraged, nor the latter refuse a little Care and Diligence when a Thing requires some Study.
Whence it is somewhat strange that any men from so mean and silly a practice should expect commendation, or that any should afford regard thereto; the which it is so far from meriting, that indeed contempt and abhorrence are due to it.
Generosity is in nothing more seen than in a candid estimation of other men?s virtues and good qualities.
Nature has concatenated our fortunes and affections together with indissoluble bands of mutual sympathy.
The fruits of the earth do not more obviously require labor and cultivation to prepare them for our use and subsistence, than our faculties demand instruction and regulation in order to qualify us to become upright and valuable members of society, useful to others, or happy ourselves.
Wherefore for the public interest and benefit of human society it is requisite that the highest obligations possible should be laid upon the consciences of men.
God designs that a charitable intercourse should be maintained among men, mutually pleasant and beneficial.
No man speaketh, or should speak, of his prince, that which he hath not weighed whether it will consist with that veneration which should be preserved inviolate to him.
The histories of ages past, or relations concerning foreign countries, wherein the manners of men are described, and their actions reported, afford us useful pleasure and pastime: thereby we may learn as much, and understand the world as well, as by the most curious inquiry into the present actions of men; there we may observe, we may scan, we may tax the proceedings of whom we please, without any danger or offence. There are extant numberless books, wherein the wisest and most ingenious of men have laid open their hearts and exposed their most secret cogitations unto us: in pursuing them we may sufficiently busy ourselves, and let our idle hours pass gratefully: we may meddle with ourselves, studying our own dispositions, examining our own principles and purposes, reflecting on our thoughts, words, and actions, striving thoroughly to understand ourselves: to do this we have an unquestionable right, and by it we shall obtain vast benefit.
Wisdom makes all the troubles, griefs, and pains incident to life, whether casual adversities or natural afflictions, easy and supportable, by rightly valuing the importance and moderating the influence of them.
He that loveth a book will never want a faithful friend, a wholesome counsellor, a cheerful companion, an effectual comforter.
No unkindness of a brother can wholly rescind that relation, or disoblige us from the duties annexed thereto.
The Mathematics which effectually exercises, not vainly deludes or vexatiously torments studious Minds with obscure Subtilties, perplexed Difficulties, or contentious Disquisitions; which overcomes without Opposition, triumphs without Pomp, compels without Force, and rules absolutely without Loss of Liberty; which does not privately overreach a weak Faith, but openly assaults an armed Reason, obtains a total Victory, and puts on inevitable Chains; whose Words are so many Oracles, and Works as many Miracles; which blabs out nothing rashly, nor designs anything from the Purpose, but plainly demonstrates and readily performs all Things within its Verge; which obtrudes no false Shadow of Science, but the very Science itself, the Mind firmly adheres to it, as soon as possessed of it, and can never after desert it of its own Accord, or be deprived of it by any Force of others: Lastly the Mathematics, which depend upon Principles clear to the Mind, and agreeable to Experience; which draws certain Conclusions, instructs by profitable Rules, unfolds pleasant Questions; and produces wonderful Effects; which is the fruitful Parent of, I had almost said all, Arts, the 47 unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human Affairs.
Wit is proper and commendable when it enlightens the intellect by good sense, conveyed in jocular expression; when it infringes neither on religion, charity, and justice, nor on peace; when it maintains good humor, sweetens conversation, and makes the endearments of society more captivating; when it exposes what is vile and base to contempt; when it reclaims the vicious, and laughs them into virtue; when it answers what is below refutation; when it replies to obloquy; when it counterbalances the fashion of error and vice, playing off their own weapons of ridicule against them; when it adorns truth; when it follows great examples; when it is not used upon subjects, improper for it, or in a manner unbecoming, in measure intemperate, at an undue season or to a dangerous end.
I pass by that it is very culpable to be facetious in obscene and smutty matters.
No virtue is acquired in an instant, but step by step.
The mind of man is able to discern universal propositions ? by its native force, without any previous notion or applied reasoning, which method of attaining truth is by a peculiar name styled intellection.
If men are wont to play with swearing anywhere, can we expect they should be serious and strict therein at the bar or in the church.
Now as to what pertains to these Surd numbers (which, as it were by way of reproach and calumny, having no merit of their own are also styled Irrational, Irregular, and Inexplicable) they are by many denied to be numbers properly speaking, and are wont to be banished from arithmetic to another Science, (which yet is no science) viz. algebra.