The Usefulness of Mathematical Learning Explained and Demonstrated: Being Mathematical Lectures Read in the Publick Schools at the University of Cambridge

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S. Austen, 1734 - Mathematics - 440 pages
 

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Page 1 - ... the economy 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...
Page 2 - ... 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...
Page 251 - For I fay, through the grace given unto me, to every man that is among you, not to think of himfelf more highly than he ought to think, but to think foberly, according as God hath dealt to every man the meafure of faith.
Page 1 - ... we make pacific separations of the bounds of lands, examine the moments of weights in an equal balance, and distribute every one 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...
Page 229 - Proposition 15. The surface of any isosceles cone has the same ratio to its base as the side of the cone has to the radius of the base. By Prop. 14, the surface of the cone is equal to a circle whose radius is a mean proportional between the side of the cone and the radius of the base. Hence, since circles are to one another as the squares of their radii, the proposition follows.
Page 25 - Newton's teacher, Isaac Barrow, said in a lecture Newton probably heard, "Magnitude is the common Affection of all physical things, it is interwoven in the Nature of Bodies, blended with all corporeal Accidents, and well nigh bears the Principal Part in the Production of every natural Effect.
Page 2 - ... 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...
Page xxxii - ... 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...
Page 1 - Vol. 8, p. 47. 1572. [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 Labour...
Page 3 - Zeit (Stuttgart, 1889), p. 40. 402. These Disciplines [mathematics] serve to inure and corroborate the Mind to a constant Diligence in Study; to undergo the Trouble of an attentive Meditation, and cheerfully contend with such Difficulties as lie in the Way. They wholly deliver us from a credulous Simplicity, most strongly fortify us against the Vanity of Scepticism, effectually restrain from a rash Presumption, most easily incline us to a due Assent, perfectly subject us to the Government of right...

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