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Algebra angle applied areas in equal Arithmetic astronomers binomial theorem capable celestial celestial mechanics centre circumference circumscribed square class of measurements cornered figure cubic curve line degrees demonstration diagonal diagram diameter diffusion diminish distance drawn earth eight inches ellipse equal areas Euclid Euclid's Elements exemplified four inches fulcrum Galileo geometry gravity Greek half hypothenuse idea illustration inches area inches in length inches radius inches sides infinite infinite series inscribed square Law of Kepler length and breadth length multiplied lever light linear magnitude mechanics method metical Mixed Mathematics moon motion Natural Philosophy nature Newton oblique observations obvious octagon orbit parallelogram planets Plate polygons pound weight principle problem of Pythagoras pure mathematics quadruple quantity radii ratio relation represent result revolution revolving right-angled short hand similar triangles square inch square number straight line telescope thickness Thomas Beddoes three inches tion triangles forming true truth Tycho Tycho Brahe universal velocity
Page 22 - But yet if we would speak of things as they are, we must allow that all the art of rhetoric, besides order and clearness, all the artificial and figurative application of words eloquence hath invented, are for nothing else but to insinuate wrong ideas, move the passions, and thereby mislead the judgment, and so indeed are perfect cheats...
Page 26 - Just so it is in the mind; would you have a man reason well, you must use him to it betimes, exercise his mind in observing the connection of ideas and following them in train. Nothing does this better than mathematics, which therefore I think should be taught all those who have the time and opportunity, not so much to make them mathematicians as to make them reasonable creatures...
Page 26 - HATE mentioned mathematics as a way to settle in the mind a habit of reasoning closely and in train ; not that I think it necessary that all men should be deep mathematicians, but that having got the way of reasoning, which that study necessarily brings the 5 mind to, they might be able to transfer it to other parts of knowledge as they shall have occasion.
Page 29 - How do the dear girls go on ? I would have them taught geometry, which is of all sciences in the world the most entertaining : it expands the mind more to the knowledge of all things in nature, and better teaches to distinguish between truths and such things as have the appearance of being truths, yet are not, than any other.
Page 30 - Newton, with some others of that strain ; it is ambition enough to be employed as an under-labourer in clearing the ground a little, and removing some of the rubbish that lies in the way to knowledge...
Page 29 - How would it enlarge their minds if they would acquire a sufficient knowledge of mathematics and astronomy to give them an idea of the beauty and wonders of the creation ! I am persuaded that the generality of people, and particularly fine ladies, only adore God because they are told it is proper and the fashion to go to church ; but I would have my girls gain real knowledge of the works of the creation, that they may have a fixed idea of the nature of that Being who could be the author of such a...
Page 107 - ... author. It is by following his reasonings, and by pursuing the train of his thoughts in his own elegant, though somewhat diffuse exposition of them, that we become acquainted with the fertility of his genius, with the sagacity, penetration, and comprehensiveness of his mind. The service which he rendered to real knowledge is to be estimated not only from the truths which he discovered, but from the errors which he detected, — not merely from the sound principles which he established, but from...
Page 111 - The squares of the times of revolution of any two planets are to each other, in the same proportion as the cubes of their mean distances from the sun.
Page 22 - ... harangues and popular addresses, they are certainly, in all discourses that pretend to inform or instruct, wholly to be avoided ; and where truth and knowledge are concerned, cannot but be thought a great fault, either of the language or person that makes use of them.
Page 27 - I think it necessary that all men should be deep mathematicians, but that, having got the way of reasoning, which that study necessarily brings the mind to, they might be able to transfer it to other parts of knowledge as they shall have occasion. For in all sorts of reasoning every single argument should be managed as a mathematical demonstration...