## Mathematical Questions and Solutions, from the "Educational Times": With Many Papers and Solutions in Addition to Those Published in the "Educational Times", Volume 42W. J. C. Miller Hodgson, 1885 - Mathematics |

### Common terms and phrases

a₁ a²X² algebraic Axiom BIDDLE bisects Brocard Brocard circle centre of similitude centroid chance chord circle circumcentre circumcircle coefficients conic coordinates cos² cosec curve diagonals distance drawn ellipse equal equation fixed point focus given HANUMANTA RAU hence horizontal hyperbola inscribed intersection inverse limaçon line joining locus mid-point nine-point circle P₁ P₂ parabola parallel perpendicular plane points of contact polar position probability Professor WOLSTENHOLME prove R₁ radical axis radii radius ratio rectangle respectively result right angles roots sides Similarly sin² Solution by W. J. C. squares straight line symmetrical symmetrical function T. C. SIMMONS t₁ tangents theorem triangle ABC trilinear coordinates values vertex vertical W. J. C. SHARP whence

### Popular passages

Page 130 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line.

Page 131 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.

Page 137 - Now, the question is, whether, if this story were related to the wild boy caught some years ago in the woods of Hanover, or to a savage without experience, and without instruction, cut off in his infancy from all intercourse with his species, and consequently under no...

Page 137 - Toranius's conduct which we feel, or not. They who maintain the existence of a moral sense ; of innate maxims ; of a natural conscience ; that the love of virtue and hatred of vice are instinctive ; or the perception of right and wrong intuitive, (all which are only different ways of expressing the same opinion,) affirm that he would. They who deny the existence of a moral sense, &c. affirm that he would not. — And, upon this, issue is joined.

Page 137 - Upon the whole, it seems to me, either that there exist no such instincts as compose what is called the moral sense, or that they are not now to be distinguished from prejudices and habits...

Page 128 - To describe an equilateral triangle upon a given finite straight line. Let AB be the given straight line : it is required to describe an equilateral triangle upon AB.

Page 136 - every one who possesses prudence ;" and you will have the celebrated argument of Aristotle, Eth. sixth book, to prove that the virtues are inseparable ; viz. He who possesses prudence, possesses all virtue ; He who possesses one virtue, must possess prudence; therefore He who possesses one, possesses all.

Page 130 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.

Page 136 - X : eg Prudence has for its object the benefit of individuals ; but prudence is a virtue ; therefore, some virtue has for its object the benefit of the individual, is part of Adam Smith's reasoning (Moral Sentiments) against Hutcheson and others, who placed all virtue in benevolence.