Ellen: Or, Whisperings of an Old Pine, Volume 2

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American Publishing Company, 1908
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Page 346 - of natural knowledge, that the various forms under which the forces of matter are made manifest, have one common origin ; or, in other words, are so directly related and mutually dependent, that they are convertible, as it were, one into another, and possess equivalents of power in their action.
Page 12 - In an obtuse-angled triangle the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, plus twice the product of one of these sides and the projection of the other side upon it.
Page 698 - "Yet all these were, when no man did them know, Yet have from wisest ages hidden beene ; And later times thinges more unknowne shall show. Why then should witlesse man so much misweene, That nothing is, but that which he hath scene
Page 12 - The spherical excess of any spherical polygon is equal to the excess of the sum of its angles over two right angles taken as many times, less two, as the polygon has sides. If we denote the spherical excess by E, the sum of the angles by S, and the number of sides by n, we have,
Page 12 - many a glorious morning have I seen, Flatter the mountain-tops with sovereign eye ; Kissing with golden face the meadows green, Gilding pale streams with heavenly alchemy.
Page 12 - lines which meet the plane at equal distances from the foot of the perpendicular, are equal : '3. Of two oblique lines which meet the plane at unequal distances from the foot of the perpendicular, the one which meets it at the greater distance is the longer.
Page 225 - Hey diddle diddle, The cat's in the fiddle, The cow jumped over the moon ; The little dog laughed to see such a craft, And the dish ran away with the spoon.
Page 12 - The area of a rectangle is equal to the product of its base and altitude, provided the unit of area is a square whose side is the linear unit.
Page 12 - In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 12 - The angle of two arcs of great circles on a spherical surface is ' I. Equal to the plane angle of the diedral angle formed by their planes. ' II. Measured by the arc of the great circle described with its vertex as a pole and included between its sides, produced if necessary.

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