Read Ellen: Or, Whisperings of an Old Pine; Volume 1

Ellen: Or, Whisperings of an Old Pine; Volume 1

Joseph Battell

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Description:Excerpt: ... XLVIII. DEGREES FALLEN will now criticise the propositions given in this *--' geometry and their demonstrations. But first let us take two straight lines of equal length, as A B, DE (see Figure I), and place one upon the other. So long as these lines coincide Figure I. in direction there is no angle, but should we make one line rotate upon a point at C, the centre of AB: "First.--Four angles will be formed at the point of divergence of the lines, two of these increasing constantly in size and two decreasing constantly, as the upper line is made to turn from left to right, until the lines shall again coincide, when all the angles will disappear. "Second.--The two angles which are opposite each other, called vertical angles, are equal; for the straight lines which form them must have the same difference in direction at cither side of the point of intersection. "Third.-- Of the four angles any two adjacent are unequal except in one position of the revolving line, when they are all equal. At this point the lines are said to be perpendicular to each other." "Can Ellen give any reason why in one position the angles are equal? " I asked. "It is evident," she answered, "from the definition of an angle--the difference in direction of two straight lines intersecting each other. For as we thus turn one line upon a pivot, as we have seen, one angle on each side of the stationary line increases, and the other decreases, thus constantly approaching each other in size, and as the difference between them is finite they must finally equal each other. And when they do the lines are said to be perpendicular to each other, and the angles are called right angles. The being perpendicular is only a name used to denote the relative direction of the lines when these angles are equal....We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Ellen: Or, Whisperings of an Old Pine; Volume 1. To get started finding Ellen: Or, Whisperings of an Old Pine; Volume 1, you are right to find our website which has a comprehensive collection of manuals listed.
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Description: Excerpt: ... XLVIII. DEGREES FALLEN will now criticise the propositions given in this *--' geometry and their demonstrations. But first let us take two straight lines of equal length, as A B, DE (see Figure I), and place one upon the other. So long as these lines coincide Figure I. in direction there is no angle, but should we make one line rotate upon a point at C, the centre of AB: "First.--Four angles will be formed at the point of divergence of the lines, two of these increasing constantly in size and two decreasing constantly, as the upper line is made to turn from left to right, until the lines shall again coincide, when all the angles will disappear. "Second.--The two angles which are opposite each other, called vertical angles, are equal; for the straight lines which form them must have the same difference in direction at cither side of the point of intersection. "Third.-- Of the four angles any two adjacent are unequal except in one position of the revolving line, when they are all equal. At this point the lines are said to be perpendicular to each other." "Can Ellen give any reason why in one position the angles are equal? " I asked. "It is evident," she answered, "from the definition of an angle--the difference in direction of two straight lines intersecting each other. For as we thus turn one line upon a pivot, as we have seen, one angle on each side of the stationary line increases, and the other decreases, thus constantly approaching each other in size, and as the difference between them is finite they must finally equal each other. And when they do the lines are said to be perpendicular to each other, and the angles are called right angles. The being perpendicular is only a name used to denote the relative direction of the lines when these angles are equal....We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Ellen: Or, Whisperings of an Old Pine; Volume 1. To get started finding Ellen: Or, Whisperings of an Old Pine; Volume 1, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Ellen: Or, Whisperings of an Old Pine; Volume 1

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