# The Elements of Euclid: With Many Additional Propositions, & Explanatory Notes, Etc, Part 1

John Weale, 1853 - Geometry - 136 pages
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### Contents

 Section 1 1 Section 2 3 Section 3 6 Section 4 9 Section 5 20 Section 6 26 Section 7 28 Section 8 30
 Section 14 64 Section 15 69 Section 16 75 Section 17 79 Section 18 80 Section 19 81 Section 20 83 Section 21 85

 Section 9 38 Section 10 43 Section 11 44 Section 12 52 Section 13 62
 Section 22 106 Section 23 113 Section 24 118 Section 25 119 Copyright

### Popular passages

Page 24 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 114 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Page xiv - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16. And this point is called the centre of the circle.
Page 13 - The difference between any two sides of a triangle is less than the third side.
Page 111 - AFC. (in. 21.) Hence in the triangles ADE, AFC, there are two angles in the one respectively equal to two angles in the other, consequently, the third angle CAF is equal to the third angle DAB ; therefore the arc DB is equal to the arc CF, (in.
Page 89 - ... the centre of the circle shall be in that line. Let the straight line DE touch the circle ABC in C, and from C let CA be drawn at right angles to DE ; the centre of the circle is in CA.
Page 70 - EQUAL circles are those of which the diameters are equal, or from the centres of which the straight lines to the circumferences are equal. ' This is not a definition, but a theorem, the truth of ' which is evident; for, if the circles be applied to one ' another, so that their centres coincide, the circles ' must likewise coincide, since the straight lines from
Page 34 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle.
Page 22 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...