Elements of Plane Geometry |
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AB² ABC and DEF AC and BC AC² adjacent angles angles are equal arc AB arc AB arc arc AC arc CD base and altitude bisect bisectors centre chord circumscribed common point construct Convex Polygon COR.-In decagon DEF are similar describe an arc diameter divided Draw the diagonal equally distant equilateral polygon exterior angles F To prove given circle given polygon given straight line homologous sides hypothenuse inscribe a regular intercepted intersect isosceles La=Lb Let ABCD lines drawn measured by arc medial line middle point parallel parallelogram perimeter perpendicular plane produced Q. E. D. THEOREM Q. E. F. PROBLEM quadrilateral quantities radius ratio rectangle regular inscribed hexagon regular polygon respectively equal rhombus right angles right-angled triangle SCHOLIUM secant similar polygons tangent trapezoid unit of measure vertex
Popular passages
Page 14 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Page 136 - AA' and BB' be perpendicular to line CD, the projection of line AB upon line CD is line A'B'. PROP. XXV. THEOREM 277. In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Page 85 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 44 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Page 83 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 14 - Axioms. 1. Things which are equal to the same thing are equal to each other. 2. If equals are added to equals, the wholes are equal. 3. If equals are taken from equals, the remainders are equal.
Page 75 - To indicate that the ratio of A to B is equal to the ratio of C to D...
Page 123 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Page 55 - A polygon of three sides is a triangle ; of four, a quadrilateral; of five, a pentagon ; of six, a hexagon ; of seven, a heptagon; of eight, an octagon; of nine, a nonagon; of ten, a decagon; of twelve, a dodecagon.
Page 149 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.