Elements of Plane Geometry |
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Page 4
... CHORDS , ARCS , ETC. 87 RELATIVE POSITION OF CIRCLES 97 MEASUREMENT OF ANGLES . 99 PROBLEMS IN CONSTRUCTION 107 EXERCISES IN INVENTION 124 BOOK IV . AREA AND RELATION OF POLYGONS . DEFINITIONS AREAS SQUARES ON LINES PROJECTION ...
... CHORDS , ARCS , ETC. 87 RELATIVE POSITION OF CIRCLES 97 MEASUREMENT OF ANGLES . 99 PROBLEMS IN CONSTRUCTION 107 EXERCISES IN INVENTION 124 BOOK IV . AREA AND RELATION OF POLYGONS . DEFINITIONS AREAS SQUARES ON LINES PROJECTION ...
Page 85
... Chord is a straight line joining any two points in the circumference ; as , P ED . The arc EPD is said to be subtended by its chord ED . Every chord subtends two E D 0 arcs , whose sum equals the whole circumference . Whenever an arc ...
... Chord is a straight line joining any two points in the circumference ; as , P ED . The arc EPD is said to be subtended by its chord ED . Every chord subtends two E D 0 arcs , whose sum equals the whole circumference . Whenever an arc ...
Page 86
... chord ; as , FGH . A Semicircle is a segment equal to one - half of the circle . F G 176. A Sector of a circle is ... chords ; as , ABE . A B C F 180. An Inscribed Polygon is one whose sides are chords of a circle ; as , ABCDEF ...
... chord ; as , FGH . A Semicircle is a segment equal to one - half of the circle . F G 176. A Sector of a circle is ... chords ; as , ABE . A B C F 180. An Inscribed Polygon is one whose sides are chords of a circle ; as , ABCDEF ...
Page 87
Franklin Ibach. CHORDS , ARCS , ANGLES AT THE CENTRE , SECANTS , AND RADII . THEOREM I. 183. Any diameter bisects the circle and its circumference . Let ABCD be a O , and AB any diameter . C A B D To prove that ABC ... CHORDS, ARCS, ETC.
Franklin Ibach. CHORDS , ARCS , ANGLES AT THE CENTRE , SECANTS , AND RADII . THEOREM I. 183. Any diameter bisects the circle and its circumference . Let ABCD be a O , and AB any diameter . C A B D To prove that ABC ... CHORDS, ARCS, ETC.
Page 88
... chord . In the O ACB , let AB be any diameter and BC any other chord . or A C B 0 To prove that AB > BC . From the centre O , draw ОС , OA = OC . ( 182 ) OC + OB > BC . ( Ax . 11 ) Substitute OA for its equal OС . Then OA + OB > BC , AB ...
... chord . In the O ACB , let AB be any diameter and BC any other chord . or A C B 0 To prove that AB > BC . From the centre O , draw ОС , OA = OC . ( 182 ) OC + OB > BC . ( Ax . 11 ) Substitute OA for its equal OС . Then OA + OB > BC , AB ...
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Common terms and phrases
AB² ABC and DEF AC and BC AC² adjacent angles angles are equal angles formed AP² arc AC base and altitude BC² bisectors centre chord circumscribed common point Concave Polygon construct Convex Polygon D To prove decagon DEF are similar describe an arc diameter divided Draw the diagonal EF² equal circles equally distant equilateral polygon F To prove given circle given polygon given straight line homologous sides hypothenuse inscribe a regular intercepted interior angles intersect isosceles La=Lb Let ABCD lines drawn measured by arc medial line middle point parallel parallelogram perimeter 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 secants 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 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 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 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 136 - 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 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 137 - 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 diminished by twice the product of one of those sides and the projection of the other upon that side.
Page 177 - From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines.