 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...a diameter, is a semi-circumference, and the included segment is a semicircle. THEOREM II. 141. In the same circle, or in equal circles, equal arcs are...and, conversely, equal chords subtend equal arcs. Let ADB and EGF be two equal circles, and let the arc AD be equal to EG ; then will the chord AD be... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...cannot meet the circumference in more than two points ; which was to be proved. PROPOSITION IV. THEOREM. In equal circles, equal arcs are subtended by equal...; and conversely, equal chords subtend equal arcs. 1°. In the equal circles ADB and EGF, let the arcs AMD and ENG be equal : then will the chords AD... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...from the center of an equal circle, and hence they are equal to each other. 126. Proposition IX.— Theorem. 'In the same circle or in equal circles,...chords; and conversely, equal chords subtend equal arcs. Let C, C', be the centers of equal circles, AmB, DnE, equal arcs. Then, AB = DE. A falls on D, and... | |
 | William Guy Peck - Conic sections - 1876 - 412 pages
...preceding proposition holds good if the angles and arcs belong to the same circle. PROPOSITION IV. THEOREM. In equal circles, equal arcs are subtended by equal...; and conversely, equal chords subtend equal arcs. Draw the radii OA, OD, QE, and QG. •Because the arcs ACD and IEBG are equal, the angles 0 ;anfi Q... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...sectors the greater has the greater angle. [By Rule of Conversion.] SECTION 2. CHORDS. THEOR. 4. In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and of two unequal minor arcs the greater is subtended by the greater chord. [By Theor. 3, and Book I,... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...the arcs are in the same circle, the demonstration is similar. Therefore, in the same circle, etc. PROPOSITION IV. THEOREM. In the same circle or in equal circles, equal angles at the centre are subtended by equal arcs; and, conversely, equal arcs subtend equal angles... | |
 | Charles Scott Venable - 1881 - 380 pages
...straight line, which is impossible (Book I., Prop. XVII. Cor. 2). .PROPOSITION IV. THEOREM. In ihe same circle, or in equal circles, equal arcs are subtended...conversely, equal chords subtend equal arcs. If the radii AC and EO are equal, and the arc AMD equal to the arc ENG, then the chord AD will be equal to the chord... | |
 | Mathematical association - 1883 - 86 pages
...sectors the greater has the greater angle. [By Rule of Conversion.] SECTION 2. CHORDS. THEOR. 4. In the same circle, or in equal circles, equal arcs are subtended by equal chords; and of two unequal minor arcs the greater is subtended by the greater chord. [By Theor. 3, and Book I,... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...DF are equally distant from the centre. QUERY. Why are AC and D 0 oblique lines? THEOREM IV. QED In the same circle or in equal circles, equal arcs are subtended by equal chords. Let C and O be two equal circles, ABD and EFG two equal arcs; then will AD = E G. For, let C be applied... | |
 | Henry Elmer Moseley - Universities and colleges - 1884 - 214 pages
...opposite these angles are unequal, and the greater side is opposite the greater angle. 5. Prove that in the same circle, or in equal circles, equal arcs are subtended by equal chords. 6. Prove that the square of a side of a triangle opposite an acute angle is equal to the sum of the... | |
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In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs. 
