A treatise on special or elementary geometry (1877)
Olney, Edward, 1827-1887, Olney, Edward, 1827-1887. Elements of trigonometry, plane and spherical · New York : Sheldon · leaf 101
0 be the centres of two equal circles, and arc AwB be less than arc C/iD; then ischord A3 < chord CD.Drawing the diametersAL and CM, place circleO upon circle O, withCM upon AL. Take arcAD = arc CiiD anddraw AD, OB, and OD.AD = CD by {W5),Now AB < AN + NB.AlsoOD<ND + NO;Fig- 135. or, as OD… … STKAIGHT LINES AND CIKCUMFEEENCES. 81 Conversely, if chord AB is less than chord CD, arc AwB is less than arcCnD. For if arc AmB = arc CnD, cliord AB = chord CD [1(S5). And, if arcAmB > arc CwD, chord AB > chord CD. But both of these conclusions arecontrary to the hypothesis. Hence, as arc…
Geometry · Trigonometry
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