An elementary treatise on geometry : simplified for beginners not versed in algebra . and z,together, equal to a right angle (page 34, 7thly); andbecause the tangent DB is perpendicular to the radiusCB, the angles x and y are together also equal to a rightangle ; therefore the angle z is equal to the angle y(Truth III, page 21) : and as the angle z is half of theangle ACB, the angle y (its equal) is also half of theangle ACB. Q. And what remark can you make with regard to thearc BK? A. That the arc BK, which measures the angle 2, mt^-4« taken also for the measure of * angle y (its equal);10 11
An elementary treatise on geometry : simplified for beginners not versed in algebra . and z,together, equal to a right angle (page 34, 7thly); andbecause the tangent DB is perpendicular to the radiusCB, the angles x and y are together also equal to a rightangle ; therefore the angle z is equal to the angle y(Truth III, page 21) : and as the angle z is half of theangle ACB, the angle y (its equal) is also half of theangle ACB. Q. And what remark can you make with regard to thearc BK? A. That the arc BK, which measures the angle 2, mt^-4« taken also for the measure of * angle y (its equal);10 110 GEOMETRY. and as the arc BK is half of the arc AB, the angle y, •made hy the tangent BD and the chord AB, may likewisehe measured hy half the arc AB. Q. What do you mean by saying that half the arc ABmeasures the angle y ? A. That if the arc AB is given in degi-ees^ minutes,seconds, &lc., the angle y measures half as many degrees,,minutes, seconds, &/C., as the arc AB. Thus if the arcAB were 12 degrees and 30 minutes, the angle y wouldmeasure 6 degrees and 15 What relation does the angle w, formed hy the tworadii CA, CF, hear to the angle y, formed hy the ticochords ABj FB, if the legs of both these angles stand onthe extremities of the same arc AF1 A. The angle w, formed by the ttvo radii CA, CF, istwice as great as the angle y, formed hy the two chordsAB, FB. Q. How can you prove it ? A. Drawing in the point B a tangent, DE, to thecircle, the angles Xj y, z, being together equal to tworight angles (duery 4, Sect. I.), will have for therrmeasure half the circumference of the circle (page 107,remark 3d). Now, the angle x, formed by the tangentDB and the chord AB, is measured by half the arc AB,as has been proved in the last query; and for the same GEOMETRY. Ill reason is the angle z measured by half the arc BF ; andtherefore the remaining angle y is measured by half thearc AF ; because half of the arc AF makes with half ofthe arcs AB and BF, half the circumferenc
Size: 1839px × 1359px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookauthorgrundfrancisjfrancisjoseph18051863, bookcentury1800
