. The principles of projective geometry applied to the straight line and conic . be described throughC, A,B and B, A, C to meet in 0, thesum of the angles CBA, COA, ACBandAOB is four right angles and thereforethe sum of the angles CAB and COBis two right angles. Hence a circle canbe described through A, C, 0, B. The angle B0C=BAC+AB0+AC0= BAC+CA0+OAB= BAC+CAB. As these angles are given the angleBOC is constant and 0 is situated on a given circle through B and C. Similarly, itis on a given circle through B and A and is therefore a fixed point. Also the angle OCA equals the angle OBC and is ther
. The principles of projective geometry applied to the straight line and conic . be described throughC, A,B and B, A, C to meet in 0, thesum of the angles CBA, COA, ACBandAOB is four right angles and thereforethe sum of the angles CAB and COBis two right angles. Hence a circle canbe described through A, C, 0, B. The angle B0C=BAC+AB0+AC0= BAC+CA0+OAB= BAC+CAB. As these angles are given the angleBOC is constant and 0 is situated on a given circle through B and C. Similarly, itis on a given circle through B and A and is therefore a fixed point. Also the angle OCA equals the angle OBC and is therefore constant. Hencethe triangle OCA is given in species. One of its vertices 0 is fixed and the othertwo move along fixed lines AB and BC. 7. Areas. (a) If Ai and A2 be the areas of the triangles P^BC and P^BC and P point on tJie line P1P2, then the area PBC equals Let PyP-i meet BC in 0, and letPj, JO2, jo be the perpendiculars fromPi, P2, P respectively on BC. Then, if A be the area of PBC, ^: : : O/i : OP : OP.^.Hence it follows that^ + any + ,
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective
