An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 39
point 0, then, by § 28, we haveBC.Ox+CO.Bx+OB.Cx=0,and AD.Ox + DO.Ax + OA.Dx=0. Hence DO. BC. Ax-CO. AD. Bx-OB.AD. Cx+OA . BC. Dx=0 ;or DO. BC. Ax+DA. CO.Bx-BO. DA . Cx-BC. AO. Dx=0. But {BCD)=iDO. 5C. sin BOD, {CDA)=iDA. CO.sin AOC, (DAB) = iDA. BO. siaAOC, {ABC)=iBC .AO.ainBOD.Also sin BOD= - sin… … CONCERNING AREAS. 23 Let the straight lines AB, CD meet in the point 0, and let Mand N be two points on these lines respectively, such thatOM=AB, and ON=GD. Then we have (PAB) = (POM), and (PCD) = (PON).Let Q be the middle point oi MN. Then, by § 35 (2), we have 2 (POQ) = (POM) + (PON).Therefore 2…
Geometry
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