An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 38
ualto (PO^)+(POjB) + (POC); and so on. Ex. 4. If A, B, C,...K be n points in a plane, and if (? be the centroid ofequal masses placed at them, show that ^{POA)=n{POG). CONCERNING AREAS. 21 Ex. 5. li A, B, C, D he any four points in a plane, find a point P on theline CD such that the area {PAB)… … B By § 35 (3) we have i {DEF). BC={CEF). BD-{BEF). CD.But {CEF) : {CAF)=CE : CA, and {CAF) : {ABC) = AF : AB. Therefore {CEF) : {ABC) = CE. AF : CA . AB. Similarly {BEF) : {ABC)=BF. AE : BA . AC. {DEF) _ BD.CE. AF-CD. BF. AE**®°*^ {ABC) BC.CA.AB It follows from this result, that when the points D,…
Geometry
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