Plane and solid geometry . CaI), and EAb, the surface of the sphere will be divided intoeight spherical triangles, four of which are seen on the hemi-sphere represented in the figure. Of these eight spherical tri-angles, abCis the one and only one that is so situated that Aand a lie on the same side of BC, B and b on the same side ofAC, and C and C on the same side of AB. This particular tri-angle abc is called the polar triangle of triangle ABC. 944. Questions. In the figure above, A ABC, the polar of A ABC,is entirely outside of A ABC. Can the two ^ be so constructed that:(rt) ABC is entirel
Plane and solid geometry . CaI), and EAb, the surface of the sphere will be divided intoeight spherical triangles, four of which are seen on the hemi-sphere represented in the figure. Of these eight spherical tri-angles, abCis the one and only one that is so situated that Aand a lie on the same side of BC, B and b on the same side ofAC, and C and C on the same side of AB. This particular tri-angle abc is called the polar triangle of triangle ABC. 944. Questions. In the figure above, A ABC, the polar of A ABC,is entirely outside of A ABC. Can the two ^ be so constructed that:(rt) ABC is entirely within ABC ?(b) ABC is partly outside of and partly within ABC? Ex. 1518. What is the polar triangle of a spherical triangle all ofwhose sides are quadrants ? BOOK IX 433 Proposition XI. Theorem 945. If one spherical triangle is the polar of another,then the second is the polar of the first.
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
