### UnivHypGeom31: Menelaus, Ceva and the Laws of proportion

The classical theorems of Menelaus and Ceva concern a triangle together with an additional line or point, and give relations between three ratios of distances (or quadrances). These results are also valid in universal hyperbolic geometry. However we also give some other lovely and simple results: the Triangle proportions theorem and the Alternate spreads theorem.CONTENT SUMMARY: pg 1: @00:11 classical results (main tool- spread law); Menelaus; remark on trigonometry @01:32 ; Menelaus' theorem @02:01pg 2: @05:20 dividing a segment into a ratio; Menelaus' vector theorem @08:23 ;pg 3: @13:24 Ceva's theorem; cevian? lines; the previous are classical results @17:55 ; relationship of results to UHG @18:15pg 4: @18:38 Back to Universal Hyperbolic Geometry; Menelaus theorem; proof;pg 5: @24:23 remark on duality; menelaus' dual theorem @25:15 ; exercises 31-(1:3)pg 6: @27:45 Triangle proportions theorem; proof (the Spread law as the main ingredient)pg 7: @31:36 Alternate spreads? theorem; proofpg 8: @34:14 Ceva's theorem; proofpg 9: @38:24 Ceva's dual theorem; exercises 31.4-6 (THANKS to EmptySpaceEnterprise)

Length:
42:05