Read e-book online Algebraic Geometry Santa Cruz 1995: Summer Research PDF

By David R. Morrison, Janos Kolla Summer Research Institute on Algebraic Geometry

ISBN-10: 0821808958

ISBN-13: 9780821808955

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Read or Download Algebraic Geometry Santa Cruz 1995: Summer Research Institute on Algebraic Geometry, July 9-29, 1995, University of California, Santa Cruz (Proceedings of Symposia in Pure Mathematics) (Pt. 2) PDF

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Additional resources for Algebraic Geometry Santa Cruz 1995: Summer Research Institute on Algebraic Geometry, July 9-29, 1995, University of California, Santa Cruz (Proceedings of Symposia in Pure Mathematics) (Pt. 2)

Example text

Let ACB have been added to both. Thus, the (angles) ACD and ACB are greater than the (angles) ABC and BCA. But, ACD and ACB are equal to two right-angles [Prop. 13]. Thus, ABC and BCA are less than two right-angles. Similarly, we can show that BAC and ACB are also less than two right-angles, and again CAB and ABC (are less than two right-angles). Thus, for any triangle, (any) two angles are less than two right-angles, (the angles) being taken up in any (possible way). (Which is) the very thing it was required to show.

But it was shown that (BAC is) also not equal (to EDF ). Thus, BAC is greater than EDF . Thus, if two triangles have two sides equal to two sides, respectively, but (one) has a base greater than the base (of the other), then (the former triangle) will also have the angle encompassed by the equal straight-lines greater than the (corresponding) angle (in the latter). (Which is) the very thing it was required to show. 59 ΣΤΟΙΧΕΙΩΝ α΄ κ ΄ ∆ Α Η Β Ε Ζ Θ Γ Ε ν δύο τρίγωνα τ ς δύο γωνίας δυσ γωνίαις σας χ καρέραν καρέρ κα µίαν πλευρ ν µι πλευρ σην τοι τ ν πρ ς τα ς σαις γωνίαις τ ν ποτείνουσαν π µίαν τ ν σων γωνι ν, κα τ ς λοιπ ς πλευρ ς τα ς λοιπα ς πλευρα ς σας ξει [ κατέραν κατέρ ] κα τ ν λοιπ ν γωνίαν τ λοιπ γωνί .

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Algebraic Geometry Santa Cruz 1995: Summer Research Institute on Algebraic Geometry, July 9-29, 1995, University of California, Santa Cruz (Proceedings of Symposia in Pure Mathematics) (Pt. 2) by David R. Morrison, Janos Kolla Summer Research Institute on Algebraic Geometry


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