The Elements of Euclid, Libros 1-6;Libro 11J.M. Dent & Sons, Limited, 1933 - 298 páginas |
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Página 36
... Corollary 2 . Therefore all the interior angles of the figure , together with four right angles , are equal to twice as many right angles as the figure has sides . COROLLARY 2. All the exterior angles of any recti- lineal figure are ...
... Corollary 2 . Therefore all the interior angles of the figure , together with four right angles , are equal to twice as many right angles as the figure has sides . COROLLARY 2. All the exterior angles of any recti- lineal figure are ...
Página 171
... COROLLARY 1. If the same hypothesis be made as in the proposition , the excess of the first and fifth shall be to the second as the excess of the third and sixth is to the fourth . The demonstration of this is the same as that of the ...
... COROLLARY 1. If the same hypothesis be made as in the proposition , the excess of the first and fifth shall be to the second as the excess of the third and sixth is to the fourth . The demonstration of this is the same as that of the ...
Página 264
... corollaries to I. 32 were added by Simson . In the second corollary it ought to be stated what is meant by an exterior angle of a rectilineal figure . At each angular point let one of the sides meeting at that point be produced ; then ...
... corollaries to I. 32 were added by Simson . In the second corollary it ought to be stated what is meant by an exterior angle of a rectilineal figure . At each angular point let one of the sides meeting at that point be produced ; then ...
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ABCD AC is equal adjacent angles angle ABC angle ACB angle BAC angle DEF angle EDF angles equal Axiom base BC bisected centre circle ABC circumference Constr Construction Corollary Definition 15 demonstration diameter double draw equal angles equal to F equiangular equimultiples Euclid Euclid's Elements exterior angle fourth given circle given straight line gnomon greater ratio greater than F Hypothesis less Let ABC Let the straight meet multiple opposite angle parallel to BC parallelogram perpendicular polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION rectangle contained remaining angle right angles segment shewn sides similar and similarly Simson square described square on AC straight line &c straight line AB THEOREM tiples touches the circle triangle ABC triangle DEF twice the rectangle Wherefore