The Elements of Euclid, Libros 1-6;Libro 11J.M. Dent & Sons, Limited, 1933 - 298 páginas |
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Página 14
... sides BA , CA do not coincide with the sides ED , FD , but have a different situation as EG , FG ; then on the same base and on the same side of it there will be two triangles having their sides which are terminated at one extremity of ...
... sides BA , CA do not coincide with the sides ED , FD , but have a different situation as EG , FG ; then on the same base and on the same side of it there will be two triangles having their sides which are terminated at one extremity of ...
Página 278
... sides equal and all their angles equal . A polygon which has all its sides equal and all its angles equal is called a regular polygon . IV . 4. By a process similar to that in IV . 4 we can describe a circle which shall touch one side ...
... sides equal and all their angles equal . A polygon which has all its sides equal and all its angles equal is called a regular polygon . IV . 4. By a process similar to that in IV . 4 we can describe a circle which shall touch one side ...
Página 284
... sides of the triangles about each of their angles are proportionals , but not in the same order , and the triangles are not necessarily equiangular to one another . For a numerical illustration we may suppose the sides of one triangle ...
... sides of the triangles about each of their angles are proportionals , but not in the same order , and the triangles are not necessarily equiangular to one another . For a numerical illustration we may suppose the sides of one triangle ...
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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