The Elements of EuclidJ. M. Dent & sons, 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 produced . Suppose , for example , that we wish to describe a circle which shall touch the side BC , and the sides AB and AC produced : bisect the angle between AB produced and BC , and bisect the angle between AC produced and BC ...
... sides produced . Suppose , for example , that we wish to describe a circle which shall touch the side BC , and the sides AB and AC produced : bisect the angle between AB produced and BC , and bisect the angle between AC produced and BC ...
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 adjacent angles angle ABC angle ACB angle BAC angle DEF angle EDF angles equal Axiom base BC BC is equal bisected centre circle ABC circumference Constr Construction 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