The Elements of EuclidJ. M. Dent & Sons Limited, 1933 - 298 páginas |
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Página 11
... shewn to be equal to GB ; therefore the two sides BF , FC are equal to the two sides CG , GB , each to each ; and the angle BFC was shewn to be equal to the angle CGB ; therefore the triangles BFC , CGB are equal , and their other ...
... shewn to be equal to GB ; therefore the two sides BF , FC are equal to the two sides CG , GB , each to each ; and the angle BFC was shewn to be equal to the angle CGB ; therefore the triangles BFC , CGB are equal , and their other ...
Página 127
... shewn that HK is double of BK . And because BK is equal to CK , as was shewn , and that HK is double of BK , and LK double of CK , therefore HK is equal to LK . [ Axiom 6 . In the same manner it may be shewn that GH , GM , ML are each ...
... shewn that HK is double of BK . And because BK is equal to CK , as was shewn , and that HK is double of BK , and LK double of CK , therefore HK is equal to LK . [ Axiom 6 . In the same manner it may be shewn that GH , GM , ML are each ...
Página 150
... shewn , that L is greater than FG but not greater than EG . And L is a multiple of D , [ Construction . and EG and FG were shewn to be equi- multiples of AB and CB . [ Construction . E Therefore D has to BC a greater ratio than it has ...
... shewn , that L is greater than FG but not greater than EG . And L is a multiple of D , [ Construction . and EG and FG were shewn to be equi- multiples of AB and CB . [ Construction . E Therefore D has to BC a greater ratio than it has ...
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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