The Elements of EuclidJ. M. Dent & sons, 1933 - 298 páginas |
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Página 41
... diameter AB bisects the parallelogram ; [ I. 34 . and the triangle DBC is half of the parallelogram DBCF , because the diameter DC bisects the parallelogram . [ I. 34 . But the halves of equal things are equal . [ Axiom 7 . Therefore ...
... diameter AB bisects the parallelogram ; [ I. 34 . and the triangle DBC is half of the parallelogram DBCF , because the diameter DC bisects the parallelogram . [ I. 34 . But the halves of equal things are equal . [ Axiom 7 . Therefore ...
Página 78
... diameter of a circle which is not the centre , of all the straight lines which can be drawn from this point to the circumference , the greatest is that in which the centre is , and the other part of the diameter is the least ; and , of ...
... diameter of a circle which is not the centre , of all the straight lines which can be drawn from this point to the circumference , the greatest is that in which the centre is , and the other part of the diameter is the least ; and , of ...
Página 114
... diameter of the circle . Let ABC be the given circle , and D the given straight line , not greater than the diameter of the circle : it is required to place in the circle ABC , a straight line equal to D. Draw BC , a diameter of the ...
... diameter of the circle . Let ABC be the given circle , and D the given straight line , not greater than the diameter of the circle : it is required to place in the circle ABC , a straight line equal to D. Draw BC , a diameter of the ...
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Términos y frases comunes
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