The Elements of EuclidJ. M. Dent & sons, 1933 - 298 páginas |
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Página 79
... circumference ; and FB is greater than FC , and FC than FG . Also , there can be drawn two equal straight lines from the point F to the circumference , one on each side of the shortest line FD . [ I. 23 . For , at the point E , in the ...
... circumference ; and FB is greater than FC , and FC than FG . Also , there can be drawn two equal straight lines from the point F to the circumference , one on each side of the shortest line FD . [ I. 23 . For , at the point E , in the ...
Página 80
... circumference two straight lines , and only two , which are equal to one another , one on each side of the shortest ... circumference , of which DA passes through the centre : of those which fall on the concave circumference AEFC ...
... circumference two straight lines , and only two , which are equal to one another , one on each side of the shortest ... circumference , of which DA passes through the centre : of those which fall on the concave circumference AEFC ...
Página 82
... circumference there fall more than two equal straight lines , namely DA , DB , DC : the point D shall be the centre of the circle . For , if not , let E be the centre ; join DE and produce it both ways to meet the circumference at F ...
... circumference there fall more than two equal straight lines , namely DA , DB , DC : the point D shall be the centre of the circle . For , if not , let E be the centre ; join DE and produce it both ways to meet the circumference at F ...
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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