The Elements of Euclid, Libros 1-6;Libro 11J.M. Dent & Sons, Limited, 1933 - 298 páginas |
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Página xvii
... demonstration of the theorem . Lastly , we have the demonstration itself , which shews that the problem has been solved , or that the theorem is true . Sometimes , however , no construction is required ; and sometimes the construction ...
... demonstration of the theorem . Lastly , we have the demonstration itself , which shews that the problem has been solved , or that the theorem is true . Sometimes , however , no construction is required ; and sometimes the construction ...
Página 273
... demonstrations of III . 9 , of which Simson has chosen the second . Euclid's other demonstration is as follows . Join D with the middle point of the straight line AB ; then it may be shewn that this straight line is at right angles to ...
... demonstrations of III . 9 , of which Simson has chosen the second . Euclid's other demonstration is as follows . Join D with the middle point of the straight line AB ; then it may be shewn that this straight line is at right angles to ...
Página 274
... demonstration in III . 11 will hold even if D and H be supposed to coincide , and that the demonstration in III . 12 will hold even if C and D be supposed to coincide . We may combine III . II and III . 12 in one enunciation thus . If ...
... demonstration in III . 11 will hold even if D and H be supposed to coincide , and that the demonstration in III . 12 will hold even if C and D be supposed to coincide . We may combine III . II and III . 12 in one enunciation thus . If ...
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Términos y frases comunes
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