The Elements of Euclid, Bøker 1-6;Bok 11J.M. Dent & Sons, Limited, 1933 - 298 sider |
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Side 81
... shown that LD is less than HD . Therefore DG is the least , and DK less than DL , and DL less than DH . Also , there can be drawn two equal straight lines from the point D to the circumference , one on each side of the least line . [ I ...
... shown that LD is less than HD . Therefore DG is the least , and DK less than DL , and DL less than DH . Also , there can be drawn two equal straight lines from the point D to the circumference , one on each side of the least line . [ I ...
Side 175
Euclid Isaac Todhunter, Robert Simson. and since it has been shown that if the base HC be greater than the base CL ... shown that the triangle ABC is to the triangle ACD as the base BC is to the base CD ; therefore the parallelogram EC ...
Euclid Isaac Todhunter, Robert Simson. and since it has been shown that if the base HC be greater than the base CL ... shown that the triangle ABC is to the triangle ACD as the base BC is to the base CD ; therefore the parallelogram EC ...
Side 248
... shown ; which is impossible . [ V. 14 . Therefore the square on BD is not to the square on FH as the circle ABCD is to any space less than the circle EFGH . In the same way it may be shown that the square on FH is not to the square on ...
... shown ; which is impossible . [ V. 14 . Therefore the square on BD is not to the square on FH as the circle ABCD is to any space less than the circle EFGH . In the same way it may be shown that the square on FH is not to the square on ...
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Vanlige uttrykk og setninger
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