The Elements of Euclid, Bøker 1-6;Bok 11 |
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Side 13
But it has been shewn to be greater ; which is impossible . But if one of the
vertices as D , be within the other triangle ACB , produce AC , AD to E , F. Then
because AC is equal to AD , in the triangle ACD , ( Hyp . the angles ECD , FDC ,
on the ...
But it has been shewn to be greater ; which is impossible . But if one of the
vertices as D , be within the other triangle ACB , produce AC , AD to E , F. Then
because AC is equal to AD , in the triangle ACD , ( Hyp . the angles ECD , FDC ,
on the ...
Side 77
But EC was shewn to be equal to EF ; therefore EF is equal to EG , [ Axiom 1 . the
less to the greater ; which is impossible . Therefore E is not the centre of the
circles ABC , CDG . Wherefore , if two circles & c . Q.E.D. PROPOSITION 6.
But EC was shewn to be equal to EF ; therefore EF is equal to EG , [ Axiom 1 . the
less to the greater ; which is impossible . Therefore E is not the centre of the
circles ABC , CDG . Wherefore , if two circles & c . Q.E.D. PROPOSITION 6.
Side 83
Therefore the same point is the centre of two circles which cut one another ;
which is impossible . [ III . 5 . Wherefore , one circumference & c . Q.E.D.
PROPOSITION 11. THEOREM . If two circles touch one another internally , the
straight line ...
Therefore the same point is the centre of two circles which cut one another ;
which is impossible . [ III . 5 . Wherefore , one circumference & c . Q.E.D.
PROPOSITION 11. THEOREM . If two circles touch one another internally , the
straight line ...
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Vanlige uttrykk og setninger
ABCD AC is equal angle ABC angle ACB angle BAC Axiom base bisected Book centre circle circle ABC circumference common Construction contained Corollary Definition demonstration described diameter divided double draw drawn edition Elements equal equal angles equiangular equilateral equimultiples Euclid exterior angle extremities fall figure four fourth given given straight line greater half Hypothesis impossible join less Let ABC magnitudes manner meet multiple namely parallel parallelogram pass perpendicular plane polygon PROBLEM produced proportionals Q.E.D. PROPOSITION ratio reason rectangle rectangle contained rectilineal figure right angles segment shewn sides similar Simson square square on AC straight line &c suppose Take taken THEOREM third triangle ABC Wherefore whole
Bibliografisk informasjon
| Tittel | The Elements of Euclid, Bøker 1-6;Bok 11 Utgave 891 av Everyman's library Utgave 891 av Everyman's library, ed. by Ernest Rhys. Science. [No. 891] Utgave 891 av Everyman's library: Science |
| Forfatter | Euclid |
| Redaktører | Isaac Todhunter, Robert Simson |
| Utgiver | J.M. Dent & Sons, Limited, 1933 |
| Original fra | University of California, Berkeley |
| Digitalisert | 5. aug 2019 |
| Lengde | 298 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |