The Elements of Euclid, Bøker 1-6;Bok 11 |
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Side 138
THEOREM , If any number of magnitudes be equimultiples of as many , each of
each ; whatever multiple any one of them is . of its part , the same multiple shall
all the first magnitudes be of all the other . Let any number of magnitudes AB , CD
...
THEOREM , If any number of magnitudes be equimultiples of as many , each of
each ; whatever multiple any one of them is . of its part , the same multiple shall
all the first magnitudes be of all the other . Let any number of magnitudes AB , CD
...
Side 148
Let A and B be equal magnitudes , and C any other magnitude : each of the
magnitudes A and B shall have the same ratio to C ; and C shall have the same
ratio to each of the magnitudes A and B. Take of A and B any equimultiples
whatever ...
Let A and B be equal magnitudes , and C any other magnitude : each of the
magnitudes A and B shall have the same ratio to C ; and C shall have the same
ratio to each of the magnitudes A and B. Take of A and B any equimultiples
whatever ...
Side 157
D Magnitudes have the same ratio to one another that their equimultiples have .
Let AB be the same multiple of C that DE is of F : C shall be to F as AB is to DĖ .
For , because AB is the same multiple of C that DE is of F , [ Hypothesis .
therefore ...
D Magnitudes have the same ratio to one another that their equimultiples have .
Let AB be the same multiple of C that DE is of F : C shall be to F as AB is to DĖ .
For , because AB is the same multiple of C that DE is of F , [ Hypothesis .
therefore ...
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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 |