The Elements of Euclid, Bøker 1-6;Bok 11J.M. Dent & Sons, Limited, 1933 - 298 sider |
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Side 134
... magnitude is said to be a part of a greater magnitude , when the less measures the greater ; that is , when the less is contained a certain number of times ex- actly in the greater . 2. A greatér magnitude is said to be a multiple of a ...
... magnitude is said to be a part of a greater magnitude , when the less measures the greater ; that is , when the less is contained a certain number of times ex- actly in the greater . 2. A greatér magnitude is said to be a multiple of a ...
Side 137
... magnitudes are taken , two and two . 19. Ex æquali . This term is used simply by itself , when the first magnitude is to the second of the first rank , as the first is to the second of the other rank ; and the second is to the third of ...
... magnitudes are taken , two and two . 19. Ex æquali . This term is used simply by itself , when the first magnitude is to the second of the first rank , as the first is to the second of the other rank ; and the second is to the third of ...
Side 148
Euclid Isaac Todhunter, Robert Simson. " 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 ...
Euclid Isaac Todhunter, Robert Simson. " 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 ...
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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