The Elements of Euclid, Bøker 1-6;Bok 11J.M. Dent & Sons, Limited, 1933 - 298 sider |
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Resultat 1-3 av 87
Side 103
... less than a semicircle , shall be greater than a right angle . . EB , Join AE , and produce BA to F. Then , because ... less than two right angles , [ I. 17 . and that BAC has been shewn to be a right angle , therefore the angle ABC is ...
... less than a semicircle , shall be greater than a right angle . . EB , Join AE , and produce BA to F. Then , because ... less than two right angles , [ I. 17 . and that BAC has been shewn to be a right angle , therefore the angle ABC is ...
Side 134
... LESS 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 ...
... LESS 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 153
... less , less . Again , because C is to D as E is to F , [ V. Definition 5 . [ Hypothesis . and that H and K are equimultiples of C and E , and M and N are equimultiples of D and F ; therefore if H be greater than M , K is and if equal ...
... less , less . Again , because C is to D as E is to F , [ V. Definition 5 . [ Hypothesis . and that H and K are equimultiples of C and E , and M and N are equimultiples of D and F ; therefore if H be greater than M , K is and if equal ...
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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