The Elements of Euclid, Libros 1-6;Libro 11J.M. Dent & Sons, Limited, 1933 - 298 páginas |
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Página 21
... Q.E.D. PROPOSITION 17. THEOREM . Any two angles of a triangle are together less than two right angles . Let ABC be a triangle : any two of its angles are together less than two right angles . Produce BC to D. Then because ACD is the ...
... Q.E.D. PROPOSITION 17. THEOREM . Any two angles of a triangle are together less than two right angles . Let ABC be a triangle : any two of its angles are together less than two right angles . Produce BC to D. Then because ACD is the ...
Página 23
... Q.E.D. PROPOSITION 20 . THEOREM . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle : any two sides of it are together greater than the third side ; namely , BA , AC greater than BC ; and AB ...
... Q.E.D. PROPOSITION 20 . THEOREM . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle : any two sides of it are together greater than the third side ; namely , BA , AC greater than BC ; and AB ...
Página 83
... Q.E.D. PROPOSITION 11. THEOREM . [ III . 5 . If two circles touch one another internally , the straight line which joins their centres , being produced , shall pass through the point of contact . Let the two circles ABC , ADE touch one ...
... Q.E.D. PROPOSITION 11. THEOREM . [ III . 5 . If two circles touch one another internally , the straight line which joins their centres , being produced , shall pass through the point of contact . Let the two circles ABC , ADE touch one ...
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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