The Elements of Euclid, Libros 1-6;Libro 11J.M. Dent & Sons, Limited, 1933 - 298 páginas |
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Página 21
... Wherefore , if one side & c . 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 ...
... Wherefore , if one side & c . 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 ...
Página 43
... Wherefore , equal triangles & c . Q.E.D. PROPOSITION 41. THEOREM . If a parallelogram and a triangle be on the same base and between the same parallels , the parallelogram shall be double of the triangle . Let the parallelogram ABCD and ...
... Wherefore , equal triangles & c . Q.E.D. PROPOSITION 41. THEOREM . If a parallelogram and a triangle be on the same base and between the same parallels , the parallelogram shall be double of the triangle . Let the parallelogram ABCD and ...
Página 83
... Wherefore , one circumference & c . 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 ...
... Wherefore , one circumference & c . 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 ...
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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