The Elements of Euclid, Bøker 1-6;Bok 11J.M. Dent & Sons, Limited, 1933 - 298 sider |
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Side 173
... the greater segment as the greater segment is to the less . 4. The altitude of any figure is the straight line drawn from its ver- tex perpendicular to the base . PROPOSITION 1. THEOREM . Triangles and parallelograms of the same Book VI.
... the greater segment as the greater segment is to the less . 4. The altitude of any figure is the straight line drawn from its ver- tex perpendicular to the base . PROPOSITION 1. THEOREM . Triangles and parallelograms of the same Book VI.
Side 174
... altitude are to one another as their bases . Let the triangles ABC , ACD , and the parallelograms EC , CF have the same altitude , namely , the perpendicular drawn from the point A to BD ; as the base BC is to the base CD , so shall the ...
... altitude are to one another as their bases . Let the triangles ABC , ACD , and the parallelograms EC , CF have the same altitude , namely , the perpendicular drawn from the point A to BD ; as the base BC is to the base CD , so shall the ...
Side 286
... altitude . It is not difficult to establish a third proposition conversely connected with the two involved in VI . 14 , and a third propo- sition similarly conversely connected with the two involved in VI . 15. These propositions are ...
... altitude . It is not difficult to establish a third proposition conversely connected with the two involved in VI . 14 , and a third propo- sition similarly conversely connected with the two involved in VI . 15. These propositions are ...
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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