The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth BooksMacmillan, 1886 - 400 Seiten |
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Seite 7
... circle BCD . [ Postulate 3 . From the centre B , at the distance BA , describe the circle ACE . [ Postulate 3 . From ... ABC shall be an equilateral triangle . Because the point A is the centre of the circle BCD , AC is equal to AB ...
... circle BCD . [ Postulate 3 . From the centre B , at the distance BA , describe the circle ACE . [ Postulate 3 . From ... ABC shall be an equilateral triangle . Because the point A is the centre of the circle BCD , AC is equal to AB ...
Seite 9
... circle DEF meeting AB at E. [ Postulate 3 . AE shall be equal to C. F ... ABC , DEF be two triangles which have the two sides AB , AC equal to the two ... ABC to the tri- angle DEF , and the other angles shall be equal , each to each , to ...
... circle DEF meeting AB at E. [ Postulate 3 . AE shall be equal to C. F ... ABC , DEF be two triangles which have the two sides AB , AC equal to the two ... ABC to the tri- angle DEF , and the other angles shall be equal , each to each , to ...
Seite 72
... circle is the figure contained by a straight line and the circumference it cuts off . 7. The angle of a segment is ... ABC be the given circle : it is required to find its centre . Draw within it any straight line AB , and bisect 72 ...
... circle is the figure contained by a straight line and the circumference it cuts off . 7. The angle of a segment is ... ABC be the given circle : it is required to find its centre . Draw within it any straight line AB , and bisect 72 ...
Seite 73
... circle ABC . For if F be not the centre , if possible , let & be the centre ; and join GA , GD , GB . Then , because DA is equal to DB , [ Construction . and DG is common to the two triangles ADG , BDG ; the two sides AD , DG are equal ...
... circle ABC . For if F be not the centre , if possible , let & be the centre ; and join GA , GD , GB . Then , because DA is equal to DB , [ Construction . and DG is common to the two triangles ADG , BDG ; the two sides AD , DG are equal ...
Seite 74
... circle . Let ABC be a circle , and A and B any two points in the circumference : the straight line drawn from A to B shall fall within the circle . For if it do not , let it fall , if possible , without , as AEB . Find D the centre of ...
... circle . Let ABC be a circle , and A and B any two points in the circumference : the straight line drawn from A to B shall fall within the circle . For if it do not , let it fall , if possible , without , as AEB . Find D the centre of ...
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ABCD angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC BC is equal bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore