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
... given finite straight line . Let AB be the given straight line : it is required to describe an equilateral triangle on AB . A A From the centre A , at the distance AB , describe the circle BCD . [ Postulate 3 . From the centre B , at ...
... given finite straight line . Let AB be the given straight line : it is required to describe an equilateral triangle on AB . A A From the centre A , at the distance AB , describe the circle BCD . [ Postulate 3 . From the centre B , at ...
Seite 8
... given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the given ... circle CGH , meeting DF at G. [ Post . 3 . From the centre D , at the dis- tance DG , describe the circle GKL , meeting ...
... given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the given ... circle CGH , meeting DF at G. [ Post . 3 . From the centre D , at the dis- tance DG , describe the circle GKL , meeting ...
Seite 17
... circle EGF , meeting AB at F and G. [ Postulate 3 . Bisect FG at H , and join CH . [ I. 10 . H The straight line CH drawn from the given point C shall be perpendicular to the given straight line AB . Join CF , CG . Because FH is equal ...
... circle EGF , meeting AB at F and G. [ Postulate 3 . Bisect FG at H , and join CH . [ I. 10 . H The straight line CH drawn from the given point C shall be perpendicular to the given straight line AB . Join CF , CG . Because FH is equal ...
Seite 25
... given straight lines , but any two whatever of these must be greater than the third . Let A , B , C be the three ... circle [ Post . 3 . describe DKL . D E H L Α B ARC From the centre G , at the distance GH , describe the circle HLK ...
... given straight lines , but any two whatever of these must be greater than the third . Let A , B , C be the three ... circle [ Post . 3 . describe DKL . D E H L Α B ARC From the centre G , at the distance GH , describe the circle HLK ...
Seite 72
... circle is the figure contained by a straight line and the circumference it cuts off . 7. The angle of a segment is ... given circle . Let ABC be the given circle : it is required to find its centre . Draw within it any straight line AB ...
... circle is the figure contained by a straight line and the circumference it cuts off . 7. The angle of a segment is ... given circle . Let ABC be the given circle : it is required to find its centre . Draw within it any straight line AB ...
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Häufige Begriffe und Wortgruppen
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