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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Ergebnisse 1-5 von 57
Seite 7
... describe an equilateral triangle on a 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 ...
... describe an equilateral triangle on a 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 ...
Seite 8
... describe the circle GKL , meeting DE at L. [ Post . 3 . AL shall be equal to BC . B Because the point B is the centre of the circle CGH , BC is equal to BG . [ Definition 15 . And because the point D is the centre of the circle GKL ...
... describe the circle GKL , meeting DE at L. [ Post . 3 . AL shall be equal to BC . B Because the point B is the centre of the circle CGH , BC is equal to BG . [ Definition 15 . And because the point D is the centre of the circle GKL ...
Seite 9
... describe the circle DEF meeting AB at E. [ Postulate 3 . AE shall be equal to C. F Because the point A is the centre of the circle DEF , AE is equal to AD . But C is equal to AD . [ Definition 15 . [ Construction . Therefore AE and Care ...
... describe the circle DEF meeting AB at E. [ Postulate 3 . AE shall be equal to C. F Because the point A is the centre of the circle DEF , AE is equal to AD . But C is equal to AD . [ Definition 15 . [ Construction . Therefore AE and Care ...
Seite 17
... describe the circle EGF , meeting AB at F and G. [ Postulate 3 . Bisect FG at H , and join CH . [ I. 10 . H The ... Definition 15 . and the base CF is equal to the base CG ; therefore the angle CHF is equal to the angle CHG ; [ I. 8 ...
... describe the circle EGF , meeting AB at F and G. [ Postulate 3 . Bisect FG at H , and join CH . [ I. 10 . H The ... Definition 15 . and the base CF is equal to the base CG ; therefore the angle CHF is equal to the angle CHG ; [ I. 8 ...
Seite 25
... circle [ Post . 3 . describe DKL . D E H L Α B ARC From the centre G , at the distance GH , describe the circle HLK , cutting the former circle at K. Join KF , KG . The triangle KFG shall have its sides equal to the three straight lines ...
... circle [ Post . 3 . describe DKL . D E H L Α B ARC From the centre G , at the distance GH , describe the circle HLK , cutting the former circle at K. Join KF , KG . The triangle KFG shall have its sides equal to the three straight lines ...
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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