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 xv
... equilateral triangle on a given finite straight line , or Any two angles of a triangle are together less than two right angles . After the general enunciation follows the discussion of the proposition . First , the enunciation is ...
... equilateral triangle on a given finite straight line , or Any two angles of a triangle are together less than two right angles . After the general enunciation follows the discussion of the proposition . First , the enunciation is ...
Seite 3
... , or polygons , by more than four straight lines . 24. Of three - sided figures , An equilateral triangle is that which has three equal sides : 25. An isosceles triangle is that which has two sides 1-2 DEFINITIONS . 3.
... , or polygons , by more than four straight lines . 24. Of three - sided figures , An equilateral triangle is that which has three equal sides : 25. An isosceles triangle is that which has two sides 1-2 DEFINITIONS . 3.
Seite 6
... lines , being continually produced , shall at length meet on that side on which are the angles which are less than two right angles . PROPOSITION 1. PROBLEM . To describe an equilateral triangle on 6 CO EUCLID'S ELEMENTS .
... lines , being continually produced , shall at length meet on that side on which are the angles which are less than two right angles . PROPOSITION 1. PROBLEM . To describe an equilateral triangle on 6 CO EUCLID'S ELEMENTS .
Seite 7
... 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 . [ Postulate 3 ...
... 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 . [ Postulate 3 ...
Seite 11
... the angle GCB , which are the angles on the other side of the base . Wherefore , the angles & c . Q.E.D. Corollary . equiangular . Hence every equilateral triangle is also PROPOSITION 6. THEOREM . If two angles of a triangle BOOK I. 5 . 11.
... the angle GCB , which are the angles on the other side of the base . Wherefore , the angles & c . Q.E.D. Corollary . equiangular . Hence every equilateral triangle is also PROPOSITION 6. THEOREM . If two angles of a triangle BOOK I. 5 . 11.
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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