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 19
... manner it may be shewn that no other can be in the same straight line with it but BD ; therefore BD is in the same straight line with CB . Wherefore , if at a point & c . X Q.E.D. PROPOSITION 15. THEOREM . If two straight lines cut one ...
... manner it may be shewn that no other can be in the same straight line with it but BD ; therefore BD is in the same straight line with CB . Wherefore , if at a point & c . X Q.E.D. PROPOSITION 15. THEOREM . If two straight lines cut one ...
Seite 20
... manner it may be shewn that the angle CEB is equal to the angle AED . Wherefore , if two straight lines & c . Q.E.D. Corollary 1. From this it is manifest that , if two straight lines cut one another , the angles which they make at the ...
... manner it may be shewn that the angle CEB is equal to the angle AED . Wherefore , if two straight lines & c . Q.E.D. Corollary 1. From this it is manifest that , if two straight lines cut one another , the angles which they make at the ...
Seite 21
... manner if BC be bisected , and the side AC be produced to G , it may be shewn that the angle BCG , that is the angle ACD , is greater than the angle ABC . [ I. 15 . Wherefore , if one side & c . Q.E.D. PROPOSITION 17. THEOREM . Any two ...
... manner if BC be bisected , and the side AC be produced to G , it may be shewn that the angle BCG , that is the angle ACD , is greater than the angle ABC . [ I. 15 . Wherefore , if one side & c . Q.E.D. PROPOSITION 17. THEOREM . Any two ...
Seite 23
... manner it may be shewn that AB , BC are greater than AC , and BC , CÅ greater than AB . Wherefore , any two sides & c . Q.E.D. PROPOSITION 21 . THEOREM . If from the ends of the side of a triangle there be drawn two straight lines to a ...
... manner it may be shewn that AB , BC are greater than AC , and BC , CÅ greater than AB . Wherefore , any two sides & c . Q.E.D. PROPOSITION 21 . THEOREM . If from the ends of the side of a triangle there be drawn two straight lines to a ...
Seite 31
... manner , it may be shewn that they do not neet towards A , C. But those straight lines which being produced ever so far both ways do not meet , are parallel . Therefore AB is parallel to CD . Wherefore , if a straight line & c . Q.E.D. ...
... manner , it may be shewn that they do not neet towards A , C. But those straight lines which being produced ever so far both ways do not meet , are parallel . Therefore AB is parallel to CD . Wherefore , if a straight line & c . Q.E.D. ...
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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