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 25
... namely , A and B greater than Ỡ ; A and C greater than B ; and B and C greater than A : it is required to make a triangle of which the sides shall be equal to A , B , C , each to each . Take a straight line DE terminated at the point D ...
... namely , A and B greater than Ỡ ; A and C greater than B ; and B and C greater than A : it is required to make a triangle of which the sides shall be equal to A , B , C , each to each . Take a straight line DE terminated at the point D ...
Seite 26
... namely , AB to DE , and AC to DF , but the angle BAC greater than the angle EDF : the base BC shall be PROPOSITION 25 . theo triangles have two de of the other greater than the base EF . Of the two sides. 26 EUCLID'S ELEMENTS .
... namely , AB to DE , and AC to DF , but the angle BAC greater than the angle EDF : the base BC shall be PROPOSITION 25 . theo triangles have two de of the other greater than the base EF . Of the two sides. 26 EUCLID'S ELEMENTS .
Seite 28
... namely , AB to DE , and AC to DF , but the base BC greater than the base EF : the angle BAC shall be greater than the angle EDF . For if not , the angle BAC must be either equal to the angle EDF or less than the angle EDF . But the ...
... namely , AB to DE , and AC to DF , but the base BC greater than the base EF : the angle BAC shall be greater than the angle EDF . For if not , the angle BAC must be either equal to the angle EDF or less than the angle EDF . But the ...
Seite 29
... namely , ABC to DEF , and BCA to EFD ; and let them have also one side equal to one side ; and first let those sides be equal which are adjacent to the equal angles in the two triangles , namely , BC to EF : the other sides shall be ...
... namely , ABC to DEF , and BCA to EFD ; and let them have also one side equal to one side ; and first let those sides be equal which are adjacent to the equal angles in the two triangles , namely , BC to EF : the other sides shall be ...
Seite 30
... namely , ÅB to DE : likewise in this case the other sides shall be equal , each to each , namely , BC to EF , and AC to DF , and also the third angle BAC equal to the third angle EDF . For if BC be not equal to EF , one of them must be ...
... namely , ÅB to DE : likewise in this case the other sides shall be equal , each to each , namely , BC to EF , and AC to DF , and also the third angle BAC equal to the third angle EDF . For if BC be not equal to EF , one of them must be ...
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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