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 5
... produced ever so far both ways do not meet . [ Note . The terms oblong and rhomboid are not often used . Practically the following definitions are used . Any four - sided figure is called a quadrilateral . A line joining two opposite ...
... produced ever so far both ways do not meet . [ Note . The terms oblong and rhomboid are not often used . Practically the following definitions are used . Any four - sided figure is called a quadrilateral . A line joining two opposite ...
Seite 10
... produced the angles on the other side of the base shall be equal to one another . Let ABC be an isosceles triangle , having the side AB equal to the side AC , and let the straight lines AB , AC be produced to D and E : the angle ABC ...
... produced the angles on the other side of the base shall be equal to one another . Let ABC be an isosceles triangle , having the side AB equal to the side AC , and let the straight lines AB , AC be produced to D and E : the angle ABC ...
Seite 20
... produced , the exterior angle shall be greater than either of the interior opposite angles . Let ABC be a triangle ... produce it to F , making EF equal to EB , [ I. 3 . and join FC . Because AE is equal to EC , and BE to EF ; [ Constr ...
... produced , the exterior angle shall be greater than either of the interior opposite angles . Let ABC be a triangle ... produce it to F , making EF equal to EB , [ I. 3 . and join FC . Because AE is equal to EC , and BE to EF ; [ Constr ...
Seite 21
... produced to G , it may be shewn that the angle BCG , that is the angle ACD , is greater than the angle ABC . [ I. 15 ... Produce BC to D. Then because ACD is the exte- rior angle of the triangle ABC , it is greater than the interior oppo ...
... produced to G , it may be shewn that the angle BCG , that is the angle ACD , is greater than the angle ABC . [ I. 15 ... Produce BC to D. Then because ACD is the exte- rior angle of the triangle ABC , it is greater than the interior oppo ...
Seite 31
... produced , do not meet to- wards B , D. In the same 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 ...
... produced , do not meet to- wards B , D. In the same 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 ...
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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