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 10
... fall on DF , because the angle BAC is equal to the angle EDF . B AA [ Hypothesis . Therefore also the point C will coincide with the point F , because AC is equal to DF . [ Hypothesis . But the point B was shewn to coincide with the ...
... fall on DF , because the angle BAC is equal to the angle EDF . B AA [ Hypothesis . Therefore also the point C will coincide with the point F , because AC is equal to DF . [ Hypothesis . But the point B was shewn to coincide with the ...
Seite 31
... falling on two other straight lines , make the alternate angles equal to one another , the two straight lines shall be parallel to one another . Let the straight line EF , which falls on the two straight lines AB , CD , make the ...
... falling on two other straight lines , make the alternate angles equal to one another , the two straight lines shall be parallel to one another . Let the straight line EF , which falls on the two straight lines AB , CD , make the ...
Seite 32
... fall on two parallel straight lines , it makes the alternate angles equal to one another , and the exterior angle equal to the interior and opposite angle on the same side ; and also the two interior angles on the same side together ...
... fall on two parallel straight lines , it makes the alternate angles equal to one another , and the exterior angle equal to the interior and opposite angle on the same side ; and also the two interior angles on the same side together ...
Seite 35
... falls on them , the alternate angles B BAC , ACE are equal . D [ I. 29 . Again , because AB is parallel to CE , and BD falls on them , the exterior angle ECD is equal to the interior and opposite angle ABC . [ I. 29 . But the angle ACE ...
... falls on them , the alternate angles B BAC , ACE are equal . D [ I. 29 . Again , because AB is parallel to CE , and BD falls on them , the exterior angle ECD is equal to the interior and opposite angle ABC . [ I. 29 . But the angle ACE ...
Seite 46
... falls on the parallels AH , EF , the angles AHF , HFE are together equal to two right angles . [ I. 29 . Therefore the angles BHF , HFE are together less than two right angles . But straight lines which with another straight line make ...
... falls on the parallels AH , EF , the angles AHF , HFE are together equal to two right angles . [ I. 29 . Therefore the angles BHF , HFE are together less than two right angles . But straight lines which with another straight line make ...
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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