The Elements of Euclid for the Use of Schools and CollegesMacmillan, 1872 - 400 Seiten |
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Seite 6
... whole is greater than its part . 10. Two straight lines cannot enclose a space . 11. All right angles are equal to one another . 12. If a straight line meet two straight lines , so as to make the two interior angles on the same side of ...
... whole is greater than its part . 10. Two straight lines cannot enclose a space . 11. All right angles are equal to one another . 12. If a straight line meet two straight lines , so as to make the two interior angles on the same side of ...
Seite 10
... whole triangle ABC coincides with the whole triangle DEF , and is equal to it . [ Axiom 8 . And the other angles of the one coincide with the other angles of the other , and are equal to them , namely , the angle ABC to the angle DEF ...
... whole triangle ABC coincides with the whole triangle DEF , and is equal to it . [ Axiom 8 . And the other angles of the one coincide with the other angles of the other , and are equal to them , namely , the angle ABC to the angle DEF ...
Seite 11
... whole AF is equal to the whole AG , of which the parts AB , AC are equal , [ Hypothesis . the remainder BF is equal to the remainder CG . [ Axiom 3 . And FC was shewn to be equal to GB ; therefore the two sides BF , FC are equal to the ...
... whole AF is equal to the whole AG , of which the parts AB , AC are equal , [ Hypothesis . the remainder BF is equal to the remainder CG . [ Axiom 3 . And FC was shewn to be equal to GB ; therefore the two sides BF , FC are equal to the ...
Seite 35
... whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC . [ Axiom 2 . To each of these equals add the angle ACB ; therefore the angles ACD , ACB are equal to the three angles CBA , BAC , ACB . But the angles ...
... whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC . [ Axiom 2 . To each of these equals add the angle ACB ; therefore the angles ACD , ACB are equal to the three angles CBA , BAC , ACB . But the angles ...
Seite 38
... whole angle ABD is equal to the whole angle 4CD . [ Ax . 2 . And the angle BAC has been shewn to be equal to the angle CDB . Therefore the opposite sides and angles of a parallelogram are equal to one another . Also the diameter bisects ...
... whole angle ABD is equal to the whole angle 4CD . [ Ax . 2 . And the angle BAC has been shewn to be equal to the angle CDB . Therefore the opposite sides and angles of a parallelogram are equal to one another . Also the diameter bisects ...
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Häufige Begriffe und Wortgruppen
ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC 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