Geometry Without Axioms; Or the First Book of Euclid's Elements. With Alterations and Familiar Notes; and an Intercalary Book in which the Straight Line and Plane are Derived from Properties of the Sphere ...: To which is Added an Appendix ...Robert Heward, 1833 - 150 σελίδες |
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Σελίδα 81
... alternate angles equal to one another , those two straight lines being prolonged ever so far both ways , shall not meet . E A G B C H D F First Case ; where the two straight lines are both in the same plane . Let the straight line EF ...
... alternate angles equal to one another , those two straight lines being prolonged ever so far both ways , shall not meet . E A G B C H D F First Case ; where the two straight lines are both in the same plane . Let the straight line EF ...
Σελίδα 82
... alternate angles taken to be equal . Second Case ; if the two straight lines are not in the same plane , they can never meet though prolonged ever so far both ways , whether the alternate angles they make with the other straight line ...
... alternate angles taken to be equal . Second Case ; if the two straight lines are not in the same plane , they can never meet though prolonged ever so far both ways , whether the alternate angles they make with the other straight line ...
Σελίδα 83
... alternate angles ; therefore ( by Cor . 1 above ) AB and CD are parallel . * Hyp . + I. 12 . Secondly ; where HGB and GHD the interior angles on the same side of the line , are together equal to two right angles . Because the angles HGB ...
... alternate angles ; therefore ( by Cor . 1 above ) AB and CD are parallel . * Hyp . + I. 12 . Secondly ; where HGB and GHD the interior angles on the same side of the line , are together equal to two right angles . Because the angles HGB ...
Σελίδα 84
... alternate angles EAD and ADC are † equal to one another , EF and BC are ‡ parallel . Therefore through the point A is drawn a straight line EAF , parallel to BC . Which was to be done . And by parity of reasoning , the like may be done ...
... alternate angles EAD and ADC are † equal to one another , EF and BC are ‡ parallel . Therefore through the point A is drawn a straight line EAF , parallel to BC . Which was to be done . And by parity of reasoning , the like may be done ...
Σελίδα 86
... alternate angles ; therefore DC and AB are + parallel . * I. 11 . D F C W G H X I E B COR . 2. If through any point in EF as G , a straight line of unlimited length both ways ( as WX ) be drawn at right angles to EF ; it shall cut the ...
... alternate angles ; therefore DC and AB are + parallel . * I. 11 . D F C W G H X I E B COR . 2. If through any point in EF as G , a straight line of unlimited length both ways ( as WX ) be drawn at right angles to EF ; it shall cut the ...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles alternate angles angle ABC angle ACB angle BAC angular points aret assigned point Axiom axis base BC bisected called CEGDHF central distances change of place circle coincide throughout Constr demonstrated double equal angles equal straight lines equal to AC equal to EF equilateral triangle Euclid exterior angle extremities four right angles Geometry given straight line greater hard body inclose a space instance INTERC Intercalary Book ist equal join line AC magnitude manner meet opposite angles parallelogram parity of reasoning pass perpendicular prolonged Prop PROPOSITION proved quadrilateral radii radius rectilinear figure remain unmoved remaining angle remains at rest respectively SCHOLIUM self-rejoining line shown side BC side opposite situation sphere whose centre straight line BC tessera THEOREM.-If third side triangle ABC turned unlimited length Wherefore