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 63
... angles . But when the adjacent angles which one straight line makes with another straight line are + I . Nom.37 . equal to one another , each of them is † a right angle ; therefore each of the angles DCF , ECF , is a right angle ...
... angles . But when the adjacent angles which one straight line makes with another straight line are + I . Nom.37 . equal to one another , each of them is † a right angle ; therefore each of the angles DCF , ECF , is a right angle ...
Σελίδα 64
... angles ABC , ABD . These are together equal to two right angles . First Case . If the angles ABC , ABD are * I.Nom.37 . equal to one another , each of them is * a right A angle , and consequently they are together D B equal to two right ...
... angles ABC , ABD . These are together equal to two right angles . First Case . If the angles ABC , ABD are * I.Nom.37 . equal to one another , each of them is * a right A angle , and consequently they are together D B equal to two right ...
Σελίδα 65
... right angles . For their sum is equal to the sum of the two angles made by any one of the straight lines that fall upon the other , on the one side . COR . 2. All the angles made by any number of straight lines proceeding from one point ...
... right angles . For their sum is equal to the sum of the two angles made by any one of the straight lines that fall upon the other , on the one side . COR . 2. All the angles made by any number of straight lines proceeding from one point ...
Σελίδα 66
... right angles , is not in the same straight line with it . For let BD , BE be two straight lines making an angle DBE less than the sum of two right angles . From B draw any straight line BA between BD and BE ; and prolong * DB to C ...
... right angles , is not in the same straight line with it . For let BD , BE be two straight lines making an angle DBE less than the sum of two right angles . From B draw any straight line BA between BD and BE ; and prolong * DB to C ...
Σελίδα 67
... right angles ; and no point in the straight line drawn from D to E shall coincide with any point in BD or BE , except the points D and E which were joined . For because BE makes with BD an angle less than the sum of two right angles ...
... right angles ; and no point in the straight line drawn from D to E shall coincide with any point in BD or BE , except the points D and E which were joined . For because BE makes with BD an angle less than the sum of two right angles ...
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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