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 xii
... wherefore its boundary can have none . And if the so - called boundary had breadth , it would not be the boundary , but part of the surface . Thus the boundaries of the black surface at the side , are lines ; which manifestly have ...
... wherefore its boundary can have none . And if the so - called boundary had breadth , it would not be the boundary , but part of the surface . Thus the boundaries of the black surface at the side , are lines ; which manifestly have ...
Σελίδα 6
... wherefore A and + I.Nom . 14. B are equal . And in the same manner if the magnitudes + I.Nom.15 . * I.Nom.15 . equal to C were more than two . And by parity of reasoning , the like may be proved in every other instance . Wherefore ...
... wherefore A and + I.Nom . 14. B are equal . And in the same manner if the magnitudes + I.Nom.15 . * I.Nom.15 . equal to C were more than two . And by parity of reasoning , the like may be proved in every other instance . Wherefore ...
Σελίδα 9
... Wherefore the double of A is greater than the double of B. And in like manner if to the double of A be added a third magnitude equal to A , and to the double of B a third magnitude equal to B. And so on . COR . 12. Magnitudes which are ...
... Wherefore the double of A is greater than the double of B. And in like manner if to the double of A be added a third magnitude equal to A , and to the double of B a third magnitude equal to B. And so on . COR . 12. Magnitudes which are ...
Σελίδα 10
... Wherefore there will be some remainder MO such , that it is a limit which they cannot pass , but if any smaller magnitude be substituted they shall pass it ; for if they would not pass such smaller magnitude , the difference might be ...
... Wherefore there will be some remainder MO such , that it is a limit which they cannot pass , but if any smaller magnitude be substituted they shall pass it ; for if they would not pass such smaller magnitude , the difference might be ...
Σελίδα 13
... Wherefore , universally , a hard body may be turned & c . Which was to be demonstrated . COR . Any solid , surface , line , or figure , may be turned about any one point , or about any two points , in it ; such point or points remaining ...
... Wherefore , universally , a hard body may be turned & c . Which was to be demonstrated . COR . Any solid , surface , line , or figure , may be turned about any one point , or about any two points , in it ; such point or points remaining ...
Άλλες εκδόσεις - Προβολή όλων
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