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 viii
... demonstrated as Theorems , or executed as Problems ; others ( as the Axiom on coincidence ) resolved into the mere declaration of the matter to which a certain Nomenclature is assigned ; and others into Corollaries from the rest . The ...
... demonstrated as Theorems , or executed as Problems ; others ( as the Axiom on coincidence ) resolved into the mere declaration of the matter to which a certain Nomenclature is assigned ; and others into Corollaries from the rest . The ...
Σελίδα 3
... demonstrated by the same steps . When the parity of reasoning is extended to all instances to which the proposition is capable of being applied , [ or in other words , to all which come under its terms ] , the proposition is said to be ...
... demonstrated by the same steps . When the parity of reasoning is extended to all instances to which the proposition is capable of being applied , [ or in other words , to all which come under its terms ] , the proposition is said to be ...
Σελίδα 6
... demonstrated . COROLLARY 1. If of equals , one be equal to some thing else , the rest are severally equal to the same . Let A and B be equal , and let B be equal to C. A shall also be equal to C. For A is equal to B , and C is equal to ...
... demonstrated . COROLLARY 1. If of equals , one be equal to some thing else , the rest are severally equal to the same . Let A and B be equal , and let B be equal to C. A shall also be equal to C. For A is equal to B , and C is equal to ...
Σελίδα 13
... 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 unmoved . For it is supposed to be represented on a hard body which may ...
... 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 unmoved . For it is supposed to be represented on a hard body which may ...
Σελίδα 16
... demonstrated . PROPOSITION V. THEOREM . - If two spheres touch one another externally , they touch only in a point . Let there be two spheres whose centres are A and B , touching one another externally . The one cannot touch the other ...
... demonstrated . PROPOSITION V. THEOREM . - If two spheres touch one another externally , they touch only in a point . Let there be two spheres whose centres are A and B , touching one another externally . The one cannot touch the other ...
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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