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 sider |
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Resultat 1-5 av 54
Side 2
... when equals to them can be assigned . XVII . The science which treats of the relations and properties of magnitudes , is named Geometry . XVIII . An assertion which it is proposed to show to be true , is called a Theorem . An operation ...
... when equals to them can be assigned . XVII . The science which treats of the relations and properties of magnitudes , is named Geometry . XVIII . An assertion which it is proposed to show to be true , is called a Theorem . An operation ...
Side 6
... THEOREM . - Magnitudes which are equal to the same , are equal to one another . Let A and B be two magnitudes , each of which is equal to C. A and B are equal to one another . A B For because A is equal to C , if their bound- aries were ...
... THEOREM . - Magnitudes which are equal to the same , are equal to one another . Let A and B be two magnitudes , each of which is equal to C. A and B are equal to one another . A B For because A is equal to C , if their bound- aries were ...
Side 12
... is con- tained in DG , so many times is AI contained in AB ; but AB is less than DG ... if from AB or any of the remainders were taken more than the half ; only the more would the last remainder AI be less than C. PROPOSITION II . THEOREM ...
... is con- tained in DG , so many times is AI contained in AB ; but AB is less than DG ... if from AB or any of the remainders were taken more than the half ; only the more would the last remainder AI be less than C. PROPOSITION II . THEOREM ...
Side 15
... is to say , one sphere will be greater + than the other ; which is impossible , for they are equal . The central distances , therefore , cannot be unequal ; that is , they are equal . PROPOSITION IV . THEOREM . - If a sphere be turned ...
... is to say , one sphere will be greater + than the other ; which is impossible , for they are equal . The central distances , therefore , cannot be unequal ; that is , they are equal . PROPOSITION IV . THEOREM . - If a sphere be turned ...
Side 16
... is its reciprocal remains unmoved . And by parity of reasoning , the like may be proved of every other sphere . Wherefore , universally , if a sphere be turned & c . Which was to be demonstrated . PROPOSITION V. THEOREM . - If two ...
... is its reciprocal remains unmoved . And by parity of reasoning , the like may be proved of every other sphere . Wherefore , universally , if a sphere be turned & c . Which was to be demonstrated . PROPOSITION V. THEOREM . - If two ...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... Thomas Perronet Thompson Uten tilgangsbegrensning - 1833 |
Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
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