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 1
... equal . Equal magnitudes may be divided into , 1. Those whose boundaries can actually be applied together and be in contact in every part at once ; as a cast to its mould , a stamp to its impression , or one side of an indenture to the ...
... equal . Equal magnitudes may be divided into , 1. Those whose boundaries can actually be applied together and be in contact in every part at once ; as a cast to its mould , a stamp to its impression , or one side of an indenture to the ...
Σελίδα 2
... equal to the second . XVI . Magnitudes are said to be given , when equals to them can be assigned . XVII . The ... equal , some particular result shall follow , as , for instance , that the sum of them shall be equal to some third ...
... equal to the second . XVI . Magnitudes are said to be given , when equals to them can be assigned . XVII . The ... equal , some particular result shall follow , as , for instance , that the sum of them shall be equal to some third ...
Σελίδα 3
... equal by construction . For one of them has been specially constituted and constructed equal to the other . XXIV . When a thing is said to be so and so by parity of reasoning , the meaning is , that what has been shown to be true in ...
... equal by construction . For one of them has been specially constituted and constructed equal to the other . XXIV . When a thing is said to be so and so by parity of reasoning , the meaning is , that what has been shown to be true in ...
Σελίδα 6
... 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 applied to one another A and C ...
... 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 applied to one another A and C ...
Σελίδα 7
... equal to equals , are equal to one another . Let A be equal to B , and C to D ; and let A B and D be equal . A and C shall also be equal . B D * I.Nom.14 . + 1.Nom . 14 . For A is equal to B , and D is equal to B ; therefore ( by Prop ...
... equal to equals , are equal to one another . Let A be equal to B , and C to D ; and let A B and D be equal . A and C shall also be equal . B D * I.Nom.14 . + 1.Nom . 14 . For A is equal to B , and D is equal to B ; therefore ( by Prop ...
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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