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 8
... equals be taken from equals , the remainders are equal . For , if this be disputed , let it be assumed that one remainder is greater than the other . Add each to the equals that were before taken away ; and because to equals unequals ...
... equals be taken from equals , the remainders are equal . For , if this be disputed , let it be assumed that one remainder is greater than the other . Add each to the equals that were before taken away ; and because to equals unequals ...
Σελίδα 9
... equal to A , and to the double of B a third magnitude equal to B. And so on . COR . 12. Magnitudes which are half of the same or of equal magnitudes , are equal to one another . And so if , instead of the half , they are the third ...
... equal to A , and to the double of B a third magnitude equal to B. And so on . COR . 12. Magnitudes which are half of the same or of equal magnitudes , are equal to one another . And so if , instead of the half , they are the third ...
Σελίδα 10
... equal to the sum of A , B , C , and D , But ( by Cor . 5 ) , the sum of A and B is equal to the sum of C and D ; therefore the sum of A , B , C , and D , is equal to double the sum of A and B. Where- fore ( by Cor . 1 ) , the double of ...
... equal to the sum of A , B , C , and D , But ( by Cor . 5 ) , the sum of A and B is equal to the sum of C and D ; therefore the sum of A , B , C , and D , is equal to double the sum of A and B. Where- fore ( by Cor . 1 ) , the double of ...
Σελίδα 11
... equal number of those magnitudes . But if the magnitudes were all equal to one another , the magnitudes A , B , C , D , and E would ( by Cor . 10 ) be together equal to the sum of an equal number of the magnitudes which should be taken ...
... equal number of those magnitudes . But if the magnitudes were all equal to one another , the magnitudes A , B , C , D , and E would ( by Cor . 10 ) be together equal to the sum of an equal number of the magnitudes which should be taken ...
Σελίδα 13
... equal to the distance of any two points that have been assigned . Let A and B be the two assigned points , in a hard body of any kind ; and let B be the point from which all the points in the surface of the required solid are to be ...
... equal to the distance of any two points that have been assigned . Let A and B be the two assigned points , in a hard body of any kind ; and let B be the point from which all the points in the surface of the required solid are to be ...
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