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 ix
... applied to what ought to have been called universal propositions ; than which nothing has given a greater handle to the supporters of practical mal - reasoning . With a view to further resisting the notion of self - evident truths , no ...
... applied to what ought to have been called universal propositions ; than which nothing has given a greater handle to the supporters of practical mal - reasoning . With a view to further resisting the notion of self - evident truths , no ...
Σελίδα 1
... applied to one another , B and D might also be applied to one another at the same time . XII . Two or more points , as B , C , D , are said to be equidistant from another point A , when B and A , C and A , D and A , are equally distant ...
... applied to one another , B and D might also be applied to one another at the same time . XII . Two or more points , as B , C , D , are said to be equidistant from another point A , when B and A , C and A , D and A , are equally distant ...
Σελίδα 3
... applied in any other instance ; it may be avouched that by parity of reasoning any other two magnitudes which are equal to a third , are equal to one another . For it is open to be demonstrated by the same steps . When the parity of ...
... applied in any other instance ; it may be avouched that by parity of reasoning any other two magnitudes which are equal to a third , are equal to one another . For it is open to be demonstrated by the same steps . When the parity of ...
Σελίδα 4
... applied , cannot be included under one specification or one construction , the proposition is said to divide itself into two or more Cases ; which may in fact be considered as so many dis- tinct propositions , each of which has , or is ...
... applied , cannot be included under one specification or one construction , the proposition is said to divide itself into two or more Cases ; which may in fact be considered as so many dis- tinct propositions , each of which has , or is ...
Σελίδα 6
... applied to one another A and C would coincide ; or else might be made capable of doing so , by a different arrange- ment of parts . And because B is equal to C , in like manner would B and C. But because A and B would each coincide with ...
... applied to one another A and C would coincide ; or else might be made capable of doing so , by a different arrange- ment of parts . And because B is equal to C , in like manner would B and C. But because A and B would each coincide with ...
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 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 half the angle 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
Δημοφιλή αποσπάσματα
Σελίδα 51 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Σελίδα 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Σελίδα 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Σελίδα 120 - If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle.
Σελίδα 72 - Any two sides of a triangle are together greater than the third side.
Σελίδα 55 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Σελίδα 103 - ... twice as many right angles as the figure has sides.
Σελίδα 70 - Any two angles of a triangle are together less than two right angles.
Σελίδα 138 - ... the exterior angle equal to the interior and opposite on the same side of the line ; and likewise the two interior angles on the same side of the line together equal to two right angles.
Σελίδα 106 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.