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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Αποτελέσματα 6 - 10 από τα 35.
Σελίδα 2
... called a Theorem . An operation which it is proposed to show how to perform , is called a Problem . And both are called by the title of Propositions . XIX . A Proposition dependent on some other that has been previously established ...
... called a Theorem . An operation which it is proposed to show how to perform , is called a Problem . And both are called by the title of Propositions . XIX . A Proposition dependent on some other that has been previously established ...
Σελίδα 3
... called a consequence . XXVI . When such preceding position is not known to be true , but is only assumed to be true for the purpose of trying its truth or falsehood by examination of the consequences , it is called an assumption . And ...
... called a consequence . XXVI . When such preceding position is not known to be true , but is only assumed to be true for the purpose of trying its truth or falsehood by examination of the consequences , it is called an assumption . And ...
Σελίδα 4
... called the enunciation . The second presents to the eye , or to the imagination , a particular instance , in respect of which the truth of the proposition is to be established ; with an understanding always , that nothing shall be done ...
... called the enunciation . The second presents to the eye , or to the imagination , a particular instance , in respect of which the truth of the proposition is to be established ; with an understanding always , that nothing shall be done ...
Σελίδα 5
... called the converse of a proposition is , when the premises and the conclusion are made to change places , and the proposition so arising is presented as a new proposition . For example , if the original proposition is , that magnitudes ...
... called the converse of a proposition is , when the premises and the conclusion are made to change places , and the proposition so arising is presented as a new proposition . For example , if the original proposition is , that magnitudes ...
Σελίδα 14
... called a sphere . And such point within , is called the centre of the sphere ; and the distance from it to every point in the surface , is called the central distance . Spheres are said to touch one another , which meet but do not cut ...
... called a sphere . And such point within , is called the centre of the sphere ; and the distance from it to every point in the surface , is called the central distance . Spheres are said to touch one another , which meet but do not cut ...
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.