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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Side vi
... centre of each a sphere be described passing through the centre of the other , and a straight line of unlimited length be drawn from the point of contact of the two smaller spheres to any point in the inter- section of the others ; this ...
... centre of each a sphere be described passing through the centre of the other , and a straight line of unlimited length be drawn from the point of contact of the two smaller spheres to any point in the inter- section of the others ; this ...
Side 14
... 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 one another . same centre , are called concentric ...
... 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 one another . same centre , are called concentric ...
Side 15
... centre which remains at rest , the sphere will be without change of place . Let the substantial sphere whose INTERC . 2. centre is B , bet turned in any man- ner whatsoever about the centre B which remains at rest . The sphere shall be ...
... centre which remains at rest , the sphere will be without change of place . Let the substantial sphere whose INTERC . 2. centre is B , bet turned in any man- ner whatsoever about the centre B which remains at rest . The sphere shall be ...
Side 16
... centres are A and B , touching one another externally . The one cannot touch the other in more than a single point at once . For if this be disputed , First Case ; let it be assumed that they coincide in the surface CEGDHF in Fig . 1 ...
... centres are A and B , touching one another externally . The one cannot touch the other in more than a single point at once . For if this be disputed , First Case ; let it be assumed that they coincide in the surface CEGDHF in Fig . 1 ...
Side 17
... centre , and they must still always coin- cide in the surface in fixed space CEGDHF and not else- where . For each of them will be * without change of place ; wherefore they must at all times coincide in that surface and not elsewhere ...
... centre , and they must still always coin- cide in the surface in fixed space CEGDHF and not else- where . For each of them will be * without change of place ; wherefore they must at all times coincide in that surface and not elsewhere ...
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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 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
Populære avsnitt
Side 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.
Side 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Side 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Side 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.
Side 72 - Any two sides of a triangle are together greater than the third side.
Side 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.
Side 70 - Any two angles of a triangle are together less than two right angles.
Side 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.
Side 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.