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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Resultat 1-5 av 23
Side vi
... 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 straight line , on the whole being turned about the two centres of the spheres , will describe a ...
... 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 straight line , on the whole being turned about the two centres of the spheres , will describe a ...
Side ix
... unlimited length which shall travel continuously from one of the angular points in the series of bases , along the straight line formed by the junction of two sides , keeping ever at right angles to it , cannot cease to cut the bases ...
... unlimited length which shall travel continuously from one of the angular points in the series of bases , along the straight line formed by the junction of two sides , keeping ever at right angles to it , cannot cease to cut the bases ...
Side 36
... length in a straight line . For ( by Cor . 5 above ) it may be multiplied [ that is to say , straight lines equal to ... unlimited length be made to pass through + INTERC . 4. B ; and because the sphere may bet turned about its centre ...
... length in a straight line . For ( by Cor . 5 above ) it may be multiplied [ that is to say , straight lines equal to ... unlimited length be made to pass through + INTERC . 4. B ; and because the sphere may bet turned about its centre ...
Side 38
... unlimited length on the side Cor . 6. of L. Let then the spheres BFGH and AFIH be united as one INTERC . 9. body , and together with the straight line CL be turned round the Nom . straight line AB which remains at rest . The straight ...
... unlimited length on the side Cor . 6. of L. Let then the spheres BFGH and AFIH be united as one INTERC . 9. body , and together with the straight line CL be turned round the Nom . straight line AB which remains at rest . The straight ...
Side 39
... unlimited length CL ( See Fig . 2 in the next page ) take any point other than F , as M ; and if about the centres A and B , with the radii AM and BM , spheres be described , THE POINT M , AT ALL TIMES DURING THE REVOLUTION OF CL ...
... unlimited length CL ( See Fig . 2 in the next page ) take any point other than F , as M ; and if about the centres A and B , with the radii AM and BM , spheres be described , THE POINT M , AT ALL TIMES DURING THE REVOLUTION OF CL ...
Andre utgaver - Vis alle
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.