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 |
Inni boken
Resultat 1-5 av 97
Side xi
... INTERC . ) See Note . 1 . II . NOMENCLATURE . AFTER a thing , or a class of things , has been rendered obvious to the senses , and either by speech , writing , pictorial representa- tion , or examination in its proper substance , has ...
... INTERC . ) See Note . 1 . II . NOMENCLATURE . AFTER a thing , or a class of things , has been rendered obvious to the senses , and either by speech , writing , pictorial representa- tion , or examination in its proper substance , has ...
Side 13
... INTERC . 2. which are the points A and B being turned * about B ; and let the line AC be expressed on a hard body in which the point B is also situate . By the turning of this last - mentioned hard body about B , let the line AC be made ...
... INTERC . 2. which are the points A and B being turned * about B ; and let the line AC be expressed on a hard body in which the point B is also situate . By the turning of this last - mentioned hard body about B , let the line AC be made ...
Side 15
... INTERC . 2. centre is B , bet turned in any man- ner whatsoever about the centre B which remains at rest . The sphere shall be without change of place . * INTERC . 3 . Cor . 3 . + Constr . For if its reciprocal be sup- posed to remain ...
... INTERC . 2. centre is B , bet turned in any man- ner whatsoever about the centre B which remains at rest . The sphere shall be without change of place . * INTERC . 3 . Cor . 3 . + Constr . For if its reciprocal be sup- posed to remain ...
Side 16
... at once . For if this be disputed , First Case ; let it be assumed that they coincide in the surface CEGDHF in Fig . 1 below , and not elsewhere . But if so , Fig . 1 . A. E 5 F · B H * INTERC . 4 . INTERC . 2 . + 16 INTERCALARY BOOK .
... at once . For if this be disputed , First Case ; let it be assumed that they coincide in the surface CEGDHF in Fig . 1 below , and not elsewhere . But if so , Fig . 1 . A. E 5 F · B H * INTERC . 4 . INTERC . 2 . + 16 INTERCALARY BOOK .
Side 17
To which is Added an Appendix ... Thomas Perronet Thompson. * INTERC . 4 . INTERC . 2 . + I. Nom . 3 . I.Nom.26 . 8ee Note . PROP . V. 17 Let now the either or both of the spheres may be turned in any manner whatsoever about its centre ...
To which is Added an Appendix ... Thomas Perronet Thompson. * INTERC . 4 . INTERC . 2 . + I. Nom . 3 . I.Nom.26 . 8ee Note . PROP . V. 17 Let now the either or both of the spheres may be turned in any manner whatsoever about its centre ...
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.