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 páginas |
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Página vi
... change of place . And on receipt of the remark mentioned above , this track was pursued with renewed vigour , and the results are presented in the sequel . For the use of those who are not disposed to go into details , the substance may ...
... change of place . And on receipt of the remark mentioned above , this track was pursued with renewed vigour , and the results are presented in the sequel . For the use of those who are not disposed to go into details , the substance may ...
Página 15
... 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 without change of place . * INTERC . 3 . Cor . 3 . + ...
... 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 without change of place . * INTERC . 3 . Cor . 3 . + ...
Página 16
... change of place ; the substantial sphere is without change of place . So also of the hollow sphere , if it be turned while the substantial one which is its reciprocal remains unmoved . And by parity of reasoning , the like may be proved ...
... change of place ; the substantial sphere is without change of place . So also of the hollow sphere , if it be turned while the substantial one which is its reciprocal remains unmoved . And by parity of reasoning , the like may be proved ...
Página 17
... change of place ; wherefore they must at all times coincide in that surface and not elsewhere ; for if they do not , one or both must have suffered change of place . Let then the sphere whose centre is A , be turned about A , till the ...
... change of place ; wherefore they must at all times coincide in that surface and not elsewhere ; for if they do not , one or both must have suffered change of place . Let then the sphere whose centre is A , be turned about A , till the ...
Página 20
... change its place ; for it cannot have its face turned to all sides in succession and be without change of place . Let it therefore , at some period during the turning , be in the situation EF . But if the spheres do at first coincide in ...
... change its place ; for it cannot have its face turned to all sides in succession and be without change of place . Let it therefore , at some period during the turning , be in the situation EF . But if the spheres do at first coincide in ...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Sin vista previa disponible - 2015 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Página 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Página 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.
Página 72 - Any two sides of a triangle are together greater than the third side.
Página 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.
Página 103 - ... twice as many right angles as the figure has sides.
Página 70 - Any two angles of a triangle are together less than two right angles.
Página 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.
Página 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.