## 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 ... |

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Resultat 1-5 av 38

Side 13

See Note. situation, as M, such that the points B and C

same places in fixed space as they did when the body was in the situation A. And

for the same reason, between the situations A and M the body may be placed in ...

See Note. situation, as M, such that the points B and C

**respectively**occupy thesame places in fixed space as they did when the body was in the situation A. And

for the same reason, between the situations A and M the body may be placed in ...

Side 25

... AE; and if about the centre B be described spheres

, as in the points G, H ; on the hard body in which are all the spheres being turned

about A and B, the points of contact G, H, will also severally remain unmoved.

... AE; and if about the centre B be described spheres

**respectively**touching these, as in the points G, H ; on the hard body in which are all the spheres being turned

about A and B, the points of contact G, H, will also severally remain unmoved.

Side 30

Also if on the one sphere the points M, N, O, P, do not coincide with the same

points on the other

spheres about the point G * I. Nom. 3. +I.Nom.26. # I. Nom. 3. *. *INTERC.10. Cor.

4.

Also if on the one sphere the points M, N, O, P, do not coincide with the same

points on the other

**respectively**, they may be made to do so by turning one of thespheres about the point G * I. Nom. 3. +I.Nom.26. # I. Nom. 3. *. *INTERC.10. Cor.

4.

Side 33

About B as a centre, with the radii BC and BD

spheres. In BC take any point as E, between B and the surfaces of both these

concentric spheres on the side of B which is towards C; and about B as a centre,

...

About B as a centre, with the radii BC and BD

**respectively**, describe" concentricspheres. In BC take any point as E, between B and the surfaces of both these

concentric spheres on the side of B which is towards C; and about B as a centre,

...

Side 42

... wherefore if AN and BN were

MQOP, for the spheres

intersections would coincide; and if AN and BN are

...

... wherefore if AN and BN were

**respectively**equal to AM and BM, N would be inMQOP, for the spheres

**respectively**would” coincide, and consequently theirintersections would coincide; and if AN and BN are

**respectively**less than AM and...

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Geometry Without Axioms Or the First Book Euclid's Elements: With ... 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 aret equal assigned point axis base BC bisected called CEGDHF central distances change of place circle coincide throughout Constr demonstrated double equal straight lines equal to AC equal to EF equilateral triangle Euclid exterior angle extremities four right angles Geometry given straight line greater 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 tryo turned unlimited length Wherefore willf

### 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.