## 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 ... |

### Inni boken

Resultat 1-5 av 22

Side vi

... and a straight line of

two smaller spheres to any point in the intersection of the others ; this straight line

, on the whole being turned about the two centres of the spheres, will describe a ...

... and a straight line of

**unlimited length**be drawn from the point of contact of thetwo smaller spheres to any point in the intersection of the others ; this straight line

, on the whole being turned about the two centres of the spheres, will describe a ...

Side ix

And this because, if a number of such figures are placed side by side, a straight

line of

points in the series of bases, along the straight line formed by the junction of two

...

And this because, if a number of such figures are placed side by side, a straight

line of

**unlimited length**which shall travel continuously from one of the angularpoints in the series of bases, along the straight line formed by the junction of two

...

Side 36

When a straight line is said to be of

is assigned at which it shall be held to be terminated, but on the contrary it shall

without further notice be considered as prolonged to any extent a motive may ...

When a straight line is said to be of

**unlimited length**, the meaning is, that no pointis assigned at which it shall be held to be terminated, but on the contrary it shall

without further notice be considered as prolonged to any extent a motive may ...

Side 38

and let CF bef prolonged to an

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.

and let CF bef prolonged to an

**unlimited length**on the side " of L. Let then thespheres 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.

Side 39

32ert them, in the straight line of

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 ...

32ert them, in the straight line of

**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 ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

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.