## 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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Side vii

And for the further convenience of this class, a Recapitulation of the principal

contents of the Intercalary Book has been given at page 46; thereby placing the

beginner in the same

And for the further convenience of this class, a Recapitulation of the principal

contents of the Intercalary Book has been given at page 46; thereby placing the

beginner in the same

**situation**as by the ordinary proceeding. The best time for ... Side 12

For the body may be placed in another

occupies the same place in fixed space as it did when the body was in the

For the body may be placed in another

**situation**, as M, such that the point Boccupies the same place in fixed space as it did when the body was in the

**situation**A. Also between the**situations**A and M, the body may be placed in other**situations**... Side 13

See Note.

same places in fixed space as they did when the body was in the

for the same reason, between the

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. Andfor the same reason, between the

**situations**A and M the body may be placed in ... Side 17

Let then the sphere whose centre is A, be turnedt about A, till the portion of its

surface which was originally in the

elsewhere, ...

Let then the sphere whose centre is A, be turnedt about A, till the portion of its

surface which was originally in the

**situation**CEGDHF, is brought into the**situation**IESF; and because the spheres will still coincide in CEGDHF and notelsewhere, ...

Side 18

Let then the sphere whose centre is A, be turned about A, till the line on its

surface which originally coincided with CEGDHF, isbrought into the

IESF; and on the sphere being returned to its former

F in ...

Let then the sphere whose centre is A, be turned about A, till the line on its

surface which originally coincided with CEGDHF, isbrought into the

**situation**IESF; and on the sphere being returned to its former

**situation**, let the points E andF in ...

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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.