## 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 15

Side 19

3. bodies on which the lines are exhibited, are hard* bodies. t I.Nom:26. The

assumptiont, therefore, which involves the impossible consequence, cannot be

true ; or the two spheres cannot coincide in the

in like ...

3. bodies on which the lines are exhibited, are hard* bodies. t I.Nom:26. The

assumptiont, therefore, which involves the impossible consequence, cannot be

true ; or the two spheres cannot coincide in the

**self**-**rejoining line**CEGDHF. Andin like ...

Side 20

20 INTERCALARY BOOK. the face towards A, will be turned to all sides in

succession; the line CD, which is not a

for it cannot have its face turned to all sides in succession and be without change

of ...

20 INTERCALARY BOOK. the face towards A, will be turned to all sides in

succession; the line CD, which is not a

**self**-**rejoining line**, must change its place;for it cannot have its face turned to all sides in succession and be without change

of ...

Side 29

If two equal spheres cut one another, their surfaces coincide only in one

Their surfaces coincide only in one

one ...

If two equal spheres cut one another, their surfaces coincide only in one

**self**-**rejoining line**. Let two equal spheres whose centres are A and B, cut one another.Their surfaces coincide only in one

**self**-**rejoining line**. Because the spheres cutone ...

Side 30

Such figure therefore (or each such, if there can be more than one) will be either

a

about A and B, revolves on its own ground in fixed space without change of place

.

Such figure therefore (or each such, if there can be more than one) will be either

a

**self**-**rejoining line**or a belt of surface, which on the united body being turnedabout A and B, revolves on its own ground in fixed space without change of place

.

Side 31

Second Case; let it be assumed that besides coinciding in CD they also coincide

in some other

same process as in the preceding case, that the two lines HOPLNM and IOPKNM

...

Second Case; let it be assumed that besides coinciding in CD they also coincide

in some other

**self**-**rejoining line**as EF, but ... Whereupon may be shown by thesame process as in the preceding case, that the two lines HOPLNM and IOPKNM

...

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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.