## 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 44

Side 38

To which is Added an Appendix ... Thomas Perronet Thompson. *INTEnc.11. their

surfaces coincide" only in one self-rejoining line. Let them coincide in FJHK; in

which take any point as F, and

To which is Added an Appendix ... Thomas Perronet Thompson. *INTEnc.11. their

surfaces coincide" only in one self-rejoining line. Let them coincide in FJHK; in

which take any point as F, and

**join**CF, ... Side 39

For,

turned round BA till M be in the same place as before. Because the extremities A

and M occupy the places previously occupied by the extremities B and M, AM

and ...

For,

**join**AM, B.M.; and afterwards let the united spheres be transposed, andturned round BA till M be in the same place as before. Because the extremities A

and M occupy the places previously occupied by the extremities B and M, AM

and ...

Side 40

... lie wholly in the surface described by CL, inasmuch as each half of it will

coincide with part of CL as it was found at some instant of the revolution by which

the surface was described. But if MQ do not pass through C,

AQ, ...

... lie wholly in the surface described by CL, inasmuch as each half of it will

coincide with part of CL as it was found at some instant of the revolution by which

the surface was described. But if MQ do not pass through C,

**join***INTERc.10, AM,AQ, ...

Side 41

... and

done before, that AS and BS are equal; wherefore the point S shall be in the self-

rejoining line which is the intersection of the spheres described with the radii AR

and ...

... and

**join**AS, BS. Because S is a point in CL, it may be shown as has beendone before, that AS and BS are equal; wherefore the point S shall be in the self-

rejoining line which is the intersection of the spheres described with the radii AR

and ...

Side 45

And the straight lines

three points are in each of the two planes, the straight lines which

formit a three-sided figure will lie wholly in each of the planes; and consequently

...

And the straight lines

**joining**them will lie wholly in that plane ... For because thethree points are in each of the two planes, the straight lines which

**join**them andformit a three-sided figure will lie wholly in each of the planes; and consequently

...

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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.