## 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 24

Side 12

For the body may be placed in another situation , as M , such that the point B

occupies the same place in fixed

situation A. Also between the situations A and M , the body may be placed in

other ...

For the body may be placed in another situation , as M , such that the point B

occupies the same place in fixed

**space**as it did when the body was in thesituation A. Also between the situations A and M , the body may be placed in

other ...

Side 13

situation , as M , such that the points B and C respectively occupy the same

places in fixed

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

other ...

situation , as M , such that the points B and C respectively occupy the same

places in fixed

**space**as they did when the body was in the situation A. And forthe same reason , between the situations A and M the body may be placed in

other ...

Side 17

1 either or both of the spheres may be turned in any manner whatsoever about its

centre , and they must still always coincide in the surface in fixed

and not elsewhere . For each of them will be * without change of place ...

1 either or both of the spheres may be turned in any manner whatsoever about its

centre , and they must still always coincide in the surface in fixed

**space**CEGDHFand not elsewhere . For each of them will be * without change of place ...

Side 18

But if So , it may be shown as before , that they must continue to coincide in the

same line in fixed

they may be turned about their respective centres . Let then the sphere whose

centre ...

But if So , it may be shown as before , that they must continue to coincide in the

same line in fixed

**space**CEGDHF and not elsewhere , in whatsoever mannerthey may be turned about their respective centres . Let then the sphere whose

centre ...

Side 23

As would be mechanically exhibited , if the

yielding substance like plaster , out of which a sphere was to be formed through

the scraping away of the greatest possible quantity of matter by the turning of the

...

As would be mechanically exhibited , if the

**space**about B were filled with someyielding substance like plaster , out of which a sphere was to be formed through

the scraping away of the greatest possible quantity of matter by the turning of the

...

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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... Thomas Perronet Thompson 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 added alternate angle ABC angle BAC applied aret assigned axis base bisected body Book called centre change of place circle coincide common consequently Constr continually demonstrated described distance double drawn equal Euclid exterior angle extremities fall figure follows formed four right angles Geometry given straight line greater half impossible instance INTERC interior join kind less magnitude manner meet moved Note opposite parallel parallelogram parity of reasoning pass perpendicular plane portion prolonged proof Prop PROPOSITION proved radius remaining angle respectively rest right angles Second self-rejoining line shown situation space sphere sphere whose centre square straight line succession surface taken terminated thing third side touch triangle triangle ABC true turned unequal universally Wherefore whole

### 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.