## 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

Side 26

A body or figure which is turned about two points in it that are also the

of a straight line , inasmuch as the whole of the straight line remains without

change of place ) is said to be turned round such straight line . When from any

point ...

A body or figure which is turned about two points in it that are also the

**extremities**of a straight line , inasmuch as the whole of the straight line remains without

change of place ) is said to be turned round such straight line . When from any

point ...

Side 27

And if two straight lines are equal , their

For if when one extremity of each are made to coincide , the other extremity of the

one cannot be also made to coincide with the other extremity of the other ; then ...

And if two straight lines are equal , their

**extremities**may be made to coincide .For if when one extremity of each are made to coincide , the other extremity of the

one cannot be also made to coincide with the other extremity of the other ; then ...

Side 28

2 . distance equal to the distance between any two points ; therefore it may be

described with a central distance equal to the distance between the

the proposed radius . CoR . 7. If two spheres touch one another externally , the ...

2 . distance equal to the distance between any two points ; therefore it may be

described with a central distance equal to the distance between the

**extremities**ofthe proposed radius . CoR . 7. If two spheres touch one another externally , the ...

Side 33

... both these concentric spheres on the side of B which is towards C ; and about

B as a centre , with the radius BE , describe a sphere , whose surface ( because it

lies within the surfaces which pass through the

... both these concentric spheres on the side of B which is towards C ; and about

B as a centre , with the radius BE , describe a sphere , whose surface ( because it

lies within the surfaces which pass through the

**extremities**C and + INTERC.10 . Side 35

А B D B line ; С D Thirdly ; If there be two straight lines as AB and CD , and their

А B D B line ; С D Thirdly ; If there be two straight lines as AB and CD , and their

**extremities**B and C are made to coincide each with a several point between the**extremities**of the other А the whole AD shall be a straight line . For if the line ...### Hva folk mener - Skriv en omtale

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### Andre utgaver - Vis alle

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.