## 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 18

Side 1

... thus imagined to coincide , may three , or any other number . X. Points which

do not coincide , are said to be distant . XI . Two points A and B are said to be

equally distant with two others C and D , or to be at a

... thus imagined to coincide , may three , or any other number . X. Points which

do not coincide , are said to be distant . XI . Two points A and B are said to be

equally distant with two others C and D , or to be at a

**distance**equal to the**distance**... Side 4

For example , a cooper knows that in every instance where he has tried it , the

to be taken in his compasses in order to describe the head that would fit . But he ...

For example , a cooper knows that in every instance where he has tried it , the

**distance**that went exactly round the rim of his cask at six times , was the**distance**to be taken in his compasses in order to describe the head that would fit . But he ...

Side 12

By the For because the body is * a hardt Hypothesis . body , the

point B in t I. Nom . 3 . it to the point C will be unaltered in every situation of the

body . Wherefore the body may be placed in another N w situation , as M , such ...

By the For because the body is * a hardt Hypothesis . body , the

**distance**from thepoint B in t I. Nom . 3 . it to the point C will be unaltered in every situation of the

body . Wherefore the body may be placed in another N w situation , as M , such ...

Side 13

To describe a solid , all the points in whose surface shall be equidistant from an

assigned point within , and at a

that have been assigned . Let A and B be the two assigned points , in a hard

body ...

To describe a solid , all the points in whose surface shall be equidistant from an

assigned point within , and at a

**distance**equal to the**distance**of any two pointsthat have been assigned . Let A and B be the two assigned points , in a hard

body ...

Side 14

And such point within , is called the centre of the sphere ; and the

to every point in the surface , is called the central

touch one another , which meet but do not cut one another . Spheres described ...

And such point within , is called the centre of the sphere ; and the

**distance**from itto every point in the surface , is called the central

**distance**. Spheres are said totouch one another , which meet but do not cut one another . Spheres described ...

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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.