## 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 20

Side 18

... and on the sphere being returned to its former situation , let the points E and F

in IESF

again , till the points on its surface G and H coincide with E and F as before ; and

let ...

... and on the sphere being returned to its former situation , let the points E and F

in IESF

**fall**on G and H. And after this let the sphere be turned round its centreagain , till the points on its surface G and H coincide with E and F as before ; and

let ...

Side 55

It is required to cut off from AB , a part equal to C. A JEB From either of the ends of

AB ( as , for + I. 2 . instance , from A ) , drawt a straight line AD equal to C ; [ which

straight line will

It is required to cut off from AB , a part equal to C. A JEB From either of the ends of

AB ( as , for + I. 2 . instance , from A ) , drawt a straight line AD equal to C ; [ which

straight line will

**fall**in some direction that will be determined by the operations ... Side 63

Nom . point A be placed in the same plane in which are the points F , H , and D. If

then BA does not coincide with ED , let it be assumed that it

which is towards H , as El . But because the angle IEF is equal to ABC , and IEH ...

Nom . point A be placed in the same plane in which are the points F , H , and D. If

then BA does not coincide with ED , let it be assumed that it

**falls**on the side of itwhich is towards H , as El . But because the angle IEF is equal to ABC , and IEH ...

Side 64

BA cannot

shown , that it cannot

does not

BA cannot

**fall**on the side of ED which is towards H. And in the same way may beshown , that it cannot

**fall**on the side of ED which is towards F ; and because itdoes not

**fall**on either side of ED , it**falls**upon it , and the angle ABC coincides ... Side 65

For their sum is equal to the sum of the two angles made by any one of the

straight lines that

made by any number of straight lines proceeding from one point and in the same

plane ...

For their sum is equal to the sum of the two angles made by any one of the

straight lines that

**fall**upon the other , on the one side . Cor . 2. All the anglesmade by any number of straight lines proceeding from one point and in the same

plane ...

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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.