## 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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Side ix

... a straight line of unlimited length which shall travel continuously from one of

the

make angles at the point of section greater than given angles, before it has

reached ...

... a straight line of unlimited length which shall travel continuously from one of

the

**angular points**in the series of bases, ... cannot cease to cut the bases andmake angles at the point of section greater than given angles, before it has

reached ...

Side xii

To which may hereafter be added

angle. Figures of all kinds, lines, and

exhibited on a hard body of some kind, which causes the position of the several

parts or ...

To which may hereafter be added

**angular**, or those of which the subject is anangle. Figures of all kinds, lines, and

**points**, will always be considered asexhibited on a hard body of some kind, which causes the position of the several

parts or ...

Side 52

In any quadrilateral figure, a straight line joining two of thc opposite

letters at two of their opposite angles, when no obscurity arises therefrom. LIV.

In any quadrilateral figure, a straight line joining two of thc opposite

**angular****points**is called a diagonal. For brevity, quadrilateral figures may be named by theletters at two of their opposite angles, when no obscurity arises therefrom. LIV.

Side 75

By the help of this, on an assigned straight line and at an assigned point in it, may

be made an angle equal to a given ... For the given rectilinear figure may be

divided into triangles, by straight lines drawn from some of its

By the help of this, on an assigned straight line and at an assigned point in it, may

be made an angle equal to a given ... For the given rectilinear figure may be

divided into triangles, by straight lines drawn from some of its

**angular points**to ... Side 89

If the

the angle GIF is greater than the angle ABC or ACB, which are the angles made

by joining the extremities of the first two straight lines of the series. For the angles

...

If the

**angular points**of any one of the tesseras be joined diagonally as I and F,the angle GIF is greater than the angle ABC or ACB, which are the angles made

by joining the extremities of the first two straight lines of the series. For the angles

...

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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.