## 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

If a tessera [or quadrilateral

sides are equal to one another and make ... And this because, if a number of

such

shall ...

If a tessera [or quadrilateral

**rectilinear**plane**figure**of which two of the oppositesides are equal to one another and make ... And this because, if a number of

such

**figures**are placed side by side, a straight line of unlimited length whichshall ...

Side 75

Hence also on an assigned straight line and at an assigned point in it, may be

described a

Hence also on an assigned straight line and at an assigned point in it, may be

described a

**rectilinear figure**having its ... respectively equal to those of a given**rectilinear figure**of any number of sides; and the two**rectilinear figures**shall be ... Side 94

3 point A in the straight line AM describet the

respects to ABNM, and having its base AC (at which are the angles that are equal

to BAM, ABN), adjacent to the base AB. In like manner at the points B and C, ...

3 point A in the straight line AM describet the

**rectilinear figure**ACOM, equal in allrespects to ABNM, and having its base AC (at which are the angles that are equal

to BAM, ABN), adjacent to the base AB. In like manner at the points B and C, ...

Side 102

All the interior angles of any plane

equal to twice as many right angles as the figure ... For First ; if the figure is one,

as ABCDE, TX that can be divided into as many triangles as the C figurehas

sides, ...

All the interior angles of any plane

**rectilinear figure**that incloses a space, areequal to twice as many right angles as the figure ... For First ; if the figure is one,

as ABCDE, TX that can be divided into as many triangles as the C figurehas

sides, ...

Side 103

Secondly; if the figure be such as cannot be divided into triangles by lines drawn

from one point within the figure, it can be divided into smaller

each severally capable of being so divided. And because the interior angles of ...

Secondly; if the figure be such as cannot be divided into triangles by lines drawn

from one point within the figure, it can be divided into smaller

**rectilinear figures**each severally capable of being so divided. And because the interior angles of ...

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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.