## 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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Resultat 1-5 av 10

Side 62

To

G. Because in the triangles CAF, CBF, CA ist equal to CB, and CF ... And by parity

of reasoning, in like manner may every other given straight line be

To

**bisect**a given straight line. ... Join CF, and let CF cut AB in G. AB is**bisected**inG. Because in the triangles CAF, CBF, CA ist equal to CB, and CF ... And by parity

of reasoning, in like manner may every other given straight line be

**bisected**. Side 68

Then join AF; the straight line AF shall

given angle BAC is

be perpendicular to BAC and

angles.

Then join AF; the straight line AF shall

**bisect**the angle BAC. ... Wherefore thegiven angle BAC is

**bisected**by the : I. 13. ... be**bisected**by the point A, and AFbe perpendicular to BAC and

**bisect**the angle BAC by dividing it into two rightangles.

Side 70

In the same manner if the side BC be

is greater than CBA. But the angle BCG ist equal to ACD, for they are vertical

angles; therefore the angle ACD is also: greater than CBA. And in the same way

...

In the same manner if the side BC be

**bisected**, may be shown that the angle BCGis greater than CBA. But the angle BCG ist equal to ACD, for they are vertical

angles; therefore the angle ACD is also: greater than CBA. And in the same way

...

Side 76

Wherefore CF will” form a triangle with them, on that side on which is the angle

CDF that is less than the sum of two right angles,

Because in the triangles CDG, FDG, DC ist equal to DF, and CG too FG, and DG

is ...

Wherefore CF will” form a triangle with them, on that side on which is the angle

CDF that is less than the sum of two right angles,

**Bisect**CF, in G.; and join DG.Because in the triangles CDG, FDG, DC ist equal to DF, and CG too FG, and DG

is ...

Side 85

... angle CED is

CEF, the sides ED and EF are equal to the sides EC and EF respectively, and the

angle DEF has been shown to be equal to the angle CEF, FD ist equal to FC; ...

... angle CED is

**bisected**by the straight line EZ ; and because in the angles DEF,CEF, the sides ED and EF are equal to the sides EC and EF respectively, and the

angle DEF has been shown to be equal to the angle CEF, FD ist equal to FC; ...

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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.