## 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 23

Side 11

But if the magnitudes were all

and E would (by Cor. 10) be together

magnitudes which should be taken afterwards ... I H B C 10

But if the magnitudes were all

**equal**to one another, the magnitudes A, B, C, D,and E would (by Cor. 10) be together

**equal**to the sum of an**equal**number of themagnitudes which should be taken afterwards ... I H B C 10

**E F**For if ... Side 30

In

surface of the hollow sphere whose centre ... as the radii of these

are"

In

**EF**take any point as G; and on the other side of CD take any point as H, in thesurface of the hollow sphere whose centre ... as the radii of these

**equal**spheresare"

**equal**); whereupon the surfaces of the two spheres willf coincide throughout. Side 56

AB to DE, and AC to DF; and the angle BAC

side BC shall be

EDF; and the other angles, to which the

...

AB to DE, and AC to DF; and the angle BAC

**equal**to the angle EDF. The thirdside BC shall be

**equal**to the third side**EF**, and the triangle BAC to the triangleEDF; and the other angles, to which the

**equal**sides are opposite, shall be**equal**...

Side 61

... sides are opposite, shall be equal respectively, viz. the angle ABC to DEF, and

ACB to DFE. For, let the triangle BAC be applied to the triangle EDF, so that the

point B may be on E, and the straight line BC on* EF. Because BC ist

...

... sides are opposite, shall be equal respectively, viz. the angle ABC to DEF, and

ACB to DFE. For, let the triangle BAC be applied to the triangle EDF, so that the

point B may be on E, and the straight line BC on* EF. Because BC ist

**equal to EF**,...

Side 63

Because CD is t

the two sides DC, CF are

DF is:

Because CD is t

**equal**to CE and CF common to the two triangles DCF and ECF,the two sides DC, CF are

**equal**to the two EC, CF respectively. Also the third sideDF is:

**equal**to the third side**EF**; therefore the angle DCF is"**equal**to ECF; and ...### Hva folk mener - Skriv en omtale

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### Andre utgaver - Vis alle

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.