## 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 84

Side v

... for the emendation of Geometry, which was, information on the nature and

construction of the

Emperor was 'to divide the circumference of a circle into four

means ...

... for the emendation of Geometry, which was, information on the nature and

construction of the

**straight line**and plane. ... that the problem given by the futureEmperor was 'to divide the circumference of a circle into four

**equal**parts bymeans ...

Side vi

If two

centre of each a sphere be described passing through the centre of the other,

and a

two ...

If two

**equal**spheres be placed touching one another externally, and about thecentre of each a sphere be described passing through the centre of the other,

and a

**straight line**of unlimited length be drawn from the point of contact of thetwo ...

Side vii

... thus acquired, before attempting what must be characterized as, in some parts,

at least

with respect to the sphere and

... thus acquired, before attempting what must be characterized as, in some parts,

at least

**equal**in complexity to anything in ... instance in the conclusions drawnwith respect to the sphere and

**straight line**from turning them about certain points. Side ix

If a tessera [or quadrilateral rectilinear plane figure of which two of the opposite

sides are

such figures are placed side by side, a

shall ...

If a tessera [or quadrilateral rectilinear plane figure of which two of the opposite

sides are

**equal**to one another and make ... And this because, if a number ofsuch figures are placed side by side, a

**straight line**of unlimited length whichshall ...

Side 1

And in like manner two

coincide. But besides this, there is an ... Two points A and B are said to be

equally distant mith two others C and D, or to be at a distance

distance of C and ...

And in like manner two

**lines**or points may actually touch one another andcoincide. But besides this, there is an ... Two points A and B are said to be

equally distant mith two others C and D, or to be at a distance

**equal**to thedistance of C and ...

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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.