## 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 74

Side viii

... and others into Corollaries from the rest. The Axiom which declared the whole

to be

... and others into Corollaries from the rest. The Axiom which declared the whole

to be

**greater**viii PR E FA C E. Side ix

The Axiom which declared the whole to be

as amounting, after the explanation of the terms '

from Euclid's Book of Data, to no more than the proposition that ' the greatest is ...

The Axiom which declared the whole to be

**greater**than its part, has been omittedas amounting, after the explanation of the terms '

**greater**' and “less introducedfrom Euclid's Book of Data, to no more than the proposition that ' the greatest is ...

Side 2

See Note. See Note. See Note, See Note. XV. A magnitude is said to be

than another by a certain magnitude, when this last-mentioned magnitude being

taken from the first, the remainder is equal to the second. And a magnitude is said

...

See Note. See Note. See Note, See Note. XV. A magnitude is said to be

**greater**than another by a certain magnitude, when this last-mentioned magnitude being

taken from the first, the remainder is equal to the second. And a magnitude is said

...

Side 5

For example, if the original proposition is, that if of equals one be

some thing else, the rest are severally

proposition is, that if of equals one be not

For example, if the original proposition is, that if of equals one be

**greater**thansome thing else, the rest are severally

**greater**than the same ; the negative of thisproposition is, that if of equals one be not

**greater**than some thing else ... Side 6

I. above) A and C are equal. CoR. 2. If of equals, one be

some thing else; the rest are severally

thing be

also.

I. above) A and C are equal. CoR. 2. If of equals, one be

**greater**, or less, thansome thing else; the rest are severally

**greater**, or less, than the same. Or if something be

**greater**, or less, than one ; it is**greater**, or less, than each of the othersalso.

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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.