## 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

Side 1

The only way in which coincidence can actually be brought to pass , is when the

The only way in which coincidence can actually be brought to pass , is when the

**things**touch**one another**or are in ... Two points A and B are said to be equally distant with two**others**C and D , or to be at a distance**equal**to the ... Side 2

And a magnitude is said to be

And a magnitude is said to be

**less than another**by a certain magnitude , when this last - mentioned magnitude being added to the first , the sum is**equal**to the**second**. XVI . Magnitudes are said to be given , when**equals**to them can be ... Side 3

For

For

**one**of them has been specially constituted and constructed**equal**to the**other**. XXIV . When a**thing**is said to be so and so by parity of reasoning , the meaning is , that what has been shown to be true in some previous instance ... Side 5

... that magnitudes which are

... that magnitudes which are

**equal to the same**, are**equal to one another**; the converse of this proposition is , that magnitudes ... that if of**equals**one be greater than some**thing**else , the rest are severally greater than the**same**... Side 6

Let A and B be two magnitudes , each of which is

Let A and B be two magnitudes , each of which is

**equal**to C. A and B are**equal to one another**. B * I. NomenFor because A is ... COROLLARY 1. If of**equals**, one be**equal**to some**thing**else , the rest are severally**equal to the same**.### Hva folk mener - Skriv en omtale

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### Andre utgaver - Vis alle

Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... Thomas Perronet Thompson 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 added alternate angle ABC angle BAC applied aret assigned assumed axis base bisected body Book called centre change of place circle coincide common consequently Constr continually demonstrated described double drawn equal establish Euclid exterior angle extremities fall figure follows formed four right angles Geometry given straight line greater half impossible instance INTERC interior join kind less magnitude manner meet moved Note opposite parallel parallelogram parity of reasoning pass perpendicular plane portion prolonged proof Prop PROPOSITION proved radius remaining angle respectively rest right angles Second self-rejoining line shown situation space sphere sphere whose centre square straight line surface taken terminated thing third side touch triangle triangle ABC true turned unequal universally Wherefore whole

### 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.