## 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 11

Side 81

If a straight line falling upon two other straight lines makes the

equal to one another , those two straight lines being prolonged ever so far both

ways , shall not meet . See Note . E First Case ; where the two straight lines are ...

If a straight line falling upon two other straight lines makes the

**alternate**anglesequal to one another , those two straight lines being prolonged ever so far both

ways , shall not meet . See Note . E First Case ; where the two straight lines are ...

Side 82

It cannot be , therefore , that AB and CD being prolonged , will meet on the side of

B and D. And in the same manner may be shown that they cannot meet on the

side of A and C. So also if HGA , GHD had been the

...

It cannot be , therefore , that AB and CD being prolonged , will meet on the side of

B and D. And in the same manner may be shown that they cannot meet on the

side of A and C. So also if HGA , GHD had been the

**alternate**angles taken to be...

Side 83

And they are

parallel . Secondly ; where HGB and GHD the interior angles on the same side of

the line , are together equal to two right angles . Because the angles HGB , GHD

are ...

And they are

**alternate**angles ; therefore ( by Cor . 1 above ) AB and CD areparallel . Secondly ; where HGB and GHD the interior angles on the same side of

the line , are together equal to two right angles . Because the angles HGB , GHD

are ...

Side 84

Because the straight line AD meets the two straight lines BC and EF which are

both in the same plane , and the

equal to one another , EF and BC are # 1.27.Cor.1 , parallel . Therefore through

the ...

Because the straight line AD meets the two straight lines BC and EF which are

both in the same plane , and the

**alternate**Constr . angles EAD and ADC aretequal to one another , EF and BC are # 1.27.Cor.1 , parallel . Therefore through

the ...

Side 86

Cor . ) .

any point in EF as G , a straight line of unlimited length both ways ( as WX ) be

drawn at right angles to EF ; it shall cut the straight lines AD and BC between

their ...

Cor . ) .

**alternate**angles ; therefore DC and AB aret parallel . COR . 2 . If throughany point in EF as G , a straight line of unlimited length both ways ( as WX ) be

drawn at right angles to EF ; it shall cut the straight lines AD and BC between

their ...

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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 axis base bisected body Book called centre change of place circle coincide common consequently Constr continually demonstrated described distance double drawn equal 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 succession 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.