## 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 8

Side 108

Or for brevity , the rectangle made by two straight lines AB , BC , is called the

rectangle AB , BC ; or more briefly still , the rectangle ABC . Nom . 2. A rectangle

of which all the sides are equal , is called a

which ...

Or for brevity , the rectangle made by two straight lines AB , BC , is called the

rectangle AB , BC ; or more briefly still , the rectangle ABC . Nom . 2. A rectangle

of which all the sides are equal , is called a

**square**. NOM . 3 . A rectangle ofwhich ...

Side 116

For such a rectangle is a parallelogram upon the same base , and between the

same parallels . Therefore ( by the Prop . above ) it is the double of the triangle . #

1.3 . PROPOSITION XLII . PROBLEM . — To describe a

For such a rectangle is a parallelogram upon the same base , and between the

same parallels . Therefore ( by the Prop . above ) it is the double of the triangle . #

1.3 . PROPOSITION XLII . PROBLEM . — To describe a

**square**upon a given ... Side 117

The side AB of the one

For if AB be not equal to EF , one of # 1.3 . them must be the greater . Let AB be

the greater ; and makef AK and AI each equal to EF ; and join Kl . Join also BD ...

The side AB of the one

**square**, is equal to the side EF of the other**square**. KB EFor if AB be not equal to EF , one of # 1.3 . them must be the greater . Let AB be

the greater ; and makef AK and AI each equal to EF ; and join Kl . Join also BD ...

Side 118

PROPOSITION XLV . upon a less .

described upon a greater straight line , is greater than the

the straight line AB be greater D С than the straight line EF . The H G ABCD

which is ...

PROPOSITION XLV . upon a less .

**square**] \ 1.3 . THEOREM . - The**square**described upon a greater straight line , is greater than the

**square**described Letthe straight line AB be greater D С than the straight line EF . The H G ABCD

which is ...

Side 119

In any right - angled triangle , the

to the right angle , is equal to the sum of the squares described on the sides

between which is the right angle . Let ABC be a triangle having the right angle

BAC .

In any right - angled triangle , the

**square**described on the side which is oppositeto the right angle , is equal to the sum of the squares described on the sides

between which is the right angle . Let ABC be a triangle having the right angle

BAC .

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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.