## The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner Corrected |

### Inni boken

Resultat 1-5 av 6

Side 41

to the triangle EBC , because it is upon the same base BC , and between the

same A D

demonstrated B that no other line but AD is

to the triangle EBC , because it is upon the same base BC , and between the

same A D

**parallels**BC , AE : but the triangle ... In the same manner , it can bedemonstrated B that no other line but AD is

**parallel**to BC ; AD is therefore**parallel**to it . Side 203

Two straight lines which are each of them

not in the same plane with it , are

of them

Two straight lines which are each of them

**parallel**to the same straight line , andnot in the same plane with it , are

**parallel**to one another . H Let AB , CD be eachof them

**parallel**to EF , and not in the same plane with it ; AB shall be**parallel**to ... Side 207

If two straight lines meeting one another , be

meet one another , but are not in the same plane with the first two , the plane

which passes through these is

BC ...

If two straight lines meeting one another , be

**parallel**to two straight lines whichmeet one another , but are not in the same plane with the first two , the plane

which passes through these is

**parallel**to the plane passing the others . * Let AB ,BC ...

Side 208

If two

their common sections with it be EF , GH ; EF is

EF ...

If two

**parallel**planes be cut by another plane , their common sections with it are**parallels**. * Let the**parallel**planes , AB , CD be cut by the plane EFHG , and lettheir common sections with it be EF , GH ; EF is

**parallel**to GH . For , if it be not ,EF ...

Side 248

X

and because KL , MN are each of them

with it , KL is

X

**parallel**to DC , and not in the same plane with it , KL is**parallel**( 9. 11. ) to BA :and because KL , MN are each of them

**parallel**to BA , and not in the same planewith it , KL is

**parallel**( 9 . 11. ) to MN ; wherefore KL , MN are in one plane .### Hva folk mener - Skriv en omtale

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### Andre utgaver - Vis alle

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Euclid,Robert Simson Uten tilgangsbegrensning - 1838 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained rectilineal figure remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 81 - The angles in the same segment of a circle are equal to one another.

Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Side 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 155 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Side 22 - ANY two angles of a triangle are together less than two right angles.

Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.

Side 24 - Any two sides of a triangle are together greater than the third side.