## 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 |

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Side vi

powers of the mind allow; and which

both of peace and war, to many of which geometry is absolutely necessary. This I

have endeavoured to do, by taking away the inaccurate and false reasonings ...

powers of the mind allow; and which

**likewise**is of the greatest use in the artsboth of peace and war, to many of which geometry is absolutely necessary. This I

have endeavoured to do, by taking away the inaccurate and false reasonings ...

Side 14

the circle DEF ; and because A F is the centre of the circle DEF , AE shall be

equal to AD ; but the straight line C is

are each of them equal to AD ; wherefore the straight line AE is equal to ( 1.

the circle DEF ; and because A F is the centre of the circle DEF , AE shall be

equal to AD ; but the straight line C is

**likewise**equal to AD ; whence AE and Care each of them equal to AD ; wherefore the straight line AE is equal to ( 1.

Side 18

to one another , but the angle ECD is greater than the angle BCD ; wherefore the

angle FDC is

greater than the angle BCD . Again , because CB is equal to DB , the angle BDC

is ...

to one another , but the angle ECD is greater than the angle BCD ; wherefore the

angle FDC is

**likewise**greater than BCD ; much more then is the angle BDCgreater than the angle BCD . Again , because CB is equal to DB , the angle BDC

is ...

Side 42

parallel to EF : there A F G fore FECG ' is a parallelogram : and because BE is

equal to EC , the triangle ABE is

since D they are upon equal bases BE , EC , and between the same parallels BC

, AG ...

parallel to EF : there A F G fore FECG ' is a parallelogram : and because BE is

equal to EC , the triangle ABE is

**likewise**equal ( 38. 1. ) to the triangle AEC ,since D they are upon equal bases BE , EC , and between the same parallels BC

, AG ...

Side 52

... the angle GBC ; and therefore the side BC is equal G ( 6. 1. ) to the side CG :

but CB is equal H K ( 34. 1. ) also to GK , and CG to BK ; wherefore the figure

CGKB is equilateral ; it is

meets ...

... the angle GBC ; and therefore the side BC is equal G ( 6. 1. ) to the side CG :

but CB is equal H K ( 34. 1. ) also to GK , and CG to BK ; wherefore the figure

CGKB is equilateral ; it is

**likewise**rectangular ; for CG is parallel to BK , and CBmeets ...

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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.