## 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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Resultat 1-5 av 6

Side 32

For , if it be not parallel , AB and CD being

D , or towards A , C ; let them be

; therefore GEF is a triangle , and its exterior angle AEF is greater ( 16. 1. ) ...

For , if it be not parallel , AB and CD being

**produced**shall meet either towards B ,D , or towards A , C ; let them be

**produced**and meet towards B , D , in the point G; therefore GEF is a triangle , and its exterior angle AEF is greater ( 16. 1. ) ...

Side 54

If a straight line be bisected , and

by the whole line thus

square of half the line bisected , is equal to the square of the straight line which is

...

If a straight line be bisected , and

**produced**to any point ; the rectangle containedby the whole line thus

**produced**, and the part of it**produced**, together with thesquare of half the line bisected , is equal to the square of the straight line which is

...

Side 58

Ir a straight line be bisected , and

line thus

of the square of half the line bisected , and of the square of the line made up of ...

Ir a straight line be bisected , and

**produced**to any point , the square of the wholeline thus

**produced**and the square of the part of it**produced**, are together doubleof the square of half the line bisected , and of the square of the line made up of ...

Side 208

For , if it be not , EF , GH shall meet , if

first , let them be

since EFK is in the plane AB , every point in EFK is in K that plane ; and K is a ...

For , if it be not , EF , GH shall meet , if

**produced**, either on the side of FH , or EG ;first , let them be

**produced**on the side of FH , and meet in the point K ; therefore ,since EFK is in the plane AB , every point in EFK is in K that plane ; and K is a ...

Side 456

If a straight line be drawn within a circle given in magnitude , cutting off a

segment containing a given angle : if the angle adjacent to the angle in the

segment be bisected by a straight line

again and the ...

If a straight line be drawn within a circle given in magnitude , cutting off a

segment containing a given angle : if the angle adjacent to the angle in the

segment be bisected by a straight line

**produced**till it meet the circumferenceagain and the ...

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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.