## 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 7

Side 50

1 B F the straight lines A , BC is equal to D E C the

, together with that contained by A , DE , and that contained by A , EC . From the

point B draw ( 11. 1. ) BF at right angles to BC , and make BG equal ( 3. 1. ) ...

1 B F the straight lines A , BC is equal to D E C the

**rectangle contained**by A , BD, together with that contained by A , DE , and that contained by A , EC . From the

point B draw ( 11. 1. ) BF at right angles to BC , and make BG equal ( 3. 1. ) ...

Side 51

1 BA , AC ; for it is contained by DA , AC , of which AD is equal to AB ; and CE is

contained by AB , BC , for BE is equal to AB ; therefore the

AB , AC , together with the rectangle AB , BC , is equal to the square of AB .

1 BA , AC ; for it is contained by DA , AC , of which AD is equal to AB ; and CE is

contained by AB , BC , for BE is equal to AB ; therefore the

**rectangle contained**byAB , AC , together with the rectangle AB , BC , is equal to the square of AB .

Side 170

If four straight lines be proportionals , the

equal to the

the extremes be equal to the

If four straight lines be proportionals , the

**rectangle contained**by the extremes isequal to the

**rectangle contained**by the means : and if the**rectangle contained**bythe extremes be equal to the

**rectangle contained**by the means , the four ... Side 171

IF three straight lines be proportionals , the

is equal to the square of the mean : and if the

extremes be equal to the square of the mean , the three straight lines are

proportionals .

IF three straight lines be proportionals , the

**rectangle contained**by the extremesis equal to the square of the mean : and if the

**rectangle contained**by theextremes be equal to the square of the mean , the three straight lines are

proportionals .

Side 448

If two straight lines contain a given parallelogram in a given angle , and if the

excess of the square of one of them above a ... to the given rectangle CB , BD ;

therefore , because the

and ...

If two straight lines contain a given parallelogram in a given angle , and if the

excess of the square of one of them above a ... to the given rectangle CB , BD ;

therefore , because the

**rectangle contained**by the straight lines FB , BC is given ,and ...

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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.