## The Elements of Euclid: 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. viz. the first six books, together with the eleventh and twelfth |

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Resultat 1-5 av 5

Side 46

If a straight line be divided into two equal , and also into two unequal parts ; the

squares of the two unequal parts are together

, and of the square of the line between the points of section . Let the straight line ...

If a straight line be divided into two equal , and also into two unequal parts ; the

squares of the two unequal parts are together

**double**of the square of half the line, and of the square of the line between the points of section . Let the straight line ...

Side 48

EG is

of EG is

EA is

...

EG is

**double**of the square of EF : and EF is equal to CD ; wherefore the squareof EG is

**double**of the square of CD : but it was de monstrated , that the square ofEA is

**double**of the square of AC ; therefore the squares of AE , EG are**double**of...

Side 87

an isosceles triangle FGH , having each of the angles at G , H ,

angle at F ; and in the circle ABCDE inscribe ( 2. 4. ) the triangle ACD

equiangular to the triangle FGH , so that the angle CAD be equal A to the angle

at F , and each ...

an isosceles triangle FGH , having each of the angles at G , H ,

**double**of theangle at F ; and in the circle ABCDE inscribe ( 2. 4. ) the triangle ACD

equiangular to the triangle FGH , so that the angle CAD be equal A to the angle

at F , and each ...

Side 89

angle FLC : and because KC is equal to CL , KL is

manner , it may be shown that HK is

KC , as was demonstrated , and that KL is

HK ...

angle FLC : and because KC is equal to CL , KL is

**double**of KC : in the samemanner , it may be shown that HK is

**double**of BK : and because BK is equal toKC , as was demonstrated , and that KL is

**double**of KC , and HK**double**of BK ,HK ...

Side 101

Take any equimultiples of each of them , as the

5th of this book , if the

, the

Take any equimultiples of each of them , as the

**doubles**of each ; then , by def .5th of this book , if the

**double**of the first be greater than the**double**of the second, the

**double**of the third is greater than the**double**of the fourth ; but if the first be ...### Hva folk mener - Skriv en omtale

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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: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1892 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone contained 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 gles greater Greek half join less likewise 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 45 - Ir a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 41 - 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 54 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.

Side 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.

Side 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.

Side 8 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 256 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Side 129 - 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 23 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...

Side 20 - ANY two angles of a triangle are together less than two right angles.