## 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 11

Side 11

the straight line AD equal to C ; ana from the centre A , and at the distance AD ,

describe ( 3. Post . ) the circle DEF ; and because A is the centre of the circle DEF

, AE shall be equal to AD ; but the straight line C is

...

the straight line AD equal to C ; ana from the centre A , and at the distance AD ,

describe ( 3. Post . ) the circle DEF ; and because A is the centre of the circle DEF

, AE shall be equal to AD ; but the straight line C is

**likewise**equal to AD ; whence...

Side 14

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

...

Side 20

to ABD , because the side AB is equal to the side AD ; therefore the angle ABD is

greater than ACB . Therefore the greater side , & c . Q. E. D. PROP . XIX . THEOR

.

to ABD , because the side AB is equal to the side AD ; therefore the angle ABD is

**likewise**greater than the angle ACB ; wherefore much more is the angle ABCgreater than ACB . Therefore the greater side , & c . Q. E. D. PROP . XIX . THEOR

.

Side 25

1. ) to the base DF , and the third angle BAC to the third angle EDF . Next let the

sides A D which are opposite to equal angles in each triangle be equal to one

another , viz . AB to DE ;

...

1. ) to the base DF , and the third angle BAC to the third angle EDF . Next let the

sides A D which are opposite to equal angles in each triangle be equal to one

another , viz . AB to DE ;

**likewise**in this case , the other side's shall be equal , AC...

Side 36

to the angle ABM , and

angle D : therefore the parallelogram LB is applied to the straight line , AB , is

equal to the triangle C , and has the angle ABM equal to the angle D. Which was

to be ...

to the angle ABM , and

**likewise**to the angle D ; the angle ABM is equal to theangle D : therefore the parallelogram LB is applied to the straight line , AB , is

equal to the triangle C , and has the angle ABM equal to the angle D. Which was

to be ...

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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.