## 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 |

### Inni boken

Resultat 1-5 av 8

Side 59

Let the point D be

there fall more than two equal straight lines , viz . DA , DB , DC : the point D is the

centre of the circle . For , if not , let E be the centre , join DE , and produce it to the

...

Let the point D be

**taken**within the circle ABC , from which to the circumferencethere fall more than two equal straight lines , viz . DA , DB , DC : the point D is the

centre of the circle . For , if not , let E be the centre , join DE , and produce it to the

...

Side 99

6 Let A the first , have to B the second , the same ratio which the third C has to the

fourth D ; and of A and C let there be

of B and D any equimultiples whatever G , H : then E has the same ratio to G ...

6 Let A the first , have to B the second , the same ratio which the third C has to the

fourth D ; and of A and C let there be

**taken**any equiinultiples whatever E , F : andof B and D any equimultiples whatever G , H : then E has the same ratio to G ...

Side 100

fore , that K is the same multiple of A , that L is of C : and because A is to B , as C

is to D , and of A and C certain equimultiples have been

of B and D certain equimultiples G , H ; therefore if K be greater than G , L is ...

fore , that K is the same multiple of A , that L is of C : and because A is to B , as C

is to D , and of A and C certain equimultiples have been

**taken**, viz . K and L ; andof B and D certain equimultiples G , H ; therefore if K be greater than G , L is ...

Side 114

from the first , is to a magnitude

the remainder , as the whole to the whole . * Let the whole AB be to the whole CD

, as AE , a magnitude

from the first , is to a magnitude

**taken**from the other ; the remainder shall be tothe remainder , as the whole to the whole . * Let the whole AB be to the whole CD

, as AE , a magnitude

**taken**from AB , to CF , a magnitude**taken**from CD ; the ... Side 281

... to this 29th , for it is necessary to none but to it , and to the 40th of this book , as

we now have it , to which last it would , without doubt , have been premised , if

Euclid had not made use of it in the 29th ; but some unskilful editor has

... to this 29th , for it is necessary to none but to it , and to the 40th of this book , as

we now have it , to which last it would , without doubt , have been premised , if

Euclid had not made use of it in the 29th ; but some unskilful editor has

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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.