## 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 5

Side 55

the

in the point F : it cuts it also at right angles . Take ( 1. 3. ) E the

and join EA , EB . Then , because AF is equal to FB , and FE common to the two ...

the

**centre**, bisect any straight line AB , which does not pass through the**centre**,in the point F : it cuts it also at right angles . Take ( 1. 3. ) E the

**centre**of the circle ,and join EA , EB . Then , because AF is equal to FB , and FE common to the two ...

Side 56

Let the two circles ABC , CDG cut one another in the points B , C ; they have not

the same

any straight line EFG meeting them in С F and G ; and because E is the

...

Let the two circles ABC , CDG cut one another in the points B , C ; they have not

the same

**centre**. For , if it be possible , let E be their**centre**: join EC , and drawany straight line EFG meeting them in С F and G ; and because E is the

**centre**of...

Side 59

If a point be taken within a circle , from which there fall more than two equal

straight lines to the circumference , that point is the

point D be taken within the circle ABC , from which to the circumference there fall

more ...

If a point be taken within a circle , from which there fall more than two equal

straight lines to the circumference , that point is the

**centre**of the circle . Let thepoint D be taken within the circle ABC , from which to the circumference there fall

more ...

Side 62

Let the straight lines AB , CD , in the circle ABDC ; be equal to one another : they

are equally distant from the

from it draw EF , EG perpendiculars to AB , CD ; then , because the straight line

EF ...

Let the straight lines AB , CD , in the circle ABDC ; be equal to one another : they

are equally distant from the

**centre**. Take E the**centre**of the circle ABDC , andfrom it draw EF , EG perpendiculars to AB , CD ; then , because the straight line

EF ...

Side 66

Ir a straight line touch a circle , and from the point of contact a straight line be

drawn at right angles to the touching line , the

line . Let the straight line DE touch the circle ABC in C , and from C let CA be

drawn ...

Ir a straight line touch a circle , and from the point of contact a straight line be

drawn at right angles to the touching line , the

**centre**of the circle shall be in thatline . Let the straight line DE touch the circle ABC in C , and from C let CA be

drawn ...

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The Elements of Euclid, Viz; The First Six Books: Together With the Eleventh ... Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2017 |

### 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.