## 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

Side 10

From the centre A , at the distance AB , describe ( 3. Postulate . ) the circle BCD ,

and from the centre B , at the distance BA , describe the circle B в ACE ; and from

the point C , in E which the circles cut one another ,

From the centre A , at the distance AB , describe ( 3. Postulate . ) the circle BCD ,

and from the centre B , at the distance BA , describe the circle B в ACE ; and from

the point C , in E which the circles cut one another ,

**draw**the straight lines ( 2. Side 11

Wherefore from the given point A a straight line AL has been

given straight line BC . Which was to be done . PROP . III . PROB . From the

greater of two given straight lines to cut off a part equal to the less . Let AB and C

be ...

Wherefore from the given point A a straight line AL has been

**drawn**equal to thegiven straight line BC . Which was to be done . PROP . III . PROB . From the

greater of two given straight lines to cut off a part equal to the less . Let AB and C

be ...

Side 16

To

in the same . Let AB be a given straight line , and C a point given in it : it is

required to

point D ...

To

**draw**a straight line at right angles to a given straight line , from a given pointin the same . Let AB be a given straight line , and C a point given in it : it is

required to

**draw**a straight line from the point C at right angles to AB . * Take anypoint D ...

Side 17

To

length , from a given point without it . Let AB be the given straight line , which may

be produced to any length both ways , and let C be a point without it . It is

required to ...

To

**draw**a straight line perpendicular to a given straight line of an unlimitedlength , from a given point without it . Let AB be the given straight line , which may

be produced to any length both ways , and let C be a point without it . It is

required to ...

Side 21

XXI . THEOR . If , from the ends of the side of a triangle , there be

straight lines to a point within the triangle , these shall be less than the other two

sides of the triangle , but shall contain a greater angle . * Let the two straight lines

BD ...

XXI . THEOR . If , from the ends of the side of a triangle , there be

**drawn**twostraight lines to a point within the triangle , these shall be less than the other two

sides of the triangle , but shall contain a greater angle . * Let the two straight lines

BD ...

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1810 |

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

### 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.