## 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 26

For , if it be not parallel , AB and CD being produced shall

D , or towards A , C ; let them be produced and

; therefore GEF is a triangle , and its exterior angle AEF is greater ( 16. 1. ) ...

For , if it be not parallel , AB and CD being produced shall

**meet**either towards B ,D , or towards A , C ; let them be produced and

**meet**towards B , D , in the point G; therefore GEF is a triangle , and its exterior angle AEF is greater ( 16. 1. ) ...

Side 160

with every straight line meeting it in that plane ; but BF , which is in that plane ,

straight line B , D , to which draw DE at right angles , in the same plane ; and

make DE ...

with every straight line meeting it in that plane ; but BF , which is in that plane ,

**meets**it : there . ... Let them**meet**the plane in the points B , D , and draw thestraight line B , D , to which draw DE at right angles , in the same plane ; and

make DE ...

Side 165

If not , they shall

section shall be a G straight line GH , in which take any point K , and join AK , BK

: then because AB is K perpendicular to the plane EF , it is perpendicular ( 3.

If not , they shall

**meet**one another when produced ; let them**meet**; their commonsection shall be a G straight line GH , in which take any point K , and join AK , BK

: then because AB is K perpendicular to the plane EF , it is perpendicular ( 3.

Side 166

For , if it be not , EF , GH shall

first , let them be produced on the side of FH , and

since EFK is in the plane AB , every point in EFK is in that plane ; K and K is a ...

For , if it be not , EF , GH shall

**meet**, if produced , either on the side of FH , or EG ;first , let them be produced on the side of FH , and

**meet**in the point K ; therefore ,since EFK is in the plane AB , every point in EFK is in that plane ; K and K is a ...

Side 369

a right angle and the angle contained by the straight line given in position , and

the straight line which joins the given point and the centre of the circle ; and from

the point in which the second line

...

a right angle and the angle contained by the straight line given in position , and

the straight line which joins the given point and the centre of the circle ; and from

the point in which the second line

**meets**the circumference again , a third straight...

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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.