## 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 9

Side 29

All the interior angles of any rectilineal figure , together with

are equal to twice as many right angles as the figure has sides . с For any

rectilineal figure ABCDE can be divided into as many triangles as the F figure has

sides ...

All the interior angles of any rectilineal figure , together with

**four**right D angles ,are equal to twice as many right angles as the figure has sides . с For any

rectilineal figure ABCDE can be divided into as many triangles as the F figure has

sides ...

Side 45

If a straight line be divided into any two parts ,

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 ...

If a straight line be divided into any two parts ,

**four**times the rectangle containedby 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 ...

Side 86

... the

described from the centre E , at the distance of one of them , shall pass through

the extremities of the other three , and be described about the square ABCD .

... the

**four**straight lines EA , EB , EC , ED are equal to one another ; and the circledescribed from the centre E , at the distance of one of them , shall pass through

the extremities of the other three , and be described about the square ABCD .

Side 169

THEOR . Every solid angle is contained by plane angles which together are less

than

angles BAC , CAD , DAB . These three together are less than

THEOR . Every solid angle is contained by plane angles which together are less

than

**four**right angles . First , let the solid angle at A be contained by three planeangles BAC , CAD , DAB . These three together are less than

**four**right angles . Side 257

Let A , B , C , D be

and also the two others either of the same kind with the two first , or of some other

, the same kind with one another . I say the ratio of the third C to the fourth D , is ...

Let A , B , C , D be

**four**magnitudes , of which the two first are of the one kind ,and also the two others either of the same kind with the two first , or of some other

, the same kind with one another . I say the ratio of the third C to the fourth D , is ...

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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.