## 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 55

the centre , bisect any straight line AB , which does not

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 ...

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 60

If two circles touch each other internally , the straight line which joins their centres

being produced shall

line which A joins the centres F , G , being produced

If two circles touch each other internally , the straight line which joins their centres

being produced shall

**pass**through ... G the centre of the circle ADE : the straightline which A joins the centres F , G , being produced

**passes**through the point ... Side 76

A E D If AC , BD

is evident , that AE , EC , BE , ED , being all equal , the B rectangle AE , EC is

likewise equal to the rectangle BE , ED . But let one of them BD

...

A E D If AC , BD

**pass**each of them through the centre , so that E is the centre ; itis evident , that AE , EC , BE , ED , being all equal , the B rectangle AE , EC is

likewise equal to the rectangle BE , ED . But let one of them BD

**pass**through the...

Side 77

Next , let BD , which

bisected in F , F is the centre of the circle . Join AF , and from F draw ( 12. 1. ) ...

Next , let BD , which

**passes**through the centre , cut the other AC , which does not**pass**through the centre , in E , but not at right angles : then , as before , if BD bebisected in F , F is the centre of the circle . Join AF , and from F draw ( 12. 1. ) ...

Side 78

which

) angle : and because the straight D line AC is bisected in E , and produced to the

...

which

**passes**Either DCA**passes**through the centre , or it does not ; first , let it**pass**through the centre E , and join EB ; therefore the angle EBD is a right ( 18.3 .) angle : and because the straight D line AC is bisected in E , and produced to the

...

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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.