## 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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Side 80

DEFINITIONS . I. A

the figure in which it is inscribed , each upon each . * II . In like manner , a figure

is said ...

DEFINITIONS . I. A

**RECTILINEAL figure**is said to be inscribed in another**rectilineal figure**, when all the angles of the inscribed figure are upon the sides ofthe figure in which it is inscribed , each upon each . * II . In like manner , a figure

is said ...

Side 138

Wherefore , because the

have their sides about the equal angles ... Next , let it be required to describe

upon a given straight line AB , a

the ...

Wherefore , because the

**rectilineal figures**ABHG , CDEF are equiangular , andhave their sides about the equal angles ... Next , let it be required to describe

upon a given straight line AB , a

**rectilineal figure**similar and similarly situated tothe ...

Side 141

In like manner , it may be proved , that similar four sided figures , or of any

number of sides , are one to another in the ... Therefore , universally , similar

sides . Cor .

In like manner , it may be proved , that similar four sided figures , or of any

number of sides , are one to another in the ... Therefore , universally , similar

**rectilineal figures**are to one another in the duplicate ratio of their homologoussides . Cor .

Side 144

for the same reason , the parallelogram ABCD is similar to the parallelogram

FHCK . Wherefore each of the parallelograms GE , KH is similar to DB ; but

to one ...

for the same reason , the parallelogram ABCD is similar to the parallelogram

FHCK . Wherefore each of the parallelograms GE , KH is similar to DB ; but

**rectilineal figures**which are similar to the same**rectilineal figure**are also similarto one ...

Side 327

the figure F , as AB to G , that is , as H to L. PROP . LV . 51 . If two straight lines

have a given ratio to one another ; the

described upon them , shall have to one another a given ratio . Let AB , CD be

two straight ...

the figure F , as AB to G , that is , as H to L. PROP . LV . 51 . If two straight lines

have a given ratio to one another ; the

**rectilineal figures**given in speciesdescribed upon them , shall have to one another a given ratio . Let AB , CD be

two 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.