## 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 21

than the angle ACB ; but B С it is not ; therefore the

and it has been shown that it is not equal to AB ; therefore AC is greater than AB .

Wherefore the greater angle , & c . Q. E. D. PROP . XX . THEOR . Any two

than the angle ACB ; but B С it is not ; therefore the

**side**AC is not less than AB ;and it has been shown that it is not equal to AB ; therefore AC is greater than AB .

Wherefore the greater angle , & c . Q. E. D. PROP . XX . THEOR . Any two

**sides**... Side 24

two triangles have two

each ...

**side**is opposite to the greater angle ; the**side**EG is therefore greater than the**side**EF ; but EG is equal to BC ; and therefore also BC is greater than EF . ... Iftwo triangles have two

**sides**of the one equal to two**sides**of the other , each toeach ...

Side 329

G. If two similar rectilineal figures have a given ratio to one another , their

homologous

CD be homologous to EF , and to CD , EF let the straight line G be a third

proportional .

G. If two similar rectilineal figures have a given ratio to one another , their

homologous

**sides**have also a given ratio to one another . * Let the ... Let the**side**CD be homologous to EF , and to CD , EF let the straight line G be a third

proportional .

Side 391

In a plane triangle , the base is to the sum of the

perpendicular upon it from the vertex , according as the square of the greater

is ...

In a plane triangle , the base is to the sum of the

**sides**, as the difference of the**sides**is to the sum or difference of the segments of the base made by theperpendicular upon it from the vertex , according as the square of the greater

**side**is ...

Side 398

IF , in a spherical triangle ABC , two of the angles BAC , ABC , be equal , the

demonstration of the preceding proposition , unto the words " and the

CB , ” & c ...

IF , in a spherical triangle ABC , two of the angles BAC , ABC , be equal , the

**sides**BC , AC , opposite to them , are equal . Read the construction anddemonstration of the preceding proposition , unto the words " and the

**sides**AC ,CB , ” & c ...

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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.