## 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 59

the base DB : but , besides DB , there can be no straight line drawn from D to the

equal to DN , and also to DB ; therefore DB is equal to DN , that is , the nearer to

the ...

the base DB : but , besides DB , there can be no straight line drawn from D to the

**circumference**equal to DK : for , if there can , let it be DN ; and because DK isequal to DN , and also to DB ; therefore DB is equal to DN , that is , the nearer to

the ...

Side 72

is equal to the

whole EDF ; the remaining part therefore of the

equal to ...

**circumferences**, when they are at the centres ; therefore the**circumference**BGCis equal to the

**circumference**EHF . But the whole circle ABC is equal to thewhole EDF ; the remaining part therefore of the

**circumference**, viz . BAC , isequal to ...

Side 151

In equal circles , angles , whether at the centres or

same ratio which the

...

In equal circles , angles , whether at the centres or

**circumferences**, have thesame ratio which the

**circumferences**on ... EDF at their**circumferences**: as the**circumference**BC to the**circumference**EF , so is the angle BGC to the angle EHF...

Side 152

the angle EHN : and it has been proved that if the

than EN , the angle BGL is greater than EHN : and if equal , equal ; and if less ,

less : as therefore the

...

the angle EHN : and it has been proved that if the

**circumference**BL be greaterthan EN , the angle BGL is greater than EHN : and if equal , equal ; and if less ,

less : as therefore the

**circumference**BC to the**circumference**EF , so ( 5. def . 5. )...

Side 385

Elem . the angle ABC is to a right angle ABD , as the arch AC to the arch AD ; and

quadrupling the consequents , the angle ABC will be to four right angles , as the

arch AC to four times the arch AD , or to the whole

Elem . the angle ABC is to a right angle ABD , as the arch AC to the arch AD ; and

quadrupling the consequents , the angle ABC will be to four right angles , as the

arch AC to four times the arch AD , or to the whole

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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.