## 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 68

to the D angle CDB , because they are in the same

angle ACB is С equal to the angle ADB , because they are in the same

ADCB : therefore the whole angle ADC is equal to the angles CAB , ACB : to

each of ...

to the D angle CDB , because they are in the same

**segment**BADC , and theangle ACB is С equal to the angle ADB , because they are in the same

**segment**ADCB : therefore the whole angle ADC is equal to the angles CAB , ACB : to

each of ...

Side 69

Also, the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books,

together with the eleventh and t Euclid, Robert Simson. For , if the

AEB be applied to the

...

Also, the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books,

together with the eleventh and t Euclid, Robert Simson. For , if the

**segment**E FAEB be applied to the

**segment**CFD , so as the point A be on C , and the straight...

Side 70

other points ; and the circle of which ABC is a

evident , that if the angle ABD be greater than the angle BAD , the centre E falls

without the

angle ...

other points ; and the circle of which ABC is a

**segment**is described : and it isevident , that if the angle ABD be greater than the angle BAD , the centre E falls

without the

**segment**ABC , which therefore is less than a semicircle ; but if theangle ...

Side 73

In a circle , the angle in a semicircle is a right angle ; but the angle in a

greater than a semicircle is less than a ... Let ABCD be a circle , of which the

diameter is BC , and centre E ; and draw CA , dividing the circle into the

In a circle , the angle in a semicircle is a right angle ; but the angle in a

**segment**greater than a semicircle is less than a ... Let ABCD be a circle , of which the

diameter is BC , and centre E ; and draw CA , dividing the circle into the

**segments**... Side 74

... this line with the line touching the circle , shall be equal to the angles which are

in the alternate

that is , the angle FBD is equal to the angle which is in the

...

... this line with the line touching the circle , shall be equal to the angles which are

in the alternate

**segments**of the circle . ... the alternate**segments**of the circle :that is , the angle FBD is equal to the angle which is in the

**segment**DAB , and 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.