## 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 29

ABC , BCA , CAB , are together equal to two

draw A CE parallel ( 31. 1. ) to the E straight line AB ; and because AB is parallel

to CE and AC meets them , the alternate angles BAC , ACE are equal ( 29 . B 1. )

...

ABC , BCA , CAB , are together equal to two

**right angles**. Through the point Cdraw A CE parallel ( 31. 1. ) to the E straight line AB ; and because AB is parallel

to CE and AC meets them , the alternate angles BAC , ACE are equal ( 29 . B 1. )

...

Side 47

CE at

through E draw ( 31. 1. ) EF parallel to AB , and through D draw DF , parallel to

CE : and because the straight line EF meets the parallels EC , FD , the angles

CEF ...

CE at

**right angles**to AB : and make it equal to AC , or CB , and join AE , EB ;through E draw ( 31. 1. ) EF parallel to AB , and through D draw DF , parallel to

CE : and because the straight line EF meets the parallels EC , FD , the angles

CEF ...

Side 73

In a circle , the angle in a semicircle is a

greater than a semicircle is less than a

less than a semicircle is greater than a

which ...

In a circle , the angle in a semicircle is a

**right angle**; but the angle in a segmentgreater than a semicircle is less than a

**right angle**; and the angle in a segmentless than a semicircle is greater than a

**right angle**. Let ABCD be a circle , ofwhich ...

Side 160

to the plane passing through them ; and therefore makes

) ... A fore the angle ABF is a

is also a right с angle ; therefore the angle ABF is equal to F the angle ABC , and

...

to the plane passing through them ; and therefore makes

**right angles**( 3. def . 11.) ... A fore the angle ABF is a

**right angle**; but the angle ABC , by the hypothesis ,is also a right с angle ; therefore the angle ABF is equal to F the angle ABC , and

...

Side 162

them is a

plane passing through BD , DA , because all three are in the plane in which are

the ...

them is a

**right angle**; therefore the base AD С is equal ( 4. 1. ) to the ... make**right angles**with every straight line meeting it in that E plane : but DC is in theplane passing through BD , DA , because all three are in the plane in which are

the ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

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.