## 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 311

in it ; the straight line drawn to C , a F E which makes a given angle with CB , is

def . ) ; let this be the angle at D : at the given A B point C , in the given straight

line ...

in it ; the straight line drawn to C , a F E which makes a given angle with CB , is

**given in position**. Because the angle is given , one equal to it can be found ( 1.def . ) ; let this be the angle at D : at the given A B point C , in the given straight

line ...

Side 312

If therefore D be equal to AE , AE B E C is the straight line given in magnitude ,

drawn Dfrom the given point A to BC : and it is evident that AE is

, ( 33. dat . ) , because it is drawn from the given point A to BC , which is

If therefore D be equal to AE , AE B E C is the straight line given in magnitude ,

drawn Dfrom the given point A to BC : and it is evident that AE is

**given in position**, ( 33. dat . ) , because it is drawn from the given point A to BC , which is

**given in**... Side 314

Let the straight line AD given in magnitude be drawn from the point A to the

straight line BC , given in posi- E A H F tion , in the given angle ADC : the straight

line EAF drawn through A parallel to BC is

...

Let the straight line AD given in magnitude be drawn from the point A to the

straight line BC , given in posi- E A H F tion , in the given angle ADC : the straight

line EAF drawn through A parallel to BC is

**given in position**. In BC take the given...

Side 315

From the given point A , let the straight line AED be drawn to the two parallel

straight lines FG , BC , and let the ratio of the segments AE , AD be given ; if one

of the parallels BC be

From the given point A , let the straight line AED be drawn to the two parallel

straight lines FG , BC , and let the ratio of the segments AE , AD be given ; if one

of the parallels BC be

**given in position**, the other FG is also**given in position**. Side 364

If from any point in the circumference of a circle

lines be drawn meeting the circumference , and containing a given angle ; if the

point in which one of them meets the circumference again be given , the point in ...

If from any point in the circumference of a circle

**given in position**, two straightlines be drawn meeting the circumference , and containing a given angle ; if the

point in which one of them meets the circumference again be given , the point in ...

### 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.