## 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 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 ...

in it ; the straight line drawn to C , a F E which makes a

**given angle**with CB , isgiven 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 317

to the

BAC , has been found , the

to the

**angle**BAC ; therefore , because the**angle**EDF which is equal to the**angle**BAC , has been found , the

**angle**BAC is**given**( 1. def . ) ; in like manner the**angles**at B , C are**given**. And because the sides AB , BC , CA are**given**, their ... Side 319

c ܠ Let the sides AB , BC about the acute

has a right

c ܠ Let the sides AB , BC about the acute

**angle**ABC of the triangle ABC , whichhas a right

**angle**at A , have a**given**ratio to one another ; the triangle ABC is**given**in species . Take a straight line DE**given**in position and magnitude ; and ... Side 323

Suppose the

together are to BC , as AB to BD , as was shown in the preceding proposition .

But the ratio of BA and AC together to BC is

to BD is ...

Suppose the

**angle**BAC to be bisected by the straight line AD : BA and ACtogether are to BC , as AB to BD , as was shown in the preceding proposition .

But the ratio of BA and AC together to BC is

**given**, therefore also the ratio of ABto BD is ...

Side 348

centre E , draw EA , EB , EC , ED ; because the

BEC at the centre , which is the double ( 20. 3. ) of it , is

to EC is

centre E , draw EA , EB , EC , ED ; because the

**angle**BAC is**given**, the**angle**BEC at the centre , which is the double ( 20. 3. ) of it , is

**given**. And the ratio of BEto EC is

**given**, because they are equal to one another ; therefore ( 44. dat . ) ...### 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.