## 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 169

Wherefore , if a

. First , let the

Wherefore , if a

**solid angle**, & c . Q. E. D. B PROP . XXI . THEOR . Every**solid****angle**is contained by plane angles which together are less than four right angles. First , let the

**solid angle**at A be contained by three plane angles BAC , CAD ... Side 176

0 which are equal to one another , each to each , and alike situated ; these

which the

0 which are equal to one another , each to each , and alike situated ; these

**solid****angles**are equal to one another . * . Let there be two**solid angles**at A and B , ofwhich the

**solid angle**at A is contained by the three plane angles CAD ; CAE ... Side 179

what multiple soever the base LF is of the base AF , the same multiple is the solid

LV of the solid AV : for the same ... At a given point in a given straight line , to

make a

what multiple soever the base LF is of the base AF , the same multiple is the solid

LV of the solid AV : for the same ... At a given point in a given straight line , to

make a

**solid angle**equal to a given**solid angle**contained by three plane angles . Side 180

G. 1 44 L it in that plane : therefore each of the angles FGD , FGE is a right angle :

for the same reason , HKA , HKB , are ... to the angle FDC : therefore , because

the three plane angles BAL , BAH , HAL , which contain the

...

G. 1 44 L it in that plane : therefore each of the angles FGD , FGE is a right angle :

for the same reason , HKA , HKB , are ... to the angle FDC : therefore , because

the three plane angles BAL , BAH , HAL , which contain the

**solid angle**at A , are...

Side 276

them are greater than the third ; therefore a

be contained by three plane angles equal to the angles C , D , E , each to each (

23. 11. ) : and by prop . 26. 11 , at the point F in the straight line FG a

them are greater than the third ; therefore a

**solid angle**may be made which shallbe contained by three plane angles equal to the angles C , D , E , each to each (

23. 11. ) : and by prop . 26. 11 , at the point F in the straight line FG a

**solid angle**...### 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.