## 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 60

... GH : but AG is equal to GD ; thereB

the greater , which is impossible . Therefore the straight line which joins the

points F , G cannot fall otherwise than upon the point A , that is , it must pass

through it .

... GH : but AG is equal to GD ; thereB

**fore**GD is greater than GH , the less thanthe greater , which is impossible . Therefore the straight line which joins the

points F , G cannot fall otherwise than upon the point A , that is , it must pass

through it .

Side 99

... is to B , as F to D. Take of E , F any equimultiples whatever K , L , and of B , D

any equimultiples whatever G , H ; then it may be demonstrated , as be* See Note

.

... is to B , as F to D. Take of E , F any equimultiples whatever K , L , and of B , D

any equimultiples whatever G , H ; then it may be demonstrated , as be* See Note

.

**fore**, that K is the same multiple of A BOOK V. 99 THE ELEMENTS OF EUCLID . Side 185

... as be- O

С L solid CF to the solid A S HT LR ; and therefore the solid AE is equal ( 9. 5. ) to

the solid CF. But let the solid parallelopipeds SE , CF be upon equal bases SB ...

... as be- O

**fore**was proved : thereB**fore**as the solid AE to the solid LR , so is theС L solid CF to the solid A S HT LR ; and therefore the solid AE is equal ( 9. 5. ) to

the solid CF. But let the solid parallelopipeds SE , CF be upon equal bases SB ...

Side 336

and K is given , where M

parallelogram AC is to the parallelogram EG , as the straight line K to the straight

line M , as is demonstrated in the 23d prop . of B. 6. Elem . ; therefore the ratio of

AC to ...

and K is given , where M

**fore**( 1. dat . ) the ratio of K to M is given : but theparallelogram AC is to the parallelogram EG , as the straight line K to the straight

line M , as is demonstrated in the 23d prop . of B. 6. Elem . ; therefore the ratio of

AC to ...

Side 349

... is given , therefore the ratio of BE to EA , and the ratio of EA to EC , as also the

ratio of BE to EC is given ( 9. dat . ) ; wherefore the ratio of EB to BC is given ( 6.

dat . ) ; and the ratio of AD to BC is given by the hypothesis , thereA

...

... is given , therefore the ratio of BE to EA , and the ratio of EA to EC , as also the

ratio of BE to EC is given ( 9. dat . ) ; wherefore the ratio of EB to BC is given ( 6.

dat . ) ; and the ratio of AD to BC is given by the hypothesis , thereA

**fore**( 9. dat . )...

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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.