## 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 |

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Resultat 1-5 av 5

Side 199

If there be two triangular

a parallelogram , and the base of the other ... its base ; if the parallelogram AF ,

be double of the triangle GHK , the

.

If there be two triangular

**prisms**of the same altitude , the base of one of which isa parallelogram , and the base of the other ... its base ; if the parallelogram AF ,

be double of the triangle GHK , the

**prism**ABCDEF is equal to the**prism**GHKLMN.

Side 205

of the triangle GFC : but when there are two

one has a parallelogram for its base , and the other a triangle that is half of the ...

to one another ; therefore the

of the triangle GFC : but when there are two

**prisms**of the same altitude , of whichone has a parallelogram for its base , and the other a triangle that is half of the ...

to one another ; therefore the

**prism**having the parallelogram EBFG for its base ... Side 207

parts in the points N , Y by the same planes : therefore the

RVFSTY are of the same altitude ; and therefore as the base LXC to the base

RVF ; that is , as the triangle ABC to the triangle DEF , so ( Cor . 32. 11. ) is the

parts in the points N , Y by the same planes : therefore the

**prisms**LXCOMN ,RVFSTY are of the same altitude ; and therefore as the base LXC to the base

RVF ; that is , as the triangle ABC to the triangle DEF , so ( Cor . 32. 11. ) is the

**prism**... Side 211

From this it is manifest , that every pyramid is the third part of a

the same base , and is of an equal altitude with it ; for if the base of the ... any

other figure than a triangle , it may be divided into

.

From this it is manifest , that every pyramid is the third part of a

**prism**which hasthe same base , and is of an equal altitude with it ; for if the base of the ... any

other figure than a triangle , it may be divided into

**prisms**having triangular bases.

Side 214

and the cylinder is less than the

ABCD : therefore the

cylinder , is greater than half of the cylinder . Bisect the circumferences AB , BC ...

and the cylinder is less than the

**prism**upon the square described about the circleABCD : therefore the

**prism**upon the square ABCD of the same altitude with thecylinder , is greater than half of the cylinder . Bisect the circumferences AB , BC ...

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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.