## 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 7

Side 40

If there be two straight lines , one of which is

the rectangle contained by the two straight lines , is equal to the rectangles

contained by the undivided line , and the several parts of the

and BC ...

If there be two straight lines , one of which is

**divided**into any number of parts ;the rectangle contained by the two straight lines , is equal to the rectangles

contained by the undivided line , and the several parts of the

**divided**line . Let Aand BC ...

Side 41

II . THEOR . If a straight line be

contained by the whole and each of the parts , are together equal to the square of

the whole line . Let the straight line AB be

point C ...

II . THEOR . If a straight line be

**divided**into any two parts , the rectanglescontained by the whole and each of the parts , are together equal to the square of

the whole line . Let the straight line AB be

**divided**into any A с в two parts in thepoint C ...

Side 133

To

into parts that shall have the same ratios to one another which the parts of the

and ...

To

**divide**a given straight line similarly to a given**divided**straight line , that is ,into parts that shall have the same ratios to one another which the parts of the

**divided**given straight line have . Let AB be the straight line given to be**divided**,and ...

Side 206

IV . THEOR . If there be two pyramids of the same altitude , upon triangular bases

, and each of them be

pyramid , and also into two equal prisms ; and if each of these pyramids be

IV . THEOR . If there be two pyramids of the same altitude , upon triangular bases

, and each of them be

**divided**into two equal pyramids similar to the wholepyramid , and also into two equal prisms ; and if each of these pyramids be

**divided**in ... Side 248

This proposition is

construction and demonstration ; therefore it is now

PROP . XXXIII . B. III . This also in the Greek is

two , viz ...

This proposition is

**divided**into three cases , of which two have the sameconstruction and demonstration ; therefore it is now

**divided**only into two cases .PROP . XXXIII . B. III . This also in the Greek is

**divided**into three cases , of whichtwo , viz ...

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1892 |

### 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.