## The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; 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 |

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Resultat 1-5 av 8

Side 51

If a straight line be

whole and one of the parts , is equal to the rectangle contained by the two parts ,

together with the square of the foresaid part Let the straight line AB be

into ...

If a straight line be

**divided**into any two parts , the rectangle contained by thewhole and one of the parts , is equal to the rectangle contained by the two parts ,

together with the square of the foresaid part Let the straight line AB be

**divided**into ...

Side 165

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 258

If there be two pyramids of the same altitude , upon triangular bases , and each of

them be

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

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 whole pyramid , and alsointo two equal prisms ; and if each of these pyramids be

**divided**in the same ... Side 289

... for if these two solids be

same order , the pyramids shall be similar to one another , each to each ;

because they have the solid angles at their common vertex , the centre of the

sphere ...

... for if these two solids be

**divided**into the same number of pyramids , and in thesame order , the pyramids shall be similar to one another , each to each ;

because they have the solid angles at their common vertex , the centre of the

sphere ...

Side 308

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: The Errors, by which Theon, Or Others, Have Long Ago ... Euclid,Robert Simson Uten tilgangsbegrensning - 1838 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone 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 greater Greek half join less likewise magnitude 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 9 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 81 - The angles in the same segment of a circle are equal to one another.

Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 49 - 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 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 155 - 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 22 - ANY two angles of a triangle are together less than two right angles.

Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.

Side 24 - Any two sides of a triangle are together greater than the third side.