## 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 : to this Edition are Also Annexed, Elements of Plane and Spherical Trigonometry |

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Resultat 1-5 av 13

Side 196

A

A

**cylinder**is a solid figure described by the revolution of a right angled parallelogram about one of its sides , which remains fixed . XXII . The axis of a**cylinder**is the fixed straight line about which the parallelogram revolves . Side 268

Upon the square ABCD erect a prism of the same altitude with the

Upon the square ABCD erect a prism of the same altitude with the

**cylinder**; this prism is greater than half of the**cylinder**: because if a square be describe about the circle , and a prism erected upon the square , of the same altitude ... Side 269

Therefore the rest of the

Therefore the rest of the

**cylinder**, thatis , the prism of which the base is the polygon AEBFCGDH , and of which the altitude is the same with that of the**cylinder**, is greater than the triple of the cone : but this prism is triple ( 1. Side 270

of the cone , and so on , there must at length remain some segments of the cone , which together shall be less than the excess of the cone above the third part of the

of the cone , and so on , there must at length remain some segments of the cone , which together shall be less than the excess of the cone above the third part of the

**cylinder**. Let these be the segments upon AE , EB , BF , FC , CG , GD ... Side 273

is the

is the

**cylinder**to the**cylinder**, because the**cylinders**are triple ( 10. 12. ) of the cone , each to each . Therefore , as the circle ABCD to the circle EFGH , so are the**cylinders**upon them of the same altitude .### Hva folk mener - Skriv en omtale

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1810 |

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base BC is given 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 greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid radius reason rectangle rectangle contained 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 11 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 155 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...

Side 329 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 20 - To draw a straight line at right angles to a given straight line, from a given point in the same.

Side 9 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Side 55 - If 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 53 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Side 318 - 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 21 - The angles which one straight line makes with another upon one tide of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.

Side 27 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.