## The Elements of Euclid; viz. the first six books, together with the eleventh and twelfth. Also the book of Euclid's Data. By R. Simson. To which is added, A treatise on the construction of the trigonometrical canon [by J. Christison] and A concise account of logarithms [by A. Robertson]. |

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Side

But indeed , this Proposition , which makes the 10th definition of the 11th Book , is not true universally , except in the case in which each of the

But indeed , this Proposition , which makes the 10th definition of the 11th Book , is not true universally , except in the case in which each of the

**solid angles**of the figures is contained by no more than three plane angles ; for in ... Side 189

A

A

**solid angle**is that which is made by the meeting of more See N. than two plane angles , which are not in the same plane , in one point . X. ' The tenth definition is omitted for reasons given in the See N. notes . ' XI . Side 190

The base of a cone is the circle described by that side containing the right

The base of a cone is the circle described by that side containing the right

**angle**, which revolves . XXI . A cylinder is a**solid**figure described by the revolution of a right**angled**parallelogram about one of its sides which remains ... Side 204

BOOK XI . their common section , are also at right angles to the other planed ; and any straight line FG in the plane DE , which is at right angles to CE the ... Q. E. D. D Let the

BOOK XI . their common section , are also at right angles to the other planed ; and any straight line FG in the plane DE , which is at right angles to CE the ... Q. E. D. D Let the

**solid angle**at A be contained by the 204 THE ELEMENTS. Side 205

Let the

Let the

**solid angle**at A be contained by the three plane angles , BAC , CAD , DAB . Any two of them are greater than the third . PROP . XX . THEOR . Ir a**solid angle**be contained by three plane angles , See N. any two of them are ...### Hva folk mener - Skriv en omtale

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The Elements of Euclid; viz. the first six books, together with the eleventh ... Euclides Uten tilgangsbegrensning - 1834 |

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added altitude angle ABC angle BAC arch base Book Book XI centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples 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 logarithm magnitude manner meet multiple 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 Take taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 43 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.

Side 20 - Any two sides of a triangle are together greater than the third side.

Side 30 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 20 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...

Side 310 - 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 8 - DL is equal to DG, and DA, DB, parts of them, are equal ; therefore the remainder AL is equal to the remainder (3. Ax.) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC.

Side 153 - 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 52 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.

Side 3 - 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 165 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.