## 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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Resultat 1-5 av 5

Side 476

The

ABC . Since CD , AE , are parallel , BD is to BC or BA , as BA to · BE . PROP . I .

Fig . 5 . In a right angled plane triangle : if the hypothe . puse be made

...

The

**radius**is a mean proportional between the cosine and secant of any angleABC . Since CD , AE , are parallel , BD is to BC or BA , as BA to · BE . PROP . I .

Fig . 5 . In a right angled plane triangle : if the hypothe . puse be made

**radius**, the...

Side 512

In right angled spherical triangles , the sine of either of the sides about the right

angle , is to the

the tangent of the angle opposite to that side . Let ABC be a triangle , having the ...

In right angled spherical triangles , the sine of either of the sides about the right

angle , is to the

**radius**of the sphere , as the tangent of the remaining side is tothe tangent of the angle opposite to that side . Let ABC be a triangle , having the ...

Side 514

... of AC , and the arch AD , which is the measure of the angle CFE , is the

complement of AB . · But ( 17 . of this ) in the triangle CEF , the sine of the side CE

is to the

... of AC , and the arch AD , which is the measure of the angle CFE , is the

complement of AB . · But ( 17 . of this ) in the triangle CEF , the sine of the side CE

is to the

**radius**, as the tangent of the other side is to the tangent of the angle ... Side 515

And since by this proposition the cosine of the angle ABC is to the

tangent of the side AB is to the tangent of the hypothenuse BC ; and as the

is to the cotangent of BC , so is the tangent of BC to the

And since by this proposition the cosine of the angle ABC is to the

**radius**, as thetangent of the side AB is to the tangent of the hypothenuse BC ; and as the

**radius**is to the cotangent of BC , so is the tangent of BC to the

**radius**; by equality , the ... Side 517

The rectangle contained by the

the rectangle contained by the cosines of the opposite parts , res These rules are

demonstrated in the following manner : First , Ler either of the sides , as BA , be ...

The rectangle contained by the

**radius**and the sine of the middle part , is equal tothe rectangle contained by the cosines of the opposite parts , res These rules are

demonstrated in the following manner : First , Ler either of the sides , as BA , be ...

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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 base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples excess figure 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 306 - 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.