## 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 475

Euclides Robert Simson. It is manifest from def . 4 . that CD is the

angle | CBF . Let CB - be produced till it meet the circle again in G ; and it is

manifest that AE is the tangent , and BE the secant , of the angle ABG or EBF ,

from def . 6 .

Euclides Robert Simson. It is manifest from def . 4 . that CD is the

**sine**of theangle | CBF . Let CB - be produced till it meet the circle again in G ; and it is

manifest that AE is the tangent , and BE the secant , of the angle ABG or EBF ,

from def . 6 .

Side 488

But because FO = EO , then will FM = MG = ON ; and so OP + FM - FI =

sum of the arcs : And OP - FM : that is , OP - ON = EL =

the arcs : which were to be found . Cor . Because the differences of the arcs BE ...

But because FO = EO , then will FM = MG = ON ; and so OP + FM - FI =

**sine**of thesum of the arcs : And OP - FM : that is , OP - ON = EL =

**sine**of the difference ofthe arcs : which were to be found . Cor . Because the differences of the arcs BE ...

Side 489

If EB be less than the o ne part of thë radius , then the difference between the

Cor . Since any arc is less than the tangent , and greater than its

If EB be less than the o ne part of thë radius , then the difference between the

**sine**and the tangent will be also less than the " 10000000 part of the tangent .Cor . Since any arc is less than the tangent , and greater than its

**sine**, and the**sine**... Side 520

18 . the

at A ) as the

the

18 . the

**sine**of the hypothenuse BC is to the radius ( or the**sine**of the right angleat A ) as the

**sine**of the side AÇ to the**sine**of the angle B . And in like manner ,the

**sine**of BC is to the**sine**of the angle A , as the**sine**of AB to the**sine**of the ... Side 525

DB or AD , the half of AB : Let BF be perpendicular to AC , and AF will be the

versed

is to AE as AB , that is , twice AE to AF ; and by halving the antecedents , half of

the ...

DB or AD , the half of AB : Let BF be perpendicular to AC , and AF will be the

versed

**sine**of the arch BA ; but , because of the similar triangles CAE , BAF , CAis to AE as AB , that is , twice AE to AF ; and by halving the antecedents , half of

the ...

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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.