## 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 99

scribed from the centre F , at the distance of one of them , Book IV . shall pass

through the extremities of the other two , and be described about the triangle

. Which was to be done . Cor . And it is manifest , that when the centre of the

...

scribed from the centre F , at the distance of one of them , Book IV . shall pass

through the extremities of the other two , and be described about the triangle

**ABC**. Which was to be done . Cor . And it is manifest , that when the centre of the

**circle**...

Side 246

Let ABCD , EFGH be two circles , and BD , FH their diameters : As the square of

BD ... For , if it be not so , the square of BD shall be to the square of FH , as the

Let ABCD , EFGH be two circles , and BD , FH their diameters : As the square of

BD ... For , if it be not so , the square of BD shall be to the square of FH , as the

**circle ABCD**is to some space either less than the circle EFGH , or greater than it . Side 248

Book XII . polygon EKFLGMHN : But the square of BD is also to m the square of

FH , as the

is to the space S , so is the polygon AXBOCPDR to the polygon EKFLGMHN : But

...

Book XII . polygon EKFLGMHN : But the square of BD is also to m the square of

FH , as the

**circle ABCD**is to the space S : € 11 . 5 . Therefore as the**circle ABCD**is to the space S , so is the polygon AXBOCPDR to the polygon EKFLGMHN : But

...

Side 249

the square of BD , so is the circle EFGH to a space less Book XII . than the

BD is not to the square of FH as the

the square of BD , so is the circle EFGH to a space less Book XII . than the

**circle****ABCD**, which has been demonstrated to be impossible : Therefore the square ofBD is not to the square of FH as the

**circle ABCD**is to any space greater . than ... Side 267

han the cowhich is greicie E F Gbut as is absurd : Therefore the

not to the cirele Boox XII . EFGH , as the cone AL to any solid which is less than

the eone EN . In the same manner it may be demonstrated , that the circle EFGH

is ...

han the cowhich is greicie E F Gbut as is absurd : Therefore the

**circle ABCD**isnot to the cirele Boox XII . EFGH , as the cone AL to any solid which is less than

the eone EN . In the same manner it may be demonstrated , that the circle EFGH

is ...

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

### Vanlige uttrykk og setninger

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.