## 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 199

plane through ED , AD , meets it : Therefore GH is per - Boox XL , pendicular to

AF ; and consequently AF is

: Therefore AF is

plane through ED , AD , meets it : Therefore GH is per - Boox XL , pendicular to

AF ; and consequently AF is

**perpendicular**to GH ; and AF is**perpendicular**to DE: Therefore AF is

**perpendicular**to each of the straight lines GH , DE . But if a ... Side 201

From the point B draw BG perpendiculara to the plane a 31 . 11 . which passes

through DE , EF , and let it meet that plane in G ; and through G draw GH parallel

b to ED , and GK • 31 . 1 . . parallel to EF : And because BG is

the ...

From the point B draw BG perpendiculara to the plane a 31 . 11 . which passes

through DE , EF , and let it meet that plane in G ; and through G draw GH parallel

b to ED , and GK • 31 . 1 . . parallel to EF : And because BG is

**perpendicular**tothe ...

Side 204

1 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

conimon section of the planes , lias been proved to be

plane ...

1 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

conimon section of the planes , lias been proved to be

**perpendicular**to the otherplane ...

Side 348

XXXVIII . B . XI . WHEN it is required to draw a

plane which is at right angles to another plane , unto this last plane , it is done by

drawing a

XXXVIII . B . XI . WHEN it is required to draw a

**perpendicular**from a point in oneplane which is at right angles to another plane , unto this last plane , it is done by

drawing a

**perpendicular**from the point to the common section of the planes ; for ... Side 423

Draw AD

wherefore the ratio of AD to AR is given : and the ratio of AR to BC is given , and

consequently the ratio of AD to BC is given ; and the triangle h 9 Dat . ABC is ...

Draw AD

**perpendicular**to BC ; therefore the triangle ARD is given in species ;wherefore the ratio of AD to AR is given : and the ratio of AR to BC is given , and

consequently the ratio of AD to BC is given ; and the triangle h 9 Dat . ABC 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.