## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. The first six books, together with the eleventh and twelfth |

### Inni boken

Side 196

And because AB is

2. 3. Def.s1 . line which meets it , and is in that plane " . therefore each of the

angles ABD , ABE , is a right angle , and because the straight line BD meets the ...

And because AB is

**perpendicular**to the plane , it is**perpendicular**to every stright2. 3. Def.s1 . line which meets it , and is in that plane " . therefore each of the

angles ABD , ABE , is a right angle , and because the straight line BD meets the ...

Side 199

therefore GH is

right angles to each ...

therefore GH is

**perpendicular**to AF , and consequently AF , is Book Xi .**perpendicular**to GH . and AF is**perpendicular**to DE ; therefore AF is**perpendicular**to each of the straight lines GH , DE . but if a straight line stands atright angles to each ...

Side 201

From the point B draw BG

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

b to ED , and GK parallel to EF . b . 31. s . and because BG is

...

From the point B draw BG

**perpendicular**to the plane which 2. 11. 11 . passesthrough DE , EF , and let it meet that plane in G ; and through G draw GH parallel

b to ED , and GK parallel to EF . b . 31. s . and because BG is

**perpendicular**to the...

Side 204

Def.si. sight angles to CE the common fection of the planes , has been proved to

be

to the plane CK . In like manner , it may be proved that all the planes which pass

...

Def.si. sight angles to CE the common fection of the planes , has been proved to

be

**perpendicular**to the other plane CK ; therefore the plane DE is at right anglesto the plane CK . In like manner , it may be proved that all the planes which pass

...

Side 297

If two straight lines which contain an angle be produced , there may be found in

either of them a point from which the

greater than any given straight line . Let AB , AC be two straight lines which make

...

If two straight lines which contain an angle be produced , there may be found in

either of them a point from which the

**perpendicular**drawn to the other shall begreater than any given straight line . Let AB , AC be two straight lines which make

...

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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ... Robert Simson Uten tilgangsbegrensning - 1775 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1762 |

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... Robert Simson Uten tilgangsbegrensning - 1827 |

### Vanlige uttrykk og setninger

added alſo altitude angle ABC angle BAC baſe becauſe Book caſe circle circle ABCD circumference common cone cylinder Definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs fame fides figure firſt folid angle fore four fourth given angle given in poſition given magnitude given ratio given ſtraight line greater half join leſs likewiſe magnitude manner meet multiple muſt oppoſite parallel parallelogram perpendicular plane produced PROP proportionals Propoſition pyramid radius reaſon rectangle rectangle contained rectilineal remaining right angles ſame ſecond ſegment ſhall ſides ſimilar ſolid ſphere ſquare ſquare of AC taken THEOR theſe third thro triangle ABC wherefore whole

### Populære avsnitt

Side 156 - 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 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 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 92 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square- of the line which meets it, the line which meets shall touch the circle.

Side 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.

Side 52 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.

Side 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Side 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.

Side 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.

Side 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...