## 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 |

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Side 165

IF F three straight lines be proportionals , the

extremes is equal to the square of the mean . and if the

the extremes be equal to the square of the mean , the three straight lines are

proportionals ...

IF F three straight lines be proportionals , the

**rectangle**contained by theextremes is equal to the square of the mean . and if the

**rectangle**contained bythe extremes be equal to the square of the mean , the three straight lines are

proportionals ...

Side 327

To apply a

line , deficient by a square . but the given square must not be greater than that

upon the half of the given line . Let AB be the given straight line , and let the

square ...

To apply a

**rectangle**which shall be equal to a given square , to a given straightline , deficient by a square . but the given square must not be greater than that

upon the half of the given line . Let AB be the given straight line , and let the

square ...

Side 328

Book VI . tangle All is equal to the given square upon the straight line C.

wherefore the

to the given straight line AB , deficient by the square GK . Which was to be done .

2.

Book VI . tangle All is equal to the given square upon the straight line C.

wherefore the

**rectangle**AH equal to the given fquare upon C , has heen appliedto the given straight line AB , deficient by the square GK . Which was to be done .

2.

Side 329

3 . the

AL the half of AB , wherefore the

of AL , that is of KG . add to each the square of KE , therefore the square bof AK is

...

3 . the

**rectangle**C , D , from the determination , is not greater than the square ofAL the half of AB , wherefore the

**rectangle**EA , AH is not greater than the squareof AL , that is of KG . add to each the square of KE , therefore the square bof AK is

...

Side 429

6 . then fall on L ; nor can PO belcfs than LM , therefore it is and consequently the

greater than GM . therefore the ratio of GM to MH is greater than the ratio of CP to

PH ...

6 . then fall on L ; nor can PO belcfs than LM , therefore it is and consequently the

**rectangle**GPII is greater than the**rectangle**GMH , and the straight line GPgreater than GM . therefore the ratio of GM to MH is greater than the ratio of CP to

PH ...

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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...