## 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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Resultat 1-5 av 23

Side 67

Take M the center of the circle ABC , and

MH . and because AM is equal to ME , add MD to each , therefore AD is equal to

EM , MD ; but EM , MD are greater b . 20. fi than ED , therefore also AD is greater

...

Take M the center of the circle ABC , and

**join**ME , MF , MC , 6. 1. 3 . MK , ML ,MH . and because AM is equal to ME , add MD to each , therefore AD is equal to

EM , MD ; but EM , MD are greater b . 20. fi than ED , therefore also AD is greater

...

Side 69

THE O R. F two circles touch each other internally , the straight line which

their centers being produced shall pass ... G beΑ . ing produced passes thro ' the

point A. For if not , let it fall otherwise , if H possible , as FGDH , and

THE O R. F two circles touch each other internally , the straight line which

**joins**their centers being produced shall pass ... G beΑ . ing produced passes thro ' the

point A. For if not , let it fall otherwise , if H possible , as FGDH , and

**join**AF , AG ... Side 77

First , Let E the center of the circle be within the angle BAC , and

produce it to F. Because EA is equal to EB , the angle EAB is equal to the angle

EBA ; therefore the angles EAB , EBA are double of the angle EAB ; but the B

angle ...

First , Let E the center of the circle be within the angle BAC , and

**join**AE , andproduce it to F. Because EA is equal to EB , the angle EAB is equal to the angle

EBA ; therefore the angles EAB , EBA are double of the angle EAB ; but the B

angle ...

Side 101

common to the triangles DAC , BAC , the two sides DA , AC are equal to the two

BA , AC ; and the base DC is equal to the base BC ; wherefore the angle DAC is ...

**Join**AC , BD cutting one another in E. and because DA is equal to AB , and ACcommon to the triangles DAC , BAC , the two sides DA , AC are equal to the two

BA , AC ; and the base DC is equal to the base BC ; wherefore the angle DAC is ...

Side 103

Bisect - the angles ACD , CDA by the straight lines CE , DB , and

DE , EA . ABCDE is the pentagon required . Because each of the angles ACD ,

CDA is double of CAD , and are bifected by the straight lines CE , DB , the five ...

Bisect - the angles ACD , CDA by the straight lines CE , DB , and

**join**AB , H BC ,DE , EA . ABCDE is the pentagon required . Because each of the angles ACD ,

CDA is double of CAD , and are bifected by the straight lines CE , DB , the five ...

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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...