## 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, to this Second Edition is Added the Book of Euclid's Data. In Like Manner Corrected. viz. the first six books, together with the eleventh and twelfth |

### Inni boken

Resultat 1-5 av 5

Side 112

N. B. “When four magnitudes are proportionals, it is usually “expressed by saying,

the first is to the second, as the

of four magnitudes (taken as in the 5th Definition) the multiple of the first is ...

N. B. “When four magnitudes are proportionals, it is usually “expressed by saying,

the first is to the second, as the

**third**to * the fourth.” VII. When of the equimultiplesof four magnitudes (taken as in the 5th Definition) the multiple of the first is ...

Side 118

T H E O R. F the first of four magnitudes has the same ratio to the second which

the

shall have the same ratio to any equimultiples of the second and fourth, viz. the ...

T H E O R. F the first of four magnitudes has the same ratio to the second which

the

**third**has to the fourth; then any equimultiples whatever of the first and**third**shall have the same ratio to any equimultiples of the second and fourth, viz. the ...

Side 121

PRO P. A. T H E O R. IF the first of four magnitudes has to the second, the same

ratio which the

the

...

PRO P. A. T H E O R. IF the first of four magnitudes has to the second, the same

ratio which the

**third**has to the fourth; then if the first be greater than the second,the

**third**is also greater than the fourth; and if equal, equal; if less, less. Take any...

Side 204

T H E O R. F two planes cutting one another be each of them perpendicular to a

the two planes AB, BC be each of them perpendicular to a

...

T H E O R. F two planes cutting one another be each of them perpendicular to a

**third**plane; their common se&tion shall be perpendicular to the same plane. Letthe two planes AB, BC be each of them perpendicular to a

**third**plane, and let BD...

Side 323

to a

to the

have it. but the antient Geometers, when they observed this Enuntiation could be

...

to a

**third**: the first parallelogram is to the second, as the first Book v1. straight lineto the

**third**. and the Demonstration would be exactly Joof the same as we nowhave it. but the antient Geometers, when they observed this Enuntiation could be

...

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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 ... Robert Simson Uten tilgangsbegrensning - 1827 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1781 |

### Vanlige uttrykk og setninger

added alſo altitude angle ABC angle BAC baſe BC is given becauſe Book caſe circle circle ABCD circumference common cone contained cylinder Definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs figure firſt fore four fourth given angle given in poſition given in ſpecies given magnitude given ratio given ſtraight line greater Greek half join leſs likewiſe manner meet muſt oppoſite P R O parallel parallelogram perpendicular plane produced Prop proportionals Propoſition pyramid reëtangle remaining right angles ſaid ſame ſame multiple ſecond ſegment ſhall ſhewn ſides ſimilar ſolid ſolid angle ſome ſquare ſquare of BC T H E O taken theſe third thro triangle ABC wherefore whole

### Populære avsnitt

Side 5 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 163 - 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 48 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.

Side 73 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle; and no straight line can be drawn from the extremity between that straight line and the circumference, so as not to cut the circle...

Side 105 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...

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 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.

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 47 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Side 37 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.