## 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

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 129

T H E OR, F the first has to the second the same ratio which the

fourth, but the

first shall also have to the second a greater ratio than the fifth has to the sixth.

T H E OR, F the first has to the second the same ratio which the

**third**has to thefourth, but the

**third**to the fourth a greater ratio than the fifth has to the fixth; thefirst shall also have to the second a greater ratio than the fifth has to the sixth.

Side 167

DEF, the duplicate ratio of that which BC has to EF. - Take BG a

to BC, EFb, so that BC is to EF, b. 11.6. as EF to BG, and join GA. then, because

as AB to BC, so DE to EF; alternately", AB is to DE, as BC to EF. but as BC to EF,

...

DEF, the duplicate ratio of that which BC has to EF. - Take BG a

**third**proportionalto BC, EFb, so that BC is to EF, b. 11.6. as EF to BG, and join GA. then, because

as AB to BC, so DE to EF; alternately", AB is to DE, as BC to EF. but as BC to EF,

...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

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.