## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. 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 |

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Side 119

Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . V The first of four magnitudes is said to have the same ratio to the second , which the third has to the

Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . V The first of four magnitudes is said to have the same ratio to the second , which the third has to the

**fourth**, when any ... Side 120

Book V. 6 or , if the multiple of the first be greater than that of the second , the multiple of the third is also greater than that of the

Book V. 6 or , if the multiple of the first be greater than that of the second , the multiple of the third is also greater than that of the

**fourth**. VI . Magnitudes which have the same ratio are called proportionals . Side 121

Permutando , or alternando , by premutation , or alternately ; this See Note . word is used when there are four proportionals , and it is inferred , that the first has the same ratio to the third , which the second has to the

Permutando , or alternando , by premutation , or alternately ; this See Note . word is used when there are four proportionals , and it is inferred , that the first has the same ratio to the third , which the second has to the

**fourth**... Side 122

Book V. second , as the third to its excess above the

Book V. second , as the third to its excess above the

**fourth**. Prop . L , book 5 . XVIII . Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance ; when there is any number of magnitudes more than two , and as many others ... Side 124

IF the first magnitude be the same multiple of the second that the third is of the

IF the first magnitude be the same multiple of the second that the third is of the

**fourth**, and the fifth the same multiple of the second that the sixth is of the**fourth**; then shall the first together with the fifth be the same ...### Hva folk mener - Skriv en omtale

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1821 |

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

### Vanlige uttrykk og setninger

ABCD added altitude angle ABC angle BAC arch base Book centre circle circle ABC circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 17 - FG; then, upon the same base EF, and upon the same side of it, there can be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise their sides terminated in the other extremity: But this is impossible (i.

Side 35 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 67 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.

Side 92 - IF a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.

Side 26 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.

Side 55 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line, which is made of the whole and that part.

Side 318 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Side 22 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.

Side 161 - If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.

Side 21 - 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.