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

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Side 110

Book IV . or , if the multiple of the first be greater than that of the second , the

multiple of the

have the same ratio are called proportionals . N . B . " When four magnitudes are

...

Book IV . 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 whichhave the same ratio are called proportionals . N . B . " When four magnitudes are

...

Side 112

second , as the

æquali ( sc . distantia , ) or ex æquo , from equality of distance , when there is any

number of magnitudes more than two ; and as many others , so that they are ...

second , as the

**third**to its excess above the fourth . Prop . E . Book 5 . XVIII . Exæquali ( sc . distantia , ) or ex æquo , from equality of distance , when there is any

number of magnitudes more than two ; and as many others , so that they are ...

Side 116

THEOR . See N . If the first of four magnitudes has the same ratio to the second

which the

THEOR . See N . If 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 . Side 119

A . THEOR . Book v . If the first of four magnitudes has to the second the See N .

same ratio which the

second , the

.

A . THEOR . Book v . If the first of four magnitudes has to the second the See N .

same ratio which the

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

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

Side 202

If two planes cutting one another be each of them perpendicular to a

their common section will also be perpendicular to the same plane , Let the two

planes AB , BC be each of them perpendicular to a

...

If two planes cutting one another be each of them perpendicular to a

**third**plane ;their common section will also be perpendicular to the same plane , Let the two

planes AB , BC be each of them perpendicular to a

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

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The Elements of Euclid: viz. the first six books, together with the eleventh ... Robert Simson Uten tilgangsbegrensning - 1835 |

The Elements of Euclid: Viz. the First Six Books Together with the Eleventh ... Euclides,A. Robertson Ingen forhåndsvisning tilgjengelig - 1999 |

### Vanlige uttrykk og setninger

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

### Populære avsnitt

Side 47 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to D : the rectangle AD, DB, together with the square of CB, shall be equal to the square of CD.

Side 306 - 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 26 - if a straight line," &c. QED PROP. XXIX. THEOR. See the Jf a straight line fall upon two parallel straight ti?isepropo- lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.

Side 54 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...

Side 170 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.* Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. • See Note. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (14.

Side 153 - 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 30 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB...

Side 28 - 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 64 - ... than the more remote: but of those which fall upon the convex circumference, the least is that between the point without the circle and the diameter; and, of the rest, that which is nearer to the least is always less than the more remote: and only two equal straight lines can be drawn from the point into the circumference, one upon each side of the least.

Side 5 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...