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

### Inni boken

Resultat 1-5 av 8

Side 103

... it may be

was demonstrated , and KL is double KC ... it may be

are each of them equal to HK or KL : Therefore the pentagon GHKLM is

equilateral .

... it may be

**shown**that HK is double BK : And because BK is equal to KC , aswas demonstrated , and KL is double KC ... it may be

**shown**that GH , GM , MLare each of them equal to HK or KL : Therefore the pentagon GHKLM is

equilateral .

Side 132

In like manner , it may be

not greater than KH , then GH , the mulG A CL tiple of AB , is always greater than

KO , the multiple of BE ; and likewise LM , the multiple of CD , is greater than ...

In like manner , it may be

**shown**, that LM is greater than NP . Therefore , if KO benot greater than KH , then GH , the mulG A CL tiple of AB , is always greater than

KO , the multiple of BE ; and likewise LM , the multiple of CD , is greater than ...

Side 276

... plane : And if PB , TK be joined , and perpendiculars be drawn from the points

P , T to the straight lines AB , AK , it may be demonstrated , that TP is parallel to

KB in the very same way that SO was

... plane : And if PB , TK be joined , and perpendiculars be drawn from the points

P , T to the straight lines AB , AK , it may be demonstrated , that TP is parallel to

KB in the very same way that SO was

**shown**to be parallel to the same KB ; a 9 . Side 279

Much more then is AZ greater than AG ; because , in the preceding proposition , it

was

plane KBOS , and is therefore the shortest of all the straight lines that can be ...

Much more then is AZ greater than AG ; because , in the preceding proposition , it

was

**shown**that KV falls without the circle FGH : and AZ is perpendicular to theplane KBOS , and is therefore the shortest of all the straight lines that can be ...

Side 349

... from the things that are laid down to be known or given , by the help of these

propositions other things are demonstrated to be given , and from these , other

things are again

be ...

... from the things that are laid down to be known or given , by the help of these

propositions other things are demonstrated to be given , and from these , other

things are again

**shown**to be given , and so on , until that which was proposed tobe ...

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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...